Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability

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1 Journal of Bionic Engineering 9 (2012) Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability Hoang Vu Phan 1, Quoc Viet Nguyen 1, Quang Tri Truong 1, Tien Van Truong 2, Hoon Cheol Park 1, Nam Seo Goo 1, Doyoung Byun 3, Min Jun Kim 4 Abstract 1. Department of Advanced Technology Fusion, Konkuk University, Seoul , Korea 2. Department of Aerospace Engineering, Konkuk University, Seoul , Korea 3. Department of Mechanical Engineering, Sungkyunkwan University, Seoul , Korea 4. Department of Mechanical Engineering and Mechanics, Drexel University, Philadelphia, USA We briefly summarized how to design and fabricate an insect-mimicking flapping-wing system and demonstrate how to implement inherent pitching stability for stable vertical takeoff. The effect of relative locations of the Center of Gravity (CG) and the mean Aerodynamic Center (AC) on vertical flight was theoretically examined through static force balance consideration. We conducted a series of vertical takeoff tests in which the location of the mean AC was determined using an unsteady Blade Element Theory (BET) previously developed by the authors. Sequential images were captured during the takeoff tests using a high-speed camera. The results demonstrated that inherent pitching stability for vertical takeoff can be achieved by controlling the relative position between the CG and the mean AC of the flapping system. Keywords: beetle, flapping-wing system, insect-mimicking, insect flight, inherent pitching stability, vertical takeoff Copyright 2012, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: /S (11) Introduction In recent decades, there has been considerable progress in developing Flapping-Wing Micro Air Vehicles (FW-MAVs) for real flight [1 6] and for basic study [7 10]. A typical FW-MAV flies by flapping its wings at a flapping angle of about 50 and a flapping frequency of about 20 Hz [1]. For attitude control, most FW-MAVs available in the literature use their horizontal and vertical control surfaces, similar to a conventional airplane [1 6]. However, the presence of fragile wings and bulky tails is a drawback as it makes FW-MAVs uneasy to handle and difficult to carry without a specially designed carrier. If we mimic insect flight to develop an FW-MAV, we may be able to design a handy MAV without control surfaces at the tail. Most insects flap their wings at relatively higher flapping frequencies with larger flapping angles to produce aerodynamic forces [11 13]. Some very informative studies on the principles of insect flight include works of Weis-Fogh [14], Ellington [15,16], Dickinson et al. [17,18], Sun and Tang [19], Sane [20], Wang et al. [21], Wu and Sun [22], Ansari et al. [23], and Shyy et al. [24]. These studies contributed to theoretically and/or experimentally explaining how an insect can produce extraordinary aerodynamic force in an unsteady environment. However, research on flight stability of an insect is relatively limited compared with the number of studies available on their aerodynamics [25,26]. The main reason for this limitation is the difficulty in direct force measurement of an insect in free flight [27]. To overcome this situation, computational fluid dynamics was used to estimate aerodynamic forces produced by a bumblebee and their derivatives in Ref. [25], and a Blade Element Theory (BET) was used to investigate longitudinal stability of an animal in Ref. [26]. For stable longitudinal flight of animals, it is suggested that the Center of Gravity (CG) be located ahead of the Aerodynamic Center (AC) and below the AC during animal flight [26]. However, the exact location of an insect may not be available when using the proposed BET to derive the quasi-static pitch equilibrium condition, because the researchers did not Corresponding author: Hoon Cheol Park hcpark@konkuk.ac.kr

2 392 include unsteady effects such as added mass and wing rotation [28,29]. de Croon et al. suggested that best CG location varies between hovering and forward flight for the double-winged ornithopter DelFly [6]. Thus, the relative location of CG and AC is an important parameter for pitch stability. For attitude control, without control surfaces at the tail, insects mostly rely on changes in the stroke plane and on differential flapping motion [12]. Realization of FW-MAVs mimicking these features requires many creative ideas. Designing an inherently stable insect-mimicking FW-MAV involves overcoming several hurdles. First, we cannot use the typical flapping mechanism used in current FW-MAVs [1] because the flapping angle of an insect is typically larger and the flapping frequency is mostly higher than those of currently available FW-MAVs. Therefore, a new flapping-wing mechanism must be designed to accommodate features of flapping motion of insects; further, the FW-MAV must be compact in size and light weight. Second, maintaining symmetry in flapping motions of paired wings is another important issue for stability of vertical and longitudinal flight. Even if we develop such a design, making it fly stably is another concern because there is no control surface at the tail. Once we design a flapping-wing mechanism, the flapping angle is typically predetermined and the stroke plane is fixed with respect to its body axis. In other words, it is hard to find a source of control force in an insect-mimicking FW-MAV, and the free flight test of an insect-mimicking flapping-wing system becomes nontrivial. For example, two thin wire guides were used to demonstrate takeoff of an insect size flapping-wing system because its stability was not guaranteed [8]. Thus, inherent stability should be implemented in an insect-mimicking FW-MAV before we install the control mechanism. Recent announcement from AeroVironment indicates that the company has developed a successful FW-MAV controlled by only flapping wings [30]. However, no technical aspect or principle on it can be acquired from literature survey. In this study, we investigated a simple but useful way to implement inherent pitching stability in an insect-mimicking flapping-wing system for stable vertical takeoff. We used a flapping-wing mechanism developed in earlier works [9,10]. The system flaps at 25 Hz to 40 Hz and creates a large flapping angle of 145. Using this flapping-wing system, we suggested how to determine Journal of Bionic Engineering (2012) Vol.9 No.4 the mean AC and examined the effect of the mean AC location on the pitching stability through vertical takeoff tests. To determine the mean AC location of the flapping-wing system, we used an unsteady BET developed in Ref. [29]. The flapping-wing system is first tested to prove that it can produce a thrust force large enough to overcome its weight. Finally, we demonstrated successful vertical takeoff of the flapping-wing system without any guide and control. 2 Vertical takeoff of a beetle Rhinoceros beetle, Allomyrina dichotoma, is one of the largest flying insects. Therefore, it is easier to observe its body and wing structure with the naked eye and examine its flapping-wing motion using a high-speed camera. In an effort to mimic the flight motion of this particular beetle [9], we observed its flight and found that it flaps its hind wings at a frequency of 34 Hz to 37 Hz with angles ranging from 165 to 180 in a well-maintained stroke plane angle of around 20 (nose down) to 10 (nose up) with respect to the horizontal line during forward and hovering flights, respectively. A beetle can rotate its hind wings around 140 and adjust its cambered shape during upstrokes and downstrokes to generate sufficient aerodynamic forces [9]. From the images taken by a high-speed camera (Photron Fastcam Ultima APX, Japan) at 2000 frames s 1, we can analyze the takeoff mechanism of the beetle. When preparing for takeoff, the beetle raises both its front legs and then starts to open its elytra (forewings) and hind wings at the same time; however, the hind wings are still in the folded configuration at the beginning. To completely unfold the hind wings, the beetle consecutively sweeps them forward, starts to flap them, and fully unfolds them after two flapping strokes. It takes about ms to completely open the hind wings. Thus, the beetle fully unfolds the outer part of its hind wings during the initial flapping motion in a relatively short time. Then, it takes off with an inclined flapping stroke plane after two to three full flapping strokes, as shown in Fig. 1. The duration from wing opening to takeoff is about ms, which is denoted by ms at the first picture in Fig. 1. The inclined flapping stroke plane seems to be almost parallel to the horizontal surface or similar to the flapping stroke plane of about 10 for hovering [9], although the angle could not be exactly quantified. From the high-speed camera video, we

3 Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability 393 Fig. 1 Takeoff of a beetle from the ground. confirmed that there is no significant leg motion to push the body up. Instead, the force produced by the flapping of the insect s hind wings is the main thrust for takeoff. However, stability could not be assessed because direct force estimation was not available. The beetle s ability to vertically take off gave us an inspiration to develop a flapping-wing system that can demonstrate stable vertical takeoff. 3 Flapping-wing system 3.1 Design and fabrication Our flapping-wing system aimed to mimic features of a beetle, namely, Allomyrina dichotoma [9]. Here, we briefly summarize the design and features of the flapping-wing system used in this study. More details on the system can be found in Refs. [9,10]. (1) Fabrication of linkage and frame In this work, we adopted the design used in Ref. [9] for the flapping-wing system: the same linkage design, motor weighing of 4.1 g from (Maxon motor, Switzerland), and a reduction gear ratio of 5:1. Fig. 2 shows parts of the present flapping-wing system including the supporting frame, links, slider, reduction gear, and motor. The dimension of each part was chosen such that the designed flapping angle can be around 150 by the analysis suggested in Ref. [9]. For all the parts of the supporting frames and linkages, we used a 0.8-mm-thick glass/epoxy sheet, which is thinner than that used in Refs. [9,10], to reduce the weight of the flapping-wing system. A precision Computer Numerical Control (CNC) machine (M300S CE, resolution = mm, Woosung E&I Co. Ltd, Korea) was used for fabrication. (2) Artificial wing The artificial wings were made of carbon prepreg strip (with a thickness of 0.1 mm and a width of 1 mm) and thin Kapton film (with a thickness of 7.7 m, Du- Pont, USA) as explained Ref. [9]. Properly tailored three layers of carbon prepreg strips were placed on the Kapton film in a pattern similar to the main wing vein structure of the beetle s hind wing [9]. The venation structure stiffens the wing to sustain wing loading during the flapping motion. For a simple fabrication, we removed some veins but kept the weight and stiffness of the wings similar to those of the previous wings, as shown in Fig. 3 [9]. The weight of each wing was about g. More detailed dimensions and weights of the two systems are compared in Table 1. Output link Front frame Couplers Slider Reduction gear Vertical columns Output link shafts Motor Supporting frame Fig. 2 Supporting frame, links, slider, gear, and motor for the flapping-wing system assembly. Fig. 3 Artificial wings: previous (left) and present (right).

4 394 Journal of Bionic Engineering (2012) Vol.9 No.4 Table 1 Summary of the dimension and weight of previous and present systems Dimensions and weight Previous system [9] Present system Length (mm) Height (mm) Wing span (mm) Wing area (cm 2 ) Wings (g) Motor (g) Linkage & Frame (g) Total weight (g) (3) Flapping angle and frequency The actual flapping angle can be determined by the angle difference between the end of upstroke and the end of downstroke based on the images taken by a high-speed camera. From the same images, we can also determine the flapping frequency. The flapping frequency was about 39 Hz for a 12 V application, which is similar to the typical flapping frequency of Allomyrina dichotoma [9]. The flapping angles of the previous and present flapping-wing systems were designed to be 145, as shown in Fig. 4. The measured flapping angle was found to be slightly larger than the designed flapping angle because of bending deformation of the wings created by the aerodynamic and inertial forces acting on the wings during the flapping motion. The flapping angle range can be modified from that in the prototype flapping system in Ref. [9], such that location of the mean AC can be shifted, as shown in Fig. 4. We assumed that the mean AC is located at approximately 25% of the wing chord from the leading edge at the middle of the flapping stroke (i.e., the bisector of the flapping angle). This assumption, that the mean AC is located at the mid-stroke, is based on the mean AC estimation using a Modified Unsteady BET (MUBET) [29]. More details are provided in the following section. 3.2 Estimation for the mean AC The MUBET was developed and validated with several examples in Ref. [29]. Here, we used this theory to locate the mean AC for thrust over a flapping cycle. As the flapping-wing system produces mostly thrust, and negligible lift [10], we decided to locate the mean AC for thrust only. The schematic drawing of flapping motion of a wing is shown in Fig. 5. The stroke plane is the xy-plane. The position of the feather axis is determined by flapping angle. A wing section located at distance r from the wing root (flapping axis) is demarked by the black strip in Fig. 5a. To present the forces acting on the wing section, we defined an orthogonal coordinate system at the wing section as shown in Fig. 5a. The -axis is the feather axis, the -axis is tangential to the flapping path of the wing section, and the -axis is perpendicular to the stroke plane. In the -plane, rotation of a wing section is expressed by the rotation angle r as shown in Fig. 5b. The flapping speed of the feather axis and rotating speed of the wing section are denoted by and r, respectively. The aerodynamic force acting on the wing section was decomposed into the - and -directions, which were denoted by df and df (thrust in this case), respectively, as shown in Fig. 5b. The center of F j (thrust) in the span-wise direction at each instant of time t = t j of the wing was calculated using the following equations: R F df d, r (1) j x y j j 0 1 F 1 F R j 0 R j 0 df rdrcos, df rdrsin, j j (2) End of upstroke 25 Mid-stroke: mean AC line 145 Mid-stroke: mean AC line (a) (b) End of downstroke Fig. 4 Flapping angle ranges: (a) previous and (b) present system. Fig. 5 Description of wing section and force components: (a) definition of a wing section and (b) forces acting on a wing section and wing rotation.

5 Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability 395 where F j and j are the thrust acting on the wing and the flapping angle at an instant time t j, respectively. x j and y j are the x, y coordinates of the center of the instant thrust acting on the wing, respectively. Finally, the mean AC for thrust over a flapping cycle can be determined as x y F y j j F, j (3) Fj xj where x, y are the coordinates of the mean AC for thrust over a flapping cycle. For the estimation of the AC we calculated the instant thrust (F j ) and its actuation location (x j /R, y j /R) by using Eqs. (1) and (2) for fifty instant times t j /T within a flapping cycle of the previous flapping-wing system. Table 2 shows the data for only twenty five instant times among the fifty data. The instant of time t j /T = 0 corresponds to the beginning of the downstroke, which means Table 2 Instant thrust force and its location during a flapping cycle for the previous flapping-wing system t j / T x j / R y j / R F j (g) F j, that the wing is located in the vertical position. By using the data in Table 2 and Eq. (3), we can determine the location of the AC for the previous flapping-wing system, which is located at a flapping angle of and at the 47% wing span in the wing span direction. We have followed the same procedure to estimate the AC of the present flapping-wing system, where flapping angle range is shifted down for 25 compared to the previous system as shown in Fig. 6b. The estimated AC of the present design is located at 4.3 with respect to the x-axis. In this case, the averaged pitching moment around the CG over a flapping cycle caused by the thrust was mostly eliminated for the stable vertical takeoff. Fig. 6 shows that the mean ACs for thrust of our flapping-wing systems are located approximately at the mid-stroke and at about mid-span. Stroke plane 4.3 Mid-stroke (b) 145 AC 25 y 0.47R End of downstroke End of upstroke AC 7.5 R Wing tip path Fig. 6 Mean aerodynamic center for thrust over a flapping cycle: (a) previous and (b) present flapping-wing system. x

6 396 For the MUBET, we included the added mass force and rotational lift to model unsteady aerodynamics. Even though they might not perfectly model the real unsteady nature of flow environment, it provided a good enough aerodynamic force estimation for our flapping-wing systems, which was proven in Ref. [29]. Since the MUBET requires wing kinematics, we need to acquire the wing kinematics by capturing the flapping motion using more than two high-speed cameras and post-process. Based on the images, we approximated the wing kinematics with a series of functions. In this procedure, some error can be included. Thus, the AC estimation possesses some uncertainty. The CG location was measured by typical hanging method. We hung the flapping-wing system with two strings, one after another, which are attached to the flapping-wing system at two different locations, and captured the images. The CG location is the intersecting point of the extended lines of the two strings. Change of the CG location due to the flapping wing motion should be negligible. 3.3 Modification of the flapping-wing system The CG of a flapping-wing system can be measured or more easily estimated. The CG of each system is expressed with black circle in Fig. 7. As shown in Fig. 6, the mean AC location strongly depends on the flapping angle range for these particular flapping-wing systems. The flapping angle range of the previous flapping-wing system, which is shown in Fig. 4a, was chosen to expect a clap-fling effect [14] to produce more aerodynamic force. Because of this arrangement, the AC for thrust is located above the CG, and it is misaligned in the vertical direction as shown in Fig. 7a, which is a side view of the previous flapping-wing system. In this case, the mean thrust produces a nose-down or counter-clockwise pitching moment about the CG, as described in Eq. (4) MG I G, (4) where M G is the sum of pitching moment about the CG, I G is the mass moment of inertial about the CG, and is the angular acceleration. Since the left hand side of the equation is not zero, the pitching angle can grow with time. However, when the flapping angle range is shifted, as shown in Fig. 4b, the estimated mean AC for thrust is located close to the x-axis as shown in Fig. 6, and the CG and mean AC are aligned in the vertical direction, as Journal of Bionic Engineering (2012) Vol.9 No.4 described in Fig. 7b. Since thrust does not contribute to pitching moment in this case, M G = 0 or I 0. (5) G Therefore, when the initial pitching angle and the initial angular velocity are all zeros, the modified flapping-wing system can demonstrate stable vertical takeoff. Thus, we expect that the present one possesses inherent pitching stability for vertical takeoff. Note that we have not included a component for the side force in the horizontal direction in this force analysis, because the two flapping-wing systems produce negligible lift in the horizontal direction due to the symmetric flapping motion during upstroke and downstroke. (a) T V AC CG H Counterclockwise moment W Estimated aerodynamic center line Fig. 7 Center of gravity and aerodynamic center locations of flapping-wing systems: (a) previous and (b) present system. 4 Flight test of flapping-wing systems We have conducted flight test for the present flapping-wing system that has the adjusted flapping angle range as explained in Section 3. Through the adjustment, the system may possess inherent pitching stability for vertical takeoff. To confirm this, we flew the flapping-wing system at the flapping frequency of 39 Hz without any vertical guide. 4.1 Demonstration of guided takeoff Before the free vertical takeoff test, we set up an experiment, as shown in Fig. 8, to confirm that the flapping-wing system can generate sufficient vertical

7 Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability 397 Fig. 8 Experimental setup for guided vertical takeoff. force for a liftoff. In this test, we intentionally added a small dummy weight to the present flapping-wing system to examine the maximum takeoff weight and to slow down the takeoff speed. The total weight reached 6.95 g after attaching the dummy weight and two carbon rods. Since the dummy weight was fixed at the bottom of the motor, it could be used to adjust the lateral location of CG when the flapping angle range is not appropriately shifted, which might happen during the fabrication process. Two small carbon rods were connected to the flapping-wing system: one at the top as a guide and the other at the bottom as a leg. The length of each rod was 100 mm. One end of the upper rod was inserted into a glass tube with a diameter of 9 mm, which was used to constrain the vertical flight direction of the flapping-wing system. The flapping-wing system was powered at 12 V by an external power supply through very thin copper electric wires (diameter = 0.15 mm), so that the effect of the electric wire on vertical takeoff can be minimized. The stroke plane was parallel to the horizontal line when it was installed to the apparatus, which is similar to the stroke plane configuration of a real beetle during takeoff from the ground as shown in Fig. 1. The takeoff motion was captured by a high-speed camera (Photron Fastcam Ultima APX, Japan) operated at 2000 frames s 1. Fig. 9 shows the sequential takeoff motions of the present flapping-wing system captured by the high-speed camera. They show that the flapping-wing system could take off for 80 mm in about 0.80 s, which means that the average vertical takeoff speed is about 10 cm s 1 at the maximum takeoff weight. These images prove that the flapping-wing system can produce a thrust large enough to lift it in the vertical direction. Since the previous flapping-wing system had the same flapping mechanism, it also could take off in this test setup. Thus, the proposed test method can be used to check whether an insect-mimicking flapping-wing system can produce a force large enough for takeoff without force measurement by using a load-cell. Now, if the flapping-wing system fails to vertically take off, it is due to lack of stability not because of lower thrust production. 4.2 Demonstration of free vertical takeoff For the free takeoff test without any guide, we attached a carbon rod to the bottom of both the flapping-wing systems. The rod was then inserted into a glass tube of 50 mm height firmly installed on the ground surface, as shown in Fig. 10 and Fig. 11. The two flapping-wing systems were powered at 12 V by an external power supply, and the motions of flapping-wing system were captured by a high-speed camera. The weights of the previous and the present flapping-wing systems were 6.40 g and 6.32 g, respectively. Fig. 9 Guided vertical takeoff of the present flapping-wing system.

8 398 Journal of Bionic Engineering (2012) Vol.9 No.4 Fig. 10 Demonstration of takeoff of the previous flapping-wing system. Fig. 11 Demonstration of takeoff of the present flapping-wing system. Fig. 10 shows a typical takeoff process of the previous flapping-wing system. After leaving the tube within about 0.90 s, it rotates about its CG and immediately falls down at about 0.95 s. The duration from leaving the tube to falling down is about 0.05 s. Thus, the previous flapping-wing system could not demonstrate pitching stability because the CG and AC were not vertically aligned, as shown in Fig. 7a. However, the present system displayed a more stable vertical takeoff after leaving the tube, as shown in Fig. 11. After leaving the tube at about 0.20 s, the flapping-wing system still maintained pitching stability. The previous one spent relatively longer time for leaving the glass tube because it experienced large lateral motions as a result of pitching moment. Fig. 12 shows images of three vertical takeoff tests for the present system, which was vertically set up with three short legs. The three images for stable takeoff tests were included in Fig. 12 to show that they are not accidentally achieved. The same flapping-wing system was used for the test. The three legs were symmetrically attached at the bottom of the motor, so that they do not change the CG location. We can see that it could stably take off as soon as power was supplied to the system. In Fig. 13, the trajectories of the CG of the system during takeoff tests are demarked with circles. The arrows in Fig. 13 indicate the direction of the body axis, which demonstrates that the flapping-wing systems tended to maintain stable vertical takeoff despite of disturbance from electric wires. We conducted many takeoff tests and all tests demonstrated similar stable takeoff if the flapping-wing system was not damaged after multiple takeoffs and crashed when the power was turned off. Video clips for the stable flight of the flapping-wing system can be found in Refs. [31,32]. Although the effect of electric wires was not fully removed in these tests, the test results provided proof that inherent pitching stability for vertical takeoff can be implemented by controlling the relative positions of the CG and mean AC. As mentioned earlier, the force analysis in Fig. 7 is rather simple for the present flapping-wing system, because it produces mostly thrust. For an insect-mimicking flapping-wing system that produces thrust and significant lift, we can still theoretically locate the mean ACs of the two force components and design a flapping-wing system such that the pitching moments created by the thrust and lift can be canceled out, which is how we implement the inherent pitching stability in a flapping-wing system.

9 Phan et al.: Stable Vertical Takeoff of an Insect-Mimicking Flapping-Wing System Without Guide Implementing Inherent Pitching Stability 399 (a) Test 1 (b) Test 2 (c) Test 3 Fig. 12 Demonstration of takeoff of the present flapping-wing system.

10 400 Journal of Bionic Engineering (2012) Vol.9 No.4 (a) Test 1 (b) Test 2 (b) Test 3 Fig. 13 Trajectories of the CG during vertical takeoff tests. 5 Conclusion In this work, we briefly summarized the design of an insect-mimicking flapping-wing system and demonstrated how we modified the configuration of the flapping-wing system for stable vertical takeoff. Flapping performance tests showed that the flapping-wing system powered at 12 V could flap at a frequency of 39 Hz, and the guided vertical flight test indicated that it could produce a thrust large enough to lift it in the vertical direction. The effect of the relative locations of the CG and mean AC on the flight was examined theoretically and experimentally. An unsteady BET suggested that the mean AC for thrust is located at about the mid-stroke and mid-span. From the free vertical takeoff tests without any guide, we proved that inherent pitching stability for vertical takeoff can be implemented by controlling relative position of the CG and the mean AC for an insect-mimicking flapping-wing system. Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant no ), and partially supported by the New & Renewable Energy R&D program of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy (No ). M.J. Kim appreciates the financial support from National Science Foundation (OISE# ). References [1] Park J H, Yoon K J. Designing a biomimetic ornithopter capable of sustained and controlled flight. Journal of Bionic Engineering, 2008, 5, [2] Thompson P, Ward G, Kelman B, Null W. Design report: Development of surveillance, endurance, and ornithoptic micro air vehicles. The 8th International Micro Air Vehicle Competition Conference, Tucson, Arizona, USA, [3] Olson D H, Silin D, Aki M, Murrieta C, Tyler J, Kochevar A, Jehle A, Shkarayev S. Wind tunnel testing and design of fixed and flapping wing micro air vehicles at the university of Arizona. International Micro Air Vehicle Competition, Seoul, South Korea, [4] Ifju P G, Jenkins D A, Ettinger S, Lian Y, Shyy W, Wazak M R. Flexible-wing-based micro air vehicles. The 40th AIAA Aerospace Sciences Meeting & Exhibit, Reno, NV, USA, 2002, AIAA [5] Krashanitsa R, Silin D, Shkarayev S, Abate G. Flight dynamics of a flapping-wing air vehicle. International Journal of Micro Air Vehicles, 2009, 1, [6] de Croon G, de Clerq K, Ruijsink R, Remes B, and de Wagter R. Design, aerodynamics, and vision-based control of the DelFly. International Journal of Micro Air Vehicles, 2009, 1, [7] Khan Z, Steelman K, Agrawal S. Development of insect thorax based flapping mechanism. IEEE International Conference on Robotics and Automation, Kobe, Japan, 2009, [8] Perez-Arancibia N O, Ma K Y, Galloway K C, Greenberg J D, Wood R J. First controlled vertical flight of a biologically inspired microrobot. Bioinspiration and Biomimetics, 2011, 6,

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