ADAPTIVE SLIDING MODE CONTROL OF UNMANNED FOUR ROTOR FLYING VEHICLE

Size: px
Start display at page:

Download "ADAPTIVE SLIDING MODE CONTROL OF UNMANNED FOUR ROTOR FLYING VEHICLE"

Transcription

1 International Journal of Robotics and Automation, Vol. 30, No. 2, 205 ADAPTIVE SLIDING MODE CONTROL OF UNMANNED FOUR ROTOR FLYING VEHICLE Shafiqul Islam, Xiaoping P. Liu, and Abdulmotaleb El Saddik Abstract This paper addresses the stability and tracking control problem of an underactuated four rotor unmanned flying robot vehicle. Algorithm design combines adaptive law with the sliding mode control term to deal with uncertainties associated with flying environment, mass, inertia, aerodynamic force and moment of the vehicle. Using Lyapunov analysis, we show that the position and orientation tracking errors and their derivatives are bounded by bounds that can be made close to the origin. Simulation examples on a quadrotor vehicle are given to demonstrate the effectiveness of theoretical development for real-world application. Key Words Quadrotor, adaptive control, Lyapunov method. Introduction Quadrotors are unmanned aerial vehicles UAVs) that have been setting the waves of the growing interest in the scientific and industrial communities because of their various applications, such as inspection and surveillance, search and rescue mission, first responders, police and military services. The interest in quadrotor UAVs has been recently pushing the limits for technology by sparking the new ideas and practical applications amongst the researchers and industrialists alike. The control system design for micro-scale quadrotor UAV is very difficult as the dynamics of the quadrotor UAV associated with inherent nonlinearity and underactuated property, nonlinear aerodynamical force and moment, strong nonlinear coupling between angular and linear dynamics and disturbances associated with the flying environments. Over the last decade, different types of autonomous tracking systems for quadrotor UAV have proposed in the literature to deal with the modeling errors and disturbance uncertainty. In [], authors developed model-based University of Ottawa, Ottawa, Canada, and Carleton University, Ottawa, Canada; sislam@sce.carleton.ca Carleton University, Ottawa, Canada; xpliu@sce. carleton.ca University of Ottawa, Ottawa, Canada; elsaddik@ uottawa.ca Recommended by Prof. J. Gu DOI: 0.236/Journal ) proportional-integral-derivative PID) and linear quadratic regulator LQR) control algorithms for quadrotor UAV. It is well known that the model-based controller cannot ensure robustness in the presence of uncertainties and disturbances. Authors in [2] [5] used backstepping control techniques to deal with the problem of coupling in the pitch-yaw-roll and the problem of coupling in kinematics and dynamics of the underactuated flying vehicle. Later, the integral action was included with the backstepping technique in [6]. The idea of including PID term with classical backstepping design was to reduce the steady tracking errors while maintaining asymptotic stability of the whole closed-loop system. Authors in [7] proposed model-based dynamic inversion mechanism for hovering control for the quadrotor system. In [8], authors developed robust H tracking controller by using backstepping controller to stabilize uncertain quadrotor UAV system. Authors in [9] proposed sliding mode design which can ensure the stability of the roll and pitch angles. Using visual feedback signal, classical control technique for quadrotor UAV system was presented in [0]. In [] [3], authors obtained perfect tracking accuracy of the quadrotor in indoor environment by using visual motion tracking system. However, the design can only be applied for a priori known tasks and indoor environment [4]. Adaptive backstepping control mechanism was proposed for quadrotor UAV system in the presence of model parameter uncertainty in [5], [6]. In our view, it can be seen from the existing designs that most reported results requires a priori known upper bound of the modeling error and disturbance uncertainty to establish stability of altitude and attitude dynamics in uncertain indoor and outdoor flying environment. In practice, it may be unrealistic to know the exact values of the uncertainty associated with the flying environment, payload mass, moment of inertia, aerodynamic friction and gyroscopic effect on the closed-loop systems. On the other hand, unpredictable changes in indoor and outdoor environment may also increase the modeling errors uncertainty significantly making the flight control system design even more complicated. Under these circumstances, available autonomous tracking system design may be unable to adapt with the change of the flight/plant dynamics during different flight mission. In this paper, we propose adaptive sliding mode control technique for stability and trajectory tracking control 40

2 problem of small size quadrotor flying vehicle in the presence of uncertainty. The overall design comprises adaptive term with the sliding mode control term. Adaptive control law is employed to learn and compensate uncertainties associated with mass, inertia matrix, external disturbances, and aerodynamic force and moment affecting the system. Algorithms for altitude, position and attitude tracking design are developed through Lyapunov-like energy functional. It is shown in our analysis that tracking errors of the position, orientation and their derivatives are bounded and asymptotically converge to zero. In contrast with the existing design, the proposed method does not rely on the upper bound of the modeling error and disturbance. The bound is obtained by using an adaptation law. To demonstrate the effectiveness of this theoretical arguments, evaluation results on a commercial quadrotor is presented. This evaluation shows that the design can be applied for quadrotor UAV with large parametric uncertainty associated with the payload mass, uncertain environment, moment of inertia, nonlinear aerodynamic friction and gyroscopic effect on the closed-loop systems. This paper is organized as follows. In Section 2, kinematics and dynamics model of the four rotor flying vehicle are given. Adaptive sliding mode control designs are introduced in Section 3. A detail stability analysis is also presented in Section 3. Simulation example is given in Section 4. Finally, conclusion and future work is given in Section Dynamical Model We first present the model dynamics of unmanned four rotor flying vehicle [], [5]. To derive the motion dynamics of the UAV system, two main reference frames are considered as earth fixed inertial reference ξ and body fixed frame δ attached to the UAV system. The quadrotor has three translational positions with respect to ξ as defined as x s =[x s,y s,z s ] T R 3 and three orientations with respect to δ represented by three Euler angles as defined as η =[φ, θ, ϕ] T. Then, we consider that the vehicle has three translational velocities as v s =[v s,v s2,v s3 ] T and three rotational velocities as Ω s =[Ω s, Ω s2, Ω s3 ] T with respect to the body fixed frame. The kinematic model of the UAV can then be written as: ẋ s = v s ) Ṙ s = R s SΩ s ) 2) where the transformation of vectors from rigid body frame to the inertial frame can be derived from the following homogenous translational rotational matrix R s R 3 3 C φ C ϕ S φ S θ C ϕ C φ S ϕ C φ S θ C ϕ + S φ S ϕ R s = C θ S ϕ S φ S θ S ϕ + C φ C ϕ C φ S θ C ϕ S φ S ϕ 3) S φ S φ C θ C φ C θ where C θ and S θ denotes cos θ and sin θ and SΩ s ) denotes the skew-symmetric matrix SΩ s ) which satisfies 4 skew-symmetric property. The skew-symmetric matrix SΩ s ) can be defined as follows: 0 Ω s3 Ω s2 SΩ s )= Ω s3 0 Ω s Ω s2 Ω s 0 Applying Newton and Euler laws in the body-fixed reference frame, the dynamic equation for the quadrotor helicopter subjected to translational forces and control torques developed in the centre of the mass can be derived as: 4) 0 m v s = mg 0 + F t + F d 5) I Ω s = Ω s IΩ s )+u t + u g + u a 6) where m R and I R 3 3 = diag[,, ] denotes the mass and symmetric positive definite constant inertia matrix of the vehicle, respectively. Using the Euler angles, the angular velocity transformation matrix can be used to relate the rate of change of the angular velocities in the body fixed frame as: Ω s 0 sin θ φ Ω s2 = 0 cos φ cos θ sin φ θ 7) 0 sin φ cos φ cos θ ϕ Ω s3 It is assumed that nonlinear aerodynamic drag forces F d varies linearly with the velocities as: F dx Δ x 0 0 F dy = 0 Δ y 0 8) F dz 0 0 Δ z where Δ x = τ v s,δ y = τ 2 v s2,δ z = τ 3 v s3 with positive constants τ i and i =, 2, 3. Now, the thrust force generated by four rotors can be derived as: 0 F t = R s dσ 4 i=ω i 0 with the trust factor d>0 and ω i is the speed of the rotors with i =, 2, 3, 4. The torques developed in the epicenter of a quadrotor helicopter by the propellers can be defined as: dlω 3 2 ω) 2 u t = dlω4 2 ω2) 2 α r ω 2 ω2 2 + ω3 2 ω4) 2 9) 0)

3 where l is the distance between the centre of the mass and the rotor axes and α r is the drag factor for the rotation. The nonlinear aerodynamic torques u a are assumed to be varying with angular velocity of flying vehicles as follows: u ax Π x 0 0 u ay = 0 Π y 0 ) u az 0 0 Π y where Π x = φ Ω s, Π y = φ 2 Ω s2,π z = φ 3 Ω s3 with the positive constants of aerodynamic coefficients φ i and i =, 2, 3. Finally, the gyroscopic torques are generated by the rotors as they move along the rotor mast with the body-fixed frame defined as: 0 u g = I r Ω s 0 ω ω 2 + ω 3 ω 4 ) 2) where I r is the inertia of the rotor blade. In flying robot vehicle, the rotational velocities of the four rotors ω i are usually used as an input variable for designing an autonomous system. Therefore, we consider new input variables for four rotors given as follows: u = dω 2 + ω ω ω 2 4), u 2 = dω 2 3 ω 2 ), u 3 = dω 2 4 ω 2 2), u 4 = α r ω 2 + ω 2 3 ω 2 2 ω 2 4) 3) Using 7) 3), one can derive overall dynamical model of the quadrotor vehicle as follows: ẍ = ÿ = z = cos φ sin θ cos ϕ + sin ϕ sin φ) u + Δ ax, cos φ sin θ sin ϕ sin φ cos ϕ) u + Δ ay cos φ cos θ) u g + Δ az 4) with = m, Δ ax = Δ x,δ ay = Δ y,δ az = Δ z and the orientation dynamics has the following form φ = p b θ ϕ)+p b u 2 p b2 F θ + Π ax, θ = p c φ ϕ)+p c u 3 + p c2 F φ + Π ay, 5) ϕ = p d θ φ)+p d u 4 + Π az with Π ax = Π x, Π ay = Π y, Π az = Π z, P b = p ), p c = p2 ), p d = p3 ), p = ), p 2 = ), l l p 3 = ), p b = ), p c = ), p d = ), ) p b2 = Ir ), p c2 = Ir and F =ω ω 2 + ω 3 ω 4 ) Algorithm Design and Stability Analysis In this section, we design sliding mode control system for autonomous tracking of four rotor flying vehicle. We assumed that the vehicle model parameters, such as flying environment, mass, inertia, damping and moment, are uncertain causing modeling errors uncertainty. In our design, we combine sliding mode control algorithm with adaptive control terms for altitude, attitude and position input such that the position and rotation angle of the flying vehicles track a time varying reference angle and position trajectory in the presence of external disturbance and uncertain model dynamics. Let us first design the altitude controller to generate the desired lifting force in order to maintain the desired distance between the ground and the vehicle. We consider that altitude between the ground and the vehicle are available for measurement. Then, we define the altitude tracking errors as: e z =z d z) 6) where z d is the altitude reference. Then, we define the auxiliary tracking error signals by combining e z and ė z as follows: S z =ė z + α z e z ) 7) with ė z =ż d ż) and α z 0. The altitude error dynamics has the following form: ë z = z d cos φ cos θ)u g + Δ ) az 8) We then introduce the following altitude control algorithm with the presence of the uncertain model dynamics: u = cos φ cos θ z d + u eqm + τ m + α z ė z + k s S z ) u eqm = g Δ ) az,τ m = ˆk z signs z ), k z =Γ z sign T S z )S z 9) where k s > 0, Γ z > 0, α z 0 and k z = k z ˆk ) z. The control term τ m is used to compensate uncertainties appearing from external disturbances and modeling errors. We now choose the following Lyapunov function: V z = 2 ST z S z + 2 Γ z k z kz 20) We then take the derivative 20) along the closed-loop system constructed by 6) 9). Then, V becomes: V z k s S T z S z 0 2) This implies that V z L 2 and V z L ensuring that the signals e z,ė z and S z are bounded. Then, using Barbalat s

4 Lemma, we can conclude that the signals e z,ė z and S z converges to zero as the time goes to infinity. We now design the position algorithm to generate the desired horizontal motion for the given time varying desired trajectories x d and y d. The horizontal motion of the vehicle is usually obtained by rolling or pitching via rotating the thrust values to the given desired motion. To design a position algorithm to keep the vehicle over the desired point, we derive the position tracking errors model: ë x =ẍ d τ x u + Δ ax 22) ë y =ÿ d τ y u + Δ ay 23) where τ x and τ y are the virtual input and x d and y d are the reference position trajectories in x and y direction. Let us define auxiliary error signals M x and N y as sliding surface as: M x =ė x + α x e x ) 24) N y =ė y + α y e y ) 25) where α x 0, α y 0, e x =x d x) and e y =y d y). We then design the following algorithms for generating motion in x and y direction corresponding to the given reference motion in x d and y d : τ x = ẍ d + α x ė x + τ xm + k x M x ) u τ xm = ˆk xm signm x ), kxm =Γ x sign T M x ) M x 26) τ y = ÿ d + α y ė y + τ yn + k y N y ) u τ yn = ˆk yn signn y ), kyn =Γ y sign T N y ) N y 27) where k x > 0, k y > 0, Γ x > 0, u > 0, α x 0, α y 0, k xm =k xm ˆk xm ), kyn =k yn ˆk yn ) and Γ y 0. The closed-loop stability of the longitudinal and lateral motion dynamics can be shown by using the following Lyapunovlike energy functional: V x = 2 MT x M x + 2 Γ x k xm kxm 28) V y = 2 N T y N y + 2 Γ y k yn kyn 29) Taking the derivative V x and V y along the closed-loop trajectory designed by using 22) 27), one can show that the errors e x, e y, M x and N y are bounded and their bounds converges to zero in the Lyapunov sense as V x k x M T x M x 0, V y k y Ny T N y 0 with V x L 2, V y L 2 and V x L, V y L. Let us now focus our attention on algorithm design for attitude dynamics of the flying vehicle. The main objective of this algorithm is to generate desired control torques for roll, pitch and yaw orientation in the presence of external disturbance and modeling error uncertainties. It is assumed that the orientation angles 43 and their derivatives are available from inertial measurement unit. The tracking errors for the given desired rolling angles can be defined as: [ ë φ = φ d p b θ ϕ)+p b u 2 p b2 F θ + Π ] ax 30) where φ d is the reference rolling angle. By knowing the values of ϕ d, τ x and τ y, φ d can be calculated from the relationship φ d = arc sinτ x sinϕ d ) τ y cosϕ d )). Then, we introduce the following control torque for generating desired rolling moment as: u 2 = [ ] φd + v eqv + τ φ + α φ ė φ + k φ B φ, p b v eqv = p b θ ϕ)+p b2 F θ Π ax τ φ = ˆk φ signb φ ), kφ =Γ φ sign T B φ ) B φ 3) where Γ φ > 0, k φ > 0, α φ 0, kφ =k φ ˆk φ ) and B φ =ė φ + α φ e φ ). For the closed-loop stability analysis under the proposed rolling moment 3), we consider the following Lyapunov energy function: V φ = 2 BT φ B φ + 2 Γ φ k φ kφ 32) Taking the time derivative of 32) along the trajectories formulated by 30) and 3), we can obtain the bound on V φ as follows V φ k φ Bφ T B φ 0. Then, using Barbalat s Lemma, we can state that the tracking errors of the rolling angles, rolling speeds and B φ are bounded and their bounds converges to zero as the time goes to infinity. We now design algorithm to generate the desired pitching moment to track the desired pitching angle θ d. The tracking errors of the pitching angles can be written as: [ ë θ = θ d p c φ ϕ)+p c u 3 + p c2 F φ + Π ] ay 33) Using ϕ d, φ d, τ x and τ y, θ d can be obtained ) by using τx sinϕ the relationship θ d = arc sin d )+τ y cosϕ d ) cosφ d ). Then, we introduce the following pitching moment for generating desired pitching motion trajectory: u 3 = ] [ θd + w eqv + τ θ + α θ ė θ + k θ C θ, p c w eqv = p c φ ϕ) p c2 F φ Π ay τ θ = ˆk θ signc θ ), kθ =Γ θ sign T C φ )C φ 34) where k θ 0, Γ θ > 0, α θ 0, kθ =k θ ˆk θ ) and C θ = ė θ + α θ e φ ). Using the following Lyapunov-like energy function: V θ = 2 CT θ C θ + 2 Γ θ k θ kθ 35)

5 Figure. The time history of uncertainty along x, y and z in metres, φ, θ and ϕ in radians. Figure 2. The time history of position tracking x and x d in metres. Figure 3. The time history of position tracking in y and y d in metres. and Barbalat s Lemma, we can show that all the signals in 33) under pitching moment 34) asymptotically converges to zero as V θ k θ Cθ T C θ 0 with V θ L 2 and V θ L. Finally, we design the following error dynamics for the yaw moment: [ ë ϕ = ϕ d p d θ φ)+p d u 4 + Π ] az 36) The desired yaw moment is generated by the following control torque: u 4 = [ ϕ d + χ eqv + α ϕ ė ϕ + τ ϕ + k ϕ D ϕ ], p d χ eqv = p d θ φ) Π az τ ϕ = ˆk ϕ signd ϕ ), kϕ =Γ ϕ sign T D φ )D φ 37) 44 with k ϕ 0, Γ ϕ > 0, α ϕ 0, kϕ =k ϕ ˆk ϕ ) and D ϕ = ė ϕ + α ϕ e ϕ ). To guarantee the closed-loop stability with the yaw moment provided by input 37), we consider the following positive definite Lyapunov function: V ϕ = 2 DT ϕ D ϕ + 2 Γ ϕ k ϕ kϕ 38) Take the time derivative 38) along the closed-loop system formulated by tracking error model 36) and control law 37), we can obtain the time derivative of V ϕ as V ϕ k ϕ D T ϕ D ϕ 0 with V ϕ L 2 and V ϕ L. In view of above equation and Barbalat s Lemma, we can conclude that the pitching error signals e ϕ,ė ϕ and D ϕ are bounded and their bounds asymptotically converges to zero in Lyapunov sense. Based on our above Lyapunov analysis, we can state our main results in Theorem.

6 Figure 4. The time history of position tracking in z and z d in metres. Figure 5. The time history of yaw tracking in ϕ and ϕ d in metres. Figure 6. The time history of position tracking x and x d in metres under large model parameters. Theorem. Let us assume that the linear and angular velocities of the quadrotor flying vehicle are bounded. Then, all the error signals in the closed-loop systems formulated by error models 8), 22), 23), 30), 33) and 36) under input algorithms 9), 26), 27), 3), 34) and 37) are bounded and their bounds asymptotically converges to zero. Proof: For the closed-loop stability analysis, we consider the following composite Lyapunov-like energy functional: V c = V x + V y + V z + V φ + V θ + V ϕ 39) In view of our above Lyapunov analysis, we can obtain the time derivative of V c as V c 0. Then, using V c 0 and Barbalat s Lemma, we can state that the signals e z, ė z, e x, ė x, e y, ė y, e φ, ė φ, e θ, ė θ, e ϕ, ė ϕ, S z, M x, N y, B φ, C θ and D ψ are bounded and their bounds converges to zero asymptotically. 4. Simulation Results To examine the stability and tracking property of the proposed algorithm, various simulation studies have been 45 performed on a commercial quadrotor UAV system [7]. Our aim in this simulation is to verify the flight control stability and tracking property developed in Theorem with respect to varying mass, aerodynamic damping, inertia matrix and uncertain outdoor environment. In our simulation, the desired motion trajectories in x and y directions are selected as x d t)= e 5t3 ) sint) and y d t)= e 2t3 ) cos0.88t). The desired trajectory for z d take-off, free flight and landing) is defined by using the following transfer function Hs)= 4 s 2 +4s +4. It is assumed that the external forces are acting on the translational and orientational motion dynamics due to the variation of uncertain flying environment, aerodynamic force and moment, mass and inertia. For our evaluation, we consider the following state independent uncertain forces that are acting along the three translational and orientational motion dynamics E x =cos0πt),e y =cos4πt),e z =sin4πt),e φ = sin2πt), E θ = sin4πt),e ϕ = cos4πt). The physical parameters for the given commercial Pelican quadrotor vehicle [7] are chosen as m =0.5kg, l =0.2m, d= , g =9.8 m s 2, = Nm s2 rad, = Nm s2 rad, = Nm s2 rad, I r = Nm s2 rad, τ =0.002 N s m,

7 Figure 7. The time history of position tracking in y and y d in metres under large model parameters. Figure 8. The time history of position tracking in z and z d in metres under large model parameters. Figure 9. The time history of yaw tracking in ϕ and ϕ d in metres under large model parameters. τ 2 =0.005 N s m, τ 3 =0.006 N s m, φ =0.00 Nm s rad, φ 2 = Nm s rad and φ 3 =0.006 Nm s rad. Then, we choose the control design parameters arbitrarily as α x =2, α y =2, α z =2, α x = 20, α y = 20, α z =2, α φ =5, α θ =5, α ϕ =5,α φ = 50, α θ = 50, α ϕ = 50, k x =00, k y =50, k s =00, k φ =300, k θ = 300, k ϕ = 300, Γ x =, Γ y =, Γ z =2, Γ φ =2, Γ θ = 2 and Γ ϕ = 2. Using these design parameters, we then apply the proposed design on the given flying vehicle with and without uncertainty. At first, from 0 to 5 s, the vehicle operates under normal condition. Then, from 5 to 0 s, the vehicle flies in the presence of uncertainty that entering into translational and rotational axes. Finally, from 0 to 20 s, the system returns to normal operating condition without using uncertainty as depicted in Fig.. The evaluation results are presented in Figs Let us now increase uncertain model parameters of the vehicle. For this evaluation, the physical parameters of the commercial Pelican quadrotor vehicle [7] are chosen 46 as m = 5 kg, l =0.2m, d = , g =9.8 m s 2, =0.235 Nm s2 rad, = Nm s2 rad, = Nm s2 rad, I r = Nm s2 rad, τ =0.2N s m, τ 2=0.5N s m,τ 3=0.6N s m, φ =0. Nm s rad, φ 2 =0.3Nm s rad and φ 3 =0.6Nm s rad. Using with these new model parameters, we then implement the proposed design with the same set up and same control design parameters as used in our previous evaluation. The evaluation results are depicted in Figs Notice from these results that the tracking errors remain closed to zero even with the increase of the modeling errors uncertainty. 5. Conclusion and Future Work In this work, we have presented adaptive sliding mode control technique for quadrotor UAV system. The proposed design can be used to ensure stability and tracking of

8 the vehicle in the presence of modeling error and disturbance uncertainty associated with aerodynamic damping and moment, mass, inertia and uncertain flying environment. Adaptive control laws have been used to learn and compensate uncertainty affecting the vehicle dynamics. Simulations studies have been carried out on a commercial Pelican quadrotor UAV to demonstrate theoretical development of this paper. In our future work, the proposed design will be implemented and evaluated on a commercial quadrotor helicopter provided by Asctec Inc. [7]. Acknowledgement Authors thank editor-in-chief, associate editor and anonymous five reviewers for their constructive comments and suggestion that definitely improves the quality and presentation of this paper. This work is partially supported in part by Natural Sciences and Engineering Research Council of Canada NSERC). References [] S. Bouabdallah and R. Siegwart, Design and control of an indoor micro quadrotor, Proc IEEE Int. Conf. on Robotics and Automation, New Orleans, USA, 53 58, [2] T. Madani and A. Benallegue, Control of a quadrotor via full state backstepping technique, Proc. 45th IEEE Conf. on Decision and Control, San Diego, CA, December 3 5, , [3] T. Madani and A. Benallegue, Backstepping control for a quadrotor helicopter, Proc. IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, 9 5 October, Beijing, China, 2006, [4] T. Madani and A. Benallegue, Backstepping sliding mode control applied to a miniature quadrotor flying robot, Proc. 32nd Annual Conf. of the IEEE Industrial Electronics Society IECON, 6 0 Nov. Paris, France, 2006, [5] S. Bouabdallah and R. Siegwart, Backstepping and slidingmode techniques applied to an indoor micro quadrotor, Proc IEEE Int. Conf. on Robotics and Automation, , [6] S. Bouabdallah and R. Siegwart, Full control of a quadrotor, Proc IEEE/RSJ Int. Conf. on Intelligent Robots and Systems, October 29 November 2, San Diego, CA, USA, 2007, [7] A. Das, F. Lewis and S. Subbarao, Dynamic inversion of the quadrotor with zero-dynamic stabilization, Proc. of the 7th IEEE Int. Conf. on Control Applications, San Diego, TX, 89 94, [8] G.V. Raffo, M.G. Ortega, and F.R. Rubio, Backstepping/nonlinear H control for path tracking of a quadrotor unmanned aerial vehicle, Proc American Control Conf., Seattle, Washington, DC, June, [9] R. Xu and U. Ozguner, Sliding mode control of a quadrotor helicopter, Proc. 45th IEEE Conf. on Decision and Control, San Diego, CA, December 3 5, , [0] E. Altug, J.P. Ostrowski, and C.J. Taylor, Quadrotor control using dual camera visual feedback, Proc IEEE Int. Conf. on Robotics and Automation, 3, , [] S. Lupashin, A. Schollig, and M. Sherback, A simple learning strategy for high-speed quadrocopter multi-flips, IEEE Int. Conf. on Robotics and Automation, 200, [2] D. Mellinger and V. Kumar, Minimum snap trajectory generation and control for quadrotors, Proc. IEEE Int. Conf. on Robotics and Automation, Shanghai International Conference Center, May 20, [3] Schoellig et al., Synchronizing the motion of a quadrocopter to music, IEEE Int. Conf. on Robotics and Automation, 47 Anchorage Convention District, Anchorage, AK, May 200, [4] M. Achtelik, T. Zhang, K. Kiihnlenz, and M. Buss, Visual tracking and control of a quadcopter using a stereo camera system and inertial sensors, Proc. Int. Conf. on Mechatronics and Automation, Changchun, China, August 2009, [5] M. Huang, B. Xian, C. Diao, K. Yang, and Y. Feng, Adaptive tracking control of underactuated quadrotor unmanned aerial vehicles via backstepping, 200 American Control Conf., Baltimore, MD, June 30 July 02, [6] D.B. Lee Huang, T.C. Bur, D.M. Dawson, D. Shu, B. Xian, and E. Talicioglu, Robust tracking control of an underactuated quadrotor aerial-robot based on a parametric uncertain model, Proc. Int. Conf. on SMC, San Antonio, TX, October 2009, [7] Ascending technologies [Online], Available: asctec.de. Biographies Shafiqul Islam earned his Ph.D. degree in Electrical and Computer Engineering from Ottawa- Carleton Institute for Electrical and Computer Engineering at the University of Ottawa and Carleton University, Canada. He has a master in Control Engineering and B.Sc. in Electrical and Electronic Engineering. His research was funded by many organizations including Natural Sciences and Engineering Research Council of Canada NSERC), CMC Electronics, Carleton University, University of Ottawa, Lakehead University, etc. He was awarded Research Excellence in Science and Engineering from Carleton University, Canada, for his outstanding contribution to research and development. He currently holds prestigious NSERC Canada Postdoctoral Research Fellowship award for visiting national and international research laboratory. His research interests are robotics and control-unmanned ground and aerial vehicles, industrial manipulators; haptics and virtual reality and interactive networked and multiagent systems. Xiaoping P. Liu received his Ph.D. degree from the University of Alberta in He has been with the Department of Systems and Computer Engineering, Carleton University, Canada, since July 2002 and is currently a professor and Canada Research Chair. He has published more than 200 research articles and serves as an associate editor for several journals including IEEE/ASME Transactions on Mechatronics and IEEE Transactions on Automation Science and Engineering. He received a 2007 Carleton Research Achievement Award, a 2006 Province of Ontario Early Researcher Award, a 2006 Carty Research Fellowship, the Best Conference Paper Award of the 2006

9 IEEE International Conference on Mechatronics and Automation and a 2003 Province of Ontario Distinguished Researcher Award. He is a licensed member of the Professional Engineers of Ontario P.Eng.) and a senior member of IEEE. His research interests are interactive networked systems: teleoperation, telerobotics and telehaptics with applications to telemedicine; haptics with applications to medical simulations; robotics, control and intelligent Systems; context-aware smart networks and wireless sensor networks. Abdulmotaleb El Saddik a University Research Chair and Professor in the School of Electrical Engineering and Computer Science at the University of Ottawa, is an internationally recognized scholar who has made strong contributions to the knowledge and understanding of multimedia computing, communications and applications, particularly in the digitization, communication and security of the sense of touch, or haptics, which is a new medium that is significantly changing the way in which human-to-human and human computer interactions are performed. He has authored and co-authored four books and more than 400 publications. He has received research grants and contracts totaling more than 8 Mio. and has supervised more than 00 researchers. He received several international awards and is ACM Distinguished Scientist, Fellow of the Engineering Institute of Canada, and Fellow of the Canadian Academy of Engineers and Fellow of IEEE. His research interests are multimedia computing, communications and applications, particularly in the digitization, communication and security of the sense of touch, or haptics. 48

Adaptive Robust Control (ARC) for an Altitude Control of a Quadrotor Type UAV Carrying an Unknown Payloads

Adaptive Robust Control (ARC) for an Altitude Control of a Quadrotor Type UAV Carrying an Unknown Payloads 2 th International Conference on Control, Automation and Systems Oct. 26-29, 2 in KINTEX, Gyeonggi-do, Korea Adaptive Robust Control (ARC) for an Altitude Control of a Quadrotor Type UAV Carrying an Unknown

More information

Nonlinear Landing Control for Quadrotor UAVs

Nonlinear Landing Control for Quadrotor UAVs Nonlinear Landing Control for Quadrotor UAVs Holger Voos University of Applied Sciences Ravensburg-Weingarten, Mobile Robotics Lab, D-88241 Weingarten Abstract. Quadrotor UAVs are one of the most preferred

More information

Modeling and Sliding Mode Control of a Quadrotor Unmanned Aerial Vehicle

Modeling and Sliding Mode Control of a Quadrotor Unmanned Aerial Vehicle Modeling and Sliding Mode Control of a Quadrotor Unmanned Aerial Vehicle Nour BEN AMMAR, Soufiene BOUALLÈGUE and Joseph HAGGÈGE Research Laboratory in Automatic Control LA.R.A), National Engineering School

More information

Mathematical Modelling and Dynamics Analysis of Flat Multirotor Configurations

Mathematical Modelling and Dynamics Analysis of Flat Multirotor Configurations Mathematical Modelling and Dynamics Analysis of Flat Multirotor Configurations DENIS KOTARSKI, Department of Mechanical Engineering, Karlovac University of Applied Sciences, J.J. Strossmayera 9, Karlovac,

More information

Control of a Quadrotor Mini-Helicopter via Full State Backstepping Technique

Control of a Quadrotor Mini-Helicopter via Full State Backstepping Technique Proceedings of the 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 3-5, 006 Control of a Quadrotor Mini-Helicopter via Full State Backstepping Technique

More information

Nonlinear and Neural Network-based Control of a Small Four-Rotor Aerial Robot

Nonlinear and Neural Network-based Control of a Small Four-Rotor Aerial Robot Nonlinear and Neural Network-based Control of a Small Four-Rotor Aerial Robot Holger Voos Abstract Small four-rotor aerial robots, so called quadrotor UAVs, have an enormous potential for all kind of neararea

More information

Nonlinear Tracking Control of Underactuated Surface Vessel

Nonlinear Tracking Control of Underactuated Surface Vessel American Control Conference June -. Portland OR USA FrB. Nonlinear Tracking Control of Underactuated Surface Vessel Wenjie Dong and Yi Guo Abstract We consider in this paper the tracking control problem

More information

LQR and SMC Stabilization of a New Unmanned Aerial Vehicle

LQR and SMC Stabilization of a New Unmanned Aerial Vehicle World Academy of Science, Engineering Technology 58 9 LQR SMC Stabilization of a New Unmanned Aerial Vehicle Kaan T. Oner, Ertugrul Cetinsoy, Efe Sirimoglu, Cevdet Hancer, Taylan Ayken, Mustafa Unel Abstract

More information

Hover Control for Helicopter Using Neural Network-Based Model Reference Adaptive Controller

Hover Control for Helicopter Using Neural Network-Based Model Reference Adaptive Controller Vol.13 No.1, 217 مجلد 13 العدد 217 1 Hover Control for Helicopter Using Neural Network-Based Model Reference Adaptive Controller Abdul-Basset A. Al-Hussein Electrical Engineering Department Basrah University

More information

Simulation of Backstepping-based Nonlinear Control for Quadrotor Helicopter

Simulation of Backstepping-based Nonlinear Control for Quadrotor Helicopter APPLICATIONS OF MODELLING AND SIMULATION http://amsjournal.ams-mss.org eissn 2680-8084 VOL 2, NO. 1, 2018, 34-40 Simulation of Backstepping-based Nonlinear Control for Quadrotor Helicopter M.A.M. Basri*,

More information

ROBUST NEURAL NETWORK CONTROL OF A QUADROTOR HELICOPTER. Schulich School of Engineering, University of Calgary

ROBUST NEURAL NETWORK CONTROL OF A QUADROTOR HELICOPTER. Schulich School of Engineering, University of Calgary ROBUST NEURAL NETWORK CONTROL OF A QUADROTOR HELICOPTER C. Nicol,C.J.B. Macnab, A. Ramirez-Serrano Schulich School of Engineering, University of Calgary Department of Electrical and Computer Engineering

More information

Control and Navigation Framework for Quadrotor Helicopters

Control and Navigation Framework for Quadrotor Helicopters DOI 1.17/s1846-1-9789-z Control and Navigation Framework for Quadrotor Helicopters Amr Nagaty Sajad Saeedi Carl Thibault Mae Seto Howard Li Received: September 1 / Accepted: September 1 Springer Science+Business

More information

Quadrotor Modeling and Control

Quadrotor Modeling and Control 16-311 Introduction to Robotics Guest Lecture on Aerial Robotics Quadrotor Modeling and Control Nathan Michael February 05, 2014 Lecture Outline Modeling: Dynamic model from first principles Propeller

More information

QUADROTOR: FULL DYNAMIC MODELING, NONLINEAR SIMULATION AND CONTROL OF ATTITUDES

QUADROTOR: FULL DYNAMIC MODELING, NONLINEAR SIMULATION AND CONTROL OF ATTITUDES QUADROTOR: FULL DYNAMIC MODELING, NONLINEAR SIMULATION AND CONTROL OF ATTITUDES Somayeh Norouzi Ghazbi,a, Ali Akbar Akbari 2,a, Mohammad Reza Gharib 3,a Somaye_noroozi@yahoo.com, 2 Akbari@um.ac.ir, 3 mech_gharib@yahoo.com

More information

Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor

Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor Proceedings of the 2005 IEEE International Conference on Robotics and Automation Barcelona, Spain, April 2005 Backstepping and Sliding-mode Techniques Applied to an Indoor Micro Quadrotor Samir Bouabdallah

More information

Nonlinear Control of a Quadrotor Micro-UAV using Feedback-Linearization

Nonlinear Control of a Quadrotor Micro-UAV using Feedback-Linearization Proceedings of the 2009 IEEE International Conference on Mechatronics. Malaga, Spain, April 2009. Nonlinear Control of a Quadrotor Micro-UAV using Feedback-Linearization Holger Voos University of Applied

More information

IDETC STABILIZATION OF A QUADROTOR WITH UNCERTAIN SUSPENDED LOAD USING SLIDING MODE CONTROL

IDETC STABILIZATION OF A QUADROTOR WITH UNCERTAIN SUSPENDED LOAD USING SLIDING MODE CONTROL ASME 206 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC206 August 2-24, 206, Charlotte, North Carolina, USA IDETC206-60060 STABILIZATION

More information

Research on Balance of Unmanned Aerial Vehicle with Intelligent Algorithms for Optimizing Four-Rotor Differential Control

Research on Balance of Unmanned Aerial Vehicle with Intelligent Algorithms for Optimizing Four-Rotor Differential Control 2019 2nd International Conference on Computer Science and Advanced Materials (CSAM 2019) Research on Balance of Unmanned Aerial Vehicle with Intelligent Algorithms for Optimizing Four-Rotor Differential

More information

Multi-layer Flight Control Synthesis and Analysis of a Small-scale UAV Helicopter

Multi-layer Flight Control Synthesis and Analysis of a Small-scale UAV Helicopter Multi-layer Flight Control Synthesis and Analysis of a Small-scale UAV Helicopter Ali Karimoddini, Guowei Cai, Ben M. Chen, Hai Lin and Tong H. Lee Graduate School for Integrative Sciences and Engineering,

More information

A Model-Free Control System Based on the Sliding Mode Control Method with Applications to Multi-Input-Multi-Output Systems

A Model-Free Control System Based on the Sliding Mode Control Method with Applications to Multi-Input-Multi-Output Systems Proceedings of the 4 th International Conference of Control, Dynamic Systems, and Robotics (CDSR'17) Toronto, Canada August 21 23, 2017 Paper No. 119 DOI: 10.11159/cdsr17.119 A Model-Free Control System

More information

Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3)

Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) 22 American Control Conference Fairmont Queen Elizabeth Montréal Canada June 27-June 29 22 Nonlinear Robust Tracking Control of a Quadrotor UAV on SE(3) Taeyoung Lee Melvin Leok and N. Harris McClamroch

More information

Unit quaternion observer based attitude stabilization of a rigid spacecraft without velocity measurement

Unit quaternion observer based attitude stabilization of a rigid spacecraft without velocity measurement Proceedings of the 45th IEEE Conference on Decision & Control Manchester Grand Hyatt Hotel San Diego, CA, USA, December 3-5, 6 Unit quaternion observer based attitude stabilization of a rigid spacecraft

More information

Nonlinear Attitude and Position Control of a Micro Quadrotor using Sliding Mode and Backstepping Techniques

Nonlinear Attitude and Position Control of a Micro Quadrotor using Sliding Mode and Backstepping Techniques 3rd US-European Competition and Workshop on Micro Air Vehicle Systems (MAV7 & European Micro Air Vehicle Conference and light Competition (EMAV27, 17-21 September 27, Toulouse, rance Nonlinear Attitude

More information

ROBUST SECOND ORDER SLIDING MODE CONTROL

ROBUST SECOND ORDER SLIDING MODE CONTROL ROBUST SECOND ORDER SLIDING MODE CONTROL FOR A QUADROTOR CONSIDERING MOTOR DYNAMICS Nader Jamali Soufi Amlashi 1, Mohammad Rezaei 2, Hossein Bolandi 2 and Ali Khaki Sedigh 3 1 Department of Control Engineering,

More information

CONTROL OF ROBOT CAMERA SYSTEM WITH ACTUATOR S DYNAMICS TO TRACK MOVING OBJECT

CONTROL OF ROBOT CAMERA SYSTEM WITH ACTUATOR S DYNAMICS TO TRACK MOVING OBJECT Journal of Computer Science and Cybernetics, V.31, N.3 (2015), 255 265 DOI: 10.15625/1813-9663/31/3/6127 CONTROL OF ROBOT CAMERA SYSTEM WITH ACTUATOR S DYNAMICS TO TRACK MOVING OBJECT NGUYEN TIEN KIEM

More information

Improving Leader-Follower Formation Control Performance for Quadrotors. By Wesam M. Jasim Alrawi

Improving Leader-Follower Formation Control Performance for Quadrotors. By Wesam M. Jasim Alrawi Improving Leader-Follower Formation Control Performance for Quadrotors By Wesam M. Jasim Alrawi A thesis submitted for the degree of Doctor of Philosophy School of Computer Science and Electronic Engineering

More information

Visual Servoing for a Quadrotor UAV in Target Tracking Applications. Marinela Georgieva Popova

Visual Servoing for a Quadrotor UAV in Target Tracking Applications. Marinela Georgieva Popova Visual Servoing for a Quadrotor UAV in Target Tracking Applications by Marinela Georgieva Popova A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate

More information

Nonlinear Control of a Multirotor UAV with Suspended Load

Nonlinear Control of a Multirotor UAV with Suspended Load Nonlinear Control of a Multirotor UAV with Suspended Load Kristian Klausen, Thor I. Fossen, Tor Arne Johansen Centre for Autonomous Marine Operations and Systems (AMOS) Department of Engineering Cybernetics,

More information

Investigation of the Dynamics and Modeling of a Triangular Quadrotor Configuration

Investigation of the Dynamics and Modeling of a Triangular Quadrotor Configuration Investigation of the Dynamics and Modeling of a Triangular Quadrotor Configuration TONI AXELSSON Master s Thesis at Aerospace Engineering Supervisor: Arne Karlsson Examiner: Arne Karlsson ISSN 1651-7660

More information

Mathematical Modelling of Multirotor UAV

Mathematical Modelling of Multirotor UAV Mathematical Modelling of Multirotor UAV DENIS KOTARSKI, Mechanical Engineering, Karlovac University of Applied Sciences Trg J.J. Strossmayera 9, CROATIA, denis.kotarski@vuka.hr PETAR PILJEK, Faculty of

More information

ENHANCED PROPORTIONAL-DERIVATIVE CONTROL OF A MICRO QUADCOPTER

ENHANCED PROPORTIONAL-DERIVATIVE CONTROL OF A MICRO QUADCOPTER ENHANCED PROPORTIONAL-DERIVATIVE CONTROL OF A MICRO QUADCOPTER Norman L. Johnson and Kam K. Leang Department of Mechanical Engineering University of Nevada, Reno Reno, Nevada 897-312, USA ABSTRACT This

More information

Backstepping sliding mode controller improved with fuzzy logic: Application to the quadrotor helicopter

Backstepping sliding mode controller improved with fuzzy logic: Application to the quadrotor helicopter Archives of Control Sciences Volume 22(LVIII), 2012 No. 3, pages 255 282 Backstepping sliding mode controller improved with fuzzy logic: Application to the quadrotor helicopter SAMIR ZEGHLACHE, DJAMEL

More information

Mini coaxial rocket-helicopter: aerodynamic modeling, hover control, and implementation

Mini coaxial rocket-helicopter: aerodynamic modeling, hover control, and implementation Mini coaxial rocket-helicopter: aerodynamic modeling, hover control, and implementation E. S. Espinoza,2, O. Garcia, R. Lozano,3, and A. Malo Laboratoire Franco-Mexicain d Informatique et Automatique,

More information

Different Approaches of PID Control UAV Type Quadrotor

Different Approaches of PID Control UAV Type Quadrotor Different Approaches of PD Control UAV ype Quadrotor G. Szafranski, R. Czyba Silesian University of echnology, Akademicka St 6, Gliwice, Poland ABSRAC n this paper we focus on the different control strategies

More information

Dynamic Modeling of Fixed-Wing UAVs

Dynamic Modeling of Fixed-Wing UAVs Autonomous Systems Laboratory Dynamic Modeling of Fixed-Wing UAVs (Fixed-Wing Unmanned Aerial Vehicles) A. Noth, S. Bouabdallah and R. Siegwart Version.0 1/006 1 Introduction Dynamic modeling is an important

More information

Attitude Regulation About a Fixed Rotation Axis

Attitude Regulation About a Fixed Rotation Axis AIAA Journal of Guidance, Control, & Dynamics Revised Submission, December, 22 Attitude Regulation About a Fixed Rotation Axis Jonathan Lawton Raytheon Systems Inc. Tucson, Arizona 85734 Randal W. Beard

More information

Robot Control Basics CS 685

Robot Control Basics CS 685 Robot Control Basics CS 685 Control basics Use some concepts from control theory to understand and learn how to control robots Control Theory general field studies control and understanding of behavior

More information

Trajectory tracking & Path-following control

Trajectory tracking & Path-following control Cooperative Control of Multiple Robotic Vehicles: Theory and Practice Trajectory tracking & Path-following control EECI Graduate School on Control Supélec, Feb. 21-25, 2011 A word about T Tracking and

More information

Adaptive Trim and Trajectory Following for a Tilt-Rotor Tricopter Ahmad Ansari, Anna Prach, and Dennis S. Bernstein

Adaptive Trim and Trajectory Following for a Tilt-Rotor Tricopter Ahmad Ansari, Anna Prach, and Dennis S. Bernstein 7 American Control Conference Sheraton Seattle Hotel May 4 6, 7, Seattle, USA Adaptive Trim and Trajectory Following for a Tilt-Rotor Tricopter Ahmad Ansari, Anna Prach, and Dennis S. Bernstein Abstract

More information

Inversion Based Direct Position Control and Trajectory Following for Micro Aerial Vehicles

Inversion Based Direct Position Control and Trajectory Following for Micro Aerial Vehicles Inversion Based Direct Position Control and Trajectory Following for Micro Aerial Vehicles Markus W. Achtelik, Simon Lynen, Margarita Chli and Roland Siegwart Abstract In this work, we present a powerful,

More information

Quadrotors Flight Formation Control Using a Leader-Follower Approach*

Quadrotors Flight Formation Control Using a Leader-Follower Approach* 23 European Conference (ECC) July 7-9, 23, Zürich, Switzerland. Quadrotors Flight Formation Using a Leader-Follower Approach* D. A. Mercado, R. Castro and R. Lozano 2 Abstract In this paper it is presented

More information

Real-time Motion Control of a Nonholonomic Mobile Robot with Unknown Dynamics

Real-time Motion Control of a Nonholonomic Mobile Robot with Unknown Dynamics Real-time Motion Control of a Nonholonomic Mobile Robot with Unknown Dynamics TIEMIN HU and SIMON X. YANG ARIS (Advanced Robotics & Intelligent Systems) Lab School of Engineering, University of Guelph

More information

TTK4150 Nonlinear Control Systems Solution 6 Part 2

TTK4150 Nonlinear Control Systems Solution 6 Part 2 TTK4150 Nonlinear Control Systems Solution 6 Part 2 Department of Engineering Cybernetics Norwegian University of Science and Technology Fall 2003 Solution 1 Thesystemisgivenby φ = R (φ) ω and J 1 ω 1

More information

Revised Propeller Dynamics and Energy-Optimal Hovering in a Monospinner

Revised Propeller Dynamics and Energy-Optimal Hovering in a Monospinner Proceedings of the 4 th International Conference of Control, Dynamic Systems, and Robotics (CDSR'17) Toronto, Canada August 21 23, 2017 Paper No. 135 DOI: 10.11159/cdsr17.135 Revised Propeller Dynamics

More information

Autonomous Mobile Robot Design

Autonomous Mobile Robot Design Autonomous Mobile Robot Design Topic: Micro Aerial Vehicle Dynamics Dr. Kostas Alexis (CSE) Goal of this lecture The goal of this lecture is to derive the equations of motion that describe the motion of

More information

The PVTOL Aircraft. 2.1 Introduction

The PVTOL Aircraft. 2.1 Introduction 2 The PVTOL Aircraft 2.1 Introduction We introduce in this chapter the well-known Planar Vertical Take-Off and Landing (PVTOL) aircraft problem. The PVTOL represents a challenging nonlinear systems control

More information

Autonomous Helicopter Landing A Nonlinear Output Regulation Perspective

Autonomous Helicopter Landing A Nonlinear Output Regulation Perspective Autonomous Helicopter Landing A Nonlinear Output Regulation Perspective Andrea Serrani Department of Electrical and Computer Engineering Collaborative Center for Control Sciences The Ohio State University

More information

Adaptive position tracking of VTOL UAVs

Adaptive position tracking of VTOL UAVs Joint 48th IEEE Conference on Decision and Control and 8th Chinese Control Conference Shanghai, P.R. China, December 16-18, 009 Adaptive position tracking of VTOL UAVs Andrew Roberts and Abdelhamid Tayebi

More information

Mini-quadrotor Attitude Control based on Hybrid Backstepping & Frenet-Serret Theory

Mini-quadrotor Attitude Control based on Hybrid Backstepping & Frenet-Serret Theory Mini-quadrotor Attitude Control based on Hybrid Backstepping & Frenet-Serret Theory J. Colorado, A. Barrientos, Senior Member, IEEE, A. Martinez, B. Lafaverges, and J. Valente Abstract This paper is about

More information

NONLINEAR PATH CONTROL FOR A DIFFERENTIAL DRIVE MOBILE ROBOT

NONLINEAR PATH CONTROL FOR A DIFFERENTIAL DRIVE MOBILE ROBOT NONLINEAR PATH CONTROL FOR A DIFFERENTIAL DRIVE MOBILE ROBOT Plamen PETROV Lubomir DIMITROV Technical University of Sofia Bulgaria Abstract. A nonlinear feedback path controller for a differential drive

More information

Design and modelling of an airship station holding controller for low cost satellite operations

Design and modelling of an airship station holding controller for low cost satellite operations AIAA Guidance, Navigation, and Control Conference and Exhibit 15-18 August 25, San Francisco, California AIAA 25-62 Design and modelling of an airship station holding controller for low cost satellite

More information

Quadcopter Dynamics 1

Quadcopter Dynamics 1 Quadcopter Dynamics 1 Bréguet Richet Gyroplane No. 1 1907 Brothers Louis Bréguet and Jacques Bréguet Guidance of Professor Charles Richet The first flight demonstration of Gyroplane No. 1 with no control

More information

Aircraft Maneuver Regulation: a Receding Horizon Backstepping Approach

Aircraft Maneuver Regulation: a Receding Horizon Backstepping Approach Aircraft Maneuver Regulation: a Receding Horizon Backstepping Approach Giuseppe Notarstefano and Ruggero Frezza Abstract Coordinated flight is a nonholonomic constraint that implies no sideslip of an aircraft.

More information

Model Reference Adaptive Control of Underwater Robotic Vehicle in Plane Motion

Model Reference Adaptive Control of Underwater Robotic Vehicle in Plane Motion Proceedings of the 11th WSEAS International Conference on SSTEMS Agios ikolaos Crete Island Greece July 23-25 27 38 Model Reference Adaptive Control of Underwater Robotic Vehicle in Plane Motion j.garus@amw.gdynia.pl

More information

Position Control for a Class of Vehicles in SE(3)

Position Control for a Class of Vehicles in SE(3) Position Control for a Class of Vehicles in SE(3) Ashton Roza, Manfredi Maggiore Abstract A hierarchical design framework is presented to control the position of a class of vehicles in SE(3) that are propelled

More information

A Nonlinear Control Law for Hover to Level Flight for the Quad Tilt-rotor UAV

A Nonlinear Control Law for Hover to Level Flight for the Quad Tilt-rotor UAV Preprints of the 19th World Congress The International Federation of Automatic Control A Nonlinear Control Law for Hover to Level Flight for the Quad Tilt-rotor UAV Gerardo R. Flores-Colunga Rogelio Lozano-Leal

More information

Design and Implementation of an Unmanned Tail-sitter

Design and Implementation of an Unmanned Tail-sitter 1 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) Congress Center Hamburg Sept 8 - Oct, 1. Hamburg, Germany Design and Implementation of an Unmanned Tail-sitter Roman Bapst,

More information

A Blade Element Approach to Modeling Aerodynamic Flight of an Insect-scale Robot

A Blade Element Approach to Modeling Aerodynamic Flight of an Insect-scale Robot A Blade Element Approach to Modeling Aerodynamic Flight of an Insect-scale Robot Taylor S. Clawson, Sawyer B. Fuller Robert J. Wood, Silvia Ferrari American Control Conference Seattle, WA May 25, 2016

More information

Adaptive Nonlinear Hierarchical Control of a Novel Quad Tilt-Wing UAV

Adaptive Nonlinear Hierarchical Control of a Novel Quad Tilt-Wing UAV Adaptive Nonlinear Hierarchical Control of a Novel Quad Tilt-Wing UAV Yildiray Yildiz 1, Mustafa Unel and Ahmet Eren Demirel Abstract Position control of a novel unmanned aerial vehicle SUAVI (Sabanci

More information

Robust Adaptive Attitude Control of a Spacecraft

Robust Adaptive Attitude Control of a Spacecraft Robust Adaptive Attitude Control of a Spacecraft AER1503 Spacecraft Dynamics and Controls II April 24, 2015 Christopher Au Agenda Introduction Model Formulation Controller Designs Simulation Results 2

More information

Dynamic Modeling and Stabilization Techniques for Tri-Rotor Unmanned Aerial Vehicles

Dynamic Modeling and Stabilization Techniques for Tri-Rotor Unmanned Aerial Vehicles Technical Paper Int l J. of Aeronautical & Space Sci. 11(3), 167 174 (010) DOI:10.5139/IJASS.010.11.3.167 Dynamic Modeling and Stabilization Techniques for Tri-Rotor Unmanned Aerial Vehicles Dong-Wan Yoo*,

More information

Dynamic Model and Control of Quadrotor in the Presence of Uncertainties

Dynamic Model and Control of Quadrotor in the Presence of Uncertainties University of South Carolina Scholar Commons Theses and Dissertations 5-2017 Dynamic Model and Control of Quadrotor in the Presence of Uncertainties Courage Agho University of South Carolina Follow this

More information

Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties

Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties Australian Journal of Basic and Applied Sciences, 3(1): 308-322, 2009 ISSN 1991-8178 Adaptive Robust Tracking Control of Robot Manipulators in the Task-space under Uncertainties M.R.Soltanpour, M.M.Fateh

More information

Modelling of Opposed Lateral and Longitudinal Tilting Dual-Fan Unmanned Aerial Vehicle

Modelling of Opposed Lateral and Longitudinal Tilting Dual-Fan Unmanned Aerial Vehicle Modelling of Opposed Lateral and Longitudinal Tilting Dual-Fan Unmanned Aerial Vehicle N. Amiri A. Ramirez-Serrano R. Davies Electrical Engineering Department, University of Calgary, Canada (e-mail: namiri@ucalgary.ca).

More information

Path Following Controller for a Quadrotor Helicopter

Path Following Controller for a Quadrotor Helicopter Path Following Controller for a Quadrotor Helicopter Ashton Roza, Manfredi Maggiore Abstract A path following controller is presented for a quadrotor helicopter model. The controller relies on input dynamic

More information

Near-Hover Dynamics and Attitude Stabilization of an Insect Model

Near-Hover Dynamics and Attitude Stabilization of an Insect Model 21 American Control Conference Marriott Waterfront, Baltimore, MD, USA June 3-July 2, 21 WeA1.4 Near-Hover Dynamics and Attitude Stabilization of an Insect Model B. Cheng and X. Deng Abstract In this paper,

More information

Adaptive Nonlinear Hierarchical Control of a Quad Tilt-Wing UAV

Adaptive Nonlinear Hierarchical Control of a Quad Tilt-Wing UAV Adaptive Nonlinear Hierarchical Control of a Quad Tilt-Wing UAV Yildiray Yildiz 1, Mustafa Unel and Ahmet Eren Demirel Abstract Position control of a quad tilt-wing UAV via a nonlinear hierarchical adaptive

More information

Geometric path following control of a rigid body based on the stabilization of sets

Geometric path following control of a rigid body based on the stabilization of sets Preprints of the 19th World Congress The International Federation of Automatic Control Geometric path following control of a rigid body based on the stabilization of sets uri A. Kapitanyuk Sergey A. Chepinskiy

More information

TTK4190 Guidance and Control Exam Suggested Solution Spring 2011

TTK4190 Guidance and Control Exam Suggested Solution Spring 2011 TTK4190 Guidance and Control Exam Suggested Solution Spring 011 Problem 1 A) The weight and buoyancy of the vehicle can be found as follows: W = mg = 15 9.81 = 16.3 N (1) B = 106 4 ( ) 0.6 3 3 π 9.81 =

More information

AN INTEGRATOR BACKSTEPPING CONTROLLER FOR A STANDARD HELICOPTER YITAO LIU THESIS

AN INTEGRATOR BACKSTEPPING CONTROLLER FOR A STANDARD HELICOPTER YITAO LIU THESIS AN INEGRAOR BACKSEPPING CONROLLER FOR A SANDARD HELICOPER BY YIAO LIU HESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical and Computer Engineering

More information

Quadrotor Modeling and Control for DLO Transportation

Quadrotor Modeling and Control for DLO Transportation Quadrotor Modeling and Control for DLO Transportation Thesis dissertation Advisor: Prof. Manuel Graña Computational Intelligence Group University of the Basque Country (UPV/EHU) Donostia Jun 24, 2016 Abstract

More information

Chapter 2 Coordinate Systems and Transformations

Chapter 2 Coordinate Systems and Transformations Chapter 2 Coordinate Systems and Transformations 2.1 Coordinate Systems This chapter describes the coordinate systems used in depicting the position and orientation (pose) of the aerial robot and its manipulator

More information

Learning a Low-Level Motor Controller for UAVs

Learning a Low-Level Motor Controller for UAVs Learning a Low-Level Motor Controller for UAVs Joseph Lorenzetti Abstract Many control algorithms for Unmanned Aerial Vehicles (UAVs) have been proven to be effective for standard flight tasks under nominal

More information

Optimal Control of Twin Rotor MIMO System Using LQR Technique

Optimal Control of Twin Rotor MIMO System Using LQR Technique Optimal Control of Twin Rotor MIMO System Using LQR Technique Sumit Kumar Pandey and Vijaya Laxmi Abstract In this paper, twin rotor multi input multi output system (TRMS) is considered as a prototype

More information

Adaptive Control of a Quadrotor UAV Transporting a Cable-Suspended Load with Unknown Mass

Adaptive Control of a Quadrotor UAV Transporting a Cable-Suspended Load with Unknown Mass rd IEEE Conference on Decision and Control December -7,. Los Angeles, California, USA Adaptive Control of a Quadrotor UAV Transporting a Cable-Suspended Load with Unknown Mass Shicong Dai, Taeyoung Lee,

More information

Towards Intelligent Miniature Flying Robots

Towards Intelligent Miniature Flying Robots Research Collection Conference Paper Towards Intelligent Miniature Flying Robots Author(s): Bouabdallah, Samir; Siegwart, Roland Publication Date: 25 Permanent Link: https://doi.org/1.3929/ethz-a-18345

More information

Design and Control of Novel Tri-rotor UAV

Design and Control of Novel Tri-rotor UAV UKACC International Conference on Control Cardiff, UK, -5 September Design and Control of Novel Tri-rotor UAV Mohamed Kara Mohamed School of Electrical and Electronic Engineering The University of Manchester

More information

WE PROPOSE a new approach to robust control of robot

WE PROPOSE a new approach to robust control of robot IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 14, NO. 1, FEBRUARY 1998 69 An Optimal Control Approach to Robust Control of Robot Manipulators Feng Lin and Robert D. Brandt Abstract We present a new

More information

WITH the development of micro-electronic technologies,

WITH the development of micro-electronic technologies, World Academy of Science, Engineering and Technology, Vol:7, No:, odeling and Control of a Quadrotor UAV with Aerodynamic Concepts Wei Dong, Guo-ing Gu, iangyang hu, Han Ding International Science Index,

More information

Aerial Robotics. Vision-based control for Vertical Take-Off and Landing UAVs. Toulouse, October, 2 nd, Henry de Plinval (Onera - DCSD)

Aerial Robotics. Vision-based control for Vertical Take-Off and Landing UAVs. Toulouse, October, 2 nd, Henry de Plinval (Onera - DCSD) Aerial Robotics Vision-based control for Vertical Take-Off and Landing UAVs Toulouse, October, 2 nd, 2014 Henry de Plinval (Onera - DCSD) collaborations with P. Morin (UPMC-ISIR), P. Mouyon (Onera), T.

More information

Chapter 2 Review of Linear and Nonlinear Controller Designs

Chapter 2 Review of Linear and Nonlinear Controller Designs Chapter 2 Review of Linear and Nonlinear Controller Designs This Chapter reviews several flight controller designs for unmanned rotorcraft. 1 Flight control systems have been proposed and tested on a wide

More information

Problem 1: Ship Path-Following Control System (35%)

Problem 1: Ship Path-Following Control System (35%) Problem 1: Ship Path-Following Control System (35%) Consider the kinematic equations: Figure 1: NTNU s research vessel, R/V Gunnerus, and Nomoto model: T ṙ + r = Kδ (1) with T = 22.0 s and K = 0.1 s 1.

More information

Robot Dynamics - Rotary Wing UAS: Control of a Quadrotor

Robot Dynamics - Rotary Wing UAS: Control of a Quadrotor Robot Dynamics Rotary Wing AS: Control of a Quadrotor 5-85- V Marco Hutter, Roland Siegwart and Thomas Stastny Robot Dynamics - Rotary Wing AS: Control of a Quadrotor 7..6 Contents Rotary Wing AS. Introduction

More information

Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays

Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays IEEE TRANSACTIONS ON AUTOMATIC CONTROL VOL. 56 NO. 3 MARCH 2011 655 Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays Nikolaos Bekiaris-Liberis Miroslav Krstic In this case system

More information

Nonlinear control of underactuated vehicles with uncertain position measurements and application to visual servoing

Nonlinear control of underactuated vehicles with uncertain position measurements and application to visual servoing Nonlinear control of underactuated vehicles with uncertain position measurements and application to visual servoing Henry de Plinval Pascal Morin Philippe Mouyon Abstract The paper concerns the stabilization

More information

Dynamic Feedback Control for a Quadrotor Unmanned Aerial Vehicle

Dynamic Feedback Control for a Quadrotor Unmanned Aerial Vehicle Dynamic Feedback Control for a Quadrotor Unmanned Aerial Vehicle N. K. M Sirdi, Abdellah Mokhtari LSIS Laboratoire de Sciences de l Information et des Systèmes, CNRS UMR 6168. Dom. Univ. St- Jérôme, Av.

More information

Carrying a Flexible Payload with Multiple Flying Vehicles

Carrying a Flexible Payload with Multiple Flying Vehicles 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) November 3-7, 2013. Tokyo, Japan Carrying a Flexible Payload with Multiple Flying Vehicles Robin Ritz and Raffaello D Andrea

More information

A trajectory tracking control design for a skid-steering mobile robot by adapting its desired instantaneous center of rotation

A trajectory tracking control design for a skid-steering mobile robot by adapting its desired instantaneous center of rotation A trajectory tracking control design for a skid-steering mobile robot by adapting its desired instantaneous center of rotation Jae-Yun Jun, Minh-Duc Hua, Faïz Benamar Abstract A skid-steering mobile robot

More information

A Simulation Study for Practical Control of a Quadrotor

A Simulation Study for Practical Control of a Quadrotor A Siulation Study for Practical Control of a Quadrotor Jeongho Noh* and Yongkyu Song** *Graduate student, Ph.D. progra, ** Ph.D., Professor Departent of Aerospace and Mechanical Engineering, Korea Aerospace

More information

Passivity Based Control of a Quadrotor UAV

Passivity Based Control of a Quadrotor UAV Preprints of the 19th World Congress The International Federation of Automatic Control Cape Town, South Africa. August 24-29, 214 Passivity Based Control of a Quadrotor UAV C. Souza G. V. Raffo E. B. Castelan

More information

AROTORCRAFT-BASED unmanned aerial vehicle

AROTORCRAFT-BASED unmanned aerial vehicle 1392 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 20, NO. 5, SEPTEMBER 2012 Autonomous Flight of the Rotorcraft-Based UAV Using RISE Feedback and NN Feedforward Terms Jongho Shin, H. Jin Kim,

More information

A GLOBAL SLIDING MODE CONTROL WITH PRE-DETERMINED CONVERGENCE TIME DESIGN FOR REUSABLE LAUNCH VEHICLES IN REENTRY PHASE

A GLOBAL SLIDING MODE CONTROL WITH PRE-DETERMINED CONVERGENCE TIME DESIGN FOR REUSABLE LAUNCH VEHICLES IN REENTRY PHASE IAA-AAS-DyCoSS-4 -- A GLOBAL SLIDING MODE CONTROL WITH PRE-DETERMINED CONVERGENCE TIME DESIGN FOR REUSABLE LAUNCH VEHICLES IN REENTRY PHASE L. Wang, Y. Z. Sheng, X. D. Liu, and P. L. Lu INTRODUCTION This

More information

Adaptive Sliding Backstepping Control of Quadrotor UAV Attitude

Adaptive Sliding Backstepping Control of Quadrotor UAV Attitude Preprints of the 9th World Congress The International Federation of Automatic Control Cape Town, South Africa. August 4-9, 04 Adaptive Sliding Backstepping Control of Quadrotor UAV Attitude Tinashe Chingozha

More information

UAV Coordinate Frames and Rigid Body Dynamics

UAV Coordinate Frames and Rigid Body Dynamics Brigham Young University BYU ScholarsArchive All Faculty Publications 24-- UAV oordinate Frames and Rigid Body Dynamics Randal Beard beard@byu.edu Follow this and additional works at: https://scholarsarchive.byu.edu/facpub

More information

Observer Based Output Feedback Tracking Control of Robot Manipulators

Observer Based Output Feedback Tracking Control of Robot Manipulators 1 IEEE International Conference on Control Applications Part of 1 IEEE Multi-Conference on Systems and Control Yokohama, Japan, September 8-1, 1 Observer Based Output Feedback Tracking Control of Robot

More information

Quadrocopter Performance Benchmarking Using Optimal Control

Quadrocopter Performance Benchmarking Using Optimal Control Quadrocopter Performance Benchmarking Using Optimal Control Robin Ritz, Markus Hehn, Sergei Lupashin, and Raffaello D Andrea Abstract A numerical method for computing quadrocopter maneuvers between two

More information

Pitch Control of Flight System using Dynamic Inversion and PID Controller

Pitch Control of Flight System using Dynamic Inversion and PID Controller Pitch Control of Flight System using Dynamic Inversion and PID Controller Jisha Shaji Dept. of Electrical &Electronics Engineering Mar Baselios College of Engineering & Technology Thiruvananthapuram, India

More information

Kostas Alexis, George Nikolakopoulos and Anthony Tzes /10/$ IEEE 1636

Kostas Alexis, George Nikolakopoulos and Anthony Tzes /10/$ IEEE 1636 2 IEEE International Conference on Robotics and Automation Anchorage Convention District May 3-8, 2, Anchorage, Alaska, USA Design and Experimental Verification of a Constrained Finite Time Optimal Control

More information

Inverse optimal control for unmanned aerial helicopters with disturbances

Inverse optimal control for unmanned aerial helicopters with disturbances Received: 4 February 8 Revised: September 8 Accepted: September 8 DOI:./oca.47 RESEARCH ARTICLE Inverse optimal control for unmanned aerial helicopters with disturbances Haoxiang Ma Mou Chen Qingxian Wu

More information

NONLINEAR BACKSTEPPING DESIGN OF ANTI-LOCK BRAKING SYSTEMS WITH ASSISTANCE OF ACTIVE SUSPENSIONS

NONLINEAR BACKSTEPPING DESIGN OF ANTI-LOCK BRAKING SYSTEMS WITH ASSISTANCE OF ACTIVE SUSPENSIONS NONLINEA BACKSTEPPING DESIGN OF ANTI-LOCK BAKING SYSTEMS WITH ASSISTANCE OF ACTIVE SUSPENSIONS Wei-En Ting and Jung-Shan Lin 1 Department of Electrical Engineering National Chi Nan University 31 University

More information