Active wing control in a Dragonfly-inspired Micro Air Vehicle

Transcription

1 Active wing control in a Dragonfly-inspired Micro Air Vehicle A Thesis Submitted for the Degree of Doctor of Philosophy by Jia Ming Kok School of Engineering, Division of Information Technology, Engineering and the Environment University of South Australia June 2016

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3 Please note that chapters 3, 4 and 5 are journal publications. Chapters 6 and 8 have been published in conferences. The related publications are listed below Chapter 3 (Journal publication) - Kok, J. M., and J. S. Chahl. Systems-level analysis of resonant mechanisms for flapping-wing flyers. Journal of Aircraft 51.6 (2014): Chapter 4 (Journal publication) - Kok, J. M., G. K. Lau, and J. S. Chahl. On the Aerodynamic Efficiency of Insect-Inspired Micro Aircraft Employing Asymmetrical Flapping. Journal of Aircraft (2016): Chapter 5 (Journal publication) - Kok, Jia-Ming, and Javaan Chahl. Optimisation of a Dragonfly-Inspired Flapping Wing-Actuation System. World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering 8.9 (2014): Chapter 6 (Conference publication) - Kok, J. M., and J. S. Chahl. A low-cost simulation platform for flapping wing MAVs. SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring. International Society for Optics and Photonics, Chapter 8 (Conference publication) - Kok, Jia Ming, and Javaan Chahl. Design and manufacture of a self-learning flapping wing-actuation system for a Dragonfly-inspired MAV. 54th AIAA Aerospace Sciences Meeting The content in these chapters have been kept the same as the publication. However, instead of an abstract, a chapter synopsis has been provided that details the outcomes of each of these publications and how it relates to the overarching concepts presented in this thesis. i

4 Contents Contents List of Figures vii List of Tables Abstract Declaration Acknowledgements xiii xv xvii xix 1 Introduction Background Fixed wing Rotary wing Motivation for work The dragonfly Dragonfly wing-actuator system Dragonfly aerodynamics and wing kinematics Operational requirements and scalability Non-aerodynamic forces Overview of contributions Survey of existing systems and their science Existing systems Wing Kinematics Optimisation Existing experimental techniques Optimisation techniques ii

5 Contents Scatter Search Algorithm Conclusion A systems level analysis of resonant mechanisms for flapping wing flyers 31 Abbreviations Introduction The dragonfly Operating Frequency Manoeuvrability Gliding Flight Discussion Conclusion On the aerodynamic efficiency of insect-inspired micro aircraft employing asymmetrical flapping 57 Abbreviations Introduction Methods Flapping modes The Quasi-Steady model System parameters Results Analysis of Dipteran flapping mode Analysis of Dragonfly mode of flapping Discussion Conclusion Appendix Dipteran flapping mode, C L, C D decreased by 50% Dipteran flapping mode, C L, C D increased by 50% iii

6 Contents Odonate flapping mode, C L, C D decreased by 50% Odonate flapping mode, C L, C D increased by 50% Optimisation of a Dragonfly-inspired Flapping Wing-actuation System 93 Abbreviations Introduction Optimisation Problem Quasi-steady Model Results Discussion Conclusion A low cost simulation platform for a flapping wing MAV 113 Abbreviations Introduction DIMAV Flight Simulator Wing Dynamics Aerodynamics Module Environmental Module Physics Module Visualisation Module Results Take-off Roll turn and Yaw Turn Discussion Conclusion On the design framework for a flapping wing MAV 127 iv

7 Contents Abbreviations Introduction Benefits of flapping wing On the question of hover Are resonant and passive modes really effective? The active mode of flapping On the question of glide Should hover be the primary mode? Glide efficiency On the question of manoeuvrability Parameters that matter The stroke plane Design guidelines Conclusion Design and manufacture of a self-learning flapping wing-actuation system for a Dragonfly-inspired MAV 155 Abbreviations Introduction Dragonfly Characterisation Wing-actuation system Flapping profile Integrated design Wing-Actuator Design Wing Design Thorax Design Actuator design Sensing and control v

8 Contents 8.4 Method Results DOF DOF Discussion Conclusion Experimental optimisation of a flapping wing system in hover 183 Abbreviations Introduction Method DOF DOF Discussion Conclusion Appendix A bio-inspired control system for a Dragonfly-inspired MAV 207 Abbreviations Introduction Hopf oscillators Synchronisation of CPG Oscillators Function mapping Conclusion Summary and Future Work Future Work References vi

9 List of Figures List of Figures 1.1 Comparison of the weight and Reynolds number regime of aircraft and natural flyers (Mueller, 2001) Efficiency of rotary winged system diminishes in forward flight Illustration of fixed (LEFT) and rotary winged (RIGHT) parcel delivery systems (adapted from dpdhl.com and amazon.com) Illustration of the wing-wake interaction phenomenon Wing-beat frequency versus wing length for natural flyers (adapted from (Greenewalt, 1960)) Existing flapping wing air vehicles. Delfly (Top Left); Harvard Robobee (Top Right); Nano Hummingbird (Bottom Left); TechJect QV (Bottom Right) An illustration of possible wing kinematics. The lines represent wing chord, the dots represent the same edge of the wing during the stroke (adapted from (Berman & Wang, 2007)) Illustration of the evolutionary algorithm optimisation process (adapted from (Eiben & Smith, 2003) ) Basic scatter search procedure Illustration of the aerodynamic forces acting on a single section of the wing. The drag force is used to calculate the aerodynamic torque exerted on the wing. The lift and drag forces are vectorially added to determine the vertical component of force (adapted from Norberg (R. A. Norberg, 1975)) Illustration of the coordinate transform required to determine the actual lift generated by the wing in the global frame of reference (adapted from Norberg) Illustration of the muscle input into a dragonfly wing in manoeuvring flight Response of two damped systems with and without elastic storage mechanisms to an instantaneous step input (Top). The dashed and solid lines represent systems with and without elastic storage respectively. The damping force (Bottom) is the performance metric for determining the manoeuvrability of the system Response of two damped systems with and without elastic storage mechanisms to an instantaneous step input (Top). The aerodynamic forces are represented by a quadratic function. The dashed and solid lines represent systems with and without elastic storage respectively. The damping force (Bottom) is the performance metric for determining the manoeuvrability of the system vii

10 List of Figures 3.6 Two different wing-actuator configurations. The wing-actuator configuration with the spring in parallel to the actuator(a) will have no effect on the gliding properties when the actuator is holding position. Conversely if the spring is in series with the actuator (B), the spring will potentially reduce the natural frequency and critical velocity of the system making it detrimental to glide Illustration of asymmetrical flapping versus symmetrical flapping Illustration of Dipteran versus Odonate flight (adapted from) The asymmetrical flapping profile is represented by two half cosine waves. The figure illustrates a flapping profile with η= Illustration of the coordinate system used. Global coordinate system (A); Stroke plane frame (B) Illustration of the aerodynamic forces due to the flapping motion acting on a single section of the wing Illustration of the pressure force due to rotational circulation acting on a single section of the wing Illustration of a dragonfly-inspired wing Mean lift generated for a Dipteran-inspired flapping mode across a range of η for different wing-beat frequencies Time-averaged angular velocity and time-averaged square of the angular velocity versus η performed for a Dipteran-inspired flapping mode (Ω = 1) Aerodynamic efficiency for a Diperan-inspired flapping mode, L/ P, across a range of η and different wing-beat frequencies Time-averaged ω 3 and ω 3 / ω 2 versus η performed for a Diperan-inspired flapping mode (Ω = 1) Lift generated for a Odonate-inspired flapping mode by the system for different values of η and different α Aerodynamic efficiency for a Odonate-inspired flapping mode, L/ P, for different values of η and different α Aerodynamic efficiency for a Odonate-inspired flapping mode, L/ P, for different values of η and different Γ (α 0 = 7π/12) Lift for a Dipteran-inspired flapping mode Aerodynamic efficiency for a Dipteran-inspired flapping mode Lift for a Dipteran-inspired flapping mode Aerodynamic efficiency for a Dipteran-inspired flapping mode viii

11 List of Figures 4.19 Lift for an Odonate-inspired flapping mode Aerodynamic efficiency for an Odonate-inspired flapping mode Aerodynamic efficiency for an Odonate-inspired flapping mode with elasticity Lift for an Odonate-inspired flapping mode Aerodynamic efficiency for an Odonate-inspired flapping mode Aerodynamic efficiency for an Odonate-inspired flapping mode with elasticity Illustration of the dependance of φ and α on K and C η (adapted from Berman and Wang (Berman & Wang, 2007)) A comparison of the periodic hyperbolic function proposed by Berman and Wang (Berman & Wang, 2007) (dashed line) with experimental results from Azuma et al. (Azuma, Azuma, Watanabe, & Furuta, 1985) (solid line) Illustration of the aerodynamic forces acting on a single section of the wing Illustration of the pressure force due to rotational circulation acting on a single section of the wing Illustration of the coordinate transform required to determine the actual lift generated by the wing in the global frame of reference (adapted from Norberg (R. A. Norberg, 1975)) Optimised flapping profile (solid lines) versus unoptimised flapping profile (dashed lines) Optimised lift profile (solid lines) versus unoptimised lift profile (dashed lines) Number of function evaluations required versus initial population size Number of function evaluations required versus Stage One population size Number of function evaluations required versus the tolerance of the local solver Lift forces generated by the optimisation algorithm as a function of the convergence tolerance criteria DIMAV simulator high level architecture Illustration of translational (A) and rotational (B) forces (adapted from Dickinson et al. (M. H. Dickinson, Lehmann, & Sane, 1999)) Illustration of the body coordinate system (adapted from (Mueller, 2001)). Circled numbers indicate actuator number Maximum vertical acceleration experienced by the DIMAV in flight ix

12 List of Figures 6.5 Angular rates experienced by the DIMAV in roll (A) and yaw (B) manoeuvre across 2 wingbeats. The dashed line represent the angular rates averaged over the period of two strokes Illustration of translational (A) and rotational (B) forces (adapted from Dickinson et al. (M. H. Dickinson et al., 1999)) Lift-to-total power and Lift-to-aero power ratio across a range of frequency ratios Illustration of the dependance of φ and α on K and C α (adapted from Berman and Wang (Berman & Wang, 2007)) Flapping angle profile optimised for β = 20, 40, 60 deg Pitch angle profile optimised for β = 20, 40, 60 deg Maximum directional thrust generated for a wing with and without stroke plane augmentation. The radial axes represents maximum achievable thrust in that direction Wing design consisting of carbon fibre spars and ribs with a Mylar skin Bearings were used in the thoracic structure to allow smooth articulation of the wing. This allows 3DOF movement of the wing Example of a compliant joint. Compliant joints are used to link the actuator to the thorax at both ends DOF Actuator configuration Illustration of optimisation process (adapted from Kok et al. (J. Kok & Chahl, 2014a)) Marking Rod. The white points are markers 1 and 2 respectively Illustration of how the marking rod works. Marker 1 is used to measure wing articulation in the flapping and rolling axis (see A). The relative position of Marker 2 to Marker 1 is used to measure the pitching angle (see B) X position of marker points 1 and 2 for a sine wave input into both actuators 1 and Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 with a negative phase change (Θ 2 = 0 o, 50 o, 100 o ) Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 with a positive phase change (Θ 2 = 0 o, 50 o, 100 o ) Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 for different values of A 1 and A Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 for different values of B 1 and B x

13 List of Figures 8.13 Tracking the centre point. A 3 = 0; Θ 3 = 0; B 3 = 400; Tracking of the movement of the centre point. Changing A 3. A 3 = 0, 200, Tracking of the movement of the centre point. Changing Θ 3. Θ 3 = 50, 0, Symmetrical inputs into solenoids 1 and Illustration of high speed cinematography of the wing root for symmetrical solenoid inputs X locations of both wing root markers with time(top); Difference in X locations between both markers (BOTTOM) Unoptimised lift profiles before and after filtering Optimised solenoid profiles High speed cinematography illustrating wing pitch and wing flap for an optimised flapping profile Comparison of flapping angle between unoptimised and optimised flapping profile Comparison of pitching angle between unoptimised and optimised flapping profile Optimised 2DOF lift profile Unoptimised solenoid inputs for a 3DOF configuration Unoptimised lift profile Solenoid inputs for basin of optimisation Solenoid inputs for basin of optimisation Lift profile for basin of optimisation Optimised lift profile from basin of optimisation X-Z positions with wing pitch for the unoptimised case X-Z positions with wing pitch for inputs from basin of optimisation Optimised X-Z positions with wing pitch for inputs from basin 3 from the optimisation ran Fast fourier transform for 2DOF basin 1 of optimisation Fast fourier transform for 2DOF basin 2 of optimisation Fast fourier transform for 2DOF basin 3 of optimisation xi

14 List of Figures 9.22 Fast fourier transform for 2DOF basin 4 of optimisation Response of Hopf oscillator (A) to control inputs (B) Response of sine-based oscillator (A) to control inputs (B) Illustration of coupling topology Step response of flap profiles for right, fore wing and right hind wing with change in phase Step response of pitch and flap profiles for right, fore wing with change in phase Illustration of the hyperbolic tan limit cycle compared to the Hopf oscillator Controller output using hyperbolic tanh mapping function (C α = 2) xii

15 List of Tables List of Tables 1.1 DARPA: MAV definition/design requirements (adapted from (Ashley, 1998)) Relevant wing-actuation parameters A summary of relevant flapping wing flyers and their characteristics Comparison of time averaged, non-dimensionalised damping force for systems with and without elastic storage Comparison of arbitrary values of damping force and energy for systems with and without elastic storage Flapping wing parameters Inertial breakdown of the wing Optimisation constraints Initial optimisation parameters Optimised flapping profile parameters Simulation parameters for all wing-actuators in take-off configuration Simulation parameters for all wing-actuators in roll configuration Simulation parameters for all wing-actuators in yaw configuration Differences between rotorcraft and flapping-wing aircraft Optimisation constraints Optimisation constraints Design constraints Test cases for different values of A 1 and A Test cases for different values of B 1 and B Optimisation constraints xiii

16 List of Tables 9.2 Test results for 2DOF optimisation DOF Optimisation constraints Test results for 3DOF optimisation xiv

17 Abstract THIS thesis addresses the science behind active control of an insect-like Micro Air Vehicle (MAV), specifically drawing inspiration from a dragonfly. The dragonfly is one of the longest surviving organisms, and its evolution has provided it with a versatile range of mission capabilities that spans hovering, gliding and manoeuvring flight. It is this capability to hover, glide, manoeuvre and switch between all three modes of flight that distinguishes the insect-inspired systems from the more prevalent fixed and rotary wing MAVs. However, much of the flapping wing science has evolved from convenience and ease of design rather than a framework for a bio-inspired system capable of expanding the mission envelope defined by existing fixed and rotary wing MAVs. This body of work employs a top-down approach which begins by reassessing the science behind flapping wing actuation in the context of a MAV system with full mission operability. The science is based on the tenet that an appropriate bio-inspired system should be able to replicate the capabilities of both fixed and rotary wing aircraft, as well as be more manoeuvrable than either system. Chapter 3 begins by addressing the effects of resonant mechanisms on the hover, manoeuvre and glide capabilities of a MAV. Results show that in an aerodynamically efficient system, the benefits of resonance are reduced and outweighed by reductions in manoeuvring and glide performance. Chapter 4 investigates the upstroke-to-downstroke ratio as a control parameter, and investigate it in the context of aerodynamic efficiency in hover. We show that in an inertia dominated system, asymmetrical flapping could be applied to optimise the aerodynamic efficiency of non-resonant systems below the natural frequency. In systems suffering from or exploiting elasticity, we also show benefits in aerodynamic efficiency. However, in an aerodynamically efficient wing system, such as that of a dragonfly, with reduced reliance on elasticity, the primary mode of energy savings is through modulation of wing pitch. Control of the upstroke-to-downstroke ratio is suitable as a secondary means for tuning the optimality of the system. In Chapter 5, we investigate a means to optimising the flapping and pitching profile using a hybrid global and local optimisation solver. We showed a 20% increase in lift generated as compared to flapping profiles obtained by high speed cinematography of a Sympetrum frequens dragonfly. Chapter 6 than looks at the active control parameters observed from high speed cinematography of dragonflies, and verifies its effects in simulation. Finally, Chapter 7 combines findings from all the chapters and proposes a design framework for future dragonfly-inspired systems. We conclude that an ideal system is achieved by using active flapping, with critical design of wing-actuator-thorax systems and efficient control and optimisation of wing kinematics. This design framework provides guiding principles and direction for future dragonfly-inspired flapping wing research. Chapter 8 then applies these principles to design of a dragonfly-inspired wing-actuation system. The final design incorporates independant and controllable actuation in 3DOF, direct drive of the wing, low inertia carbon and mylar wing and a compliant thoracic structure. A method is also presented for estimating the wing kinematics based on high speed cinematography of the wing root. This method is used xv

18 List of Tables to investigate the effects of different solenoid parameters on the wing kinematics, and hence demonstrate the controllability of the system. The optimisation approach from chapter 5 was then applied to this design and the findings are shown in Chapter 9. With no prior knowledge of the system, and no physical model of electro-mechanical interactions, we demonstrate the ability to optimise the system in 2DOF and 3DOF, with a 71% and 47% increase in lift respectively. Most of the work has focussed on the articulation of a single wing, however in Chapter 6, we show that the interaction between all four wings is critical to manoeuvring flight of the dragonfly. Chapter 10 proposes a control design which is able to modulate all four wings in phase, frequency, amplitude, upstroke-to-downstroke ratio and kinematic profile, and is able to do so for both wing pitching and flapping. The design also minimises large initial errors and is not wing-beat to wing-beat timing critical. xvi

19 Declaration I declare that: this thesis presents work carried out by myself and does not incorporate without acknowledgement any material previously submitted for a degree or diploma in any university; to the best of my knowledge it does not contain any materials previously published or written by another person except where due reference is made in the text; and all substantive contributions by others to the work presented, including jointly authored publications, is clearly acknowledged. xvii

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21 Acknowledgements I would like to express my appreciation to Professor Chahl, the DSTG and all those who have accompanied and supported me throughout my PhD journey. Their support and guidance made this journey one of the most rewarding, instructive, and enjoyable experiences of my life. I would like to give special thanks to Lao Shi and Shi Mu. Had it not been for their years of guidance and nourishment I would not have made it this far. I would like to thank my dad for contributing to half of my brain. Finally, I would like to thank my Mom for seeing me to this point. Her love and compassion, whilst not always reciprocated, has never faltered, something I will always appreciate. xix

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23 CHAPTER 1 INTRODUCTION 1

24 CHAPTER 1. INTRODUCTION 1.1 Background IN recent years, Unmanned Aerial Vehicles (UAVs) have been a growing area of research. A UAV is defined as an aerial platform capable of autonomously sustaining controlled level flight using some means of propulsion. Since the inception of UAVs, these unmanned aircraft have begun replacing piloted aircraft particularly in Defence applications. Their operational uses include aerial surveillance, reconnaissance and support to ground forces. One particular branch of UAV research has been Micro Air Vehicles (MAVs). This has been facilitated by technological advancements in many fields including micro-electronics, sensors, microelectromechanical systems, and micro-manufacturing. MAVs are defined mainly by their size which is of the order of 15cm in wingspan, and are proposed to be useful predominantly for surveillance and reconnaissance purposes. A formal definition by DARPA for MAVs is presented in Table 1.1. Table 1.1: DARPA: MAV definition/design requirements (adapted from (Ashley, 1998)) Specifications Requirements Details Size <15.24cm (6in) Maximum dimension Weight 100g ( 4 ounces) Objective GTOW Range < 9.7km (6 miles) Operational range Endurance 20 min to 2 hrs Loiter time or station Altitude < 150m Operational ceiling Speed 13.4 m/s (30mph) Maximum flight time Costs $1000 Cost for a throw-away system Their inherently low speed and small size means that they operate in the low Reynolds number regime (see Fig. 1.1). MAVs can be subdivided into three main categories fixed wing, rotary wing and flapping wing Fixed wing Fixed wing aircraft refer to aircraft configurations whereby the wings remain stationary relative to the body of the aircraft. Fixed wing aircraft have been flown reliably in many scenarios, 2

25 1.1 Background Figure 1.1: Comparison of the weight and Reynolds number regime of aircraft and natural flyers (Mueller, 2001) however they lack the capability to hover and are subject to aerodynamic stall at low speeds and high angles of attack. Such aircraft are unable to take-off and land vertically. Such limitations restrict the mission profile of fixed wing MAVs (Morris & Holden, 2000). However, fixed wing aircraft are proficient at travelling longer distances and for longer times due to the higher lift-to-drag ratios. In fixed wing MAV designs, lift-to-drag ratios greater than 5 are not uncommon (Lundström & Krus, 2012; Spoerry & Wong, 2001; Mueller, 2000) Rotary wing Rotary wing aircraft rely on rotary motion of an aerodynamic surface to provide lift, and can have any number of rotors. Rotary wing aircraft are able to take-off and land vertically as well as hover, providing mission capability that fixed wing aircraft cannot achieve. However, they have poor efficiencies at low Reynolds numbers (Ashley, 1998; Mueller, 2001). Additionally, rotary winged aircraft are not suited to long periods of forward flight, due to the low lift-tothrust ratios which are inherent in rotary-winged aircraft (see Fig. 1.2). 3

26 CHAPTER 1. INTRODUCTION Figure 1.2: Efficiency of rotary winged system diminishes in forward flight 1.2 Motivation for work Currently the MAV design space is dominated by fixed and rotary winged aircraft. These systems are employed in a wide variety of missions spanning commercial, defence and recreational activities (Zhou, Zhou, & Zhou, 2014; Gómez, 2015; Gupte, Mohandas, & Conrad, 2012; Asadpour, Burger, Schuiki, & Hummel, 2015; Bernardini, Fox, & Long, 2014; Cantelli, Mangiameli, Melita, & Muscato, 2013). Cantelli suggested the use of drones combined with ground vehicles for de-mining (Cantelli et al., 2013). Bernardini et. al has investigated the use of drones for surveillance (Bernardini et al., 2014). Recent drone applications have also looked at parcel delivery (Murray & Chu, 2015). Murray suggested the use of trucks to cover long distance aspects and drones to supplement the short range operations, also known as the Last-mile delivery. However the operational capabilities of fixed and rotary wing configurations tend to be limited. Fixed wing aircraft are highly efficient in forward flight and have the capability to cover long distances. Rotorcraft are excellent at hovering and can take-off and land vertically, but are not efficient flyers. This leaves a gap in the MAV design space for a system which is able to replicate the capabilities of both fixed and rotary winged aircraft. With the increasing roles for MAVS, such a configuration would have benefits in missions such as law enforcement, 4

27 1.3 The dragonfly complex surveillance, and many others. It s mission envelope would allow it to perform long endurance flight like a fixed-wing aircraft. It would also be able to perform complex manoeuvres characteristic of rotary winged aircraft, such as VTOL, which would allow it to operate in tight spaces or an urban environment. This opens up the mission envelope of MAVs and also presents a robust and elegant solution to many of its operational limits. Figure 1.3: Illustration of fixed (LEFT) and rotary winged (RIGHT) parcel delivery systems (adapted from dpdhl.com and amazon.com) Such a configuration already exists in nature, and is a class of flyers called flapping wing flyers. These systems in nature can be broadly categorised into bird-like and insect like configurations. Technical systems that attempt to draw inspiration from such flyers are called ornithopters and entomopters respectively. Of such bio-inspired flyers, dragonflies in particular are one of the most versatile flyers. They are able to hover, take-off and land vertically like a rotorcraft, and have been demonstrated to share the glide capabilities of a fixed-wing aircraft. Additionally, they cover a large range of strategic manoeuvers not singularly capable by either fixed or rotary wing aircraft. This ability to manoeuvre potentially gives them the capability to operate indoors. Such a versatile range of motion in glide, forward flight, hovering and agile manoeuvres increases the mission envelope of such a system, making it a worthy topic for intensive research. 1.3 The dragonfly Insects are some of the most amazing natural flyers. Amongst these, dragonflies in particular were amongst the first to evolve and is arguably the longest surviving flying organisms. 5

28 CHAPTER 1. INTRODUCTION Observations of the dragonflys genealogy show that its ancestry can be traced back to the Protodonata, which are amongst the earliest winged insect fossils discovered. This suggests that the evolution of dragonflies dates back 300 million years (Wootton, 1976; May, 1982). These dragonflies have wingspans in the order of 50cm (Beckemeyer, n.d.; Tillyard, 1925). Some recorded wingspans of the Protodonata were up to 70cm. The optimisation of dragonflies via natural selection over the millions of years has made them excellent flyers. In addition to being able to hover, they are also efficient at forward flight like a fixed wing aircraft. This is supported by studies of its migratory patterns, which shows dragonflies travelling 140km/day even with the additional load of transmitters (May, 2013). Azuma et al. (Azuma & Watanabe, 1988) demonstrated the excellent flight characteristics of the dragonfly using numerical methods and experimental methods. Dragonfly wings were attached to a shaft and glide tested that showed lift-to-drag ratios of 3.5 which is significantly higher than that of a rotory wing aircraft. Their lift and drag profiles were compared to other species of insects that also showed better gliding performance. Wakeling and Ellington (Wakeling & Ellington, 1997a) performed a similar analysis using measurements in a wind tunnel, as well as observations of dragonflies in flight. Wind tunnel results showed lift-to-drag ratios in excess of 17. Newman (Newman, Savage, & Schouella, 1977) showed lift-to-drag ratios of 11.5, whilst Okamoto (Okamoto, Yasuda, & Azuma, 1996) showed lift-to-drag values in the order of 6. Experimental studies of the glide slope by Wakeling and Ellington showed lift-to-drag ratios of 6 as well. Similar work performed by Ruppell (Ruppell, 1989) showed the excellent glide properties of dragonflies, which were comparable with some birds. Dragonflies also exhibit an aerial agility that allows it to out-manoeuvre and prey on other insects (Chahl, Dorrington, & Mizutani, 2013; Mizutani, Chahl, & Srinivasan, 2003; Corbet et al., 1999, p.345). In addition to having a versatile range of manoeuvres (May, 1991; H. Wang, Zeng, Liu, & Yin, 2003; D. E. Alexander, 1984, 1986; Ruppell, 1989), they are also able to accelerate very quickly (Chahl, Dorrington, & Mizutani, 2013; Ruppell, 1989; May, 1991). Slow motion footage taken by Ruppell (Ruppell, 1989) provides one of the most comprehensive studies on symmetrical flight manoeuvres of dragonflies. Ruppell shows the ability of the dragonfly to take-off vertically, dive downwards, fly forwards at speeds up to 10m/s and fly 6

29 1.3 The dragonfly backwards rapidly. He also noticed intermittent transitions to a glide mode between wing beat cycles, which could be an attempt at energy efficient flight. Another capability of the dragonfly is the ability of the dragonfly to carry another payload (i.e. female dragonfly, or prey) and still operate. High speed cinematography of dragonflies by Alexander (D. E. Alexander, 1986) also show the capability for non-symmetrical flight manoeuvres. Alexander demonstrated that dragonflies use asymmetrical flapping between their left and right wings to produce more lift and thrust on one side of the body, hence leading to a rolling force which leads to a banking motion. He also observed another manoeuvre, the Yaw turn, whereby the dragonfly turns 90 degrees in the yaw axis in the time span of one or two wing strokes. Slow motion footage taken by (Ruppell, 1989; Mizutani et al., 2003) show instantaneous accelerations of up to 4g and sustained and take-off accelerations of up to 2g. Other studies have demonstrated similar capabilities in the dragonfly (H. Wang et al., 2003; D. E. Alexander, 1984; Azuma et al., 1985; Azuma & Watanabe, 1988; Wakeling & Ellington, 1997b). One commonality between these papers is that the dragonfly s capability is the result of control over a large number of wing kinematic parameters. From past work it can be inferred that there are two predominant issues surrounding this research problem which need to be addressed in order to replicate the performance capabilities of dragonflies in nature: Replicating the dragonfly wing-actuation system Replicating the wing kinematics of a dragonfly-inspired system Dragonfly wing-actuator system The extensive capabilities of the dragonfly can be attributed to the unique degree of control the dragonfly has over its flapping actuators and resulting flapping profile (Sviderskiĭ, Plotnikova, & Gorelkin, 2008). High speed cinematography by Ruppell (Ruppell, 1989) shows a large amount of control over its wing parameters. The dragonfly is able to modulate its wings in frequency, amplitude, wing pitch, upstroke-to-downstroke ratio, stroke plane and phase between fore and hind wings. It is able to do so asymmetrically allowing for the wide range of 7

30 CHAPTER 1. INTRODUCTION manoeuvres described in 1.3. This finding is further supported by Alexander (D. E. Alexander, 1984, 1986) who showed that dragonflies were able to adjust the phase lag between the fore and hind wings to switch between normal flight and flight manoeuvres requiring high forces, such as take-off and yaw turning. He further performed high speed cinematography in a wind tunnel (D. E. Alexander, 1986) to demonstrate the capability of the dragonfly to adjust both stroke plane angle and angle of attack of the individual wings to perform complex yawing or banking turns. Similarly, these parameters are modulated to generate symmetrical flight manoeuvres (Ruppell, 1989). The importance of the stroke plane and the wing pitch angle have been further emphasized by Wang (Z. J. Wang, 2004, 2005). Even during hovering flight, Wang (Z. J. Wang, 2005) proposed that dragonflies rely on adjusting the angle of attack of the wing to reduce the energy costs of hover. Certainly observations of the wing actuators of dragonflies support these theories. An investigation of the actuation system in dragonflies shows their capability to actively control and effect wing rotation (Sviderskiĭ et al., 2008; Simmons, 1977). Svidersky (Sviderskiĭ et al., 2008) compared the anatomy of the dragonfly to its less manoeuvrable four wing counterpart - the locust. His studies showed that the wing base and muscles of the dragonfly give it the ability to actuate each of the wings individually, and it is able to do so in phase, frequency and amplitude, all of which have been suggested by Ruppell to be important for manoeuvring flight (Ruppell, 1989). Dragonflies are also able to pitch their wings independently of each other, and more importantly are able to actively regulate the wing rotation. Locusts are only able to do so passively. The large number of motor units in the muscles of the dragonfly also enable it to more precisely regulate their flapping profiles. Finally, whilst the standard configuration for dragonfly flapping is in an inclined stroke plane, the dragonfly is able to flap its wings along the horizontal plane as well, suggesting the ability of the dragonfly to modulate its stroke plane angle. A summary of wing-actuator parameters is found in table 1.2. A final characteristic of the dragonfly wing-actuation system is its wing-muscle interface. Dragonflies employ a direct-drive mechanism (Dudley, 2002), whereby the muscles are directly attached to the root of the wing, and are directly responsible for wing kinematics. This is 8

31 1.3 The dragonfly Table 1.2: Relevant wing-actuation parameters Parameter Source Flapping Frequency (Ruppell, 1989) (H. Wang et al., 2003) Flapping Amplitude (Ruppell, 1989) (H. Wang et al., 2003) (D. E. Alexander, 1986) (Azuma et al., 1985) Wing pitch (Ruppell, 1989) (H. Wang et al., 2003) (D. E. Alexander, 1986) (Azuma et al., 1985) Stroke Plane (Ruppell, 1989) (Azuma et al., 1985) Phase (Ruppell, 1989) (D. E. Alexander, 1986) Upstroke-to-downstroke ratio (Ruppell, 1989) in contrast to the indirect mode of actuation, common to Diptera, whereby insect muscles are attached to a highly elastic thorax. The thoracic structure modulates and transmits the force from the muscles to the wing Dragonfly aerodynamics and wing kinematics Through evolution over the course of 300 million years, insects have tuned and optimized flapping profiles unique to their evolutionary trajectory that are capable of generating the aerodynamics required for aerial acrobatics as well as efficient hover. While these systems exist in nature, it is extremely difficult to replicate the exact aerodynamics and wing kinematics that make these systems successful. Between different species of insects, wing kinematics differs in 3DOF. Many insects utilize different transient lift enhancement techniques not captured in quasi-steady analyses. The Clap-and-fling mechanism was first suggested by Weis-Fogh (Weis-Fogh, 1973) whereby vortices generated by the clapping and flinging apart of a pair of wings aid in lift generation. Many 9

32 CHAPTER 1. INTRODUCTION insects rely on wing wake interactions to boost lift. This phenomenon was first observed by Dickinson (M. Dickinson, 1994) during 2D motion of an inclined plate and is called wake capture. A vortex wake is generated prior to stroke reversal of the wing. When the wing reverses direction, it interacts with the wake. It is during this period that maximum forces are recorded. The Wake capture phenomenon is illustrated in Figure 1.4 respectively. It is likely that the dragonfly uses the mode of vortex interaction (Z. J. Wang & Russell, 2007; Usherwood & Lehmann, 2008) whereby the wakes of the fore and hind wings interact with each other constructively. Figure 1.4: Illustration of the wing-wake interaction phenomenon Other phenomenon that could affect the dragonfly aerodynamics include rotational circulation and delayed stall (M. H. Dickinson et al., 1999). Rotational circulation occurs due to the rotation of the wing pitch that generates additional circulation and hence lift. Delayed stall occurs due to the high angle of attack the wing makes when translating through the air. Flow structures form at the leading edge of the wing which generate additional circulatory forces that impact lift generation. 10

33 1.3 The dragonfly Wing kinematics plays a significant role in reducing the energy required for flapping actuation. This is crucial for systems being implemented on air vehicles as it has a direct effect on the endurance of the system. Wang (Z. J. Wang, 2004, 2005) proposed that dragonflies employ an asymmetric flapping profile in an inclined stroke plane that explains their anomalously high lift coefficients. In this model, both lift and drag forces are used to support the weight of the dragonfly on the downstroke. On the upstroke, the wing is rotated in such a way as to generate negligible forces. Wang further proposed that such a means of flapping could reduce the power consumption required by a factor of 2/ 2 compared to a conventional hovering profile (Z. J. Wang, 2005). As demonstrated, wing kinematics has a very significant impact on the aerodynamic forces and performance of the system. As such, it is important that it is taken into consideration when designing the flapping wing-actuation system. In addition to being able to generate the range of motion needed to realise the optimal flapping wing profile, the flapping wing-actuation system should also be able to achieve the desired wing beat frequency. Controllability is another factor that must be considered with regards to wing kinematics. Studies performed by Svidersky et al. (Sviderskiĭ et al., 2008) suggests that owing to the significantly larger number of muscle motor units, dragonflies are able to regulate their wing strokes more finely, hence achieving more manoeuvrability. In order to replicate the diverse range of motion of the dragonfly, a wing-actuator configuration should be able to regulate the wing kinematics in 3DOF with reasonable precision. Whilst the dragonfly mode of flapping is unique, it should be noted that there is not a single, globally optimal flapping profile. The flapping profile differs between all species of dragonflies (Ruppell, 1989; Schilder & Marden, 2004; Azuma et al., 1985; Azuma & Watanabe, 1988), and even within the same species, the flapping profiles can differ between dragonflies (Wakeling & Ellington, 1997b). This suggests that in the design of a dragonfly-inspired system, it is not just sufficient to design an efficient wing-actuation system, it is also important to optimise the wing kinematics to that particular system. Additionally, the wing kinematics is specific to that actuation system, and is unlikely to remain optimal if the parameters of the wing-actuation system are modified. 11

34 CHAPTER 1. INTRODUCTION 1.4 Operational requirements and scalability Practical MAVs weigh in the 100g regime. Taking into account the operational aspects of the system, the design and optimisation of the flapping wing-actuator configuration should be targeted at systems between 80g to 100g. This will have a direct impact on the design of the wing-actuator configuration. Data on prehistoric dragonflies is scarce and direct measurements of weight and stiffness is impossible from a fossil. Thus scaling laws and benchmarking against other systems will be used to determine certain parameters of the flapping wing MAV. These parameters include wing area and flapping frequency. Karpelson et. al (Karpelson, Wei, & Wood, 2009) used a blade-element aerodynamic analysis to show that the aerodynamic power and wing area follows a set of power laws, whereby the required aerodynamic power is given by : P aero F requency 0.5 W ingspan 1.25 (1.1) while the wing area is given by W ingarea F requency 1 W ingspan 0.5 (1.2) A parametric study of natural flyers by Greenwalt (Greenewalt, 1960) also derived a relationship between the length of the wing and the wing beat frequency. This is shown in Fig Natural flyers with a longer wing span often flap their wings at a lower frequency. This is to be expected as flyers with a longer wing span will have larger inertial costs, and to compensate for that would be limited to actuation at a lower wing beat frequency. As our system is expected to be representative of a 100 gram MAV, this places it in the weight category of small birds. As such, we can expect wing lengths to be greater than 100mm, and wing-beat frequencies of 5Hz. An additional requirement on the system is to ensure that it has the potential to be further miniaturized if required. With technological advancements in many fields including microelectronics, sensors, micro-electromechanical systems, and micro-manufacturing, components will become progressively smaller and more functional. To maintain a competitive edge, it is crucial that flapping-wing MAV designs are adaptable to changes in size and weight of critical 12

35 1.5 Non-aerodynamic forces Figure 1.5: Wing-beat frequency versus wing length for natural flyers (adapted from (Greenewalt, 1960)) subsystems such as the payload and avionics. 1.5 Non-aerodynamic forces The cyclic nature of the flapping wing system generates significant aerodynamic and nonaerodynamic forces (Greenewalt, 1960; Weis-Fogh, 1973). The non-aerodynamic forces mainly include inertial forces attributed to accelerating/decelerating the wing and elastic forces attributed to the wing and thorax of the insect. The relative contributions of these forces differ between insects and have a strong effect on performance. These forces are coupled, with aerodynamic and inertial forces affecting the degree of elastic wing deformation and vice versa (Z. J. Wang, 2004; Lehmann, Gorb, Nasir, & Schtzner, 2011). The multi-physics nature of the flapping wing system will have a significant influence on wing-actuator design and the optimisation process. Firstly, the non-linear combination of aerodynamic and non-aerodynamic forces increases the complexity of modelling the performance of any flapping wing system. An accurate com- 13

36 CHAPTER 1. INTRODUCTION putational model of the flapping wing system accounting for all three parameters would require significant computational power and time. This raises the question as to the most cost efficient method for modelling the performance of a flapping wing system, and the best approach to optimising the system. Certainly, several methods exist for being able to optimise the wing profile. This will be explored further in section 2.3. The presence of non-aerodynamic forces presents additional loads which need to be overcome by the actuator. The interaction between these forces results in the phenomenon of resonance, whereby the performance of the system is highly frequency dependant. At a particular frequency, called the natural frequency, the forces interact in such a way as to eliminate inertial and elastic forces, hence allowing enhanced efficiency (Dimarogonas, n.d.; Hutton, 1981). This phenomenon has been utilised by some researchers (Ratti & Vachtsevanos, 2010; Ratti, Jones, & Vachtsevanos, 2011; Ratti & Vachtsevanos, 2012) as a means to recover some of the inertial energy expended during flapping actuation. An alternative view to this would be that the resonant effect could be used to reduce the force required by flapping actuators to generate sufficient lift. However, counter arguments exist against the use of resonance as well (Ramananarivo, Godoy-Diana, & Thiria, 2011; Yin & Luo, 2010). As mentioned previously, in natural flyers, the contribution of each force varies significantly between insects (Greenewalt, 1960; Weis-Fogh, 1973). Greenewalt (Greenewalt, 1960) showed that this produced significant variation in the aerodynamic efficiency of the flyers. In systems where the inertial forces dominate over aerodynamic forces, which are normally characterized by systems with a low damping ratio, the use of elastic storage mechanisms can reduce the power requirements for flapping actuation. However, in systems whereby aerodynamic forces dominate inertial forces, the energy saving effect of actuation at resonance becomes less or negligible. Work performed by Yin and Luo (Yin & Luo, 2010) have shown that systems with aerodynamic forces dominating, such as in the dragonfly (Azuma & Watanabe, 1988; Sun & Lan, 2004; Azuma et al., 1985; May, 1991) exhibit optimal performance at frequencies lower than the natural frequency of the system. This is consistent with findings by Chen et al. (Chen, Chen, & Chou, 2008) that show dragonflies flapping at a frequency approximately 6 times lower than the natural frequency of the wings. A similar result was shown using computational methods by Jongerius and Lentink (Jongerius & Lentink, 2010). 14

37 1.6 Overview of contributions 1.6 Overview of contributions The main contributions of this thesis are presented in 8 chapters. summary of contributions of this thesis is given below The chapter by chapter Chapter 2 provides an overview of existing systems, the science and its limitations. Of note are the challenges present in flapping wing systems, including large inertial forces and complex interactions between aerodynamic, inertial and elastic forces. Chapter 3 discusses the use of resonance for energy savings and its effect on the mission capability of a flapping wing system. We show that whilst resonance is capable of reducing the inertial costs associated with hover, it comes with reduced glide performance and manoeuvrability. Chapter 4 will look at the significance of the upstroke-to-downstroke ratio in hover. Asymmetrical up-to-downstroke ratio is commonly observed in insects, and is an active control parameter in dragonflies. However, its effect on the performance in hover is often neglected. Chapter 5 will discuss a method for the optimisation of an actively controlled wing in hover. It presents a hybrid global/local method that gives the increased accuracy of a global solver with the reduced computational effort of a local solver. In chapter 6 we introduce the development of a low cost simulation platform for investigating flight dynamics in insects, specifically in manoeuvring flight. We show similarities between experimental and theoretical results in both pitching and rolling modes of flight. Chapter 7 collates findings from previous chapters and provides additional analysis that forms the basis for a design framework for an actively actuated dragonfly-inspired MAV. The construction of a representative test bench is then presented in chapter 8. Chapter 9 reuses the optimisation method in Chapter 5 to demonstrate the optimisation of wing kinematics for the experimental test bench. Chapter 10 then discusses a control methodology suitable for a 4 winged dragonfly-inspired system based on limit cycle oscillators. It should be noted that chapters 3, 4 and 5 are journal publications. Chapters 6 and 8 have been published in conferences. The related publications are highlighted below Chapter 3 (Journal publication) - Kok, J. M., and J. S. Chahl. Systems-level analysis of resonant mechanisms for flapping-wing flyers. Journal of Aircraft 51.6 (2014):

38 CHAPTER 1. INTRODUCTION Chapter 4 (Journal publication) - Kok, J. M., G. K. Lau, and J. S. Chahl. On the Aerodynamic Efficiency of Insect-Inspired Micro Aircraft Employing Asymmetrical Flapping. Journal of Aircraft (2016): Chapter 5 (Journal publication) - Kok, Jia-Ming, and Javaan Chahl. Optimisation of a Dragonfly-Inspired Flapping Wing-Actuation System. World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering 8.9 (2014): Chapter 6 (Conference publication) - Kok, J. M., and J. S. Chahl. A low-cost simulation platform for flapping wing MAVs. SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring. International Society for Optics and Photonics, Chapter 8 (Conference publication) - Kok, Jia Ming, and Javaan Chahl. Design and manufacture of a self-learning flapping wing-actuation system for a Dragonfly-inspired MAV. 54th AIAA Aerospace Sciences Meeting The content in these chapters have been kept the same as the publication. However, instead of an abstract, a chapter synopsis has been provided that details the outcomes of each of these publications and how it relates to the overarching concepts presented in this thesis. 16

39 CHAPTER 2 SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE 17

40 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE 2.1 Existing systems AS mentioned previously, flapping wing flyers in nature have the potential to offer capabilities not singularly possible by fixed or rotary wing air vehicles. Some of the more mature flapping-wing inspired robotic flyers are the Delfly, Harvard Robobee, and Nano Hummingbird. Figure 2.1: Existing flapping wing air vehicles. Delfly (Top Left); Harvard Robobee (Top Right); Nano Hummingbird (Bottom Left); TechJect QV (Bottom Right) The Delfy is a bio-inspired flapping wing MAV developed by Delft University of Technology. The second revision of the Delfly system weighed 16g and had a 28cm wingspan (Lentink, Jongerius, & Bradshaw, 2009). The system was capable of hover for 8 minutes and fast flight for 15 minutes. A single brushless motor was used to drive a crankshaft and gearbox combination that allowed synchronous flapping of four wings. The wing design was based on the dragonfly (Sympetrum vulgatum), and constructed using carbon fibre stiffeners and 0.5m thick one-sided film as the wing skin. Two magnetic actuators control rudder and elevator. The system is capable of carrying an on-board 2g camera. 18

41 2.1 Existing systems Another flapping wing vehicle is the Harvard Robobee designed by the team at Harvards School of Engineering and Applied Sciences. A 83mg vehicle with a wing span of 3cm was developed capable of open loop flight manoeuvers of lift-off, pitch and roll (Wood, 2008; Finio & Wood, 2012; Karpelson et al., 2009; Karpelson, Whitney, Wei, & Wood, 2010). A bimorph piezoelectric clamped-free bending cantilever is used to actuate the flapping motion of the wings. Two other similar actuators are attached either side of the vehicle providing directional control via changing the flapping profile. A small hovering ornithopter was developed as part of the Defence Advanced Research Project Agency (DARPA) Nano Air Vehicle (NAV) program by AeroVironment the Nano Hummingbird (Karpelson et al., 2010). The Nano Hummingbird has a wing span of 16.5cm, weighs 19g and has the capacity to transmit colour video to a remote ground station. In addition to sustained hover, it is capable of flying forward at speeds of up to 6.7 m/s. The Nano Hummingbird used servo motors to actuate a pair of wings (Roll, 2012). Roll, pitch and yaw control was achieved by individually modulating the lift generated on each wing. A system of string transmissions was used to provide passive wing pitch control about the leading edge of the wing. The wing twist was adjusted by applying and removing tension through the trailing edge spar of the wing. Another bio-inspired flapping wing MAV is the TechJect MAV, originally designed at the Georgia Institute of Technology (Ratti & Vachtsevanos, 2010, 2012). Inspired by the properties of a dragonfly, the TechJect QV utilises a four wing configuration. Each wing could be independently articulated in one DOF, with passive wing rotation. This 4-wing system utilizes electromechanical actuators to independently control each wing. Different variations of the system come with different actuator configurations. The first uses solenoid actuators (Ratti et al., 2011) to generate a fluctuating magnetic field that repeatedly flips a permanent magnet to generate the flapping motion. The second configuration uses a hypo-cycloidal gear train attached to a rotary actuator to convert rotary to linear flapping motion. This system weighs 25g and has a wing span of 15.2 cm. Whilst all the flapping wing systems mentioned are impressive feats of research, none of them are able to mimic the range of flight modes exhibited by the dragonfly. The Harvard 19

42 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE Robobee has only recently demonstrated lift-off, pitch and roll capabilities (Wood, 2008; Finio & Wood, 2012; Karpelson et al., 2009, 2010). The system is still in its infancy and has yet to demonstrate powered flight without an external power supply. This suggests an actuation system which is underpowered and is unable to generate the demanding forces required for dragonfly flight. Additionally, analysis of high speed motion footage of the Robobee shows limited control over its pitch and roll capabilities. The Delfly (Lentink et al., 2009; Jongerius & Lentink, 2010), like the Harvard Robobee, exhibits limited control of its flapping wings. A single brushless motor drives a carbon fibre transmission mechanism that converts the rotary motion of the brushless motor to a linear flapping motion. Additional control is provided by a tail which gives it turning capabilities. However, we know that this type of control is characteristic of fixed wing aircraft, and will only operate at higher speeds. This is not representative of what happens in dragonflies, which are able to perform complex manoeuvres even from a low speed or hover state (D. E. Alexander, 1986). The Aerovironment Nano Hummingbird has demonstrated precision hover flight, and fast forward flight. It also has gust tolerance of up to 2m/s. Videos of it flying have demonstrated capability to yaw and perform 360 degree lateral flips. However, the use of a string based transmission system places limits on the control of the wing, and hence the manoeuvrability of the system (Roll, 2012). In addition to the flapping amplitude being fixed, both wings are coupled which prevents asymmetric flapping which is crucial to manoeuvrability (Ruppell, 1989). The passive nature of the wing rotation also limits the controllability of the system. Whilst the amplitude of wing rotation can be adjusted, its timing cannot, meaning that instantaneous force modulation cannot be achieved unlike in active systems. We surveyed the literature to determine the configuration of flapping wing systems that have been designed for the purpose of flight. Table 2.1 shows an extensive list of existing flapping wing systems, and highlights the state of the art. We see that most configurations lend themselves to 2 wing configurations with a single DOF control per wing and often use passive wing rotation. Many of these systems also have a very specific operating wing-beat frequency, whereby beyond this frequency, the performance of the system begins to drop considerably. It is conceivable that most of these systems employ some form of resonance, or have some 20

43 2.2 Wing Kinematics Optimisation resonant point whereby the system is able to operate. However, observations of the dragonfly (see section 1.3) shows that the wing actuation system of a high performance flyer is more complex than the under-actuated, over simplified designs present in many studies. 2.2 Wing Kinematics Optimisation Following the design of a wing-actuator configuration capable of replicating insect wing motion, the flapping profile will need to be determined and optimised. The multi-physics nature of flapping wing systems makes accurate quantification of the performance of the flapping wing system and hence optimisation of the flapping profile difficult. Certainly within insects, the flapping profile is highly system specific as illustrated in Fig As shown there are a myriad of possible flapping profiles, all of which differ in 3DOF. Extending a similar principal to MAV systems, we can expect the optimal flapping profile to be unique to each system. Several methods exist to optimise the flapping profile mainly for hover which will be further discussed later. Figure 2.2: An illustration of possible wing kinematics. The lines represent wing chord, the dots represent the same edge of the wing during the stroke (adapted from (Berman & Wang, 2007)) Numerical analyses were one of the earliest techniques used in the literature to try and predict the forces generated on a flapping wing. One such method is the quasi-steady analysis that assumes instantaneous forces on a wing are independent of the transients and determined only by its current state. An example of a quasi-steady analysis is the blade element analysis that divides a wing section into discrete slices and obtains forces by summing the forces 21

44 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE Table 2.1: A summary of relevant flapping wing flyers and their characteristics Author Defining characteristics (Yan, Wood, Avadhanula, Sitti, & Fearing, 2001) (Yan & Fearing, 2003) (Madangopal, Khan, & Agrawal, 2005) (Madangopal, Khan, & Agrawal, 2006) (Syaifuddin, Park, & Goo, 2006) (Nguyen et al., 2008) (Wood, 2007) (Yang, Hsu, Ho, & Feng, 2007) (Park & Yoon, 2008) (Bejgerowski, Ananthanarayanan, Mueller, & Gupta, 2009) (Finio, Eum, Oland, & Wood, 2009) (Krashanitsa, Silin, Shkarayev, & Abate, 2009) (Tsai & Fu, 2009) (Baek, Ma, & Fearing, 2009) (Dileo & Deng, 2009) (Mukherjee & Ganguli, 2010) (Sahai, Galloway, Karpelson, & Wood, 2012) (Sahai, Galloway, & Wood, 2013) (Roll, Cheng, & Deng, 2013) (Hines, Campolo, & Sitti, 2014) 22 2DOF/2 wings Resonance 1DOF/2 wings Non-adjustable kinematics Passive wing twist Resonance 1DOF/2 wings Resonance Passive wing pitch 1DOF/2 wings Non-adjustable kinematics 1DOF/2 wings Non-adjustable kinematics 1DOF/2 wings Non-adjustable kinematics 2DOF/2 wings Resonance 1DOF/2 wings Non-adjustable kinematics 1DOF/2 wings Non-adjustable kinematics 1DOF/2 wings Non-adjustable kinematics 1DOF/4 wings Passive wing rotation 1DOF/wing Resonance 1DOF/ 2 wings Passive wing rotation 1DOF/wing Passive wing rotation Resonance 1DOF/wing Passive wing rotation Resonance

45 2.2 Wing Kinematics Optimisation acting on each individual slice. Weis-Fogh (Weis-Fogh, 1973, 1972) used such an analysis to perform a comparison of forces and power of several natural flyers. Computational Fluid Dynamics (CFD) analyses, which is an extension of a numerical analyses targeted at solving the Navier Stokes equations, have also been performed to better understand the forces and power requirements associated with flapping flight. Sun and Lan (Sun & Lan, 2004) performed threedimensional CFD analyses of a fore and hind dragonfly wing pairs flapping in tandem and observed the aerodynamic torque and power required. This was compared to the inertial power obtained using techniques presented by Sun and Tang (Sun & Tang, 2002). These analyses serve to provide insight into the mechanics of flapping wing actuation. However the complexity of the flapping actuation problem is such that no one method can be used to accurately and efficiently model the forces and power requirements associated with flapping wing actuation. The numerical analysis allows for a low cost, low fidelity simulation model to be generated, however the model is not sufficiently robust that it can account for the effects of inertial and elastic forces on the aerodynamics of the system. The CFD analysis is a higher cost, higher fidelity model than the numerical analysis. Whilst this form of analysis allows integration of the effects of the inertial and elastic forces, and is more accurate, the amount of computational effort required to resolve a model of such complexity would not justify the improvement in performance at an initial stage of design. The third method for quantifying and hence optimising the performance of a flapping wing system is through real world experimentation. Certainly experimental methods present a means by which we can capture the effects of real world physics on the flapping wing optimisation problem and is a more accurate method than conventional numerical methods. It does not require the prohibitive computational effort and time that a CFD simulation involves. Methods for the treatment of elasticity and inertial forces have been presented in research performed by Armanini et al. (Armanini, de Visser, de Croon, & Mulder, 2015). These methods however are specific to their platform and requires experimental results to augment the model. Therefore, the focus of this research was targeted at using experimental techniques for resolving and optimising the performance of a flapping wing system. Numerical methods were used to qualitatively explore, and potentially disprove, research trends that dominate flapping wing science. The performance criteria can be a range of parameters including lift or lift-to- 23

46 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE power. In this thesis we will focus on maximum lift generation Existing experimental techniques Experimental techniques provide a robust, low cost means for quantifying and optimising the performance characteristics of a flapping wing system. In addition, it allows real world, multiphysics effects to be accurately captured. The use of experimental techniques to measure the performance of a flapping wing system is not unique. Researchers at the Delft University of Technology (Lentink et al., 2009; Jongerius & Lentink, 2010) have performed experimental observations of the effect of the flapping profile on MAV system specific parameters. Flapping frequency and amplitude was varied to measure the effect it had on the total lift and power requirements. Variations were however only made in one degree of freedom, hence limiting the degree to which the system can be optimised. Wang and Kalyanasundaram (Y. Wang, Kalyanasundaram, Young, et al., 2008) developed a 1DOF test platform with a passive wing rotation to compare experimental and CFD results. Researchers at the Georgia Institute of Technology have also developed a 4 wing test bench to demonstrate control aspects of the MAV (Ratti & Vachtsevanos, 2012). Each wing was actuated in one DOF. The test bench specimen was allowed to rotate in three global axes. Genetic algorithms were used to tune the gains of the system to obtain faster settling and response time. Experimental flapping wing test benches capable of actuating a wing in 3 DOF have also been developed as early as Dickinson et al. (M. H. Dickinson et al., 1999) developed a 3DOF test bench to measure the effects of the aerodynamic structures such as rotational circulation, delayed stall, and wake recapture on the performance of the flapping wing system. Wing patterns and flapping profiles were designed around a scaled up variant of the fruit fly, the Drosophila Melanogaster. The wings were immersed in mineral oil to provide an environment that allowed for slower wing movements whilst still maintaining a Reynolds number regime representative of that experienced by the Fruitfly. Their results indicated that rotational circulation, delayed stall and wake recapture did indeed have an improvement on the aerodynamic performance of the system. Thomson et al. (S. L. Thomson et al., 2009) performed a similar experiment using the wing profile of the Manduca Sexta. A 3DOF test bench was designed and built with the purpose of using optimisation algorithms to determine the optimal flapping profile that maximised lift generation. 24

47 2.3 Optimisation techniques Similar to the experiment performed by Dickinson et al., the wing was scaled up and immersed in oil to match the Reynolds numbers. Whilst both of these sets of research methods meaningfully investigated the aerodynamic effects on flapping wing performance, they suffer from the same fundamental flaw. The flapping wings were subject to an artificial environment that did not fully account for the real world physics behind the flapping wing problem. 2.3 Optimisation techniques The problem of flapping wing actuation is a complex interaction of aerodynamic, inertial and elastic forces. When evaluating the performance of the wing-actuation system, there is the potential for multiple optima. To resolve this issue, optimisation techniques that rely on finding global optima can be used. Ghommem et al. (Ghommem et al., 2010) used a deterministic global optimization algorithm called VTDirect which subdivides regions where a global optimum is likely to be located. More precise analysis is than performed on these regions. Another optimization technique worth mentioning is the use of evolutionary algorithms. These algorithms attempt to mimic the process of natural selection in nature (Eiben & Smith, 2003). A random set of solutions, or candidates, are initially selected and assessed against a fitness function. The stronger candidates will have a higher likelihood of transferring their parameters to the next generation, which is done through recombination with another candidate or mutation. This process is repeated, producing a new set of improved candidates each iteration, until a termination criteria is addressed (see Fig. 2.3). This results in an optimised global solution. A commonly used evolutionary algorithm is the genetic algorithm. Rakotomamonjy et al. (Rakotomamonjy, Ouladsine, & Moing, 2007) used artificial neural networks to represent flapping wing profiles based on a parameter set of weightings and biases. Genetic algorithms were then used to evolve this set of parameters to produce a configuration that maximised the mean lift. Their results showed gains in mean lift from 30 to 40%. A potentially more computationally efficient extension of the genetic algorithm would be to use global methods to obtain an initial estimate of where the optimum solution is located and then apply local optimisation techniques to converge on a more precise solution. Berman and Wang (Berman & Wang, 2007) used a hybridised genetic algorithm to minimise energy 25

48 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE Figure 2.3: Illustration of the evolutionary algorithm optimisation process (adapted from (Eiben & Smith, 2003) ) requirements for hover. A clustering genetic algorithm (Milano & Koumoutsakos, 2002) was used initially to group the solutions into a globally minimal basin and then using a Powell simplex algorithm (Powell, 1970) for local optimization within that basin Scatter Search Algorithm Another evolutionary method that has been applied to the global optimisation process is the Scatter Search algorithm (Martí, Laguna, & Glover, 2006; Glover, 1997; Resende, Ribeiro, Glover, & Martí, 2010) which was first introduced by Glover in the 1970s as a heuristic for integer programming (Glover, 1977). Since then the scatter search algorithm has been applied to a wide range of problems that include unconstrained continuous optimisation problems (Fleurent, Glover, Michelon, & Valli, 1996), complex system optimisation (Laguna, 1997), neural network training (Kelly, Rangaswamy, & Xu, 1996) and other non-linear, multidimensional optimisation problems. Unlike other evolutionary algorithms such as genetic algorithms, the scatter search approach applies a set of rules to selecting members fit for inves- 26

49 2.3 Optimisation techniques tigation (Martí et al., 2006). The selection criteria initially is not just based on improving the objective function of the optimisation process, but also on the diversity of the solution space. This method differs from genetic algorithms in that it does not rely on a large, randomly generated initial population, which reduces the computational effort required. The most common template for implementing scatter search is described below. Diversification generation method that grows a set of trial points from an initial starting point Improvement method that aims to improve the existing set of trial points Reference set update method which narrows the additional set of trial points to a smaller, higher quality set. Criteria for selection is based on the objective function value as well as the uniqueness of the solution. Subset generation method that works on the reference set and produces subsets that can be used for creating combined solutions Solution generation method which transforms a given subset of solutions produced by the Subset generation method into a combined set of solutions. The diversification generation method generates a large set of diverse solutions and is often significantly larger than the reference set. The diversification method is based on controlled randomisation to grow an initial seed solution. The design space is broken down into equally spaced sub ranges, and then variables are randomly selected within each of these sub ranges. This produces a set of P init samples. The improvement method is then used to improve the selected samples. The reference set update method is then implemented. This generates a population of b ref samples, half of which consists of members with high objective values, whilst the other half consists of members significantly diverse from the other solutions in P init. Once this initial reference set has been produced, the subset generation method is then applied to divide the initial reference set into a group of subsets. Members within each subset are then allowed to combine, as part of the solution combination method, to produce additional trial 27

50 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE solutions which are then tested. Entry into the b ref population is allowed under the following conditions: The new trial point has a higher objective function value The new trial point is more unique The procedure terminates after all subsets have been subjected to the solution combination method, and none of the trial solutions are admitted into b ref. Figure 2.4 shows the pseudocode for such a procedure. Once the scatter search has been performed, local optimisation techniques can be applied to further optimise and refine the solution 28

51 2.3 Optimisation techniques Figure 2.4: Basic scatter search procedure 29

52 CHAPTER 2. SURVEY OF EXISTING SYSTEMS AND THEIR SCIENCE 2.4 Conclusion In the introduction (see chapter 1), we see that there is a gap in the MAV design space for a platform that is able to replicate the capabilities of both fixed and rotary winged aircraft. As an integrated system, it would be capable of independantly performing complex missions not singularly achievable by either fixed or rotary wing platforms. Examples of these missions include the last mile delivery problem. The solution to this design gap has been provided in nature through 300 million years of optimisation, and exists in the form of a flapping wing system. Of these, the dragonfly has proven itself to be one of the most versatile flyers, able to perform glide, forward flight and efficient hover. They have also demonstrated agile and versatile flight manoeuvres such as yaw turns, roll banks, reverse flight and have generated accelerations in excess of 4Gs. This makes them a suitable candidate from which to draw inspiration. Section 1.3 discusses the factors that make the dragonfly such a versatile flyer - the wingactuation system and the flapping profile associated with it. We see that the dragonfly wingactuation system is characterised by a four wing configuration, and that it has an extraordinary control over its parameters, including in phase, frequency, amplitude, wing pitch, stroke plane angle. This is in contrast to many of the under-actuated systems outlined in section 2.1 that have evolved out of simplicity of design. The second defining feature of the dragonfly wing-actuation system is that it can achieve a flapping profile over an inclined stroke plane. This flapping profile varies between different dragonfly species and even between dragonflies of the same species, suggesting that the flapping profile is highly system specific, and is tuned to the parameters of the system. There is no one globally optimal flapping profile which will work for every system. Therefore, we propose that the solution to the problem of a bio-inspired flapping wing flyer can be described as the development of a wing-actuation system capable of replicating the kinematics of a dragonfly, and opimising the flapping profile to the wing-actuation system. 30

53 CHAPTER 3 A SYSTEMS LEVEL ANALYSIS OF RESONANT MECHANISMS FOR FLAPPING WING FLYERS Synopsis In Chapter 2, Table 2.1, we see research that is targetted at the use of resonance to mitigate the inertial costs associated with hover. Whilst the use of resonance can result in energy savings in hover, its effect on the performance of the flapping wing system mission envelope is unknown. This chapter analyses the system level consequences of energy saving resonant mechanisms across the full flight envelope of hover, manoeuvre and glide of flapping wing systems. This is consistent with the motivation to develop a bio-inspired air vehicle capable of mulit-mission flight. A review of the extent to which resonant mechanisms are employed in a dragonfly and how useful they are to a manoeuvring flapping wing MAV system shows that the value of resonance is limited. We show that employing resonant elastic mechanisms in real world configurations on an aerodynamically efficient flyer could produce insignificant energy savings. This benefit is further reduced by at least 14% across the operational flapping frequency band of dragonflies, suggesting that resonance is not the major driver for aerodynamically efficient flyers. Using a simple harmonic oscillator as a simplified model, we demonstrate a significant reduction of 50 to 70% in manoeuvring limits for a system employing elastic elements. In systems with elastic storage, aeroelastic instabilities leading to reductions in maximum glide speed are possible, particularly for aerodynamically dominated systems. We conclude that the system level cost of implementing resonant mechanisms indicate against resonance in hover being a primary factor in the design of a dragonfly or dragonfly-inspired 31

54 aircraft. CHAPTER 3. A SYSTEMS LEVEL ANALYSIS OF RESONANT MECHANISMS FOR FLAPPING WING FLYERS This work has been published in a journal: Kok, J. M., and J. S. Chahl. Systems-level analysis of resonant mechanisms for flappingwing flyers. Journal of Aircraft 51.6 (2014):

55 Abbreviations Nomenclature UAV s MAV s K I φ Φ ω α Unmanned Aerial Vehicles Micro Air Vehicles Elastic constant Inertia Flapping angle Flapping amplitude Flapping frequency Pitch angle α Mean pitch angle Θ β V r C L C D L D S Pitch amplitude Stroke plane angle Local velocity of blade element Radius of blade element Lift coefficient Drag coefficient Lift Drag Blade area 33

56 Abbreviations ρ Density H r Vertical force in wing reference frame H r,vert P τ Vertical force in global frame of reference Power Torque ω n Resonant frequency B Damping constant E a Aerodynamic energy ω d Damped natural frequency λ K φ K h U s c B/2I Torsional stiffness Translational stiffness Critical velocity Semispan Mean chord of the wing 34

57 3.1 Introduction 3.1 Introduction IN recent years, Unmanned Aerial Vehicles (UAVs) have been a growing area of research. Since the inception of UAVs, these unmanned aircraft have begun replacing piloted aircraft particularly in Defence applications. Their operational uses include aerial surveillance and reconnaissance and support to ground forces. One particular branch of UAV research has been focussed on biologically inspired flapping wing aircraft. This area of research has been facilitated by technological advancements in many fields including micro-electronics, sensors, microelectromechanical systems, and micromanufacturing. Bio-inspired flapping wing aircraft differ from conventional fixed aircraft in that they offer potential benefits including the ability to hover. They are also capable of operating at lower Reynolds numbers (Mueller, 2001, pp.74-78) as compared to rotary aircraft which display reduced performance at low Reynolds numbers (Bohorquez & Pines, 2003). This makes them a viable design for small size, low speed aircraft, otherwise known as Micro Air Vehicles (MAVs) (Ashley, 1998; Sirohi, 2013). In addition, flapping wing flyers cover a large range of strategic manoeuvres not singularly capable by their fixed or rotary wing counterparts. Dragonflies in particular are able to take-off and land vertically, fly backwards and sideways and accelerate rapidly (D. E. Alexander, 1986; Chahl, Dorrington, & Mizutani, 2013; Mizutani et al., 2003; Ruppell, 1989). Such a versatile range of motion expands the mission envelope of the aircraft system, making it worth investigating. Whilst flapping wing MAVs present many possible applications, the science behind the actuation system is yet to be fully understood and is far from being convincingly replicated by technical systems. The cyclic nature of the flapping wings introduces coupled inertial, aerodynamic and elastic loads that must be overcome to successfully actuate a wing. Additionally, these loads vary between different insects and have a strong influence on the performance of the system. Greenewalt (Greenewalt, 1960) used a simple harmonic oscillator (SHO) model to show the variations in the actuation force required between different insects while Weis-Fogh (Weis-Fogh, 1973) used experimental data combined with quasisteady numerical analysis that showed significant variations in the proportion of aerodynamic to inertial loading between dif- 35

58 Abbreviations ferent insect species. Some researchers have proposed the presence of resonance as a means to reduce the inertial power requirements associated with flapping actuation via elastic storage (Ratti & Vachtsevanos, 2012). Certainly some systems such as the Harvard Microrobotic Fly rely heavily on the use of resonance to enable the system to take-off (Wood, 2008). Other studies have also demonstrated energy savings of 20% by using elastic storage mechanisms (Sahai et al., 2013; Baek et al., 2009). Certainly in systems whereby the dominant force is inertial forces, the use of resonant mechanisms will allow for significant energy savings. However in systems that are dominated by aerodynamic forces, the use of resonance is questionable (Ramananarivo et al., 2011; Sahai et al., 2013). Ramananarivo et al. (Ramananarivo et al., 2011) demonstrated that flapping flyers improve performance by tuning their wing shapes to optimize aerodynamics as opposed to optimising for resonance. Researchers should also be aware that the amount of energy that can be saved through resonance is dependant on the inertial requirements of the system. Additionally, studies by Yin and Luo (Yin & Luo, 2010) have shown that systems dominated by inertial forces have lower performance as compared to systems dominated by aerodynamic forces. Yin and Luo showed that a low inertia wing has better lift performance and power efficiency. This suggests that aerodynamically dominated flapping wing systems, such as the dragonfly, have the potential to offer better performance than inertia dominated systems. This chapter aims to explore the energetics behind flapping wing actuation and the effect of resonant mechanisms on the hovering, gliding and manoeuvring performance specific to a aerodynamically efficient, four winged dragonfly-inspired flyer capable of all three modes of flight (dragonfly inspired). 3.2 The dragonfly Insects are amazing natural flyers. Amongst insects, the dragonfly planform was amongst the first to evolve and is thus amongst the longest surviving flying organisms. Observations of the dragonfly genealogy show that its ancestry can be traced back to the Protodonata, which are 36

59 3.2 The dragonfly amongst the earliest winged insect fossils discovered (Wootton, 1976; May, 1982). This suggests that the evolution and optimization of dragonflies dates back 300 million years. Certainly, dragonflies have ruled the skies as the supreme aerial predator for over 100 million years. This evolutionary process has made dragonflies extremely versatile flyers. In addition to being able to hover, they are able to glide efficiently as well. Azuma et al. (Azuma & Watanabe, 1988) demonstrated the excellent glide properties of dragonflies using numerical methods, whilst Wakeling and Ellington (Wakeling & Ellington, 1997a) performed a similar analysis using measurements in a wind tunnel. Dragonflies also exhibit an aerial agility that allows it to out manoeuvre and prey on other insects, in particular the more common diptera. Slow motion footage taken by Ruppell (Ruppell, 1989) show instantaneous accelerations of up to 4g and sustained and take-off accelerations of up to 2g. Maximum speeds demonstrated by dragonflies were up to 10m/s which are in the order of the operational speeds of some MAVs. Analysis of a video of dragonflies in combat by Chahl et al. (Chahl, Dorrington, & Mizutani, 2013; Mizutani et al., 2003) showed accelerations in turns exceeding 4g. Wind tunnel studies performed by Alexander (D. E. Alexander, 1986) show that at low speeds, dragonflies employ a yaw turn manoeuvre whereby a 90 o yaw is achieved in 2 wing beats. It is these properties that allow for sophisticated predation strategems (Mizutani et al., 2003) that make dragonflies excellent aerial predators. The extensive capabilities of the dragonfly can be attributed to the unique degree of control the dragonfly has over its flapping actuators and hence flapping profile. Alexander showed that dragonflies were able to adjust the phase lag between the fore and hind wing to switch between normal flight and flight manoeuvres requiring high forces (D. E. Alexander, 1984). He further showed through high speed cinematography in a wind tunnel the capability of the dragonfly to adjust both its stroke plane angle and angle of attack of the individual wings to perform complex yawing or banking turns (D. E. Alexander, 1986). Even during hovering flight, Wang proposed that dragonflies rely on adjusting the angle of attack of the wing to reduce the energy costs of hover (Z. J. Wang, 2004). Certainly observations of the wing actuators of dragonflies support these theories. An investigation of the actuation system in dragonflies shows their capability to actively control and effect wing rotation (Sviderskiĭ et al., 2008; Simmons, 1977). 37

60 Abbreviations Svidersky et al. (Sviderskiĭ et al., 2008) expand on this investigation by comparing the actuation system of the dragonfly to a less manoeuvrable four winged insect, the locust. Their findings showed that the following factors give dragonflies its increased manoeuvrability over locusts The structure of the wing base and characteristics of the muscles gave the dragonfly the ability to actuate all four wings independently by the phase, frequency and amplitude. Dragonflies have active supination and pronation while locusts have passive supination Dragonflies have a large number of motor units in their muscles used for supination and pronation. This gives it the ability to more finely regulate the strength of their strokes Dragonflies are able to shift their wings along the horizontal plane as well Studies (Dudley, 2002) have shown that the dragonfly employs a direct drive mechanism whereby the actuators/muscles of the dragonfly are attached to the wing root and actuate the wing directly. This is in contrast to the indirect mechanism commonly found in insects that dragonflies prey on (i.e. diptera). In the indirect mechanism, the muscles are attached to the wings via the thorax. The contraction and expansion of the muscles deform the thorax which in turn articulates the wing. In addition to the indirect attachment of flight muscles to the base, the flight muscles are also asynchronous (Boettiger & Furshpan, 1952; M. H. Dickinson, Lehmann, & Chan, 1998). Thus a signal in motor neurones in the muscle does not produce a corresponding wing beat, but rather several wing beats. Additional wing beats are produced by the restorative forces applied by the elastic mechanism (Josephson, Malamud, & Stokes, 2000; Jewell & Ruegg, 1966). Such a configuration explains the capability of indirect muscles to operate at high wing-beat frequencies, however it also adds the requirement for an elastic storage mechanism. In addition, the indirect muscles are incapable of steering the wing (M. H. Dickinson, 2005). Wing articulation is controlled predominantly by smaller direct drive muscles (M. H. Dickinson, 2005; Heide, 1983; Wisser & Nachtigall, 1984). The direct drive mechanism in dragonflies is therefore significant in producing the high degree of controllability the dragonfly has on its wing articulation. The addition of a direct drive mechanism and the 38

61 3.3 Operating Frequency low wing-beat frequencies of the dragonfly also suggests that the requirement for the elastic restorative forces required by flies is not necessary in every configuration, and might be detrimental to the controllability of the dragonfly. This raises questions about the extent to which elastic mechanisms are employed in dragonflies. 3.3 Operating Frequency Another contributing factor to the discussion of resonance is the band of flapping frequencies in which dragonflies operate. For a resonant system to be efficient requires flapping motion to occur at the natural frequency. High speed videos taken by Ruppell (Ruppell, 1989) show different dragonflies operating over a broad range of frequencies with deviations from the maximum frequency of as large as 25-72%. To quantify the effect of having such a large flapping frequency band on resonance, a numerical quasisteady simulation was performed on a single wing taking into account the inertial, aerodynamic and elastic forces. Similar studies have been performed by Weis-Fogh and Norberg (Weis-Fogh, 1973; R. A. Norberg, 1975). In both studies, the effect of the wing-beat frequency spread was not taken into account. Using the numerical quasisteady simulation, the forces acting on the wing and power expenditure across its full range of motion was calculated and compared between a case employing resonant mechanisms and the case without. Morphological parameters of an Aeshna juuncea dragonfly (R. k. Norberg, 1972; R. A. Norberg, 1975) were used to determine the inertial and elastic forces acting on the dragonfly. The inertial and elastic forces were modelled as linear functions, proportionate to angular acceleration and position respectively, i.e. ElasticF orce = Kφ (3.1) InertialF orce = I φ (3.2) To determine the aerodynamic forces acting on the wing, a three dimensional, quasisteady model was employed. The wing was divided into spanwise sections, and the instantaneous forces calculated on each section based on the local velocity. The forces across all slices were then summed to obtain the forces/torques acting on the wing at any point in time. The wing 39

62 Abbreviations kinematics were represented using equations from Wang (Z. J. Wang, Birch, & Dickinson, 2004; Z. J. Wang, 2004) for a wing flapping in an inclined stroke plane with angle β. This inclined stroke plane is more characteristic of a dragonfly flapping profile. The flapping angle, φ, and angle-of-attack, α, in the stroke plane is represented by φ = Φ cos(ωt) (3.3) 2 α = α 0 + Θsin(ωt) (3.4) Using this information, the local velocity at each spanwise section of the wing as well as the lift and drag coefficients can be determined, and used to calculate the lift and drag forces (see Fig. 3.1). Figure 3.1: Illustration of the aerodynamic forces acting on a single section of the wing. The drag force is used to calculate the aerodynamic torque exerted on the wing. The lift and drag forces are vectorially added to determine the vertical component of force (adapted from Norberg (R. A. Norberg, 1975)). 40

63 3.3 Operating Frequency Equations for the lift and drag coefficients were obtained from three-dimensional experiments performed by Dickinson (M. H. Dickinson et al., 1999; Z. J. Wang et al., 2004). Similar coefficients were obtained by Wang computationally and used as the basis for analysing dragonfly flight (Z. J. Wang, 2004; Z. J. Wang et al., 2004). Morphological parameters for the wing shape were obtained from Norberg (R. k. Norberg, 1972). V = r φ (3.5) C L = sin(2.13α 7.2) (3.6) C D = cos(2.04α 9.82) (3.7) The aerodynamic forces and torques were then calculated at each section of the wing. The overall aerodynamic torque can then be calculated by summing the torques of all wing sections. L = 0.5ρV 2 SC L (3.8) D = 0.5ρV 2 SC D (3.9) It should be noted that the direction of the lift and drag forces are with respect to the velocity of the wing section. To determine the actual lift force generated by the wing in the global reference frame, a coordinate transformation was employed (see Fig. 3.2). The vertical force in the frame of reference of the wing is given by H r = Lcos(β) + Dsin(β) (3.10) and the vertical force with respect to the global frame of reference is H r,vert = H r cos(φ P roj ) (3.11) An equation for cos(φ P roj ) was calculated using the formulation from Norberg (R. A. Norberg, 41

64 Abbreviations Figure 3.2: Illustration of the coordinate transform required to determine the actual lift generated by the wing in the global frame of reference (adapted from Norberg). 1975). Therefore the vertical force with respect to the global frame of reference is H r,vert = H r 1 sin2 αsin 2 β (3.12) In previous work performed by Kok et al (J. Kok & Chahl, 2014b) using this model, they demonstrated that across the operational range of a dragonfly, the use of resonant mechanisms has minimal, if not detrimental effects on efficiency of the system. Their analysis also shows that at lower wing-beat frequencies, the lift-to-power ratio is reduced by the use of resonant mechanisms. 3.4 Manoeuvrability As mentioned previously, dragonflies are some of the most agile natural flying predators, able to perform 90 o turns in the time span of 2 wing beats (D. E. Alexander, 1986), and sustain accelerations of up to 4g (Ruppell, 1989; Chahl, Dorrington, & Mizutani, 2013; Mizutani et al., 2003). A system which relies purely on the effect of resonance for lift generation is less 42

65 3.4 Manoeuvrability adaptable to sudden changes in force due to the inherent build-up time required to achieve the steady state condition. This is apparent in a comparison between Anisoptera and the small Diptera on which they prey. The ability of the dragonfly to hunt and feed on diptera suggests a higher requirement for manoeuvrability (Woodward, 2001, p.345). A comparison of the aerodynamic efficiencies of typical Anisoptera and typical Diptera showed that in general the Dipteran order of insects has a lower aerodynamic efficiency in the order of 40% (Weis-Fogh, 1973) and hence is more likely to rely on the effect of resonance to overcome their inherently higher inertial forces. This presents a qualitative argument that systems employing resonance, or elastic storage, are less manoeuvrable. In this section we explored the effect of elastic storage or stiffness on the manoeuvrability of the system. To do this we employed an extension of the simple harmonic analysis and explored the response of a system to a step force input. This was done for two different damping/aerodynamic models, the first being a linear model, the latter being a quadratic model. The linear aerodynamic damping model can be represented by the following linear second order differential equation I φ + B φ + Kφ = F (3.13) where 1, t < T/2 F = 0, t T/2 (3.14) The step force input was selected as it is analogous to the sudden and instantaneous downstroke of a dragonfly employed during high acceleration manoeuvres such as take-off and yaw turns. The damping forces and damping energy were derived and used as the performance metrics to compare the manoeuvrability between systems with and without elastic storage mechanisms. The damping force is assumed to be proportionate to the angular velocity, i.e F Damping = B φ (3.15) The system is represented in Figure

66 Abbreviations Figure 3.3: Illustration of the muscle input into a dragonfly wing in manoeuvring flight. To obtain an estimate for the damping coefficient, B, morphological parameters from Norberg (R. k. Norberg, 1972; R. A. Norberg, 1975) and computational data from Sun and Lan (Sun & Lan, 2004) were used. Through computational simulations, Sun and Lan determined the power expanded on overcoming aerodynamic forces over the period of the wing stroke. The aerodynamic energy expended per wing stroke was calculated to be J by integrating the power profile over the period of the wing stroke. From first principles, the aerodynamic energy per wing-stroke is given by B φ 2 dt where φ is the angular rate. For a damped simple harmonic oscillator (SHO) model, φ = ωφcos(ωt). Therefore, the aerodynamic energy is given by E A = B(ω Φ 2 )2 cos 2 (ωt)dt (3.16) which when integrated over the period of the wing stroke equates to πωb Φ 2 2. The equation can be rearranged to give an estimate of the average damping coefficient, B B = E A πω Φ 2 2 (3.17) Equations for the angular velocity φ for a system with and without elastic storage was derived from literature (Dimarogonas, n.d., pp ) and first principles respectively. No Elastic Storage: A system with no elastic storage and a step force input was represented by the following 44

67 3.4 Manoeuvrability equation I φ + B φ = F (3.18) and solved using integration by applying the substitution Φ = φ and the initial conditions, Φ = 0 when t = 0. The final equation was given by φ = F B F B e (B/I)t (3.19) Elastic Storage: λf [ φ = Iω d (λ 2 + ωd 2) λe λt (sin(ω d t) ω d λ cos(ω dt)) e λt ω d (cos(ω d t) + ω ] d λ sin(ω dt)) (3.20) Using these equations, the velocity and hence damping force over the period of the step was calculated for a system with and without elastic storage (see table 3.1). The damping force was time averaged over the period of the wing stroke and non-dimensionalised against the actuator input force. As shown in Table 3.1, a system with no elastic storage is able to instantaneously generate twice the amount of force that a system with elastic storage can. This ability to generate more aerodynamic force for the same actuator input suggests that the system without an elastic storage mechanism is more manoeuvrable. Table 3.1: Comparison of time averaged, non-dimensionalised damping force for systems with and without elastic storage Property With elastic storage Without elastic storage Non-dimensionalised damping force To verify the analytic solution, a numerical analysis was performed using the Simulink tool kit in Matlab. A unit step was applied to the systems with and without elastic storage and the response recorded (see Fig. 3.4). As shown, a similar result to the previous analytic solution was observed. The system without an elastic storage mechanism was able to generate more damping force than a system with an elastic storage mechanism. Based on the results obtained analytically and numerically, we concluded that an actuator with no elastic mechanism is better suited to instantaneous force transmission akin to that required during highly manoeuvrable flight. 45

68 Abbreviations To provide a more accurate representation of this model, we investigated the effect of using a quadratic aerodynamic damping term. Similar to the previous quasisteady aerodynamic model as well as models presented by Norberg and Weis-Fogh (R. A. Norberg, 1975; Weis- Fogh, 1973), aerodynamic forces are proportional to the square of the relative air velocity and hence square of the angular velocity of the wing (i.e. F Damping = B φ φ). A quadratic model will allow us to capture these factors. No Elastic Storage: I φ + B φ φ = F (3.21) Elastic Storage: I φ + B φ φ + Kφ = F (3.22) Using the energy method described previously, we estimated the new damping coefficient. The Figure 3.4: Response of two damped systems with and without elastic storage mechanisms to an instantaneous step input (Top). The dashed and solid lines represent systems with and without elastic storage respectively. The damping force (Bottom) is the performance metric for determining the manoeuvrability of the system. 46

69 3.4 Manoeuvrability aerodynamic energy expanded per wing stroke is given by E A = B ( ω Φ ) 3 cos 3 (ωt) 1 dt = 2 3 Bω2 Φ 3 (3.23) Rearranging equation 3.23, we can obtain a value for the damping coefficient. Using this new value, we solved this model in Simulink. The following results (see Fig. 3.5) shows the damping/aerodynamic forces acting on the system which are modelled as quadratic terms. Similar to results obtained from the linear SHO model, the damping force for the same actuator input was greater for a system that did not employ resonant mechanisms. Figure 3.5: Response of two damped systems with and without elastic storage mechanisms to an instantaneous step input (Top). The aerodynamic forces are represented by a quadratic function. The dashed and solid lines represent systems with and without elastic storage respectively. The damping force (Bottom) is the performance metric for determining the manoeuvrability of the system. Table 3.2 summarises the results from the Simulink simulation for both the linear and quadratic aerodynamic models. The damping force was non-dimensionalised with the actuation force, F and averaged over the period of a downstroke. As shown, in both the linear and quadratic aerodynamic models, for the same actuator input, the system without an elastic storage mechanism generated 2 times more damping force than the system that used an elastic 47

70 Abbreviations storage mechanism. This would suggest that a system designed for manoeuvrability would sacrifice that manoeuvrability if it were to employ resonant mechanisms. Table 3.2: Comparison of arbitrary values of damping force and energy for systems with and without elastic storage Time averaged damping force With elastic storage Without elastic storage Linear model Quadratic model Gliding Flight In addition to being able to hover and manoeuvre rapidly, dragonflies are also relatively efficient gliders. The ability to glide is critical for fixed wing MAVs. However, like fixed wing MAVs, dragonfly wings potentially suffer from the same aeroelastic effects, in particular flutter (R. k. Norberg, 1972). Flutter is the condition whereby elastic forces generated by the bending and twisting of the wing couple with aerodynamic forces to generate a oscillatory motion which is not only detrimental to glide performance and controllability but can lead to structural divergence and failure of the system. The speed at the onset of flutter is referred to as the critical speed and is dependent on the overall stiffness of the system. By filming Sympetrum sanguineum in flight, Wakeling and Ellington (Wakeling & Ellington, 1997a) showed that dragonflies periodically glide between wing strokes. Their results showed glide speeds of up to 2.6m/s. Ruppell (Ruppell, 1989) showed maximum speeds of 7.5 to 10m/s for bigger species of dragonflies. Experimental studies performed by Norberg on similary sized dragonflies (R. k. Norberg, 1972) have shown that dragonfly wings are able to withstand flutter up to speeds of 9.1 to 10.6m/s. This suggests that flutter is the major factor affecting the maximum speed of the dragonfly. Therefore bio-inspired aircraft designs looking at replicating the mission capabilities of the dragonfly, including its glide characteristics, should take into account the effects that resonant mechanisms could potentially have on the aeroelastic properties of the system. Fung (Fung, 1955, pp ) presented a set of criterion relating the critical speed to the stiffness of the system based on Kussner s formula. 48

71 3.5 Gliding Flight Torsional stiffness: Flexural stiffness: K φ Constant (3.24) ρu 2 s c 2 K h Constant (3.25) ρu 2 s3 Kussner s formula showed that the critical speed U is proportional to k. This suggests that for an air vehicle to be able to operate at higher speeds and hence be proficient and controllable in gliding flight, requires it to have a stiffer wing-actuator system. Observations of dragonflies showed that they had relatively stiff wings that allowed them to maintain high critical speeds. Certainly dragonfly wings have evolved span-wise and chordwise corrugations as well as an extensive system of wing venation that modulates the stiffness of their wings (Rees, 1975; Combes & Daniel, 2003). Combes (Combes & Daniel, 2003) further showed that compared to many other insect species, Odonata in general have wings with higher span-wise and chord-wise stiffness. This theory is further reinforced by experimental results from Chen et al. (Chen et al., 2008) and later verified computationally by Jongerius and Lentink (Jongerius & Lentink, 2010). Both studies found that the dragonfly wing has a natural frequency 5-6 times greater than the wing beat frequency, suggesting a wing system which is relatively stiff. Similar results were observed for the torsional stiffness of the wing as demonstrated by experiments performed by Sunada et al. (Sunada, Zeng, & Kawachi, 1998). Their results demonstrated torsional natural frequencies twice the wing beat frequency. It is unclear as to the impact of aeroelastic conditions on the viability of resonant mechanisms on dragonflies, it is however a factor that bio-inspired aircraft designers will have to account for. This is particularly true for systems with high aerodynamic efficiency due to the relatively low inertial forces. Systems with low inertial forces required proportionately lower elastic coefficients to tune the natural frequency of the system to the wingbeat frequency. If unmanaged, this could result in significantly lower critical speeds, and hence reduced glide properties. 49

72 Abbreviations 3.6 Discussion Throughout this chapter we discussed the relevance of resonant mechanisms with regards to a high performance natural flyer, the dragonfly. A review of the literature suggested that the theoretical energy savings as a result of employing resonant mechanisms could be as low as 19%, assuming 100% efficient elastic storage. Similar results were obtained from numerical quasisteady analysis on a dragonfly wing, that showed time-averaged power savings of 14%. However, in real world systems, 100% elastic storage efficiency is not possible. Lehmann et al. (Lehmann et al., 2011) performed experiments on fly wings that showed 77-80% elastic efficiency. Estimates of elastic efficiency of the locust thorax and inactive muscles (Andersen & Weis-Fogh, 1964) showed values of 86% and 80% respectively. Certainly the most energy efficient storage springs in realistic configurations have been quoted to have 33% elastic storage efficiency by (Tooley, 2009, p.543), suggesting that in a real world system, the effect of using elastic storage mechanisms for heavily damped flapping wing actuators could be insignificant. Depending on the mission profile of the aircraft system, in particular the expected time in hover, such energy savings may or may not be significant to the designer. Flapping wing aircraft design must also take into consideration the wing beat frequency range at which the aircraft will operate. Observations of dragonflies showed that they operate over such a large range of wing beat frequencies that any resonant mechanism would significantly degrade in performance, and possibly even have detrimental effects. We demonstrated this, using a quasisteady numerical analysis to represent the system of forces acting on the dragonfly wing. The power saved and lift-to-power ratios were derived and used to quantify the efficacy of the resonant mechanism. It should be noted that certainly more advanced models exist that use computational means (Sun & Lan, 2004). These models are more accurate in capturing the time-dependant system of forces acting on a wing based on known flapping wing kinematics. However the additional accuracy of these models does not justify the amount of time required to generate them. The quasisteady model is sufficient to demonstrate the fundamental principles and drawbacks associated with the resonant concept as used in a flapping wing context. The results showed that across the range of dragonfly operating frequencies, significant reduction in the power savings was observed. This brings into question 50

73 3.6 Discussion the theory of resonance being employed on aerodynamically efficient flyers such as the dragonfly. Results by Yin and Luo (Yin & Luo, 2010) also support this theory. They showed that for wings dominated by aerodynamic effects, the wing-beat frequency for optimal power efficiency was almost 50% of the natural frequency. Similar results were obtained by Ramananarivo et al. (Ramananarivo et al., 2011) who showed optimal thrust performance at a wing-beat frequency of 70% of the natural frequency. Power and thrust performance peaking at frequencies so far below the natural frequency supports the hypothesis that resonance is not employed in dragonflies. An analysis of the lift-to-power ratios also showed that a system without elastic storage had the potential to outperform a similar system with elastic storage at lower wingbeat frequencies. A potential solution that aircraft designers could employ to reduce the effect of the wing-beat frequency spread would be to employ a thorax with active stiffness modulation. This would allow the natural frequency of the system to be tuned to the wing beat frequency. Whilst the stiffness of the wing-actuation system in insects can change during a wing stroke (Hollenbeck, 2012), a review of the existing literature shows no known cases of active stiffness tuning in dragonflies. The significant degradation in the performance of resonant systems further from the resonant frequency suggests flapping-wing aircraft designs looking at implementing resonant mechanisms can only operate within a very narrow band of wing beat frequencies. This implies that aircraft designs utilising elastic storage for flapping wing flyers will require Fixed Frequency Variable Amplitude (FiFVA) actuators (Ratti et al., 2011). These actuators use amplitude modulation as opposed to frequency modulation to manipulate aerodynamic loads. However, this in itself presents problems. Whilst effective control of the dynamics of the system can be achieved using the FiFVA actuation, we know that in dragonflies, frequency modulation is used to control aerodynamic forces as well (Ruppell, 1989). One possible explanation for this phenomenon could include the fact that frequency modulation provides a means of varying the lift and thrust forces additional to amplitude modulation hence giving finer control. Additionally, the combined effect of using both frequency and amplitude modulation could also explain the large forces that the dragonfly requires to achieve accelerations of up to 4g (Chahl, Dorrington, & Mizutani, 2013; Ruppell, 1989; Mizutani et al., 2003), giving it its highly manoeuvrable characteristics. 51

74 Abbreviations From a systems perspective, we saw that practical implementation of resonant mechanisms comes at a cost to manoeuvrability. To model this further, we modified the simple harmonic oscillator analysis and used a constant step force input as opposed to a sinusoidal input. The time averaged damping force was selected to arbitrarily compare the manoeuvring capabilities of flapping wing systems with and without resonant mechanisms. Results showed that a system without an elastic storage mechanism was able to generate more aerodynamic force for the same force input. It was also able to impart more energy to the air, via the damping effect, suggesting that it is converting more of the actuator input energy into aerodynamic work. This was true for both linear and quadratic aerodynamic models. This enhanced performance can be explained by the fact that the system without a resonant mechanism was not required to overcome the inherent elastic forces. It should be noted that a step input is not an accurate model of the actual forces applied at the base of the dragonfly wing. However, a step input is representative of a sudden and instantaneous force being applied to the wing, which is similar to the effect of rapid manoeuvres by dragonflies (D. E. Alexander, 1986). Certainly other force inputs could also be considered, such as an impulse function to test the manoeuvrability of the system. Close agreement between analytical and numerical results suggested that the numerical model is sufficiently accurate for this purpose. An alternative to the computational approach would be to perform real world experimentation on a test bench that is capable of replicating the wing kinematics of a dragonfly in 3 DOF. This would allow us to accurately capture the real world aerodynamic, inertial and elastic forces acting on the dragonfly wing. In addition to a reduction in manoeuvring capability, the use of elastic storage potentially has detrimental effects on the glide properties of a flapping wing flyer. Using Kussner s formula (Fung, 1955, pp ), we demonstrated the relationship between the critical speed and stiffness of the wing-actuation system, U cr K. Like a fixed wing aircraft, the dragonfly wing in glide is subject to the same aeroelastic principals. Similarly, the effects of torsional and translational stiffness as it applies to critical velocity (or velocity in which flutter occurs) in a fixed wing aircraft should apply to a dragonfly-like system in glide. The use of elastic storage could reduce the natural frequency of the system and hence the critical speed at which aerodynamic flutter occurs. This probability is higher for aerodynamically efficient flyers in particular. Additionally, aircraft designs not implementing the dragonflies gliding mode should take into account the impact of the critical speed on gust stability. Systems with lower critical speeds are more 52

75 3.6 Discussion susceptible to gusts. Therefore aircraft designs that implement elastic mechanisms to tune the natural frequency of the system to the wing-beat frequency should take into consideration the real-world impact of the elastic mechanism on the critical speed. The configuration of the actuation system will have a significant role. For example, flapping wing systems that employ a relatively stiff wing with the actuator attached directly to the wing base (see Fig. 3.6) will find that the elastic mechanism has no effect on the glide performance when the actuator is holding position. However, systems that are using an elastic mechanism as a transmission medium between the actuator and the wing (see Fig. 3.6) will find that reducing the natural frequency to match the wing beat frequency does indeed have an effect on the critical speed. Similarly aircraft systems that rely on reducing the stiffness of the wings to achieve resonance will face a similar issue. In summary, we saw that for aerodynamically efficient systems, such as in a dragonfly, the energy savings as a result of employing resonant mechanisms in hover had heavy penalties on the other flight modes. This brings into question if other methods for achieving more efficient hover might be more effective at the systems level. For a system dominated by damping effects, regulation of the aerodynamic forces through altering wing kinematics might be preferable. Certainly much work has been published on the aerodynamics behind flapping wing flyers. Figure 3.6: Two different wing-actuator configurations. The wing-actuator configuration with the spring in parallel to the actuator(a) will have no effect on the gliding properties when the actuator is holding position. Conversely if the spring is in series with the actuator (B), the spring will potentially reduce the natural frequency and critical velocity of the system making it detrimental to glide. 53

76 Abbreviations In particular, work performed by Wang (Z. J. Wang, 2004, 2005) has suggested that by using wing kinematics that differ from the conventional horizontal stroke pattern, dragonflies are potentially capable of consuming less power by a factor of 2/2. In further work (Z. J. Wang & Russell, 2007), Wang also proposed that the counter-stroking pattern between the fore and hind wings of the dragonfly had the effect of reducing the overall energy required for hover. In an extension of the same study, Wang also showed that the ability of the dragonfly to regulate the wing beat phase between the fore and hind wings allows the dragonfly to alternate between energy efficient hover and manoeuvres requiring large forces (i.e. take-off). From this we see that proper regulation of wing kinematics would not only allow for improvements in hover efficiency, but also the instantaneous bursts of force required for manoeuvring flight. This suggests that instead of resonance, aircraft designers looking at replicating the glide, hover and manoeuvring capabilities of the dragonfly should be focussing on wing articulation. Throughout our study, the numerical quasisteady and SHO models were used to demonstrate the effects of resonant mechanisms on hover and manoeuvring flight. It might be argued that these simpler models and analysis do not capture the subtlety and complexity of dragonfly flight mechanisms. This is certainly the case. Likewise, arguments that propose resonance as a primary enabler of insect flight are implicitly based on a conceptual SHO. The reality is that understanding of the details of insect flight at a system level is lacking, and hypotheses are being tested inside a largely unknown terrain. There is a clear need for more multidisciplinary research. 3.7 Conclusion Throughout this chapter, we explored the effects of employing a resonant mechanism on the hovering, manoeuvring and gliding performance of dragonflies and technical flyers. A review of previous work performed on the use of such a mechanism in solving the flapping wing actuation problem showed that for systems dominated by inertial forces, the use of elastic storage may improve some aspects of performance. However, in aerodynamically efficient systems like dragonflies, the energy savings and force reduction associated with using elastic elements is minimal. We further showed via a numerical quasisteady analysis, that the idea of using res- 54

77 3.7 Conclusion onance to improve performance breaks down when considering the operational band of wing beat frequencies in dragonflies. Using a damped SHO model, we demonstrated that the use of elastic storage mechanisms for achieving a resonant state is detrimental to the instantaneous manoeuvring capabilities of a flapping wing system. Employing Kussner s formulas, reductions in gliding performance were observed when elastic elements were used to reduce the natural frequency of the overall system. A reduction in natural frequency reduces the critical speed of an aircraft. We conclude that from a systems perspective, practical implementation of resonant mechanisms would present improvements in hover performance. However, depending on the configuration of the aircraft and the operational requirements, the improvements brought about by the use of resonance might not be sufficient to justify the potential reductions in gliding and manoeuvring performance. 55

78

79 CHAPTER 4 ON THE AERODYNAMIC EFFICIENCY OF INSECT-INSPIRED MICRO AIRCRAFT EMPLOYING ASYMMETRICAL FLAPPING Synopsis Studies have shown that asymmetrical flapping (i.e. unequal upstroke-to-downstroke periods) is employed in dragonflies (see section 1.3). However, its effects on the performance of a flapping wing system is unclear, particularly its aerodynamic efficiency. Using a quasi-steady, blade-element analysis, this chapter investigates the role of asymmetrical flapping mechanisms on the aerodynamic efficiency of insect inspired MAVs. The current analysis was applied to a 30cm half-span wing, beating at not more than 6Hz. An implementation of asymmetrical flapping exhibited significantly greater lift generation which can be attributed to the increase in angular velocity squared form for lift that occurs with increasing asymmetry. Significant improvements in the lift-to-power ratio were observed, for a house-fly like mode of flapping, when the wing-beat frequency was below the natural frequency. At a frequency ratio of 0.3 a 75% increase in performance was observed with the use of asymmetrical flapping. At flapping frequencies above the natural frequency however, asymmetry was found to be detrimental to performance, due to an increase in inertial forces. In a low inertia, inclined stroke plane system, characteristic of dragonflies, we see that in its most efficient flapping condition asymmetrical flapping is detrimental to performance. Significant gains are obtained from active control of pitch, which is consistent with findings from section 1.3. However, in compliant systems where 57

80 CHAPTER 4. ON THE AERODYNAMIC EFFICIENCY OF INSECT-INSPIRED MICRO AIRCRAFT EMPLOYING ASYMMETRICAL FLAPPING elastic forces are significant, we see that asymmetry can improve the aerodynamic efficiency of the wing-actuation system. This work has been published in a journal: Kok, J. M., G. K. Lau, and J. S. Chahl. On the Aerodynamic Efficiency of Insect-Inspired Micro Aircraft Employing Asymmetrical Flapping. Journal of Aircraft (2016):

81 Abbreviations Nomenclature UAV s MAV s k I Unmanned Aerial Vehicles Micro Air Vehicles Elastic constant Inertia ω n Resonant frequency f Ω φ Flapping frequency Frequency ratio Flapping angle φ Flapping amplitude η T α Downstroke-to-total stroke ratio Flapping period Pitch angle α Mean pitch angle α m Θ β K C α Pitch amplitude Pitch amplitude Stroke plane angle Transformation factor for sine to triangle wave Transformation factor for sine to rectangular wave 59

82 Abbreviations L D Lift Drag 60

83 4.1 Introduction 4.1 Introduction AN active topic of UAV research considers biologically inspired flapping wing aircraft. The topic has been facilitated by technological advances in many fields including micro-electronics, sensors, microelectromechanical systems (MEMS), and micro-manufacturing. Bio-inspired flapping wing aircraft may offer benefits including increased efficiency at low Reynolds numbers (Ashley, 1998; Sirohi, 2013) exhibited by Micro Air Vehicles (MAVs) and small Unmanned Aerial Vehicles (UAVs). In addition, flapping wing flyers exhibit a range of flight manoeuvres not achievable by any single fixed wing or rotary wing device. When modelling the aerodynamics of flapping wings, researchers often use sinusoidal flapping profiles with symmetrical upstroke to downstroke to simplify the modelling of the wing articulation (Z. J. Wang, 2004; Weis-Fogh, 1973; Azuma et al., 1985). However, studies have shown that insect flapping profiles vary according to aerodynamic demands (Baker & Cooter, 1979; Betts & Wootton, 1988; Yu & Tong, 2005) and can be asymmetrical (Dudley, 2002; Ennos, 1989). An asymmetrical stroke is one defined by different periods spent in upstroke versus downstroke (see Fig. 4.1). Figure 4.1: Illustration of asymmetrical flapping versus symmetrical flapping This phenomenon is present in many insect species, including Diptera and Odonata. Dudley (Dudley, 2002) suggested that an asymmetrical flapping profile could be more apparent in 61

84 Abbreviations insects with synchronous muscles such as Odonata (Dudley, 2002)). These insects tend to rely less on resonance (J. Kok & Chahl, 2014b), and consequently are not limited to the simple harmonic sinusoidal flapping profile characteristic of a resonant system. Stroke asymmetry is also present in Dipteran insects, although it is less pronounced (Ennos, 1989; Wakeling & Ellington, 1997a). Dipteran insects appear to rely on non-sinusoidal flapping profiles, or click mechanisms (R. Alexander & Bennet-Clark, 1977; Ellington, 1984; A. J. Thomson & Thompson, 1977). These click mechanisms modulate the elasticity of the thorax structure in such a way as to produce a non-symmetrical downstroke-to-upstroke. Such mechanisms have been shown in some studies to improve efficiency in lift generation (Chin & Lau, 2012, 2013; Tang & Brennan, 2011). Computational work performed by Yu and Tong (Yu & Tong, 2005) shows that asymmetrical flapping increases thrust generation in forward flight. Whilst it is known that stroke asymmetry is present in most insects, the advantages associated with asymmetrical flapping are relatively unknown. This chapter aims to simulate and analyse asymmetrical flapping, the extent to which it is beneficial to the aerodynamic efficiency in hover, and how it could be applied in the context of a real world MAV platform. This will be performed for two distinct modes of flapping - Dipteran and Odonate 4.2 Methods Flapping modes This chapter will focus on the two most commonly studied modes of insect-inspired flapping, namely an inertial-dominated, horizontal stroking mode characteristic of Diptera and an aerodynamically-dominated, inclined stroking mode characteristic of Odonata. One of the characteristics of Dipteran flapping is the horizontal stroke plane (see Fig. 4.2) (Z. J. Wang, 2004; Weis-Fogh, 1973). Additionally, Dipteran flight relies on indirect actuation whereby the muscles attach to an elastic thorax that transfers force to the wing (Dudley, 2002). Inherent in this is the use of resonance to amplify the displacements from the actuator to the wing (J. Kok & Chahl, 2014b). As a result, the elasticity of the thorax plays a dominant role in the dynamics of the system, in particular influencing the natural frequency of the system. The 62

85 4.2 Methods natural frequency is the excitation frequency whereby inertial and elastic forces are in balance and the aerodynamic loads are the only loads that need to be overcome (Dimarogonas, n.d.; Fung, 1955). The natural frequency is related to the elasticity and inertia of the system by ω n = k I (4.1) Matching the wing-beat frequency to the resonance point helps to reduce the energy otherwise lost to inertial work which can be significant in Diptera (Weis-Fogh, 1973; J. Kok & Chahl, 2014b). This is one of the methods proposed for reducing the energy costs associated with flapping flight (Wood, 2008; Baek et al., 2009; Greenewalt, 1960). The elastic thorax in Diptera promotes the theory of resonance. This would suggest that Dipteran flapping follows a simple harmonic motion. Whilst studies by Ennos (Ennos, 1989) show that the asymmetry in Diptera is significantly less as compared to other insects, an asymmetry still exists which is contrary to simple harmonic theory. In fact, studies have suggested that the elastic thoracic structure is used as a click mechanism that modulates the forces acting on the wing to produce non-sinusoidal, asymmetric flapping profiles. Such a mechanism produces similar energy Figure 4.2: Illustration of Dipteran versus Odonate flight (adapted from) 63

86 Abbreviations savings compared to a resonant system, but allows for efficient operation at lower wing-beat frequencies. Through the use of numerical methods, and a quadratic damping term, Tang et al. (Tang & Brennan, 2011) showed that the click mechanism improves the aerodynamic efficiency even at frequency ratio as low as, Ω = 0.1, where Ω is defined as Ω = 2πf ω n (4.2) In dragonflies, it is believed that elastic mechanisms could be present although much reduced (J. Kok & Chahl, 2014b). This is due to several characteristics that define the dragonfly wing-actuation system. Studies (Dudley, 2002) have shown that the dragonfly employs a direct drive mechanism whereby the actuators/muscles of the dragonfly are attached to the wing root and actuate the wing directly. Additionally, dragonflies flap their wing in an inclined stroke plane, and use active control of the angle of attack to modulate the aerodynamic forces acting on the wing (Z. J. Wang, 2000, 2004). It is these features that define the dragonfly planform, and differentiate it from other insect species (see Fig. 4.2). Another significant difference between Odonate and Dipteran flight is the proportion of aerodynamic work to inertial work. Dipteran insects have a significantly higher proportion of inertial to aerodynamic work (Weis-Fogh, 1973; J. Kok & Chahl, 2014b; Sun & Lan, 2004). It is these differences which make the Odonate mode of flapping distinct from the Dipteran. As such, the assumptions and idealisations used to analyse both these modes are different. This chapter will analyse the effects of asymmetrical flapping as it applies to both these unique styles of flapping. It should however be noted that we do not attempt to apply comparison between the two modes of flapping. We simply aim to analyse what is a phenomenon observed in both modes of flapping respective to those modes The Quasi-Steady model To quantify the performance of the asymmetrical profile, a numerical quasi-steady blade element model of the aerodynamic forces acting on the flapping wing was produced. Similar 64

87 4.2 Methods studies have been performed by Weis-Fogh and Norberg (Weis-Fogh, 1973; R. A. Norberg, 1975). Sane and Dickinson (Sane & Dickinson, 2002) also presented a similar analysis, with additional aerodynamic effects due to wing rotation. The wing was divided into spanwise sections, and the instantaneous forces calculated on each section based on the local translational and angular velocity. The forces across all slices were then summed to obtain the forces/torques acting on the wing at any point in time. The wing kinematics were represented using equations from Wang (Z. J. Wang, 2000) for a wing flapping in an inclined stroke plane with angle β (see Fig. 3.1). In Wang s representation of the Dragonfly flapping profile, the flapping angle, φ, is represented using a sinusoid. A similar flapping profile is employed in this study. To model the asymmetric flapping, two half-cosine waves were used with different angular velocities (see Fig. 4.3). The downstroke can be expressed as φ(t) = φ 0 cos( πt ηt ) (4.3) for 0 < t < ηt where η = T Downstroke /T. The upstroke is represented by π φ(t) = φ 0 cos( (t ηt ) + π) (4.4) (η 1)T for ηt < t < T. Therefore, η represents the degree of asymmetry in the flapping profile. If η = 0.5, the flapping profile is symmetric. However if η < 0.5, the downstroke period is shorter than the upstroke. The opposite is true for η > 0.5. The angle-of-attack, α, in the stroke plane is represented using a sinusoid. α = α m α 0 sin(2πft ) (4.5) Once the flapping and pitch profile have been determined, the local velocity at each spanwise section, or blade element, of the wing as well as the lift and drag coefficients can be deter- 65

88 Abbreviations Figure 4.3: The asymmetrical flapping profile is represented by two half cosine waves. The figure illustrates a flapping profile with η=0.3. mined, The local velocity is calculated by V = r φ (4.6) where r and φ are illustrated in Fig

89 4.2 Methods Figure 4.4: Illustration of the coordinate system used. Global coordinate system (A); Stroke plane frame (B) Equations for the lift and drag coefficients were obtained from three-dimensional experiments performed by Dickinson (Z. J. Wang et al., 2004; M. H. Dickinson et al., 1999). Similar coefficients were obtained by Wang computationally and used as the basis for analysing dragonfly flight (Z. J. Wang, 2004; Z. J. Wang et al., 2004). C L = sin(2.13α 7.2) (4.7) C D = cos(2.04α 9.82) (4.8) Similarly, the rotational pressure forces (Sane & Dickinson, 2002; M. H. Dickinson et al., 1999) for each section of the wing were modelled as C rotational = π(0.75 ˆx 0 ) (4.9) where ˆx 0 is the non-dimensional axis of rotation from the leading edge. Following that, the forces due to the translational (refer to Fig. 3.1) and rotational (refer to Fig. 4.6) motion of the wing can be calculated. 67

90 Abbreviations Figure 4.5: Illustration of the aerodynamic forces due to the flapping motion acting on a single section of the wing. The aerodynamic forces at each section of the wing are given by dl = 0.5ρV 2 C L ds (4.10) dd = 0.5ρV 2 C D ds. (4.11) df rotational = C rotational ρc 2 V αdr. (4.12) The overall aerodynamic force can then be calculated by summing the force of all wing sections. The wing was divided into 27 wing sections. The stroke was analysed over a

91 4.2 Methods Figure 4.6: Illustration of the pressure force due to rotational circulation acting on a single section of the wing. time-steps. It should be noted that the direction of the lift and drag forces are with respect to the velocity of the wing section. To determine the actual lift force generated by the wing in the global reference frame, a coordinate transformation was employed. The vertical force in the frame of reference of the blade element is given by (4.13). H r = L cos β + D sin β + F rotational sin (α β) (4.13) 69

92 Abbreviations The vertical force with respect to the global frame of reference is H r,vert = H r cos φ P roj (4.14) An equation for cos φ P roj was calculated using the formulation from Norberg (R. A. Norberg, 1975). Therefore the vertical force with respect to the global frame of reference is H r,vert = H r 1 sin 2 α sin 2 β (4.15) To determine the feasibility of asymmetrical flapping, we used the aerodynamic efficiency as the performance metric, which is the ratio of the mean aerodynamic lift to the mean power consumed (i.e. L/P ). This is a common performance metric used in the design of aircraft, as it relates to how much power is required to maintain steady flight (Raymer, 1999). In platforms that are capable of hovering, it also relates to how much power is required to keep the platform in a steady hover mode (Chin & Lau, 2012). To determine the power consumed in the wing stroke due to just the flapping motion, we use the equation P = τω (4.16) where τ = τ Aero + τ Inertial + τ Elastic (4.17) ω = φ (4.18) The torques due to inertial and elastic forces were modelled as being linear, i.e. τ Inertial = I φ and τ Elastic = kφ. In addition to the power associated with the flapping motion, we also investigate the aerodynamic and inertial power associated with wing rotation, which is one of the main mechanisms of lift generation (M. H. Dickinson et al., 1999). The power associated with wing rotation is given as P Rotation = τ Rotation α (4.19) 70

93 4.2 Methods where τ Rotation = τ Rotation,Aero + τ Rotation,Inertial (4.20) To determine the τ Rotation,Aero, we assume the aerodynamic forces act through a constant centre of pressure at 75% of chord (Sane & Dickinson, 2002; M. H. Dickinson et al., 1999). Whilst this is only an approximation, it should be noted that studies have shown that τ Rotation,Aero is small compared to the aerodynamic torques generated by the flapping mode (Sun & Lan, 2004). As such any inaccuracies resulting from such an approximation will be minimal. A linear model, i.e. I Rotational α, was used to represent the torque due to the rotational inertia, τ Rotation,Inertial System parameters The parameters used in the simulation are selected to best represent the characteristics of Diptera and Odonata as described by Wang (Z. J. Wang, 2004, 2005). These parameters are highlighted in Table 4.1. The wing size was selected to be representative of birds or prehistoric dragonflies (Wootton, 1976; May, 1982) which are in the order of MAVs and small UAVs. Table 4.1: Flapping wing parameters Property Diptera-inspired flapping mode Dragonfly-inspired flapping mode f (Hz) 1.6, 2.5, 5.0, β (deg) φ 0 (deg) α 0 (deg) α m (deg) , 90.0, 105.0, The design of the wing was based off a dragonfly wing profile. A larger 30cm wing design was selected, operating at lower wing-beat frequencies. This wing size is of the order of that found on prehistoric dragonflies (i.e. the Meganeuropsis Permiana had a wingspan of 70cm (Kalkman et al., 2008)). The larger wing allows for larger aerodynamic forces to be generated, while the lower wing-beat frequencies reduces the effect of mechanical loads on the system. 5Hz was selected as the nominal wing-beat frequency as studies of birds and insects by Greenewalt (Greenewalt, 1960) have shown that similarly sized birds flap at 3-10Hz. Whilst 71

94 Abbreviations the wing-beat frequencies and wing spans differ from that of the Diptera and Odonates, the wing kinematics copy from the Diptera and Dragonfly respectively. The inertia of the wing was based of a Mylar and carbon construct described by Lentink et al. (Lentink, Jongerius, & Bradshaw, 2010). The final design is shown in Fig The moment of inertia of the wing in the flapping and pitching axis was calculated and shown in table 4.2. It should be noted that this wing design was dragonfly-inspired and as such is low inertia, aerodynamically dominated. This is different to the Dipteran system which is inertially dominated. As such the Dipteran mode of flapping will use the same wing shape, but with a different treatment of inertia. This will be presented in section Figure 4.7: Illustration of a dragonfly-inspired wing. Table 4.2: Inertial breakdown of the wing Object Flapping Inertia (kg m 2 ) Rotational Inertia (kg m 2 ) Skin Spars + ribs Total Results Analysis of Dipteran flapping mode As mentioned previously in section 4.2.1, studies performed by Tang et al. (Tang & Brennan, 2011) showed that the click mechanism improves the aerodynamic efficiency even at a 72

95 4.3 Results frequency ratio of Ω = 0.1. We expand on this analysis by using the quasi-steady, blade element model listed in section We compared the effects of implementing varying degrees of asymmetry on a Dipteran flapping profile by changing η. This was performed for a range of frequency ratios centred around the resonant frequency. Rather than using the wing inertias calculated in Table 4.2, the inertia of the wing was selected to better represent the inertia dominated characteristics of Dipteran insects. Weis-Fogh (Weis-Fogh, 1973) showed that the proportion of inertial work for Dipteran insects was on average 0.52 of the combined aerodynamic and inertial work. Using this ratio and knowing the aerodynamic work is calculated by integrating the aerodynamic power over time, the inertial work can be determined. The inertia can thus be calculated using I = InertialW ork 8π 2 f 2 φ 2 0 (4.21) Once the inertia is known, the elasticity of the system, k, is calculated using equation 4.1, assuming a natural frequency of 5Hz. We firstly observe the changes in lift associated with the frequency change and asymmetrical flapping. This was performed for a range of wingbeat frequencies above and below the resonant frequency (i.e. Ω = 0.3, 0.5, 1.0, 1.2). Lift was calculated for values of η between 0.1 and 0.5. As expected lift generation decreases with decreased wing-beat frequency. The mean lift of the system is shown in Fig However, we notice that across all wing-beat frequencies there is an increase in mean lift with decreasing η. To explain this phenomenon, we observe the relationship between η and the time-averaged square of the angular velocity, ω 2. This is significant because lift is approximately proportional to the square of the angular velocity (i.e. L ω 2 ). The time-averaged square of the angular velocity can be calculated according to equation ω 2 = T 0 ω2 dt T (4.22) The results are illustrated in Fig. 4.9 for the case of Ω = 1. The effect of decreasing η is to increase ω in the downstroke and decrease ω in the upstroke, leading to no significant change in 73

96 Abbreviations Figure 4.8: Mean lift generated for a Dipteran-inspired flapping mode across a range of η for different wing-beat frequencies. time-averaged ω. However,we see that when taken across the entire period of the wing-stroke, ω 2 is higher. Correspondingly, as lift is ω 2, there is an increase in lift with decreasing η. Following the analysis of lift, the lift-to-power ratios were calculated across a range of η values. This is illustrated in Fig At the resonant frequency, it can be seen that the use of asymmetrical flapping has detrimental effects on the aerodynamic efficiency of the system. However at wing-beat frequencies below the natural frequency, the benefits of asymmetrical flapping becomes more pronounced. We see that as the wing-beat frequency decreases, the value of η that produces the optimal L P decreases. This would suggest that at progressively lower wing beat frequencies, the wing stroke that produces maximum L P is more asymmetrical. In addition, the improvements in efficiency achieved between the optimal asymmetrical flapping profile and a symmetrical profile (i.e. η = 0.5) become more significant. At Ω = 0.3, the 74

97 4.3 Results Figure 4.9: Time-averaged angular velocity and time-averaged square of the angular velocity versus η performed for a Dipteran-inspired flapping mode (Ω = 1) value of η that produces the ideal L P the use of asymmetry. is 0.18, and there is a 75% increase in performance with 75

98 Abbreviations Figure 4.10: Aerodynamic efficiency for a Diperan-inspired flapping mode, L/ P, across a range of η and different wing-beat frequencies. We also observe the change in time-averaged ω 3 (i.e. ω 3 ) with η (see Fig. 4.11). This value is important for analysing the inertial power of the system. The significance of this will be discussed in Section Analysis of Dragonfly mode of flapping As discussed in Section 4.1, the dragonfly mode of flapping differs from the Dipteran mode in a few ways. The dragonfly mode of flapping is characterised by motion in an inclined stroke plane and active modulation of the angle of attack (AoA) of the wing to manipulate aerodynamic forces. Another characteristic of the dragonfly flapping profile is reduced reliance on resonant mechanisms as demonstrated by the energetic and functional requirements of a dragonfly wing-actuation system (J. Kok & Chahl, 2014b). This is further supported by their use of a direct-drive mechanism which largely by-passes the elastic thorax. To simulate this effect, 76

99 4.3 Results Figure 4.11: Time-averaged ω 3 and ω 3 / ω 2 versus η performed for a Diperan-inspired flapping mode (Ω = 1) we initially model the system as a direct drive mechanism with no elasticity (i.e. k=0). Another characteristic of the dragonfly wing-actuation system is the significantly larger proportion of aerodynamic work versus inertial work (J. Kok & Chahl, 2014b; Sun & Lan, 2004; Azuma & Watanabe, 1988; May, 1991). Initial quasi-steady analyses performed on the dragonfly flapping profile without asymmetrical flapping shows the ratio of aerodynamic work to inertial work is 12.0 for the system described in section This shows that the simulated system is dominated by aerodynamic forces and is congruent with the dragonfly mode of flapping. We compare the effects of implementing varying degrees of asymmetry on the dragonfly flapping profile by changing η. This was performed for a range of α 0. The flapping amplitude, φ 0, was kept at 45 o to remain consistent with the flapping amplitude used in section The elasticity of the system was initially assumed to be zero to better represent the direct drive wing-actuation system design. The mean lift of the system is shown in Fig Across all 77

100 Abbreviations α 0, there is an increase in the mean lift generation with decreasing values of η. The increases in lift due to asymmetrical flapping are substantially more pronounced in the dragonfly mode of flapping. This can be explained by the fact that a dragonfly generates most of its lift on the downstroke (Z. J. Wang, 2005; Sun & Lan, 2004). By decreasing η, the velocity in the downstroke is increased, resulting in more lift being generated across a shorter time. This is in contrast to the Dipteran mode of flapping which generates substantial lift in both the upstroke and downstroke. During Dipteran flapping, increases in lift due to a quicker downstroke are largely countered by a reduction in lift in the upstroke. Figure 4.12: Lift generated for a Odonate-inspired flapping mode by the system for different values of η and different α 0 78

101 4.3 Results Figure 4.13: Aerodynamic efficiency for a Odonate-inspired flapping mode, L/ P, for different values of η and different α 0 We then observe the aerodynamic efficiency of the lift generation mechanism. The metric used to quantify this efficiency is the mean lift to mean power ratio, i.e. L/ P. As shown in Fig. 4.13, aerodynamic efficiency of the system is significantly effected by varying the asymmetry in the flapping profile. For lower values of α 0, improvements in aerodynamic efficiency of up to 9.8 times are observed with the implementation of asymmetrical flapping versus symmetrical. However, the highest values of aerodynamic efficiency are observed where α 0 = 8π 12 and no asymmetry is used. The previous cases assumed an idealised Odonate mode of flapping with no elasticity present in the system. However, elasticity is a characteristic that is inherent in all natural systems and compliant designs (Neville, 1960; Sunada et al., 1998; Lehmann et al., 2011). To model the effects of elasticity in the dragonfly wing system, the elasticity was varied such that the ratio of elastic to aerodynamic torques, i.e. Γ = τ Elastic, max τ Aero, max, were 1.0, 2.0 and

102 Abbreviations respectively. The aerodynamic efficiencies are illustrated in Fig With increasing elasticity of the system, improvements to aerodynamic efficiency are apparent. At Γ = 3, there is a 50% increase in aerodynamic efficiency with the implementation of asymmetry in the flapping profile (η = 0.23). Figure 4.14: Aerodynamic efficiency for a Odonate-inspired flapping mode, L/ P, for different values of η and different Γ (α 0 = 7π/12) 4.4 Discussion In this chapter, we investigated the effect of an asymmetric flapping profile for hover in the context of a real-world insect-inspired wing-actuation system. To model the aerodynamics of the system, we used a quasi-steady blade element model. This is a modification of the work performed by Sane and Dickinson (Sane & Dickinson, 2002). The quasi-steady blade element model detailed in section allows us to capture 80

103 4.4 Discussion representative lift and drag forces in 3-dimensional space, whilst also allowing us to investigate the combined effects of flapping and pitching wing movements. Sinusoidal wing kinematics were prescribed, that included a factor of asymmetry, η, which changed the time spent in the upstroke to that in the downstroke. Elastic and inertial models were developed which were proportional to the prescribed angular position, φ, and angular acceleration, φ, respectively. This was performed for two distinct modes of flapping, namely Dipteran and Odonate. Due to the differences between these two flapping modes, the treatment of inertia and elasticity differed. Analysis of the Dipteran mode of flapping used inertial values derived from the inertial work which studies have shown to be approximately 0.52 of the combined aerodynamic and inertial work (Weis-Fogh, 1973). Assuming resonant flapping, which is characteristic of Diptera, the elastic constant is calculated using equation 4.1. For Odonates, the assumption of resonant flapping is not applicable. As such, we have opted to perform the quasi-steady analysis over a range of elastic values from an idealised, zero-elasticity case to a case with dominant elastic forces. This allowed us to analyse the effects of asymmetrical flapping for a range of elasticity values. Inertial values were based off a dragonfly-inspired wing design used in a representative MAV system (J. Kok & Chahl, 2014a, 2015; J. M. Kok & Chahl, 2016). The same wing inertia is too low for use in a Dipteran system as Diptera are characterised by dominant inertial forces. Another fundamental difference between the Odonate and Dipteran mode is the inclined stroke plane used by Odonata. This has also been reflected in the analysis. The quasi-steady model does have its limitations in analyzing the aerodynamic forces being applied to the system. However it should also be noted that effects like unsteady wake and added mass forces, whilst important, are not the primary means of lift generation. This chapter aims to investigate the effects of asymmetrical flapping on the primary mode of lift generation to determine system level suitability. Another assumption was the use of lift and drag coefficients presented by Dickinson (Z. J. Wang et al., 2004; M. H. Dickinson et al., 1999). Similar coefficients were obtained by Wang computationally and used as the basis for analysing dragonfly flight (Z. J. Wang, 2004; Z. J. Wang et al., 2004). To determine the effect of lift and drag coefficients on the results of the quasi-steady analysis, a sensitivity analysis was performed in which lift and drag coefficients were simultaneously increased by ±50% and the analysis redone. The results are shown in the Appendix. These results demonstrate that changing the 81

104 Abbreviations lift and drag coefficients has no significant impact on the overall trends. Whilst the accuracy of the quasi-steady analysis might not be absolute in nature, it is a fair investigation of the relationship between the aerodynamic modes, inertial effects and elasticity. Without simplifying assumptions any sort of coherent design considerations become infeasible. This chapter will set the basis for further, more accurate analysis which includes non-linear elasticity, and non-steady aerodynamic effects. In section we analyse the effects of asymmetrical flapping on the aerodynamics of the Dipteran flapping mode. Previous studies by Brennan and Tang (Tang & Brennan, 2011) showed that the improvements in aerodynamic efficiency with the use of a click mechanism could be attributed to the phase shifting effect and the generation of higher wing velocities, both of which are also present in asymmetrical flapping. This also potentially explains how a Dipteran system in resonance could have an asymmetrical wing stroke. The phase shifting effect introduced by aerodynamic damping on a resonant system is offset by the inherent phase shifting effects of an asymmetrical stroke. Initially, the mean lift over the wing stroke period was considered. We see an increase in lift generated with increased wing-beat frequency. As lift is proportional to ω 2, a quicker wing-beat frequency would result in greater lift forces being generated. We then observe the changes in lift associated with changing asymmetry. Increasing asymmetry (i.e. reducing η) increases the lift that is being generated. To understand why, we observed the change in the time-averaged ω and ω 2 across the wing-beat with changing η (see Fig. 4.9). We observe that asymmetry has no effect on ω, as any gains in angular velocity from a quicker downstroke are balanced by the losses in angular velocity in the upstroke. However, when we consider the change in ω 2 with η, we see that ω 2 increases with increasing asymmetry, which explains the observed increases in lift. Following the lift force analysis, the aerodynamic efficiency was considered. The mean lift over mean power was used as the measure of aerodynamic efficiency. The analysis was performed for a range of wing-beat frequencies from high frequency, inertially dominated systems to low frequency elastically dominated systems. It was observed that with inertially dominated systems, there was no advantage to using asymmetrical flapping However in systems dominated by elasticity, this non-resonant mode of asymmetrical flapping has the potential to improve the aerodynamic efficiency. At a frequency ratio, Ω = 0.3 a 75% increase in performance was observed with the use of asymmetrical flapping 82

105 4.4 Discussion (see Fig. 4.10). An explanation for this can be derived from observations of the forces applied to a compliant flapping wing mechanism. In a harmonic system with both elastic and inertial forces, the ratio of elastic to inertial forces is given by k. At lower wing-beat frequencies, Iω 2 elastic forces are dominant, and a portion of work is used to overcome excess elasticity. Elastic power is proportionate to ω whilst lift generation is proportionate to ω 2. Therefore, when η is decreased, ω 2 increases, while ω stays approximately the same (see Fig. 4.9) leading to higher aerodynamic efficiency. The opposite is true at higher wing-beat frequencies. Inertial forces dominate, however inertial power is proportional to ω 3. As shown in Fig. 4.11, with decreasing η, both ω 2 and ω 3 increases, however ω 3 increases faster than ω 2. ω3 is an indication of the amount of inertial power that is consumed during the wing-beat as inertial power is proportional to ω 3. This indicates that as η reduces, the amount of inertial power required increases faster than the lift generated, which explains the reduction in aerodynamic efficiency with decreasing η. This suggests that in a non-resonant flight mode below the natural frequency, asymmetrical flapping can be used to tune the system to obtain increased aerodynamic efficiency in hover. In fixed frequency systems, it can also serve as a secondary or alternate means to modulate the lift of the system. Brennan and Tang (Brennan, Elliott, Bonello, & Vincent, 2003) and Chin and Lau (Chin & Lau, 2012, 2013) observed improved aerodynamic efficiency at low frequencies with the use of a click-induced asymmetrical flapping profile. Caution must be used when testing theory about insect flight against empirical results from synthetic artifacts due to the gap that appears to exist between the level of optimisation of insects compared to current mechanical systems (Chahl, Mizutani, & Dorrington, 2013). Differences also exist between the wings used by insects, which appear to have complex and optimized aerostructural properties (Chahl & Khurana, 2014) and those used in current mechanical systems. With these considerations in mind, it seems that unlike our linear-elastic system, they have observed improved aerodynamic efficiency even at higher, inertial-dominated wing-beat frequencies. This would suggest that the energy saving mechanism is in part due to the non-linear elastic nature of the click mechanism. Results from Chin and Lau (Chin & Lau, 2012, 2013) suggests that the click mechanism is at least a third order polynomial which has the potential to offer finer optimisation of the force profile, and hence aerodynamic efficiency, then just a linear elastic storage mechanism. Another variable which needs to be considered is the effect asymmetrical flapping has on wing flexure. Insect wings have finite stiffness, and as such will experience chordwise 83

106 Abbreviations and spanwise bending when aerodynamically or inertially loaded (Combes & Daniel, 2003; Lentink et al., 2010; Jongerius & Lentink, 2010). Asymmetrical flapping serves to modulate velocity in the up and down strokes which in turn influences the degree of passive wing rotation and hence the angle-of-attack of the wing. In section 4.3.2, we modified the flapping model to reflect the key characteristics of dragonfly flight, which include an inclined stroke plane and a lower reliance on elasticity. This allows us to determine if the asymmetry observed in dragonfly flight is beneficial to hover performance. Varying degrees of asymmetrical flapping were applied to the model and tested for different mean angles-of-attack. It was found that for lower values of α 0, varying the downstroke-to-upstroke ratio resulted in a significant improvement in performance. The best aerodynamic efficiencies were observed when α 0 was high, and no asymmetry was used. This can be attributed to the fact that like the previous case, which was inertially dominated (section 4.3.1, Ω > 1.0), the increases in lift are proportional to ω 2, whilst the required power is proportional to ω 3. As such the increase in flapping velocity in the down-stroke is not beneficial to the aerodynamic efficiency of the system. The improvements in performance using asymmetrical flapping at lower α 0 values are associated with the phase shifting effect. This leads to the suggestion that the use of asymmetrical flapping in hover is secondary to modulating the angle-of-attack in the dragonfly flapping profile. This is congruent with findings by Wakeling and Ellington (Wakeling & Ellington, 1997a) who showed significant but small variations in the downstroke-to-upstroke ratio in the Odonate mode of flight. Another explanation for these variations could be the elasticity in the dragonfly. In many flapping wing systems, including the dragonfly, some elasticity will be present. Whilst the elasticity might not be introduced to tune a resonant system, it is a design parameter in many compliant flapping-wing systems (Chin & Lau, 2012, 2013; Finio & Wood, 2012). Therefore it is necessary to observe the dragonfly wing-actuation system with elasticity introduced. Results showed that asymmetrical flapping improved performance significantly with an increase in elasticity. The increases in performance can be attributed to the fact that the power required to overcome elastic forces are proportional to ω. Therefore, by increasing the speed of the downstroke, the aerodynamic forces increase faster than the power required to overcome elastic forces. So in systems where elastic forces are significant the benefits of having asymmetrical flapping can be realised. 84

107 4.5 Conclusion 4.5 Conclusion In this chapter we have presented the use of a quasi-steady blade element model that we used to investigate the benefits of asymmetrical flapping in both an inertia-dominated, horizontal stroking system and an aerodynamically-dominated, inclined stroke plane system, characteristic of Dipteran and Odonate insects respectively. Our results show that in a Diptera-inspired system, stroke asymmetry increases the lift generation, which can be attributed to higher ω 2 across the wing-beat. Additionally, at wing-beat frequencies below the natural frequency, asymmetrical flapping improves aerodynamic efficiency. At and above the natural frequency, asymmetrical flapping is detrimental to performance, which we explain by the higher proportion of inertial power above the natural frequency, which is sensitive to the time-averaged ω 3. We also note that this finding is contradictory to results for a click mechanism that shows higher aerodynamic efficiencies up to, and at the resonant frequency. This suggests that the energy savings of a click mechanism is not just an aerodynamic effect, but rather a non-linear elastic phenomenon. Asymmetrical flapping could be a means to optimise the aerodynamic efficiency of non-resonant systems below the natural frequency. It can also be used as an alternate means of lift modulation. The use of asymmetrical flapping was then investigated in an idealised dragonfly mode of flight with no elasticity initially. Asymmetrical flapping was found to improve aerodynamic efficiency for some mean angles of attack. However, the most efficient flight was still achieved via tuning the angle-of-attack of the wing. With the introduction of elasticity into the system, it was observed that asymmetrical flapping produced significant improvements to aerodynamic efficiency. This suggests that the benefits of asymmetrical flapping in hover can be better realised in systems suffering from or exploiting elasticity. 85

108 Abbreviations 4.6 Appendix Dipteran flapping mode, C L, C D decreased by 50% Figure 4.15: Lift for a Dipteran-inspired flapping mode Figure 4.16: Aerodynamic efficiency for a Dipteran-inspired flapping mode 86

109 4.6 Appendix Dipteran flapping mode, C L, C D increased by 50% Figure 4.17: Lift for a Dipteran-inspired flapping mode Figure 4.18: Aerodynamic efficiency for a Dipteran-inspired flapping mode 87

110 Abbreviations Odonate flapping mode, C L, C D decreased by 50% Figure 4.19: Lift for an Odonate-inspired flapping mode Figure 4.20: Aerodynamic efficiency for an Odonate-inspired flapping mode 88

111 4.6 Appendix Figure 4.21: Aerodynamic efficiency for an Odonate-inspired flapping mode with elasticity 89

112 Abbreviations Odonate flapping mode, C L, C D increased by 50% Figure 4.22: Lift for an Odonate-inspired flapping mode Figure 4.23: Aerodynamic efficiency for an Odonate-inspired flapping mode 90

113 4.6 Appendix Figure 4.24: Aerodynamic efficiency for an Odonate-inspired flapping mode with elasticity 91

114

115 CHAPTER 5 OPTIMISATION OF A DRAGONFLY-INSPIRED FLAPPING WING-ACTUATION SYSTEM Synopsis In the previous chapters we have seen the significance of active wing kinematic control over passive methods. However, the wing kinematics that produces optimal flight in a dragonfly or dragonfly-inspired system is still relatively unknown. This chapter applies the Scatter Search algorithm to determine the flapping profile which will produce the most lift for a theoretical wing-actuation system. The optimisation method was assessed using a numerical quasi-steady analysis. Results of an optimised flapping profile show a 20% increase in lift generated as compared to flapping profiles obtained by high speed cinematography of a Sympetrum frequens dragonfly. Initial optimisation procedures showed 3166 objective function evaluations. The global optimisation parameters - initial sample size and stage one sample size, were altered to reduce the number of function evaluations. Altering the stage one sample size had no significant effect. It was found that reducing the initial sample size to 400 would allow a reduction in computational effort to approximately 1500 function evaluations without compromising the global solvers ability to locate potential minima. To further reduce the optimisation effort required, we increase the local solver s convergence tolerance criterion. An increase in the tolerance from 0.02N to 0.05N decreased the number of function evaluations by another 20%. However, this potentially reduces the maximum obtainable lift by up as much as 0.025N. This technique will be relevant to optimising the wing kinematics in Dragonfly-inspired systems, which will form a significant part of the design framework presented in Chapter 7. We will see 93

116 CHAPTER 5. OPTIMISATION OF A DRAGONFLY-INSPIRED FLAPPING WING-ACTUATION SYSTEM an implementation of this method in Chapter 9. This journal publication has been published in: Kok, Jia-Ming, and Javaan Chahl. Optimisation of a Dragonfly-Inspired Flapping Wing- Actuation System. World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering 8.9 (2014):

117 Abbreviations Nomenclature φ φ m K C α ω α Flapping angle Flapping amplitude Factor changes sine wave to triangular wave Factor changes sine wave to rectangular wave Flapping frequency Pitch angle α Mean pitch angle α m Φ α β V r C L C D C rotational Pitch amplitude Pitch phase offset Stroke plane angle Local velocity of blade element Radius of blade element Lift coefficient Drag coefficient Rotational lift coefficient ˆx Non-dimensional location of pitch axis L D Lift Drag 95

118 Abbreviations S Blade area ρ ] Density H r Vertical force in wing reference frame H r,vert F rotational Vertical force in global frame of reference Rotational wing aerodynamic force contribution 96

119 5.1 Introduction 5.1 Introduction LIKE many other insects, the dragonfly has evolved a flapping wing-actuation system that allows it to perform efficiently. The extensive capabilities of the dragonfly can be attributed to the unique degree of control the dragonfly has over its flapping actuators and hence flapping profile (Sviderskiĭ et al., 2008). Alexander showed through high speed cinematography in a wind tunnel (D. E. Alexander, 1986) the capability of the dragonfly to adjust both its stroke plane angle and angle of attack of the individual wings to perform complex yawing or banking turns. Even during hovering flight, Wang (Z. J. Wang, 2005) proposed that dragonflies rely on adjusting the angle of attack of the wing to reduce the energy costs of hover. Certainly observations of the wing actuators of dragonflies support these theories. An investigation of the actuation system in dragonflies shows their capability to actively control and effect wing rotation (Sviderskiĭ et al., 2008; Simmons, 1977). These factors highlight the importance of wing articulation and the flapping profile in dragonfly flight. High speed cinematography of dragonflies in hover shows that the optimal flapping profile varies between different dragonflies (Azuma & Watanabe, 1988; Azuma et al., 1985; Wakeling & Ellington, 1997a). This suggests that the optimal flapping profile is highly system specific, requiring the use of optimisation methods to determine the optimal wing kinematics. This chapter will present a dragonfly-inspired wing-actuation system design and the methods used to tune the flapping-wing profile to produce optimal performance for that wing-actuation system. 5.2 Optimisation Problem Both computational and experimental methods can be used to optimise the flapping profile. Berman and Wang (Berman & Wang, 2007) used blade element theory analysis to minimise the power requirements of their prescribed flapping profile whilst maintaining sufficient lift for three different insects. Ghommem et al. (Ghommem et al., 2010) used a modified blade element theory analysis to obtain maximum lift generation. Thomson et al. (S. L. Thomson et al., 2009) used experimental methods to determine the optimal flapping profile for a scaled-up moth, Manduca Sexta wing. 97

120 Abbreviations Regardless of the method, all the optimisation techniques share a common issue. The non-linear flapping-wing dynamics leads to multiple optima across the response surfaces, and depending on the initial solution the obtained local optima might not correspond to the global optima. That is particularly true for the problem of flapping wing actuation. To resolve this issue, optimisation techniques that rely on global search methods will have to be used. To do this, we employ a Global Search algorithm presented by Ugray et al. (Ugray et al., 2007). This is a combination of global and local search methods for finding multiple local optima. Global methods are used to determine basins where optima are likely to occur, and local gradient-based methods are used to refine the location of the optima within those basins. An initial set of points are produced by using a Scatter Search approach (Glover, Laguna, & Martí, 2000). Similar to Genetic algorithms, this is a heuristic approach. However, unlike genetic algorithms that require a large initial populations to generate sample points, the Scatter Search approach uses a small initial set of samples and grows the sample size based on not just the value of the objective function, but also the diversity of that solution. Therefore, the Scatter Search method produces a set of sample points that both satisfy the objective function but are sufficiently diverse from each other that the probability of locating the true global optima is increased. Once an initial population of sample points have been determined, local Quasi-Newton optimisation techniques (P. E. Gill, Murray, Saunders, & Wright, 1984; P. Gill, Murray, & Wright, n.d.) were employed to refine the location of the optima to within a userspecified convergence criterion. The objective function being optimised is the lift generated by the wing-actuation system Quasi-steady Model To tune the parameters of the optimisation routine and demonstrate its functionality, a numerical quasi-steady blade element model of the aerodynamic forces acting on the flapping wing was produced. Similar studies have been performed by Weis-Fogh, Norberg (Weis-Fogh, 1973; R. A. Norberg, 1975). Sane and Dickinson (Sane & Dickinson, 2002) also presented a similar analysis, with additional aerodynamic effects due to wing rotation. The wing was divided into spanwise sections, and the instantaneous forces calculated on each section based on the local 98

121 5.2 Optimisation Problem Figure 5.1: Illustration of the dependance of φ and α on K and C η (adapted from Berman and Wang (Berman & Wang, 2007)). translational and angular velocity. The forces across all slices were then summed to obtain the forces/torques acting on the wing at any point in time. The wing kinematics were represented using equations from Berman and Wang (Berman & Wang, 2007; Z. J. Wang et al., 2004; Z. J. Wang, 2004) for a wing flapping on an inclined stroke plane with angle β. The inclined stroke plane is more characteristic of a dragonfly flapping profile. The flapping angle, φ, and angle-of-attack, α, in the stroke plane is represented by α(t) = φ(t) = φ m sin 1 (K)) sin 1 [Kcos(ωt)] (5.1) α m tanhc α tanh[c α cos(ωt + Φ α )] + α 0 (5.2) where 0 < K < 1 and C η > 0. In the limit where K 0, φ becomes sinusoidal, and in the limit where K 1, a triangular waveform is generated. Similarly, as C η 0, α becomes a sinusoidal waveform, as C η, α tends towards a square wave (refer to Fig. 5.1). To determine if such a model is able to represent the key characteristics of the flapping wing profile, we compare the output of this model against known experimental results obtained by high speed cinematography of a Sympetrum frequens dragonfly undertaken by Azuma et 99

122 Abbreviations al. (Azuma et al., 1985).The flapping and pitch angles at 20 different locations along the wing path were measured. A Fourier series expansion was performed to fit a continuous curve with the experimental results. The curve-fitted experimental results shows that the flapping profile, φ(t) is approximated by a sinusoid and hence Berman and Wang s representation for the flapping angle (refer to (5.1)) is appropriate. The curve fitted experimental results for the pitch angle, α(t), have components of a second and third harmonic and hence cannot be represented by a sinusoidal profile. However, a comparison of the experimental pitch angles with the periodic hyperbolic function suggested by Berman and Wang (refer to (5.2)) shows that the periodic hyperbolic function is able to approximate the wing pitch profile (refer to Fig. 5.2). Additionally, the periodic hyperbolic function is fully defined by 4 variables as opposed to the 7 variables required by a triple harmonic Fourier series representation. Figure 5.2: A comparison of the periodic hyperbolic function proposed by Berman and Wang (Berman & Wang, 2007) (dashed line) with experimental results from Azuma et al. (Azuma et al., 1985) (solid line) 100

123 5.2 Optimisation Problem Once the flapping and pitch profile were determined, the local velocity at each spanwise section of the wing as well as the lift and drag coefficients could be determined, and used to calculate the forces due to the translational (refer to Fig. 5.3) and rotational (refer to Fig. 5.4) motion of the wing. Figure 5.3: Illustration of the aerodynamic forces acting on a single section of the wing. Equations for the lift and drag coefficients were obtained from three-dimensional experiments performed by Dickinson (Z. J. Wang et al., 2004; M. H. Dickinson et al., 1999). Similar coefficients were obtained by Wang computationally and used as the basis for analysing dragonfly flight (Z. J. Wang et al., 2004; Z. J. Wang, 2004). Morphological parameters for the wing shape were obtained from Norberg (R. k. Norberg, 1972). V = r φ (5.3) C L = sin(2.13α 7.2) (5.4) 101

124 Abbreviations Figure 5.4: Illustration of the pressure force due to rotational circulation acting on a single section of the wing. C D = cos(2.04α 9.82) (5.5) The aerodynamic forces were then calculated at each section of the wing. dl = 0.5ρV 2 C L ds (5.6) dd = 0.5ρV 2 C D ds (5.7) Similarly, the rotational pressure forces for each section of the wing were modelled as C rot = π(0.75 ˆx 0 ) (5.8) df rot = C rot ρc 2 U αdr (5.9) 102

125 5.2 Optimisation Problem Figure 5.5: Illustration of the coordinate transform required to determine the actual lift generated by the wing in the global frame of reference (adapted from Norberg (R. A. Norberg, 1975)). where ˆx 0 is the non-dimensional axis of rotation from the leading edge. The overall aerodynamic force can then be calculated by summing the force of all wing sections. It should be noted that the direction of the lift and drag forces are with respect to the velocity of the wing section. To determine the actual lift force generated by the wing in the global reference frame, a coordinate transformation was employed (refer to Fig. 5.5). The vertical force in the frame of reference of the wing is given by (5.10). H r = Lcos(β) + Dsin(β) + F rot sin(α β) (5.10) The vertical force with respect to the global frame of reference is H r,vert = H r cos(φ P roj ) (5.11) 103

126 Abbreviations An equation for cos(φ P roj ) was calculated using the formulation from Norberg (R. A. Norberg, 1975). Therefore the vertical force with respect to the global frame of reference is H r,vert = H r 1 sin2 αsin 2 β (5.12) With a method of calculating the objective function now defined, the optimisation problem can be expressed as: subject to the following optimisation restrictions min X = [β, K, C η, Φ α, α 0, α m ] H r,vert (5.13) X i,min X i X i,max i {1, 2, 3, 4, 5, 6} (5.14) and constraints α m α 0 10 o (5.15) α m + α o (5.16) These restrictions are selected to constrain the solution space within the limits of a physically realisable test bench design. Additionally, C η was constrained, to limit the maximum angular pitch velocity of the system. The constraints are given in Table 5.1. The flapping and pitch parameters refer to the flap and pitch angles at the root of the wing. Table 5.1: Optimisation constraints Property Lower Limit Upper Limit β (deg) K C η Φ α (deg) α η (deg) α 0 (deg)

127 5.3 Results 5.3 Results Prior to running the optimisation process, the lift generated was calculated for the flapping profile suggested by Azuma et al.(azuma et al., 1985). Previously we determined that Berman and Wang s (Berman & Wang, 2007) representation of the flapping and pitch profile was sufficient to represent the experimental results obtained through high speed cinematography by Azuma et al (refer to Fig. 5.2). The values used to approximate the experimental flapping and pitch curves are as follows: Table 5.2: Initial optimisation parameters Property Value β (deg) 37.0 K 0.1 C η 1.3 Φ α (deg) α η (deg) 70.8 α 0 (deg) 99.1 The wing-beat frequency for the Sympetrum frequens dragonfly quoted by Azuma et al was 41.5Hz, which is not achievable by our flapping wing system. Therefore the wing-beat frequency was capped at 10Hz. A quasi-steady numerical analysis was performed on that flapping profile, and the mean lift obtained was 0.55N. The optimisation algorithm was run to determine the flapping profile which would produce the most lift.the Scatter Search algorithm, working from the initial flapping profile, produced a population consisting of a 1000 members which was filtered to 200 Stage One members. Local Quasi-newton methods were then used to refine the solution and determine the optimal flapping profile. Fig. 5.6 shows the optimised flapping and pitch profile versus the unoptimised profile. The lift profiles across the wing stroke for both the optimised and initial cases are shown in Fig The final optimised parameters were: Results of the quasi-steady analysis showed that the mean lift over the wing stroke increased to 0.67N from 0.55N initially. This corresponds to an increase of 22%. However, this was achieved after 3166 objective function evaluations. Whilst this is appropriate for computer 105

128 Abbreviations Table 5.3: Optimised flapping profile parameters Property Value β (deg) 10.0 K 0.1 C η 1.3 Φ α (deg) α η (deg) 56.1 α 0 (deg) 94.5 Figure 5.6: Optimised flapping profile (solid lines) versus unoptimised flapping profile (dashed lines) simulations, it is not ideal for an experimental optimisation. The reason for this is the finite time required to experimentally measure the lift associated with each sample. Additionally, the progressive wear associated with running the experimental wing-actuation system for extended periods of time could result in changes to the system being optimised. Therefore, the number of objective function evaluations will have to be reduced in order for the optimisation algorithm to be applicable to experimental conditions. As mentioned previously, the global Scatter Search algorithm generates a population of a 1000 initial trial points initially from which it then selects 200 of the best points to perform 106

129 5.3 Results a local Quasi-Newton optimisation. Minimising the initial number of trial points reduces the number of function evaluations required. However, this comes at the risk of potentially missing the global optimum. To investigate this effect, we progressively reduced the number of initial sample points and measured the optimised lift. Due to the random nature of the scatter search algorithm, we execute the optimisation algorithm 10 times for each point of interest to ensure consistent results. Fig. 5.8 shows the change in the number of objective function evaluations required with a change in the initial number of trial points used. The error bars represent the scatter in the results obtained from the optimisation method. When the initial population size is reduced to 200, there is a reduction in the number of function evaluations to an average of 481. However, it was observed that there was a variation in the lift generated between 0.65 to 0.67N, even though the objective function convergence tolerance was set to 0.01N. This suggests that using 200 initial samples is not sufficient to consistently capture the global optima. Therefore, an initial population size of 400 was used. Figure 5.7: Optimised lift profile (solid lines) versus unoptimised lift profile (dashed lines) 107

130 Abbreviations Figure 5.8: Number of function evaluations required versus initial population size We next investigate the effect of reducing the number of Stage 1 samples (refer to Fig. 5.9). As shown, there is no significant change in the number of function evaluations required with a change in Stage one sample size. Adjusting the number of initial trial points and Stage one points both affected the global optimisation process. It was also possible to reduce the number of function evaluations by adjusting the convergence tolerance of the local, Quasi-newton optimisation algorithm. As shown in Fig. 5.10, there was a clear decrease in the number of function evaluations required by approximately 20% when the tolerance size was increased to 0.05N from 0.02N. There was no significant change with further tolerance increase above 0.05N. Increasing the tolerance of the convergence criterion comes at the cost of the ability of the local optimiser to refine the optimised solution. As shown in Fig. 5.11, the optimised lift averages 0.65N for a tolerance size of 0.05N as opposed to 0.67N for a tolerance size of 0.01N. 108

131 5.4 Discussion Figure 5.9: Number of function evaluations required versus Stage One population size At 0.1N tolerance, the scatter in the lift obtained becomes too large, suggesting a solver with inconsistent performance. 5.4 Discussion A quasi-steady blade element model was generated to investigate the functionality of a combined global and local optimisation algorithm. Results showed a 20% increase in lift between the optimised and unoptimised flapping profile. It was found that by reducing the initial sample size from 1000 to 400, and increasing the convergence tolerance criterion to 0.05N, significant reductions in the number of function evaluations could be achieved. Reductions in the number of function evaluations is critical to an experimental wingactuation system optimisation. Using a tolerance of 0.05N was found to decrease the lift by up to 4%, however this could be insignificant in comparison to the variation in lift due to the 109

132 Abbreviations Figure 5.10: Number of function evaluations required versus the tolerance of the local solver noise generated by the experimental test bench. Results from an optimisation by Thomson et al. (S. L. Thomson et al., 2009) showed the significance of noise in an experimental set-up. The noise was sufficiently large that using an iteration step size of 5 o produced no convergence. Increasing the iteration step size of the local solver was another factor which will potentially allow reductions in the number of function evaluations. However, this could also result in a reduction in the precision of the solution. In section we discussed the adaptation of Berman and Wang s methodology to representing the flapping and pitch profile of a dragonfly. By comparison with experimental results, we demonstrated that Berman and Wang s model is able to model the flapping profile of a dragonfly with reasonable accuracy. Whilst it is possible to use a Fourier expansion with second and third harmonics to better model the flapping profile, it also introduces additional parameters which need to be optimised and hence the optimisation effort required. This was done 110

133 5.5 Conclusion Figure 5.11: Lift forces generated by the optimisation algorithm as a function of the convergence tolerance criteria. by Thomson et al.(s. L. Thomson et al., 2009). However, their results showed that an iterative step of 10 o was required in order to achieve convergence, which raises the question as to the benefits of having the additional precision of a Fourier expansion in a real world system. Further work will focus on implementing the optimisation algorithm on the experimental wing-actuation system. This is described in Chapter 9. Initial efforts would be targeted at maximising lift, however other objective functions would be investigated, including maximum lift-to-power and maximum yaw moment. 5.5 Conclusion The nature of the flapping wing problem is such that the flapping wing profile is unique to each system. Therefore, optimisation methods are required in order to determine the flapping pro- 111

134 Abbreviations file that will deliver optimal performance. However, flapping wing systems are characterised by non-linear lift dynamics that produces multiple optima across its response surface. In this chapter, we present a method that uses both global and local optimisation to determine the flapping profile which will produce the most lift for an experimental wing-actuation system. The optimisation method was first tested using a numerical quasi-steady analysis to determine the functionality of the optimisation algorithm. Results after optimising the flapping profile show a 20% increase in lift generated as compared to flapping profiles obtained by high speed cinematograhy of a Sympetrum frequens dragonfly. An initially untuned optimisation algorithm showed that the objective function was evaluated 3166 times which is not suitable for a physical experimental setup. Initial sample size and stage one sample size, were altered to determine the effect on the number of function evaluations. Whilst the stage one sample size had no significant effect on reducing the optimisation effort, reducing the initial sample size reduced the number of function evaluations significantly. It was found that reducing the initial sample size to 400 would allow a reduction in computational effort to approximately 1500 function evaluations without compromising the global solvers ability to determine the locations of potential minima. To further reduce the optimisation effort required, we increase the local solver s convergence tolerance criterion. An increase in the tolerance from 0.02N to 0.05N decreased the number of function evaluations by another 20%. However, this potentially reduces the maximum obtainable lift by up to 0.025N. In summary, using a quasi-steady numerical analysis we have demonstrated the ability of the optimisation algorithm to converge on an optimised flapping wing solution in 1200 function evaluations to within 0.025N accuracy. 112

135 CHAPTER 6 A LOW COST SIMULATION PLATFORM FOR A FLAPPING WING MAV Synopsis In chapter 1, we discuss high speed cinematography of dragonflies and the observed parameters that contribute to the manoevrability of a Dragonfly-Inspired Micro Air Vehicle (DI- MAV). This chapter describes the design of a flight simulator for investigating the effects of these parameters on the manoeuvrability of the DIMAV. A quasi-steady blade element model is used to analyse the aerodynamic forces. Aerodynamic and environmental forces are then incorporated into a real world flight dynamics model to determine the dynamics of the DIMAV system. The chapter also discusses the implementation of the flight simulator for analysing the manoeuvrability of a DIMAV, specifically several modes of flight commonly found in dragonflies. This includes take-off, roll turns and yaw turns. Our findings with the simulator are consistent with results from wind tunnel studies and slow motion cinematography of dragonflies. In the take-off mode of flight, we see a strong dependence of take-off accelerations with flapping frequency. An increase in wing-beat frequency of 10% causes the maximum vertical acceleration to increase by 2g which is similar to that of dragonflies in nature. For the roll and yaw modes of manoeuvring, asymmetrical inputs are applied between the left and right set of wings. The flapping amplitude is increased on the left pair of wings which causes a time averaged roll rate to the right of 1.76rad/s within two wing beats. In the yaw mode, the stroke plane angle is reduced in the left pair of wings to initiate the yaw manoeuvre. In two wing beats, the time averaged yaw rate is 2.54rad/s. These results show the importance of flapping 113

136 CHAPTER 6. A LOW COST SIMULATION PLATFORM FOR A FLAPPING WING MAV frequency, flapping amplitude and stroke plane angle as actively controlled parameters which will be discussed further in Chapter 7. This conference publication has been published in: Kok, J. M., and J. S. Chahl. A low-cost simulation platform for flapping wing MAVs. SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health Monitoring. International Society for Optics and Photonics,

137 Abbreviations Nomenclature MAV DIMAV φ Micro Air Vehicle Dragonfly-Inspired MAV Flapping angle φ Mean flapping amplitude ω α Flapping frequency Pitch angle α Pitch amplitude α m β X B, Y B, Z B V L D Mean pitch angle Stroke plane angle Roll, pitch and yaw axes reespectively Local velocity of blade element Lift Drag H r Vertical force in wing reference frame V wind V b ω r Wind velocity due to body movement Body translational velocity Body rotational velocity Radius of blade element 115

138 Abbreviations C L C D C rotational Lift coefficient Drag coefficient Rotational lift coefficient ˆx Non-dimensional location of pitch axis S ρ F rotational Blade area Density Rotational wing aerodynamic force contribution F b Body forces M b I Body moments Body inertia 116

139 6.1 Introduction 6.1 Introduction FLAPPING wing systems present clear advantages as described in Chapter 1. However, the manufacturing and flight testing of such systems can often be costly and time consuming. To facilitate the design of UAVs, flight simulation and visualisation packages are often used. These tools allow UAV designs to be tested in a non-destructive, relatively low cost simulation environment prior to real world testing. This gives the UAV designer flexibility in the selection of design parameters and gives insight into how these parameters affect the performance of the system without the overheads associated with airframe manufacture and flight testing. A myriad of flight simulation and visualisation packages exist (Perry, 2004; Berndt, 2004; Garcia & Barnes, 2010) for fixed wing and rotary wing aircraft. However, for flapping wing aircraft, much research is focussed on the performance of individual wings using numerical, computational and experimental methods rather than the effect that each wing has on the dynamics of a multi-winged flapping MAV at the full system level. To determine the effects that a wing-actuation system has on systems level performance of a MAV, we propose to develop a low computational effort flapping wing flight simulator capable of incorporating flapping wing forces with real-world flight dynamics. This tool will enable us to compare against existing fixed and rotary wing systems, investigate different control methods, and provide insight into the system parameters that produce efficient flight. Our design is similar to the flight simulator developed by the researchers at Berkeley (Schenato, Deng, Wu, & Sastry, 2001). However, unlike the Berkeley design, our simulator is designed to specifically investigate the manouevrability and glide characteristics of a four-winged dragonflyinspired MAV (DIMAV). This chapter will discuss the design of a flight simulator specific to a manoeuvring fourwinged dragonfly-inspired MAV. The manoeuvres investigated will include take-off (Ruppell, 1989) roll turn and the yaw turn (D. E. Alexander, 1986). 117

140 Abbreviations 6.2 DIMAV Flight Simulator It is envisaged that the DIMAV flight simulator will be capable of analysing the performance of a DIMAV in its three modes of flight - glide/forward flight, hover and manoeuvre. Figure 6.1 illustrates the proposed high level architecture of the DIMAV flight simulator. The mission profile is defined initially by the user. An autopilot module is included that simulates the functioning of an autopilot. The autopilot is responsible for execution of the mission profile by determining the difference between the desired state of the DIMAV and its current state, and manipulating wing articulation to minimise the error. The autopilot uses a suite of sensors (i.e. GPS, accelerometers) to determine the current state of the DIMAV which can be modelled in the sensor block. To determine how the DIMAV behaves when the wing articulation is changed, a Physics model is used. Characteristics of the DIMAV are defined in the physics model and the equations-of-motion are solved using force inputs from the aerodynamics model and the environment model. Environmental factors include wind and gravity. The aerodynamic model solves for aerodynamic forces based on a prescribed wing motion and body dynamics. This chapter will discuss specifically the implementation of the wing dynamics, aerodynamics, physics and environment modules as it relates to the manoeuvrability of the DIMAV (see dotted section, Fig. 6.1) Wing Dynamics The wing kinematics were modelled using equations from Wang (Z. J. Wang, 2004, 2005; Z. J. Wang & Russell, 2007) for a wing flapping in an inclined stroke plane with angle β (see Fig. 6.2). It should be noted that the wings were assumed rigid. In Wang s representation of the Dragonfly flapping profile, the flapping angle, φ, is represented using a sinusoid. A similar flapping profile is employed in this study. φ(t) = φ 0 cos(ωt) (6.1) The angle-of-attack (AOA) is represented using α = α m α 0 sin(ωt) (6.2) 118

141 6.2 DIMAV Flight Simulator This was done for all four wings. Figure 6.2 illustrates the coordinate system. Figure 6.1: DIMAV simulator high level architecture 119

142 Abbreviations Aerodynamics Module The aerodynamic model comprises of a numerical quasi-steady blade element model of the aerodynamic forces acting on the flapping wing was produced. Similar studies have been performed by Weis-Fogh and Norberg (Weis-Fogh, 1973; R. A. Norberg, 1975). Sane and Dickinson (Sane & Dickinson, 2002) also presented a similar analysis, with additional aerodynamic effects due to wing rotation. The wing was divided into spanwise sections, and the instantaneous forces calculated on each section based on the local translational and angular velocity. The forces across all slices were then summed to obtain the forces/torques acting on the wing at any point in time. Figure 6.2: Illustration of translational (A) and rotational (B) forces (adapted from Dickinson et al. (M. H. Dickinson et al., 1999)) High speed footage of dragonflies show that it has excellent manoeuvring capabilities (Ruppell, 1989). The dragonflies have instantaneous accelerations of up to 4g and sustained and takeoff accelerations of up to 2g. Wind tunnel studies performed by Alexander (D. E. Alexander, 1986) show that at low speeds, dragonflies employ a yaw turn manoeuvre whereby a 90 o yaw is achieved in just 2 wing beats. Maximum speeds demonstrated by the dragonfly were also up to 10m/s (Ruppell, 1989). At these speeds, the relative wind as a result of the movement of the DIMAV is significant and must be taken into consideration. The wind due to the movement of the body is given as V wind = V b + r ω (6.3) 120

143 6.2 DIMAV Flight Simulator where V b and ω are defined as V b = [u b v b w b ], ω = [p q r] (6.4) This is combined with the relative wind due to the movement of the wing. This is calculated in the body-coordinate frame (see Fig. 6.3) as defined by Azuma (Mueller, 2001). Figure 6.3: Illustration of the body coordinate system (adapted from (Mueller, 2001)). Circled numbers indicate actuator number. Equations for the lift and drag coefficients were obtained from three-dimensional experiments performed by Dickinson (Z. J. Wang et al., 2004; M. H. Dickinson et al., 1999). Similar coefficients were obtained by Wang computationally and used as the basis for analysing dragonfly flight (Z. J. Wang, 2004; Z. J. Wang et al., 2004). C L = sin 2.13α 7.2 (6.5) C D = cos 2.04α 9.82 (6.6) Similarly, the rotational pressure forces for each section of the wing were modelled as C rot = π(0.75 ˆx 0 ) (6.7) Following that, the forces due to the translational (refer to Fig. 6.2A) and rotational (refer to 121

144 Abbreviations Fig. 6.2B) motion of the wing can be calculated. The aerodynamic forces at each section of the wing are given by dl = 0.5ρV 2 C L ds (6.8) dd = 0.5ρV 2 C D ds. (6.9) df rot = C rot ρc 2 U αdr. (6.10) where ˆx 0 is the non-dimensional axis of rotation from the leading edge. The AOA used to calculate the lift and drag forces are with respect to the wind vector Environmental Module Environmental factors include gravity and wind. Due to the nature of the operating envelope of the DIMAV, the gravitational acceleration was assumed to be constant at 9.81m/s Physics Module Forces from the aerodynamics module and environment module are converted into the body coordinate system, and input into the physics module to determine the dynamics of the DIMAV. The physics module consists of a 6 Degree-of-freedom, equation-of-motion solver (6DOF EOM) (Raol & Singh, 2008). The relationship that governs the body forces [F x F y F z ] applied to the system and its translational dynamics are given by F b = [F x F y F z ] = m( V b + ω V b ) (6.11) Similarly the rotational dynamics of the body-fixed frame to applied moments [L M N] are given as M b = [L M N] = I ω + ω (Iω) (6.12) These equations are solved to give velocity and angular rates in the body coordinate system, which is also converted to an Earth-fixed-earth-centred coordinate system. 122

145 6.3 Results Visualisation Module A visualisation module was also included in the simulator that replicates the wing and body dynamics in a virtual environment which provides visual clarity of the performance of the DIMAV. 6.3 Results Take-off Ruppell (Ruppell, 1989) describes the take-off manoeuvre as one in which the dragonfly uses in-phase stroking of the fore and hind wings to generate lift for take-off. In this mode, the dragonfly can experience accelerations of up to 2.5g (Ruppell, 1989). We investigate the effects of frequency modulation on the acceleration of the DIMAV. The parameters used in the simulation are listed in Table 6.1. Table 6.1: Simulation parameters for all wing-actuators in take-off configuration Actuator Frequency (Hz) β (deg) φ 0 (deg) α 0 (deg) α m (deg) 1, 2, 3, 4 5, 6, 7, 8, 9, The maximum vertical accelerations experienced during flight as a function of wing-beat frequency is shown in Fig The acceleration increases with frequency. At a wing-beat frequency of 10Hz, accelerations of up to 20g is experienced by the 40 gram DIMAV Roll turn and Yaw Turn Wind tunnel studies by Alexander (D. E. Alexander, 1986) show that the dragonfly is also capable of roll and yaw manoeuvres which are initiated by asymmetrical flapping of the left and right wings. In roll manoeuvres, the flapping amplitude is varied, whilst in yaw manoeuvres, both stroke plane and flapping amplitude are varied. These were investigated in the DIMAV simulator (see Table 6.2 and Table 6.3). The inertia in the roll and yaw axis were I x = kg m 2 and I z = kg m 2 respectively. 123

146 Abbreviations Figure 6.4: Maximum vertical acceleration experienced by the DIMAV in flight Table 6.2: Simulation parameters for all wing-actuators in roll configuration Actuator Frequency (Hz) β (deg) φ 0 (deg) α 0 (deg) α m (deg) 1, , Table 6.3: Simulation parameters for all wing-actuators in yaw configuration Actuator Frequency (Hz) β (deg) φ 0 (deg) α 0 (deg) α m (deg) 1, , The results for roll rate are shown in Fig. 6.5A. With asymmetrical left and right flapping profiles, a significant roll moment is generated that produces a mean roll rate of 1.76rad/s. Similarly in the yaw turn mode, a yaw rate of 2.54rad/s is generated (see Fig. 6.5B). 124

147 6.4 Discussion Figure 6.5: Angular rates experienced by the DIMAV in roll (A) and yaw (B) manoeuvre across 2 wingbeats. The dashed line represent the angular rates averaged over the period of two strokes 6.4 Discussion In this chapter we described the design of a flight simulator for DIMAV applications. DIMAVs are characterised by its four wings, but more notably by its proficiency in all three modes of flight - glide, hover and manoeuvre. Whilst the DIMAV flight simulator is envisaged to have the capacity to model all three modes of flight in a mission-like scenario (see Fig. 6.1), we specifically focus on the manoeuvrability aspects of the modelling. This is important as the ability to perform agile manoeuvres is what differentiates flapping wing MAVs from their counterparts (J. Kok & Chahl, 2014b, 2014a). The manoeuvrability modes we investigated were take-off, roll turn and yaw turn. In the take-off mode we see the dependence of vertical acceleration on the wing-beat frequency. At 5Hz, a 10% increase in wing-beat frequency to 5.5Hz results in an increase in maximum acceleration of 2g. These are similar accelerations to those experienced by a dragonfly in take-off (Ruppell, 1989). It should be noted that these results are for a 40gram DIMAV. Heavier airframes will require higher frequencies to achieve similar accelerations. In the roll and yaw modes of flight, different parameters were applied to the left (Actuator 3 and 4) and the right (Actuators 1 and 2). Having a larger flapping amplitude on actuators 3 and 4 caused significant roll to the right. Similarly reducing the stroke plane angles (i.e. more horizontal 125

148 Abbreviations stroke) on actuators 3 and 4 caused a yawing motion to the right. It should however be noted that similar to fixed wing aircraft, the roll and yaw modes are coupled. Such a phenomenon was described by Alexander (D. E. Alexander, 1986) who observed the roll mode leading into a banking mode similar to that in aircraft. This was particularly true at higher wind speeds, whereby the inherent drag of the dragonfly torso makes yaw turns difficult. This would suggest that a more accurate DIMAV flight simulator model would require body drag to be analysed as well. Additional modules that could also be beneficial to analysing a real world DIMAV system would include and actuator module, sensor module and ground control module. 6.5 Conclusion In this chapter we ve described the architecture and implementation of a flight simulator for investigating the systems level parameters affecting four-winged flapping MAV applications. We have specifically focussed on the manoeuvring capabilities of the DIMAV, which include take-off, roll turns and yaw turns. Key parameters that influence these individual modes were input into the flight simulator. We showed the importance of flapping frequency, flapping amplitude and stroke plane angle on the manoeuvrability of the system. 126

149 CHAPTER 7 ON THE DESIGN FRAMEWORK FOR A FLAPPING WING MAV Synopsis This chapter proposes a set of design criteria for a bio-inspired flapping wing system. We address many of the design choices of existing systems, including the use of resonance and passive wing pitching and how they relate to the full capability of a flapping wing MAV system. The conclusion of this chapter is a design framework by which a Micro Air Vehicle can be developed that truly replicates and benefits from dragonfly inspiration. This work, like the previous chapters, is based on the premise that the primary need for a flapping wing MAV is a system capable of all three modes of flight - hover, glide, manoeuvre. Commonly postulated systems employing resonant flapping and passive wing pitching are unlikely to meet these requirements. In addition, we show that in certain cases, achieving a resonant mode reduces the efficiency of lift generation. We propose an active flapping mode with optimisation of wing kinematics to achieve energy efficient hover. We show that the effects of optimisation are significant particularly at higher stroke plane angles of more than 20 degrees, such as those found in dragonflies. We highlight the importance of optimisation in designing efficient wings for gliding flight. We also demonstrate that in manoeuvring flight the use of stroke plane modulation can increase thrust by 100%. We conclude that an ideal system may be achieved by using active flapping, with optimised design of wing-actuator-thorax systems and efficient control and optimisation of wing kinematics. It is envisaged that these rules will introduce a paradigm shift towards a new generation of bio-inspired MAVs defined by function as opposed to conve- 127

150 CHAPTER 7. ON THE DESIGN FRAMEWORK FOR A FLAPPING WING MAV nience of design. Further exploration and development of these design rules are presented in the next chapters. 128

151 Abbreviations Nomenclature MAV DIMAV DOF β V L P τ k θ Ω φ Micro Air Vehicle Dragonfly-Inspired MAV Degrees of Freedom Stroke plane angle Local velocity of blade element Lift Power Torque Elastic coefficient in the pitch axis Frequency ratio Flapping angle φ Flapping amplitude η T α Downstroke-to-total stroke ratio Flapping period Pitch angle α Mean pitch angle α m D Pitch amplitude Drag 129

152 Abbreviations H r Vertical force in wing reference frame V wind V b ω r C L C D C rotational Wind velocity due to body movement Body translational velocity Body rotational velocity Radius of blade element Lift coefficient Drag coefficient Rotational lift coefficient ˆx Non-dimensional location of pitch axis S ρ F rotational Blade area Density Rotational wing aerodynamic force contribution F b Body forces M b I Body moments Body inertia 130

153 7.1 Introduction 7.1 Introduction WHILST flapping wing MAVs present many possible applications, the concept design of the actuation system is yet to be fully understood and is far from being convincingly replicated by technical systems (see Section 2.1). The cyclic nature of the flapping wings introduces coupled inertial, aerodynamic and elastic loads that must be overcome to successfully actuate a wing. Additionally, these loads vary between different insects and have a strong influence on the performance of the system. Greenewalt (Greenewalt, 1960) used a simple harmonic oscillator (SHO) model to show the variations in the actuation force required between different insects while Weis-Fogh (Weis-Fogh, 1973) used experimental data combined with quasisteady numerical analysis that showed significant variations in the proportion of aerodynamic to inertial loading between different insect species. Some researchers have proposed the presence of resonance as a means to reduce the inertial power requirements associated with flapping actuation through elastic storage and recovery (Ratti & Vachtsevanos, 2012). Certainly some systems such as the Harvard Microrobotic Fly rely heavily on the use of resonance to enable the system to take-off (Wood, 2008). Other studies have also demonstrated energy savings of 20% by using elastic storage mechanisms (Sahai et al., 2013; Baek et al., 2009). Certainly in systems in which the dominant forces are inertial, the use of resonant mechanisms will allow for significant energy savings. However in systems that are dominated by aerodynamic forces, the use of resonance is questionable (Ramananarivo et al., 2011; Sahai et al., 2013). Ramananarivo et al. (Ramananarivo et al., 2011) demonstrated that flapping flyers improve performance by tuning their wing shapes to optimize aerodynamics as opposed to looking for resonance. Designers should be aware that the amount of energy that can be saved through resonance is dependant on the inertial load on the system. Additionally, studies by Yin and Luo (Yin & Luo, 2010) have shown that systems dominated by inertial forces have lower performance as compared to systems dominated by aerodynamic forces. Yin and Luo showed that a low inertia wing has better lift performance and power efficiency. This suggests that aerodynamically dominated flapping wing systems, such as the dragonfly, have the potential to offer better performance than inertia dominated systems. Another common flapping configuration is the use of passive wing rotation (see Sec- 131

154 Abbreviations tion 2.1). This is common in single DOF systems, as it allows for simplicity of design as well as a reduction in actuator weight. This chapter explores the energetics of flapping wing actuation and the effect of resonant and passive wing pitching mechanisms on the hovering, gliding and manoeuvring capabilities specific to a aerodynamically efficient, four winged flyer capable of all three modes of flight. We explore the use of techniques presented in section for optimising active wing parameters that relate to aerodynamic efficiency and manoeuvrability. A review of the glide performance of dragonflies, as well as what makes it an efficient glider will also be provided. The aim of this chapter is to produce a design framework for the development of a dragonfly inspired MAV and the full realisation of its mission capabilties. 7.2 Benefits of flapping wing Before defining a framework for flapping wing system design, it is necessary to understand the benefits of deriving inspiration from insects for MAV designs. Numerous studies surrounding flapping wing systems has shown that insect-inspired systems are extremely versatile flyers, able to hover, glide while also being capable of performing complex and rapid manoeuvres (D. E. Alexander, 1986; Ruppell, 1989; Chahl, Dorrington, & Mizutani, 2013; Mizutani et al., 2003). We will show that this flight envelope is larger than what is achievable by any fixed or rotary-winged craft. Early glide tests of real-world dragonfly wings have shown lift-to-drag ratios of around 3.5 (Azuma & Watanabe, 1988), which is in the order of real world MAVs. Wakeling and Ellington (Wakeling & Ellington, 1997a) performed a similar analysis using measurements in a wind tunnel, and showed lift-to-drag ratios in excess of 17. Other studies include Newman (Newman et al., 1977) and Okamoto (Okamoto et al., 1996) that showed lift-to-drag values of 6 to The aerodynamic performance of such systems to be able to glide is in part due to corrugations on the wing which alter the airflow over the wing. It has the added benefit of stiffening the wing allowing for a light, stiff wing system which is crucial for gliding flight (J. Kok & Chahl, 2014b). Both experimental and computational studies show that insectinspired MAVs have excellent gliding characteristics (Ruppell, 1989; Azuma & Watanabe, 132

155 7.3 On the question of hover 1988; Okamoto et al., 1996; Vargas & Mittal, 2004; Vargas, Mittal, & Dong, 2008). This differs from most rotorcraft which whilst capable of hover, are not designed for efficient forward flight relative to fixed wing aircraft. Insect-inspired systems are potentially extremely versatile flyers, able to perform rapid and complex manoeuvres that include take-off, forward flight, yaw turns, bank turns, and more. Slow motion footage taken by Ruppell (Ruppell, 1989) show instantaneous accelerations of up to 4g and sustained and take-off accelerations of up to 2g. Maximum speeds demonstrated by dragonflies were up to 10m/s which are of the order of the operational speeds of some MAVs. Analysis of a video of dragonflies in combat by Chahl et al. (Chahl, Dorrington, & Mizutani, 2013; Mizutani et al., 2003) showed accelerations in turns exceeding 4g. Wind tunnel studies performed by Alexander (D. E. Alexander, 1986) show that at low speeds, dragonflies employ a yaw turn manoeuvre whereby a 90 o yaw is achieved in 2 wing beats. Finally, insects are able to hover, similar to rotorcraft. This gives them an advantage over most conventional fixed wing MAVs. Many studies have been undertaken to investigate the aerodynamic efficiency of flapping wing systems in hover (Tantanawat & Kota, 2007; Baek et al., 2009; Azhar, Campolo, Lau, Hines, & Sitti, 2013). This will be further discussed in later sections. It is the ability of insects to hover, glide and manoeuvre as well as alternate effortlessly between all three modes of flight which is what makes it a unique and valuable system in the MAV design space. 7.3 On the question of hover This section will explore the mode of hover in insects. Hover is the ability of an aircraft to generate enough lift to fly with zero forward speed. Operationally, it allows a MAV to maintain position in the air for an extended period of time with no external forces. A significant amount of research into insect-inspired flight has targeted the problem of hover. It has been shown that in addition to the translational lift generation modes experienced by rotorcraft, insect-inspired systems generate lift via other means, namely wing rotation (M. H. Dickinson et al., 1999) and 133

156 Abbreviations forewing-hindwing interactions (Z. J. Wang & Russell, 2007; Usherwood & Lehmann, 2008; Weis-Fogh, 1973) (i.e. L = L T ranslational + L Rotational + L fw,hw ). Another difference between rotorcraft and flapping flight is the constant accelerations and decelerations experienced by the flapping wing. The differences between rotorcraft and flapping flight are listed in table 7.1. Table 7.1: Differences between rotorcraft and flapping-wing aircraft Rotorcraft Flapping Wing Continuous rotation Periodic starting and stopping Dominated by aerodynamic forces Combination of aerodynamic and inertial loads Lift generation through translational Lift generation through translature means tional, rotational and vortex recap- Constant AOA Variable AOA From this, we see that specific to hover, insect-inspired systems and rotorcraft each have advantages and disadvantages. Flapping wing systems rely less on translational lift generation, relying more on wing rotation and vortex recapture to generate additional lift. Rotorcraft utilise continuously rotating propellers using carefully designed airfoil profiles operating at angles of attack optimised for their operation. As such, they are not subject to the inertial loads present in insect-inspired systems that are constantly accelerating and decelerating their wings. The work required to overcome inertial loads can be as high as 66% of the total work required for aerodynamic and inertial loading (Weis-Fogh, 1973), suggesting that inertial loading is dominant in such systems. This is one of the fundamental problems limiting insect-inspired technical systems from achieving rotorcraft efficiencies. This has resulted in a trend of research that introduces additional elastic forces to recover energy otherwise lost to inertia. This is achieved through the use of resonance, whereby at a particular wing-beat frequency, the elastic and inertial forces balance each other completely and in-principle the only force that needs to be overcome are aerodynamic forces. This method is common in single DOF systems whereby the only control parameter is the wing-beat frequency (see section 2.1). The underactuated nature of these systems also means that they rely on passive wing pitching to generate the appropriate angles-of-attack needed for modulation of aerodynamic forces (Madangopal et al., 2005; Tantanawat & Kota, 2007; Baek et al., 2009; Hines et al., 2014). However, there are fundamental technical and system issues surrounding the use of such a mechanism. 134

157 7.3 On the question of hover Are resonant and passive modes really effective? Significant research has been performed on aerodynamic efficiency (Madangopal et al., 2005; Tantanawat & Kota, 2007; Baek et al., 2009; Hines et al., 2014) The challenge is inherent in the fact that flapping wing systems are expected to overcome large inertial loads due to constant acceleration and deceleration of the wing. This reduction in aerodynamic efficiency is supposedly offset by the additional lift generation mechanisms that a flapping system has, namely vortex recapture and wing rotation (i.e. L V ortexrecapture and L W ingrotation ) (Z. J. Wang & Russell, 2007; Usherwood & Lehmann, 2008; Weis-Fogh, 1973; M. H. Dickinson et al., 1999). There is a stream of research investigating the use of an elastic mechanism to mitigate the additional power requirements from inertial loads, by tuning the elasticity of the system to achieve resonance at a particular wing-beat frequency. However, the science behind such a system as well as its effects on the system level performance are neglected in favour of oversimplifying assumptions (J. Kok & Chahl, 2014b). Firstly, the suggestion that all the energy from inertial work can be converted to elastic energy and back is false. All energy transactions in physics come at a costs. Even the most efficient springs in realistic configurations have been quoted to have 33% elastic storage efficiency (Tooley, 2009, p.543). Natural systems perform better with thorax and inactive muscles having storage efficiencies of 80% (Andersen & Weis-Fogh, 1964; Lehmann et al., 2011; J. Kok & Chahl, 2014b). However, realistically, this means that at least 20% of inertial energy is unrecoverable by the elastic element. Secondly, the concept of resonance suggests a dependance on frequency. Previous studies by Kok et al. (J. Kok & Chahl, 2014b) have shown that performance of the system decreases with deviation from the natural frequency. Dragonfly systems in nature are known to have a wide operating band of wing-beat frequencies. If such a band is applied to a resonant system it can be seen that a drop of as much as 71% in performance is possible. Certainly this suggests that the use of an elastic mechanism would limit MAV operation to a particular wing-beat frequency and as such would limit the use of frequency modulation as a means of control. Lastly, many systems neglect the effects that the resonant mechanism has on the many lift 135

158 Abbreviations generation modes of the system. Studies have been performed on the use of resonant mechanisms cycled over a range of wing-beat frequencies to calculate the aerodynamic efficiencies without questioning if the benefits gained are due to recapturing of inertial energy from an inefficiently designed system or if it is due to the enhancement of aerodynamic effects such as vortex recapture, delayed stall, etc. We hypothesize that in poorly designed systems, it is possible that attempts at achieving a resonant mode could result in degraded aerodynamic performance. For such systems, it is still possible to achieve a resonant point with relatively better aerodynamic efficiencies, however, such systems are likely to be far from optimal when considered holistically. To demonstrate this, we ran a simulation that included translational and rotational lift generation mechanisms using a quasi-steady lift generation model proposed by Sane and Dickinson (Sane & Dickinson, 2002) (see Fig. 7.1). The details of the analysis have been described in chapters 4, and 5, and will not be repeated in this chapter Figure 7.1: Illustration of translational (A) and rotational (B) forces (adapted from Dickinson et al. (M. H. Dickinson et al., 1999)) However, it should be noted that unlike the other models used by Kok et al. (J. Kok & Chahl, 2014a; J. Kok, Lau, & Chahl, 2016), this model prescribes the flapping kinematics only. Passive wing pitch is modelled in the system as a coupled linear elastic model. Additionally, the wing selected was a semi-elliptical wing with semispans a = 60 and b = 40 to be more representative of the systems described in Chapter 2. θ = τ aero /k θ (7.1) 136

159 7.3 On the question of hover where τ aero = τ aero,flap + τ aero,pitch. The aerodynamic efficiencies, L/P T otal and L/P Aero, were derived and compared against each other over a range of frequency ratios. The L/P T otal is the aerodynamic efficiency that includes power consumed in overcoming elastic and inertial mechanisms. The L/P Aero term only accounts for power consumed by aerodynamic effects. This should be the ideal case whereby the only forces that need to be overcome are aerodynamic forces. We see that when we compare the L/P T otal and L/P Aero, over a range of frequency ratios, there are different optimal points. When we consider the L/P T otal there is an optimal frequency (ω/ω n = 0.85) whereby the efficiency is a maximum. However, the L/P Aero increases with decreasing frequency ratio. It eventually reaches a maximum when the lift begins to reduce due to significantly lower wingbeat frequencies. This suggests that in the process of recovering energy lost to inertia, it is possible to compromise the efficiency of the lift generating mechanism. MAV designers must then solve for optimal aerodynamic and inertial performance. k θ was chosen to provide a wing pitch of [40 o 140 o ] at the natural frequency. Figure 7.2: Lift-to-total power and Lift-to-aero power ratio across a range of frequency ratios 137

160 Abbreviations The active mode of flapping From the previous section, we see that resonant and passive modes of flapping are not ideal for improving aerodynamic efficiency in hover. Performing frequency sweeps to determine an ideal operating frequency is an inefficient method and is questionable as to how energy saving benefits are derived. Furthermore, its effects on system level performance in manoeuvring and gliding flight are likely to be detrimental, defeating the original purpose of deriving inspiration from nature. This suggests that a better solution might be the use of active wing pitch as a regulator of aerodynamic forces. In such a configuration, active wing control regulates aerodynamic forces as opposed to the passive alternative whereby aerodynamic forces manipulate wing kinematics. The use of active wing modulation introduces additional design parameters beyond wing-beat frequency. This introduces the question of what the optimal wing kinematic profile is. Studies by Thomson et al. (S. L. Thomson et al., 2009) have suggested the use of harmonic series to represent wing kinematics. Sine waves and their harmonics are weighted and added together to produce different flapping profiles. This method however results in high dimensionality as well as non-monotonic flapping profiles which are impractical for a flapping wing system. Berman and Wang proposed an alternative kinematic waveform model (Berman & Wang, 2007; Z. J. Wang, 2004). The flapping angle, φ, and angle-of-attack, α, in the stroke plane is represented by α(t) = φ(t) = φ m sin 1 (K)) sin 1 [Kcos(ωt)] (7.2) α m tanhc α tanh[c α cos(ωt + Φ α )] + α 0 (7.3) where 0 < K < 1 and C α > 0. In the limit where K 0, φ becomes sinusoidal, and in the limit where K 1, a triangular waveform is generated. Similarly, as C α 0, α becomes a sinusoidal waveform, as C α, α tends towards a square wave (refer to Fig. 7.3). Doman et al. (Doman, Oppenheimer, & Sigthorsson, 2010b, 2010a) introduced a split cycle parameter that modulates upstroke-to-downstroke ratio, providing an added level of control over conventional 1DOF-per-wing systems. There are many different ways to represent the 138

161 7.3 On the question of hover Figure 7.3: Illustration of the dependance of φ and α on K and C α (adapted from Berman and Wang (Berman & Wang, 2007)). kinematic waveforms, however, they all share the requirement that there are a number of parameters which are variable and hence some method of optimisation is needed to produce the ideal flapping profile. Regardless of the method, all wing kinematics optimisation techniques share a common issue. The non-linear flapping-wing dynamics leads to a complex force response surface, and depending on the initial solution the obtained local optima might not correspond to the global optima. That is particularly true for the problem of flapping wing actuation. To resolve this issue, optimisation techniques that rely on global search methods are required (see Section 2.3.1). Kok et al. (J. Kok & Chahl, 2014a) previously present on a method for optimising a flapping profile based on wing kinematics presented by Berman and Wang (Berman & Wang, 2007; Z. J. Wang et al., 2004; Z. J. Wang, 2004), with the objective function aiming to maximise the mean vertical force. To do this, we employ a Global Search algorithm presented by Ugray et al. (Ugray et al., 2007). This is a combination of global and local search methods for finding multiple local optima. Global methods are used to determine basins where optima are likely to occur, and local gradient-based methods are used to refine the location of the optima within those 139

162 Abbreviations basins. An initial set of points was produced by using a Scatter Search approach (Glover et al., 2000). Similar to Genetic algorithms, this is a heuristic approach. However, unlike genetic algorithms that require a large initial populations to generate sample points, the Scatter Search approach uses a small initial set of samples and grows the sample size not just based on the value of the objective function, but also on the diversity of that solution. Therefore, the Scatter Search method produces a set of sample points that satisfy both the objective function but are sufficiently diverse from each other that the probability of locating the true global optima is increased. Once an initial population of sample points have been determined, local Quasi- Newton optimisation techniques (P. E. Gill et al., 1984; P. Gill et al., n.d.) are employed to refine the location of the optima to within a user-specified convergence criterion. Previously, this technique has been employed to demonstrate improvements in lift (see Chapter 5). In this chapter, we advance this body of work by investigating the aerodynamic efficiency of a 2 dimensional wing section. Note that we used a simplified version of the quasisteady model that accounts for translational lift only. This is more akin to the quasisteady model used by Kok (J. Kok & Chahl, 2014b). We do not attempt to accurately model the aerodynamic efficiency, but rather show at a fundamental level, the relationships between stroke plane angle and wing pitch angle, and how the use of active wing control can impact performance. The objective function being optimised is the global lift-to-drag ratio, whereby lift and drag are represented by L Global = T 0 (Lcosβ + Dsinβ)dt (7.4) D = T 0 D dt (7.5) The lift-to-drag ratio is a performance metric which is commonly used in aircraft design, and is used to quantify the aerodynamic efficiency of a system. In this case, it provides an indication of the aerodynamic forces which need to be overcome in order to produce lift. The optimisation routine can be represented as 140

163 7.3 On the question of hover min X = [Φ α, α 0, α m, K, C α ] L global D (7.6) β i subject to the following optimisation restrictions X i,min X i X i,max i {1, 2, 3, 4, 5} (7.7) and constraints α m α 0 40 o (7.8) α m + α o (7.9) These restrictions were selected to constrain the solution space within the limits of a realistic biomimetic wing MAV design (J. M. Kok & Chahl, 2016). Additionally, C α was constrained, to limit the maximum angular pitch velocity of the system. The constraints are given in Table 7.2 Table 7.2: Optimisation constraints Property Lower Limit Upper Limit β (deg) 0 70 Φ α (deg) α m (deg) 0 80 α 0 (deg) K C α Figures 7.4 and 7.5 show the flapping and pitching profiles respectively before and after optimisation. We see that the flapping profile remains relatively unchanged (see Fig. 7.4). A consistent sinusoidal profile is maintained. However, when we observe the pitch angle (see Fig. 7.5), we see that the optimisation produces a pitching profile quite distinct to a baseline, unoptimised profile. This effect is particularly apparent at stroke plane angles (β > 20deg), where greater asymmetry in the stroking profile is required, such as those found in dragonflies. These results show the importance of being able to modulate the angle-of-attack, particularly 141

164 Abbreviations in modes of flight that utilise large stroke plane angles. It also highlights the necessity for an optimisation routine for determining the flapping profile. Figure 7.4: Flapping angle profile optimised for β = 20, 40, 60 deg 7.4 On the question of glide Should hover be the primary mode? The previous sections have highlighted a trend of research into resonant and passive modes for improving aerodynamic efficiency in hover. Whilst we have demonstrated that resonance may not be the optimal means of energy savings, we also need to ask ourselves the question as to whether hover is really the primary mode of flight that technical UAV designers should be pursuing, and if optimisation for hovering flight is indeed the most important design parameter. Many natural systems whilst capable of hover, are in a constant state of motion (Ruppell, 1989; May, 1991). High speed cinematography of dragonflies have shown that dragonflies operate anywhere between 2 to 10m/s (Wakeling & Ellington, 1997b; May, 1991; Ruppell, 142

165 7.4 On the question of glide Figure 7.5: Pitch angle profile optimised for β = 20, 40, 60 deg 1989). Studies performed by May (May, 1991) show that dragonflies spend a significant proportion of their time in motion. Dragonflies are constantly alternating between stroking and gliding flight (Ruppell, 1989). Even in technical systems, MAVs are in a constant state of motion (Gómez, 2015; Gupte et al., 2012; Asadpour et al., 2015; Bernardini et al., 2014; Cantelli et al., 2013). Having a system with a dominant hover mode is impractical even in technical systems. Work performed by Mueller (Mueller, 2001) suggests that most MAV systems are designed to perform missions that involve surveillance, detection, communication and placement of unattended sensors. Additionally, MAV systems are expected to perform in a wide range of possible operational environments, such as urban, jungle, desert, maritime, alpine and arctic. All of these would require the MAV to be robust in its manoeuvring capabilities. Mueller further adds that the long term goal of MAV design should be to develop aircraft systems which have endurances of 20 to 30 minutes at speeds between 30 and 65 km/h, and that flapping wing MAVs would begin to fill such a gap, not because of its ability to hover but because of its increased efficiencies at such Reynolds numbers. Whilst the ability to hover is important, in most cases, it is not the primary mode of flight. As such MAVs usually should not be designed 143

166 Abbreviations around hover that ignores or compromises the capability of the system to perform the other modes of flight Glide efficiency In addition to hovering and manoeuvring modes, Odonates are excellent gliders. They are able to soar without impulse from the wings for more than 20m corresponding to a gliding ratio of 1:6, which is in the order of some birds (Ruppell, 1989). Certainly odonates have demonstrated themselves to be quite efficient gliders. This energy efficient mode gives odonates the ability to travel long distances efficiently giving it mission capabilities akin to fixed wing flyers. Studies have shown that this glide capability is due to a series of peaks and troughs on the dragonfly wing described here as corrugations. These corrugations serve the additional purpose of stiffening the dragonfly wing (Rees, 1975) with minimal weight increase so as to improve the overall stiffness to weight of the system. Initial studies on dragonfly wings were performed by Azuma and Watanabe (Azuma & Watanabe, 1988) and Okamoto (Okamoto et al., 1996). Okamoto showed improved lift-todrag ratios as well as high maximum lift coefficients from the use of a corrugated profile (Re <24,000) in a wind tunnel and in glide tests. Wind tunnel studies by Wakeling and Ellington (Wakeling & Ellington, 1997a) at Reynolds numbers from 700 to 2400 as well as from free flying dragonflies also come to the same conclusion, recording abnormally high lift coefficients compared to other insect species. Wakeling and Ellington attributed this to corrugations found in the wing structure. Similarly, wind tunnel testing by Kesel (Kesel, 2000) at Reynolds numbers of 7,880 and 10,000 show improved lift-to-drag ratios. Computational studies by Vargas et al (Vargas et al., 2008) (Re<6000) show a similar result, when compared against a flat plate and profiled airfoil. Levy et al. (Levy & Seifert, 2009) performed a similar numerical study on corrugated profiles at Reynolds numbers less than 8,000. Comparisons against an Eppler E-61 airfoil, commonly used for low Reynolds number flows, showed better aerodynamic performance of the corrugated airfoil. Most of these studies have shown improved performance at low Reynolds numbers, despite them being unoptimised. At higher Reynolds numbers, representative of MAVs (Re 144

167 7.4 On the question of glide 34,000 to 125,000) the conclusions are mixed. This Reynolds number range is relevant because studies have shown that dragonflies with wing span of 4.5cm are capable of flying up to 10m/s (Ruppell, 1989). It is perceivable that a dragonfly-inspired technical system with the same dragonfly-like qualities should be able to achieve similar speeds/reynolds numbers. The Delfly with passive wing pitch and a wing span of 27.4cm is able to achieve velocities up to 5.5m/s (Armanini et al., 2015). At these Reynolds numbers, Tamai et al. (Tamai, Wang, Rajagopalan, Hu, & He, 2007) and Hu et al. (Hu & Tamai, 2008) demonstrated using Particle Image Velocimetry that these wings have improved resistance to stall compared to profiled and flat plate sections. Murphy and Hu (Murphy & Hu, 2010) extended on this investigation by performing wind tunnel testing of corrugated, smooth and flat plate profile sections at Re 58,000 to 125,000. Their results showed improved aerodynamic performance of the corrugated airfoil at Re = 58,000. The opposite was true at Re = 125,000, suggesting that corrugated airfoils might not perform as well at higher Reynolds numbers. Computational studies performed by Khurana and Chahl (Khurana, Chahl, et al., 2013) show a similar result, with limited aerodynamic efficiency for a corrugated profile at low angles of attack compared to a flat plate and Eppler 61 airfoil at Reynolds numbers of 34,000. However, further work by Khurana and Chahl suggests that Reynolds number specific optimisation of the corrugated profile is necessary to achieve improvements in aerodynamic efficiency (Khurana & Chahl, 2013). This was further verified by Khurana and Chahl (Khurana & Chahl, 2014) who showed significant improvement is lift-to-drag ratio of an airfoil with optimised leading and trailing edge angles as opposed to a baseline profile. This suggests that previous attempts at improving aerodynamic efficiency of airfoils have been unsuccessful not because of the validity of the corrugated airfoil concept at higher Reynolds numbers, but rather the lack of an optimisation based design methodology. 145

168 Abbreviations 7.5 On the question of manoeuvrability Parameters that matter Dragonflies demonstrate an aerial agility that allows them to out manoeuvre and prey on other insects. In Chapter 1 and 2, we showed the excellent manoeuvring capabilities of the dragonfly. In section 1.3 we see that this capability of the dragonfly can be attributed to having an extremely controllable wing-actuation system. The dragonfly is able to control its wings in flapping frequency, amplitude, phase, upstroke-to-downstroke ratio and stroke plane. The frequency and amplitude of flapping is important in any system for modulating aerodynamic forces. High speed cinematography by Ruppell (Ruppell, 1989) showed that in dragonflies, variation in flapping frequencies away from the maximum value can be as high as 72% across all modes of flapping, suggesting strong reliance on flapping frequency for modulating aerodynamic forces. The effects of resonant mechanisms on frequency modulation have been discussed by Kok et al. (J. Kok & Chahl, 2014b), and shown to be detrimental to manoeuvring performance. Alexander showed that left-right asymmetries were employed in the wing stroke amplitude to produce rolling maneouvres (D. E. Alexander, 1986). This was further verified in chapter 6. Several studies (D. E. Alexander, 1984; Ruppell, 1989; Wakeling & Ellington, 1997b) have also discussed the effects of modulating the phase between the wings, particularly between the fore and hind wings. These studies have shown that in periods of high aerodynamic loading, such as in take-off or rapid manoeuvres, the fore and hindwings stroke in tandem, whereas in a normal energy efficient hover mode, the wings are stroked out of phase. This lends to the argument that a manoeuvrable system should be able to control its flapping frequency, amplitude and phase. Other parameters that could affect the manoeuvrability of a flapping system includes the upstroke-to-downstroke ratio, η, and the stroke plane angle. Ruppell (Ruppell, 1989) showed that η has an influence on the forward flight capabilities of the dragonfly. As the flight speed increases, η decreases. A similar result was presented by Doman et al. (Doman et al., 2010b) 146

169 7.5 On the question of manoeuvrability who used a split cycle parameter to introduce asymmetry into the flapping profile, giving it control over the forward thrust. Work performed by Yu and Tong (Yu & Tong, 2005) demonstrate thrust generation by modulating the upstroke-to-downstroke ratio. High speed cinematography (Ruppell, 1989; D. E. Alexander, 1986) has demonstrated changes in the stroke plane angle with a forward-down tilt of the stroke plane resulting in greater forward velocity. However, the actual effects of the stroke plane on the thrust bucket of the system has not been investigated. The next section utilises the concept of optimisation to determine how incorporating stroke plane control affects the available thrust, and hence manoeuvrability of the system The stroke plane The effects of flapping frequency and amplitude on aerodynamic force generation are quite well known. In general, an increase in flapping frequency and flapping amplitude produces greater aerodynamic forces which in turn increase the manoeuvrability of the system. The effects of wing phase variation have also been observed through high speed cinematography (Ruppell, 1989) and demonstrated computationally through the work performed by Wang (Z. J. Wang & Russell, 2007; D. E. Alexander, 1984). Wang showed that phase variations between the fore and hind wings allows the dragonfly to switch from an energy efficient flapping mode to a highly manoeuvrable mode of flight characterised by large aerodynamic forces. In this section, we investigate the effects of the stroke plane angle on the aerodynamic forces and hence manoeuvrability of the system. We use the same quasi-steady model described in section We compare the maximum forces generated between two systems - with and without the use of stroke plane modulation. This is performed for a range of directions from forward of the insect to upwards of the insect. In addition to the stroke plane angle, the effects of AOA modulation must also be taken into consideration as it is a significant factor in dragonfly flight (Sviderskiĭ et al., 2008; Ruppell, 1989; D. E. Alexander, 1986). Without a tuned AOA profile, it is impossible to achieve optimal flight conditions. The AOA flapping 147

170 Abbreviations profile can be represented as α = α m sin(ωt + Φ α ) + α 0 (7.10) The stroke plane combined with the range of AOA parameters forms an optimisation problem where the objective function is the maximum force generated. We also constrain the range of AOA movements to ± 50 degrees. The optimisation problem can thus be defined as: min X = [β, Φ α, α 0, α m ] F orce Manoeuvre (7.11) subject to the following optimisation restrictions X i,min X i X i,max i {1, 2, 3, 4} (7.12) and constraints α m α 0 40 o (7.13) α m + α o (7.14) These restrictions are selected to constrain the solution space within the limits of a realistic MAV system (J. M. Kok & Chahl, 2016). Other constraints are given in Table 7.3 Table 7.3: Optimisation constraints Property Lower Limit Upper Limit β (deg) 0 70 Φ α (deg) α η (deg) α 0 (deg) The results for simulations with and without the stroke plane are shown in Fig They show that in all directions from forwards to upwards, the inclusion of a stroke plane variable is able to generate greater manoeuvring force than a wing limited to flapping in the horizontal stroke plane. This is particularly apparent when forward thrust is required. We see that the inclusion of the stroke plane angle as a parameter increases the maximum thrust by 100%. 148

171 7.6 Design guidelines Figure 7.6: Maximum directional thrust generated for a wing with and without stroke plane augmentation. The radial axes represents maximum achievable thrust in that direction 7.6 Design guidelines In the previous sections, we discussed the benefits of a flapping wing system as well as some of the issues surrounding current flapping wing MAV designs. The design of a flapping wing MAV system is a challenging problem. However prior to designing the system, designers should realise the position that nature-inspired systems play in the MAV design space. Hovering and gliding/forward modes of flight are currently dominated by rotorcraft and fixed wing aircraft. The advantage of a flapping wing aircraft is its ability to perform both modes of flight while being extremely manoeuvrable. Any flapping wing design choices should take into consideration effects on all 3 modes of flight, and not just focus on hover, which is the case with many current research systems. Whilst aerodynamic efficiency in hover is important, it should not come at the expense of 149

172 Abbreviations compromising the performance of the other modes of flight. This is the case for many MAV systems that rely on passive wing pitching with a resonant mode for recovering inertial losses. This is the case with the use of elastic mechanisms for recovering energy lost to inertia. In section we showed that this energy saving mode was not the optimal means for reducing the inertial costs associated with a flapping wing, as its effects on the aerodynamic performance is unclear. Previous work done by Kok et al (J. Kok & Chahl, 2014b) discusses the effects of elastic members on the manoeuvring and gliding performance of an insect-inspired system. We demonstrated that the use of an elastic mechanism can reduce the inertial cost in hover, at the cost of reduced system rate of response to instantaneous actuator inputs such as those experienced during sharp manoeuvres performed by MAVs. We also showed that under certain conditions, the use of elastic members reduces the maximum gliding velocity. This would suggest that systems that rely on resonant modes with passive wing pitching are in violation of the primary design rule - effective glide, hover and manoeuvring flight. However, active flapping introduces increases the dimensionality of the control space and as such requires optimisation to determine what the wing kinematics are that will produce optimal flight. In section 7.3.2, we demonstrated improvements in aerodynamic performance through optimisation of the wing kinematics. We showed that the effects of optimisation were most apparent in the wing pitch profile at high stroke plane angles, which is the case with dragonfly-inspired systems. Another potential method for improving the aerodynamic efficiency of the wing-actuator system is through reducing the inertia. Two main sources of inertia would be the mass of the wing as well as the inertia of the actuators itself. To reduce the inertial costs of the flapping system requires that the inertias of both the wing and the actuators be reduced. There are several ways to do this. The first would be to reduce the inertia of the wing. Studies show that the dragonfly wing is extremely stiff in both the spanwise and chordwise direction (Jongerius & Lentink, 2010). However, despite its stiffness, the dragonfly wing also has quite low inertial contribution of 25% (Azuma & Watanabe, 1988; May, 1991). This would suggest that the dragonfly wing is extremely optimised. This is due in part to the fact that dragonflies have optimal wing corrugations which gives it additional stiffness, with minimal increases in weight. Existing technological wing designs use Mylar films with carbon rein- 150

173 7.6 Design guidelines forcement either as rods or cut carbon sheets (Lentink et al., 2009; Doman, Tang, & Regisford, 2011; J. M. Kok & Chahl, 2016). Lentink et. al (Lentink et al., 2009) also presents a design of a 3 dimensional corrugated carbon wing structure that replicates the dragonfly wing profile. Another way to minimise inertial loads is to reduce the movement of the actuator. In SHM, the inertial load is given by Iω 2 x stroke. Reducing x stroke reduces the inertial cost. By keeping the actuator stroke small, the inertial load is reduced, whilst allowing the actuator to perform at its optimal point with minimal deviations. For example, in a solenoid, this allows operation in a particular stroke length which will provide the greatest forces for the same current draw. In motors, this could be a particular velocity. Proper optimisation of the angle of attack profile is also important in improving aerodynamic efficiency as shown in section These stratagem allows improvements to the aerodynamic efficiency in hover without compromising the other modes of flight. In order for this to be achieved, the wing-actuator needs to be designed in such a way as to provide active control over the flapping parameters in 3DOF (i.e. flap, pitch, stroke plane), which must be controlled in software. Additionally, the actuators should be designed in such a way as to prevent actuator stacking. Actuator stacking is a design configuration whereby actuators are stacked orthogonally on each other to provide 3DOF operation (S. L. Thomson et al., 2009). Whilst this is a simplistic solution, it means that each actuator is supporting the weight of another actuator which is an inefficient configuration, particularly at high flapping frequencies, whereby the inertia of the actuators becomes significant. A better configuration would be a differential mode whereby two actuators contribute to the flapping mode of the wing where wing pitch is achieved via alternating the phase between the actuators (J. M. Kok & Chahl, 2016). A third actuator is required to manage stroke plane or out-of-plane motion. The use of such a wing-actuator configuration also presents advantages in the manoeuvring mode of flight. The previous sections showed that the versatility of the dragonfly was due to its ability to control the flapping amplitude, frequency, phase and upstroke-to-downstroke ratio. Such a system is not mechanically limited to having particular kinematic patterns, these variables can be varied in real time to produce versatile flight manoeuvres. An effective method of controlling such a system would be through the use of central pat- 151

174 Abbreviations tern generators (Ijspeert, 2001; Ijspeert & Kodjabachian, 1999; Seo, Chung, & Slotine, 2010; Chung & Dorothy, 2010; Kuang, Dorothy, & Chung, 2011; Dorothy & Chung, 2010). The use of central pattern generators reduces the dimensionality of the control signal and also gets rid of the high gains and large initial errors common in high gain, linear control mechanisms. It also removes the need for individual wing-beat control whereby information about the next wing-beat is passed to the control system prior to each wing-beat. In a real world configuration, this presents many timing issues, particularly if frequency modulation is employed. One final point to note, in the design of flapping wing MAV systems, is the design of the thorax. The thorax serves to transmit force from the actuator to the wing. The previous sections have shown that it is important that the wing be able to move in 3DOF. The thorax should be designed in such a way as to support such movements. This leads to the question of compliant versus non-compliant thorax structures (Bejgerowski, Gerdes, Gupta, Bruck, & Wilkerson, 2010; Bejgerowski, Gerdes, Gupta, & Bruck, 2011; Kota, Hetrick, Li, & Saggere, 1999). The use of non-compliant mechanisms is difficult as most mechanical linkages are designed to work in one direction. Such mechanisms cannot withstand out-of-plane movements and in poorly designed systems, this could lead to prismatic lock of the actuator or thorax. However despite this non-compliant mechanisms have advantages. Compared to compliant mechanisms, revolute joints do not have to overcome elastic forces inherent in flexure joints which could otherwise affect the dynamics of the system. Additionally, traditional mechanical systems have a linear response and have a simpler control system solutions. Kok et al. presented a system that uses aspects of both compliant and non-compliant mechanisms (J. M. Kok & Chahl, 2016). The wing axis was suspended in a system of bearings that allows actuation in 3DOF. Elastic members were used to attach actuators to the root of the wing, giving it properties of a compliant mechanism. 7.7 Conclusion In this chapter, we discussed some of the issues that surround conventional flapping wing MAV designs and proposed a set of design criteria for a dragonfly-inspired MAV. One of the design criteria often neglected by many MAV designers is the need for the flapping wing system to be 152

175 7.7 Conclusion able to achieve efficient hover, glide and manoeuvrable flight. We show that systems which use use resonance and passive flapping may be inefficient in improving aerodynamic efficiency in hover, and can also impact on the systems level performance of the MAV. We propose a multi DOF, actively controlled wing-actuator, using optimisation techniques to achieve hover, glide and manoeuvring flight. Energy savings should not be achieved by resonant mechanisms or passive flapping modes, but rather by optimal design of the wing-actuator-thorax systems and efficient control and optimisation of wing kinematics. 153

176

177 CHAPTER 8 DESIGN AND MANUFACTURE OF A SELF-LEARNING FLAPPING WING-ACTUATION SYSTEM FOR A DRAGONFLY-INSPIRED MAV Synopsis This chapter discusses the design and manufacturing process for replicating the dragonfly wing-actuation system for use in MAVs. The design methodology begins initially with understanding the characteristics of the dragonfly which makes it such an excellent flyer, that include independant and controllable actuation in 3DOF, direct drive of the wing, low inertia wings, and a compliant thoracic structure. It is based on the design philosophy developed in Chapter 7. The design features three solenoid actuators that replicate the linear muscles present in dragonfly wings. Two solenoids drive the flapping motion, and the wing pitch motion is modulated by asymmetrically varying the current in the solenoids. The third solenoid actuator generates out-of-plane wing motion. The wings were manufactured from a mylar and carbon composite construct. A semi-compliant thoracic structure was also developed that allows efficient transmission of forces from the solenoid to the wing, whilst preventing actuator lock-up. A method is also presented for estimating wing kinematics based on high speed cinematography of the wing root. This method is used to investigate the effects of different solenoid parameters on the wing kinematics and hence demonstrates the controllability of the system. The optimisation of the wing kinematics is performed in the next chapter. 155

178 CHAPTER 8. DESIGN AND MANUFACTURE OF A SELF-LEARNING FLAPPING WING-ACTUATION SYSTEM FOR A DRAGONFLY-INSPIRED MAV This conference publication has been published in: Kok, Jia Ming, and Javaan Chahl. Design and manufacture of a self-learning flapping wing-actuation system for a Dragonfly-inspired MAV. 54th AIAA Aerospace Sciences Meeting

179 Abbreviations Nomenclature MAV DIMAV SMA MF C DEAP IP MC DOF φ ψ θ A 1, A 2, A B 1, B 2, B Micro Air Vehicle Dragonfly-Inspired MAV Shape Memory Alloy Macro Fibre Composite Dielectric Electro Active Polymer Ionic Polymeric Metal Composite Degrees of Freedom Flapping angle Out-of-plane flapping angle Pitch angle Amplitude of input signal Offset of input signal Θ 2, Θ Phase offset of input signal X Location of marker in image plane 157

180 Abbreviations 8.1 Introduction DRAGONFLIES have the potential to perform the mission profiles of both fixed and rotary wing MAVs. They are able to perform manoeuvres not singularly achievable by existing MAV configurations. This chapter will present a brief review of the characteristics of the dragonfly wing-actuation system that allows such versatile flight, and discusses the design and manufacturing process for replicating the dragonfly s wing-actuation system for use in MAVs. 8.2 Dragonfly Characterisation The dragonfly planform was amongst the first to evolve and is amongst the longest surviving flying organisms. Observations of the dragonfly genealogy show that its ancestry can be traced back to the Protodonata, which are amongst the earliest winged insect fossils discovered (Wootton, 1976; May, 1982). This suggests that the evolution and optimization of dragonflies dates back 300 million years. Certainly, dragonflies had ruled the skies as the supreme aerial predator for over 100 million years prior to the evolution of flying dinosaurs. In this section, we isolate and discuss the characteristics that make the dragonfly such a versatile flyer Wing-actuation system The extensive capabilities of the dragonfly can be attributed to the degree of control the dragonfly has over its flapping actuators and hence the flapping profile. Wang (Z. J. Wang, 2005) proposed that during hovering flight, dragonflies rely on adjusting the angle of attack of the wing to reduce the energy costs required for hover. Wang (Z. J. Wang & Russell, 2007) further showed using Computational Fluid Dynamics (CFD) simulations that a Dragonfly was able to alternate between an energy efficient hover mode and a highly manoeuvrable state. This theory was reinforced by Alexander (D. E. Alexander, 1984) who showed that dragonflies were able to adjust the phase lag between the fore and hind wings to switch between normal flight and flight manoeuvres requiring high forces. Alexander further showed through high speed cinematography in a wind tunnel (D. E. Alexander, 1986) the capability of the dragonfly to adjust 158

181 8.2 Dragonfly Characterisation both its stroke plane angle and angle of attack of the individual wings to perform complex yawing or banking turns. Certainly observations of the wing actuation of dragonflies support these theories. An investigation of the actuation system in dragonflies shows their capability to actively control and effect wing rotation (Sviderskiĭ et al., 2008; Simmons, 1977). Anatomical studies (Dudley, 2002) have shown that the dragonfly employs a direct drive mechanism whereby the muscles of the dragonfly are attached to the wing root and actuate the wing directly. This is in contrast to the indirect mechanism commonly found in insects that dragonflies prey on (i.e. diptera). In an indirect mechanism, the muscles are attached to the wings via the thorax. Svidersky et al. (Sviderskiĭ et al., 2008) expand on this investigation by comparing the actuation system of the dragonfly to a less manoeuvrable four winged insect, the locust. Their findings showed that the following factors give dragonflies its increased manoeuvrability over locusts: The structure of the wing base and characteristics of the muscles gave the dragonfly the ability to actuate all four wings independently by the phase, frequency and amplitude. Dragonflies have active supination and pronation while locusts have passive supination Dragonflies have a large number of motor units in their muscles used for supination and pronation. This gives it the ability to more finely regulate the strength of their strokes Dragonflies are able to shift their wings along the horizontal plane as well Another characteristic of flapping-wing systems in nature, is the use of compliant mechanisms. Unlike traditional mechanical systems that are formed from rigid, discrete components, compliant mechanisms utilise the inherent flexibility of the structure to generate force or transmit motion (Bejgerowski et al., 2011; Kota et al., 1999). As such compliant mechanisms present benefits over non-compliant mechanisms. These include reduction of wear between joint members and reduction in backlash (Bejgerowski et al., 2011). However, more notably, the nature of compliant mechanisms lends it to out-of-plane flexibility which makes the system suitable for 3-dimensional motion (Kota et al., 1999). This is in contrast to mechanical systems whereby the linkages are often designed to bear load or transmit movement in one 159

182 Abbreviations direction. Non-compliant mechanisms do however have advantages as well. This includes a linear response, making control of the system easier. Additionally, compliant mechanisms also have elastic loads which could potentially affect the dynamics of the system (Bejgerowski et al., 2010). These loads are not present in traditional mechanical systems Flapping profile In addition to their wing-actuation system, Dragonflies also have a unique flapping profile. Wang (Z. J. Wang, 2004, 2005; Z. J. Wang & Russell, 2007) proposed Dragonflies employ an asymmetric flapping profile in an inclined stroke plane whereby both lift and drag forces are used to support the weight of the dragonfly on the downstroke. On the upstroke, the wing is rotated in such a way as to generate negligible forces. Wang further proposed that such a means of flapping could reduce the power consumption required by a factor of 2 2 compared to a conventional hovering profile (Z. J. Wang, 2005). This is in contrast to Dipteran insects that flap their wings in a near-horizontal stroke plane (Z. J. Wang, 2005). Another point to note is that whilst the odonata flapping profile is unique, the optimal flapping profile also differs between species, and even between individuals in the same species (Azuma et al., 1985; Wakeling & Ellington, 1997a). This would suggest that the optimal flapping profile is system specific Integrated design In sections and 8.2.2, we argued that both wing-actuator design as well as the wing flapping profile are important. However, it should be noted that these two systems cannot be designed independently of each other which is often the case in existing technical systems. This phenomenon is observed in dragonflies in nature. Whilst dragonflies have a flapping profile that is unique, even between different species of dragonflies, or even different dragonflies of the same species, their flapping profiles are distinct (Azuma et al., 1985; Wakeling & Ellington, 1997a). This would suggest that the flapping profile of each dragonfly is tuned to the wingactuation system of that particular dragonfly. Analogous to this would be humans learning to swim. Whilst the strokes between swimmers may appear similar in general, however each 160

183 8.3 Wing-Actuator Design swimmer has differences in his stroke profile which has been optimised through countless repetition. Therefore, it is fair to say that there is not one specific flapping profile that is the most efficient. Certainly proper design of a wing-actuator gives the system the best chance of achieving robust and efficient flight across all three flight modes, however more important is the wing-actuator and wing profile combination. Therefore each actuator should be designed with the capability to optimise its profile for a user selected performance criteria. This is the justification for a self-learning DI-MAV flapping-wing actuator. Computational quasisteady aerodynamic analyses performed by Kok et al (J. Kok & Chahl, 2014a) using maximum lift as the optimisation criteria has demonstrated almost 22% improvement in performance using a hybrid local-global optimisation scheme. This will allow the DI-MAV to acquire the ideal flapping profile for its wing-actuation system which will allow it to perform efficiently in all modes of flight. However, in order for this to occur, the wing-actuator system must be controllable. This chapter will focus mainly on the actuator design and manufacture. The actuator was cycled through a range of inputs to determine their effect on the flapping profile. Its controllability was demonstrated in 2 and 3DOF. 8.3 Wing-Actuator Design In section 8.2 we presented the main characteristics of the dragonfly that make it an excellent flyer. In this section we discuss the design of a flapping wing-actuation system inspired by the dragonfly planform. We developed a wing-actuation system capable of mimicking dragonfly wing kinematics. Constraints were imposed on the design of the actuator and listed in table 8.1. Table 8.1: Design constraints Design constraints Ability to alter the phase, frequency and amplitude of the flapping motion Ability to actuate wing in 3DOF (Flapping, pitching and perpendicular to wing stroke plane) Direct drive wing mechanism Active wing rotation The wing-actuator design comprised the wing, thoracic structure and the actuation mech- 161

184 Abbreviations anism. A sense-and-control system was also required to determine the forces acting on the wing as well as to control the articulation of the wing. The following sections will describe the design process involved in each of these components Wing Design The wing is responsible for generating the aerodynamic forces required to propel the DI-MAV. Wing sizing was targeted at producing a wing capable of lifting a MAV system which had a weight of approximately 100g. Aerodynamic quasi-steady analysis (J. Kok & Chahl, 2014a, 2015) was performed to determine if the initial wing sizing was appropriate. At a wing length of 30cm, operating at 10Hz, it was found that a lift of 55g was generated. Certainly, the wing size could be reduced further to achieve this objective, however larger aerodynamic forces were desirable as it becomes easier to obtain high precision, low noise results. Design and material selection of the wing was critical in minimising the overall inertia and energy requirements of the system. This has a significant effect on its aerodynamic efficiency (Weis-Fogh, 1973). A wing with high mass or inertia requires higher actuation forces to generate similar aerodynamic effects, and hence is energetically less efficient. To generate a low-inertia wing with significant wing area for aerodynamic force generation, we employed a modified wing construction method described by Lentink et al. (Lentink et al., 2010). Carbon rod was used to form the spar and rib structure which were bonded together using cyanoacrylate glue. The placement of the carbon rod was selected to provide stiffness to the leading edge and root of the wing. Such a structure is representative of a dragonfly wing structure (Jongerius & Lentink, 2010; Lentink et al., 2010). 2.2g/m 2 Mylar was used to cover the spar and rib structure due to its low weight and strength. Figure 8.1 shows the schematic of the wing. The original design utilised a wing with only 2 spars. It was observed that the wing would buckle under aerodynamic load hence not generating any lift. The wing design was then modified to use 3 spars to increase the spanwise stiffness of the wing. This is congruent with the dragonfly wing that also exhibits wings that are significantly stiffer than other insects (Combes & Daniel, 2003). The overall weight of the wing was 2.2g. 162

185 8.3 Wing-Actuator Design Figure 8.1: Wing design consisting of carbon fibre spars and ribs with a Mylar skin Thorax Design The thorax serves to transmit forces from the actuator to the wing, and it needs to be able to do so in 3DOF. This makes the use of non-compliant mechanisms difficult as most mechanical linkages are designed to work in one plane. Such mechanisms cannot withstand out-of-plane movements, and in poorly designed systems, this could lead to the lock-up of the actuator. Non-compliant mechanisms have advantages. Compared to compliant mechanisms, revolute joints do not have to overcome elastic forces inherent in flexure joints which could otherwise affect the dynamics of the system. Additionally, traditional mechanical systems have a linear response and have a simpler control system. It was decided that a semi-compliant system would be employed. A system of bearings was employed that allowed movement in 3DOF (see Fig. 8.2). To prevent actuator lock-up, compliant joints were used to attach the actuator to the root of the wing. This ensured that the actuator was able to transmit force to the wingbase without the need to utilise complicated revolute joints for preventing actuator or joint lock-up. The flexure mechanism was generated by bonding 0.5mm flexible carbon rod to the wing root using a rubber member (see Fig. 8.3). Additionally, a torsional return spring was applied which returned the wing to its original position when at rest, as well as prevents the wing from exceeding its range of motion. 163

186 Abbreviations Figure 8.2: Bearings were used in the thoracic structure to allow smooth articulation of the wing. This allows 3DOF movement of the wing Figure 8.3: Example of a compliant joint. Compliant joints are used to link the actuator to the thorax at both ends. 164

187 8.3 Wing-Actuator Design Actuator design Flapping wing actuation creates large cyclic inertial, aerodynamic and elastic forces. The choice of actuation system has an impact not only on the design of the experimental setup, but also the optimal flapping profile. In addition, the choice of actuation system should be scalable to sizes that need to be implemented in MAV applications. Therefore, design of the actuation system presented additional challenges, that had to be overcome prior to optimizing the flapping profile. Existing actuator options for MAVs include electromechanical, as well as solid state options - shape memory alloys, piezoelectric and electro-active polymers. Electromechanical actuators can be divided into linear and rotary actuators. Rotary actuators have been commercially available for a long time, and have been miniaturized over the years in particular for fixed wing MAVs. They are certainly a well understood and utilized form of actuation (Karpelson et al., 2010; Ratti & Vachtsevanos, 2010; Ratti et al., 2011; Ratti & Vachtsevanos, 2012). Whilst different actuators are operated slightly differently, they all obey the same basic principles of operation. Coils or solenoids are used to generate a magnetic field that interact with a rotor or stator to generate movement. Rotary actuators require transmission mechanisms for converting the rotary motion to a linear motion such as in a parallel crank rocker system (Conn, Burgess, & Ling, 2007). Linear actuators, such as a solenoid actuator (Kato & Ohnishi, 2004; Roll, 2012), are a reduced form of the rotary motors. Similar to the rotary motors, solenoid cores are used to generate a magnetic field that interacts with permanent magnet cores to generate bidirectional actuation. Shape memory alloys (SMAs) are a material used in solid state, linear actuators for microrobotic applications (Hunter, Lafontaine, Hollerbach, & Hunter, 1991; Tobushi, Hayashi, & Kojima, 1992). As an actuator, SMAs generate relatively large forces and have substantial strain of approximately 10%. SMAs operate by pulsing current through them and rely on expansion of the SMA to generate the forces required for actuation. The bandwidth of SMA actuators are between 1-5 Hz, which is less than the required wing beat frequency range and hence unsuitable. Piezoelectric actuators are solid state actuators used in microrobotics. Piezoelectric actua- 165

188 Abbreviations tors have been used in many flapping wing actuator systems, the most notable of which is the Harvard Robobee. Sitti et al. fabricated and characterized the performance characteristics of a unimorph piezoelectric actuator (Sitti, Campolo, Yan, & Fearing, 2001). Their design relied on the use of differential expansion and contraction between the piezoelectric and elastic layers to generate a bending moment. A similar design was presented by Ming et al. (Ming, Huang, Fukushima, & Shimojo, 2009) who used a material called Macro Fiber Composites (MFC). MFC comprises of piezoelectric fibres embedded in polymeric materials. Ming et al. attached these materials directly to the spars of the wings to generate wing flexure directly. While designs may vary between different actuation systems, the use of piezoelectric material as an actuator presents disadvantages. In (Sitti et al., 2001) and (Ming et al., 2009), both actuation systems had low strains. Sitti et al. reported strain values of 1.7%. In addition both systems relied on the use of resonance for amplifying their displacement output. This limits the operational wing beat frequency to a very narrow band centered on the resonant frequency of the system. Any deviation from the resonant frequency would incur penalties on performance. The disadvantages of such an arrangement are discussed by Kok et al. (J. Kok & Chahl, 2014b). Finally both systems require voltages of the order of 1kV to operate, which is above the breakdown voltage of most electronics (Leistiko & Grove, 1966; Rusu, Pietrareanu, & Bulucea, 1980) requires complex circuitry and elaborate safety procedures. In recent years, a new branch of materials have also been investigated, Electro-active polymers (EAPs), as a means to mimic the performance capabilities of muscles in nature (Tondu, 2007). EAPs show promise due to their large strain and low weights. There are two main classes of EAPs, ionic polymeric metal composites (IPMCs) or dielectric electro-active polymers (DEAPs). A significant advantage of using IPMCs is the low voltages required for actuation, in the order of 3V. However, their results also showed that, like the aforementioned piezoelectric unimorph actuator, the maximum displacement of the actuator was highly sensitive to changes in frequency. In addition, IPMCs are constrained by their need for a humid environment (Segalman, Witkowski, Adolf, & Shahinpoor, 1992). DEAPs, like IPMCs, rely on generating an electric field to provide actuation, however unlike IPMCs, they can be operated in dry environments (Segalman et al., 1992). DEAPs behave as a compliant capacitor. When voltage is applied between two parallel plates, a force of attraction between the two 166

189 8.3 Wing-Actuator Design plates compresses an elastomer. The high maximum stress (1.36MPa) and strain (41%) coupled with the low response time ( 2ms) makes DEAPs a promising technology (Pelrine et al., 2000) for flapping wing actuation. They do however have one disadvantage in that these actuators tend to operate at voltages of up to 4kV (Pelrine et al., 2000; Kovacs, Düring, Michel, & Terrasi, 2009). The high voltages associated with DEAPs, renders them undesirable for use as a flapping actuator at this time. An electromechanical solution to the problem of flapping wing actuation was chosen. Linear actuators was selected, as it was more representative of the geometry of dragonfly flight muscles and also it had the potential to minimize the weight and complexity of the actuator as it is a reduced form of the rotary actuator. To achieve 3DOF wing articulation, three actuators were required. Two actuators were used to drive the flapping motion of the wing - Solenoids 1 and 2. Wing rotation was achieved by altering the phase of the stroke between the two linear actuators. A third actuator, solenoid 3, was used to produce out-of-plane wing articulation. This is shown in Fig The actuators were manufactured in-house Sensing and control In order for the wing-actuation system to optimise the flapping profile, it needed to be able to sense the aerodynamic forces acting on it, and be able to modify the flapping profile of the wing. Fig. 8.5 illustrates the optimisation process. An optimisation function was defined first. A sample flapping profile was then applied, and the aerodynamic forces generated by the system measured. This was repeated until the flapping profile that generated the best aerodynamic configuration. To measure the aerodynamic loads, a ATI Nano17 Force Torque transducer was attached to the base of the flapping actuator. An Atmega2560 was used to control the motor drivers which in turn drove the solenoid. A work station computer was used to communicate with the Atmega2560 via a USB UART serial interface. 167

190 Abbreviations Figure 8.4: 3DOF Actuator configuration 8.4 Method In section 8.3, we discussed the requirements for a dragonfly-inspired wing-actuation system based on observations of the anatomy of the dragonfly. Amongst those requirements was the need for a system that was at least controllable in 3DOF. However, for it to be optimisable, we also need to be able to measure the parameters that determine the performance of the system. In section , we discussed the use of a force/torque transducer to measure aerodynamic forces. Also important is the ability to track the position of the wing. Whilst the position of the wing is not critical in the optimisation process, being able to measure the wing position provides information about the dynamics of the system as well as the ability to measure the degree of variability in the flapping profile. In this section, we present a method for tracking the position of the wing using high speed video. 168

191 8.4 Method Figure 8.5: Illustration of optimisation process (adapted from Kok et al. (J. Kok & Chahl, 2014a)) A Phantom Miro Ex 2 Vision high speed camera was used to record the position of the wing. This camera was set to record images at 1000 frames-per-second. Due to the short exposure times, additional lighting was provided in the form of an LED head lamp. At a flapping frequency of 5Hz, this gives 200 frames per flapping cycle, which is sufficient to resolve the position of the wing. Figure 8.6: Marking Rod. The white points are markers 1 and 2 respectively. 169

192 Abbreviations A marking rod was attached to the root of the wing, parallel to the chord of the wing, and at a known distance from the wing pivot. The high speed camera was used to track two points on the marking rod. The central point lay directly on the wing axis and was used to measure movement in the flapping axis as well as out-of-plane movements (i.e. φ and ψ). Measuring the position of the other point relative to the central point gives the pitch angle of the wing. This is illustrated in Fig It should be noted that the pitch angle is not the same as the angle-of-attack (AOA). The pitch angle is relative to the body of the DI-MAV, whilst the AOA is the angle made by the wing relative to the airflow. An image recognition software, Tracker, is used to track the points on the high speed video footage. Figure 8.7: Illustration of how the marking rod works. Marker 1 is used to measure wing articulation in the flapping and rolling axis (see A). The relative position of Marker 2 to Marker 1 is used to measure the pitching angle (see B). An Atmega2560 was used to control the motor drivers which in turn drove three solenoids. A computer was used to communicate with the Atmega2560 via UART serial interface. Predefined profiles were input into the PC and uploaded to the motor drivers which then run the solenoids. The waveforms input into the solenoid were sinusoidal profiles represented by equations 8.1, 8.2, 8.3. A set of 8 parameters defined the entire flapping profile - A 1, A 2, A 3, B 1, B 2, B 3, Θ 2, Θ 3. Input 1 = A 1 sin(ωt) + B 1 (8.1) Input 2 = A 2 sin(ωt + Θ 2 ) + B 2 (8.2) Input 3 = A 3 sin(ωt + Θ 3 ) + B 3 (8.3) 170

193 8.5 Results 8.5 Results DOF Initial tests were performed with the third DOF in the roll axis constrained so as to limit the system to variations in 2DOF - the flapping axis and the pitching axis. Section 8.3 discussed the use of solenoids 1 and 2 as the predominant actuators that controlled the flapping and pitching motion of the wing. Both marker points 1 and 2 were measured across the period of the flapping motion. The position of the marker point 1 represents the flapping profile φ, of the wing, whilst the difference in X-position between marker points 1 and 2 gives an indication of the pitching angle of the wing (see Fig 8.7). This was the main variable measured, as it relates directly to the ability of the system to modulate its AOA, which is critical in a DI-MAV (see Section 8.2). The parameters which will be varied are A 1, A 2, B 1, B 2, Θ 2. In the first test case, we input the same waveforms into solenoids 1 and 2 (i.e. A 1 = A 2 = 500; B 1 = B 2 = 0; Θ 2 = 0). We see in Figure 8.8 that there were slight differences between the movements of Marker 1 and Marker 2 even though the inputs into solenoids 1 and 2 were the same, suggesting that there is an inherent passive wing rotation, which was expected to be the case in a compliant system. We also take the difference in X-positions between Marker 2 and Marker 1 (i.e. X = X Marker2 X Marker1 ). To give us an approximation of the pitch angle, we use the formula θ = sin 1 ( X/R), where R is the distance between the two markers. As shown, the pitching angle, θ, initially started as a positive value indicating a negative AOA when the pitch angle was compared against the relative movement of the wind acting on the wing. We then altered the phase between actuators 1 and 2 (i.e. Θ 2 = 0 o, 50 o, 100 o ) and observed the changes in X (see Fig. 8.9). Changes in phase changed the phase of wing rotation whilst also increasing the amplitude of wing rotation at Θ 2 = 100 o. 171

194 Abbreviations Figure 8.8: X position of marker points 1 and 2 for a sine wave input into both actuators 1 and 2 Figure 8.9: Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 with a negative phase change (Θ 2 = 0 o, 50 o, 100 o ) 172

195 8.5 Results We also observed the effects of altering the phase between actuators 1 and 2 in the positive direction (i.e. Θ 2 = 0 o, 50 o, 100 o ). There was an increase in the extent of wing rotation, with increasing Θ 2, however there was insignificant phase change (see Fig. 8.10). Figure 8.10: Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 with a positive phase change (Θ 2 = 0 o, 50 o, 100 o ) We then altered other parameters A 1, A 2, B 1, B 2, to observe the effect on wing kinematics. We altered A 1 and A 2 for 3 different cases (see table 8.2). The results are shown in figure We see that varying the parameters A 1 and A 2 changed the magnitude of rotation depending on whether A 1 or A 2 was higher. When A 1 was higher, the magnitude of rotation was increased as compared to the symmetrical case. When A 2 was higher, the reverse was true. Changing the values of A 1 and A 2 also had a phase shifting effect on the wing rotation. Table 8.2: Test cases for different values of A 1 and A 2 Case A 1 A 2 B 1 B

196 Abbreviations Figure 8.11: Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 for different values of A 1 and A 2 We altered B 1 and B 2 for 3 different cases (see table 8.3). The results are shown in figure Changing B 1 and B 2 had the effect of changing the magnitude of the angle of rotation. Increasing B 1 and decreasing B 2 caused the magnitude of rotation to increase. It also caused a decrease in the mean AOA. The reverse was true when B 1 was reduced and B 2 was increased. The magnitude of rotation decreased, but the mean AOA was higher. Table 8.3: Test cases for different values of B 1 and B 2 Case A 1 A 2 B 1 B

197 8.5 Results Figure 8.12: Difference in X position, X, between marker points 1 and 2 for a sine wave input into both actuators 1 and 2 for different values of B 1 and B DOF We then varied the profile in the third degree of freedom to observe the changes in the flapping profile. The input into the third solenoid was represented by Equation 8.3. Due to the wing generating lift forces, a positive offset, B 3, was required to prevent the wing from moving too far out of plane. The magnitude, A 3, and phase, Θ 3, were varied to determine its effect on the flapping profile. The third DOF was critical because it determined the stroke plane of the wing, as well as the out-of-plane wing motion. To track the motion of the wing, the method described in section 8.4 was used. Only the centre point was tracked (see Fig. 8.13). 175

198 Abbreviations Figure 8.13: Tracking the centre point. A 3 = 0; Θ 3 = 0; B 3 = 400; First of all, the magnitude of oscillation, A 3, was varied. The phase of solenoid 3, Θ 3, was kept at zero. A Figure-of-eight pattern was generated (see Fig. 8.14). The phase of oscillation, Θ 3, was then varied to see its effect on the flapping profile. In both cases, changing the phase, changed the profile significantly. An O-shaped pattern was formed as opposed to a Figure-of-eight pattern (see Fig. 8.15). Changing the sign of the phase also caused the wing to rotate in a different direction. 176

199 8.5 Results Figure 8.14: Tracking of the movement of the centre point. Changing A 3. A 3 = 0, 200, 400. Figure 8.15: Tracking of the movement of the centre point. Changing Θ 3. Θ 3 = 50, 0,

200 Abbreviations 8.6 Discussion This chapter discusses the design and manufacture of a Dragonfly-inspired wing-actuation system. In section 8.2, we isolate the biological parameters that make the dragonfly such a versatile flyer. We argue that all of the characteristics can be achieved with its highly controllable wing-actuation system and variable flapping profile. We replicated the characteristics of the wing actuator system by designing and manufacturing a 3DOF, direct drive wing-actuation system with a mylar/carbon wing. Compliant joints were used where the actuator connects to the wing root to prevent actuator lock-up. Additionally, a return spring was used to ensure that the system would not overshoot its limits as well as make sure it always returned to home. Whilst the system was a test-bench configuration, the wing-actuation system was designed with scalability in mind. The configuration can be further miniaturised using commercial-offthe-shelf solenoids, and with the assistance of high resolution 3D printing technologies such as Stereolithography. Whilst the design and manufacture of the wing-actuator is important, it needs to be coupled with a highly tuned flapping profile before efficient lift generation can occur. Many technical designs have separate treatments for the wing-actuation system and flapping profile, however, the biology suggests that investigating one aspect separate of the other is unlikely to be successful. Systems in nature have flapping profiles which are tuned to the mechanical system, and are unique to that system. It should be the pre-requisite of any dragonfly-like flapping wing system that it can be optimised to determine its ideal flapping profile. In order for this to be achieved, we need to be able to measure the forces generated by the system, but more importantly, the system needs to be controllable. In section 8.3.4, we discussed the use of motor drivers that control solenoid actuators. Sinusoidal profiles were input into each of the solenoids which gave a total of 8 parameters that could be controlled to give wing-actuation in 3DOF. These 8 parameters include the magnitude and offsets of the three sine waves, and the phase shift of two of the sine waves. It should be noted that we did not attempt to produce a predetermined output based on the input parameters. The complex underlying physics makes predicting the output based on the input parameters 178

201 8.6 Discussion difficult. This output will change when environmental or hardware conditions change. We aimed to optimize input parameters using black box approaches that do not depend on us being able to predict wing kinematics. This is demonstrated in Chapter 9. Initial experiments were limited to movement in 2DOF, namely the flapping axis and the pitching axis. A high speed camera was used to track a marking rod located at the root of the wing. Two points were located on the marking rod. One point, Marker 1, was on the axis of the wing and gave information on the φ and ψ angles respectively. The difference in X-positions of the other point, Marker 2, relative to Marker 1 gives AOA information. Tracking of the X and Y positions of both points are shown in Figures 8.14 and It should however be noted that the equation used to convert X to AOA information is an approximation which is more valid at smaller flapping angles. Whilst, larger flapping angles might produce a more inaccurate result, being able to accurately measure position is not relevant to optimising the flapping profile. After all, it is highly unlikely that the dragonfly itself would know accurately what the position of its wing is at high rate. Obtaining position information in this experiment is to demonstrate that there is controllability in the system, and that we are able to cycle the wing-actuation system through a range of flapping profiles. Therefore, highly accurate measurements of the flapping angles was not essential. Initially, the phase was altered in solenoid 2 in the negative direction. Changing the phase increased the range over which the pitch angle of the wing varied. More importantly, it altered the phase of the wing rotation, such that there was a predominantly positive AOA relative to the wind direction. This is apparent in Θ 2 = 100 o whereby the pitching angle, θ, started negative, indicating a positive angle of attack relative to the wind. This was a mode which is suitable for lift generation. When the phase of the actuators were varied in the positive direction, it was observed that whilst the amplitude of wing rotation increased, the phase did not change. This could be due to the inherent elasticity in the joints or return spring that was asymmetrical in nature. Additionally, the wing rotation was such that the wing produced a negative AOA to the direction of the wind, and as such was not conducive for lift generation. Therefore, Θ 2 should be limited to negative values only. Following that, we alter the amplitude of the sine waves. It was observed that by increasing the amplitude in solenoid 1 and reducing it in solenoid 2, the amplitude of rotation increased. The reverse was true by decreasing the amplitude in solenoid 1 and increasing it in solenoid 2. We 179

202 Abbreviations then changed the offset of the sine waves. This had an effect on both the amplitude of rotation as well as the mean pitch angle. By changing the phase, amplitude and offset of solenoids 1 and 2, we demonstrated controllability over the pitch angle of the wing which is critical in achieving efficient dragonfly flight. This is similar to how a dragonfly actively modulates the AOA of the wing to generate efficient flight. In addition to 2DOF, the dragonfly is able to actuate its wing in 3DOF. In section 8.5.2, we altered parameters associated with solenoid 3, including its phase, and magnitude. We demonstrated complex patterns such as Figure-of-eights as well as O-shaped patterns. We also observed changes in the stroke plane angle, and direction of rotation. This demonstrated that the system was controllable in 3DOF, which is critical for a dragonfly-inspired system, particularly when optimising for manoeuvring and forward flight. In the next chapter, we will combine these findings with the methods discussed in Chapter 5 to optimise the wing kinematics for maximum lift. The wing kinematics will be displayed in that chapter. 8.7 Conclusion In this chapter we discussed the design and manufacture of a wing-actuation system for a Dragonfly-inspired micro air vehicle. We isolated the characteristics of dragonfly anatomy that makes it such a versatile flyer, which is its wing-actuation system and flapping profile. Solenoids were selected as the actuator as they resembled the linear muscles found in dragonflies. A semi-compliant system was designed, with bearings to support wing articulation, and elastic members to prevent actuator lock-up. The wing was constructed out of a carbon/mylar construct to optimise stiffness-to-weight. Additional to the design and manufacture of the wing-actuation system, was the ability to control it. By controlling 8 parameters, we have demonstrated the ability to actively control the wing rotation as well as movement in 3DOF. Future work will be targeted at optimising the flapping profile using the 8 parameters isolated in this study. The algorithm used will be that detailed in Kok et al. (J. Kok & Chahl, 2014a). This will bring us a step closer to producing a truly dragonfly-inspired Micro Air 180

203 8.7 Conclusion Vehicle. 181

204

205 CHAPTER 9 EXPERIMENTAL OPTIMISATION OF A FLAPPING WING SYSTEM IN HOVER Synopsis This chapter incorporates optimisation techniques reported in Chapter 5 with the design suggested in Chapter 8. It begins to explore the development of a functional dragonfly-inspired system that is able to tune its wing kinematics to achieve optimal flight. In this example, we optimise a one wing system for maximum lift. The wing was driven by three solenoids. Initial optimisation was done in 2DOF - pitch and flap. Symmetrical solenoid inputs were used as a starting solution, and asymmetries between solenoid inputs were optimised with the objective of maximising lift generation. This was then repeated in 3DOF, using a solenoid to actuate outof-plane movement. We demonstrated the ability to optimise the system in 2DOF and 3DOF, with a 71% and 47% increase in lift respectively from a equivalent-to-passive flapping profile. 183

206 Abbreviations Nomenclature A B Θ ω Amplitude of input signal Offset of input signal Phase offset of input signal Flapping frequency X, Z Location of marker in image plane 184

207 9.1 Introduction 9.1 Introduction DRAGONFLIES have an exceptional amount of control over their wing kinematics. This gives them the ability to hover, glide and perform manoeuvres. Existing technological systems fail to fully replicate this capability (see Chapter 1), and are often mechanically constrained to operate in a limited range of flapping profiles often at a fixed frequency or fixed amplitude. Our studies have justified the use of a fully software controllable system. Unlike existing systems, the wing kinematics of our system would not be defined by mechanical constraints, but rather by what is optimal for the mission profile. Such a wingactuation system is described in Chapter 8. However, the complexity of the flapping wing problem is such that the wing kinematics are often tuned to the system and are highly system specific. We see this in the way wing kinematics differ between different species of dragonflies and even between dragonflies of the same species (see Chapter 1). We have previously discussed this in Chapters 5 and 8. This chapter combines findings from both of these chapters and applies them to solving the problem of lift generation in a single wing, actively-controlled wing-actuation system. 9.2 Method As discussed in Chapter 8, a wing-actuation system was developed with inspiration from a dragonfly. The system is able to actuate the wing in 3DOF - flapping profile, wing pitch and out-of-plane oscillations. Three solenoids were used to drive the wing, with two of the solenoids responsible for generating the flapping motion. These two solenoids were coupled in a differential mode such that it was possible to drive wing pitch by altering the two solenoid inputs. The inputs into each of the solenoids are represented by equations 8.1, 8.2, 8.3. Altering these parameters varied the force profile produced by the solenoids and in turn the wing kinematics of the system. Similar to flapping wing systems in nature, this test bench is subject to the complex interaction between elastic, inertial and aerodynamic forces (see 1.5). Additionally, it has electromagnetic forces in the form of actuator output from the solenoids. This leads to uncertainty between forced actuator inputs versus wing kinematics. To mitigate 185

208 Abbreviations this problem, many experimental test benches use position encoders and over designed servos to control and optimise wing kinematics (see section 2.2.1). However, these systems tend to have low wingbeat frequencies, operate in non-atmospheric conditions and are unsuitable for implementation on an actual MAV system. Our system does not attempt to optimise the system by controlling and altering wing positions, but rather we do so through modulating the forces generated by the solenoid on the wing. We employ the scatter search optimisation algorithm previously described in section 2.3.1, with the objective function being the lift generated by the system. It provided the location for potential basins where local optima could exist and local search methods were used to optimise within these basins. However, due to the presence of noise in experimental procedures, the use of gradient based local optimisation techniques were unsuitable. We therefore used a simplified stepping method to try to further optimise within the basins. The scatter search algorithm is a global stochastic algorithm, thus presence of noise does not influence the results significantly. The objective function, the lift force, was measured by an ATI Nano 17 force torque sensor, but sampled using a National Instruments DAQ at 2000Hz. The wing-beat frequency is kept at 3.3Hz. Sampling was performed for 2 seconds and the lift averaged over this period. This was done initially for a 2DOF optimisation whereby the wing was constrained to move within a particular stroke plane, followed by a 3DOF optimisation that includes out-of-plane movements. Wing movements were recorded using a Phantom MIRO high speed camera at 300 frames-per-second. This process is detailed in Chapter 8. The following sections further describe the optimisation results, and the findings obtained DOF We initially optimised the system in 2DOF. The system was constrained to flap within the stroke plane. This reduced the dimensionality of the problem to 5 variables. To further reduce the dimensionality of the problem, we modified the inputs into solenoids 1 and 2 as Input 1 = (A 1,2 + A)sin(ωt) + B (9.1) 186

209 9.3 2DOF Input 2 = (A 1,2 A)sin(ωt + Θ 2 ) + B (9.2) It is intuitive that if inputs to solenoid 1 and solenoid 2 are both reduced, this will produce lower actuation force, lower flapping amplitudes and hence lower lift. The reverse is true and hence is a Monotonic function, which does not require optimisation. We instead attempt to exploit active control of the asymmetrical characteristics between solenoids 1 and 2, hence the use of differential terms in equation 9.1 and 9.2. A 1,2 was chosen to be 800. Chapter 8 shows that this value for A 1 1, 2 provided a good initial flapping amplitude, and allowed for margin to adjust the A values. The solenoid input was constrained to be between [ 1200, 1200] which corresponds to a voltage input of [ 23V, 23V ] for solenoids 1 and 2 and [ 12V, 12V ] for solenoid 3. The constraints of the test bench are described in table 9.1. Table 9.1: Optimisation constraints Property Lower Limit Upper Limit A B Θ o 50 o The optimisation problem can be described as min X = [ A, B, Θ 2 ] Lift (9.3) The scatter search begins from an initial point, [ A, B, Θ 2 ] = [0, 0, 0], which describes a symmetrical input into both solenoids 1 and 2. See Fig As symmetrical inputs had been applied to both solenoids 1 and 2, we expected a purely flapping motion, with no wing pitch. However, high speed cinematography (see Fig. 9.2) of the wing root shows a slight wing rotation present in the system. 187

210 Abbreviations Figure 9.1: Symmetrical inputs into solenoids 1 and 2 Figure 9.2: Illustration of high speed cinematography of the wing root for symmetrical solenoid inputs 188

211 9.3 2DOF We capture the horizontal positions of the marker points and show as well that there was variation between the horizontal positions of the markers, which exhibit sinusoidal characteristics (see Fig. 9.3). The wing was angled at an angle-of-attack positive with respect to the direction of the wind. Figure 9.3: X locations of both wing root markers with time(top); Difference in X locations between both markers (BOTTOM) Considering the lift profile, we observe that positive lift was generated. To mitigate the noise, we perform a FFT-iFFT transform. A fourier transform was used to obtain the power spectra (see Fig. 9.19, 9.19, 9.21, 9.22), and then a 0-40Hz window was applied that eliminated frequencies above 40Hz. 40Hz was chosen as the cut-off frequency to remove noise without losing signal integrity. An inverse fourier transform was than performed to restore the signal. These filtered results are plotted with the noisy signal and shown in figure 9.4. The mean lift was 3.8 grams. We then performed the scatter search. An initial set of 100 iterations was performed before selecting points for local optimisation based on the quality of the objective function and its 189

212 Abbreviations Figure 9.4: Unoptimised lift profiles before and after filtering diversity from the rest of the solutions. A total of 4 basins were generated that were local maxima within the global domain. Contrary to the methods employed in chapters 5 and 7, a local optimisation was not performed at each of the basins. The presence of noise made local gradient-based methods unsuitable for optimisation. Rather, simple stepping was performed at each of these points in different directions to further optimise the system. The results are shown in Table 9.2. Table 9.2: Test results for 2DOF optimisation Basin A B Θ 2 Lift (grams) o o o o 6.4 Finally, the solution for basin 4 was chosen, because it generated the least amount of noise (see appendix 9.7) but also produced lift forces comparable to the other solutions within experimental uncertainty. The solenoid inputs are shown in figure

213 9.3 2DOF Figure 9.5: Optimised solenoid profiles High speed cinematography (see Fig. 9.6) of the wing root showed significantly greater wing rotation, as well as wing rotation at the end of the stroke as opposed to during the stroke. These results are further illustrated in figures 9.7 and 9.8 that show the flapping angles and wing pitch angles of the unoptimised and optimised profiles respectively. The method used to obtain this is highlighted in Chapter 8. We see that the flapping angle was greater in the optimised profile which can be attributed to reduced aerodynamic drag. The pitching angle was also significantly increased, which explains the better aerodynamic performance (see Fig. 9.9). The mean lift was found to be 6.46 grams. 191

214 Abbreviations Figure 9.6: High speed cinematography illustrating wing pitch and wing flap for an optimised flapping profile Figure 9.7: Comparison of flapping angle between unoptimised and optimised flapping profile 192