Quadrotor UAVs formation suffers from the problems of model uncertainties, unknown external disturbances and collision between UAVs. In this paper, a safety control scheme is proposed based on prescribed performance. Firstly, the inequality constraint problem which will prevent collision between UAVs is transformed into the unconstrained problem according to the Prescribed Performance Function (PPF) and the error transfer function. To tackle model uncertainty, the neural network is used for approximation. The unknown approximation errors and the unknown external disturbances are treated as a compound disturbance, which is then estimated by the nonlinear disturbance observer. By using the transformed tracking errors and the values obtained by the observer, controllers are designed for the position and attitude subsystems, thus the collision between quadrotor UAVs is avoided. Then, the convergence of all the closed-loop system signals under the designed controller is proved by the Lyapunov method. Finally, numerical simulations verify the effectiveness of the proposed scheme.
[1] NAIR R R, BEHERA L, KUMAR S. Event-triggered finite-time integral sliding mode controller for consensus-based formation of multirobot systems with disturbances[J]. IEEE Transactions on Control Systems Technology, 2019, 27(1):39-47.
[2] LIAO R W, HAN L, DONG X W, et al. Finite-time formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input[J]. Neurocomputing, 2020, 415:234-246.
[3] KAMEL M A, YU X, ZHANG Y M. Formation control and coordination of multiple unmanned ground vehicles in normal and faulty situations:a review[J]. Annual Reviews in Control, 2020, 49:128-144.
[4] WANG Y Q, WU Q H, WANG Y. Distributed cooperative control for multiple quadrotor systems via dynamic surface control[J]. Nonlinear Dynamics, 2014, 75(3):513-527.
[5] LIU H, MA T, LEWIS F L, et al. Robust formation control for multiple quadrotors with nonlinearities and disturbances[J]. IEEE Transactions on Cybernetics, 2020, 50(4):1362-1371.
[6] ISLAM S, LIU P X, EL SADDIK A. Robust control of four-rotor unmanned aerial vehicle with disturbance uncertainty[J]. IEEE Transactions on Industrial Electronics, 2015, 62(3):1563-1571.
[7] ZHAO W B, LIU H, LEWIS F L, et al. Data-driven optimal formation control for quadrotor team with unknown dynamics[J]. IEEE Transactions on Cybernetics, 9486, PP(99):1-10.
[8] ZHAO W B, LIU H, LEWIS F L. Robust formation control for cooperative underactuated quadrotors via reinforcement learning[J]. IEEE Transactions on Neural Networks and Learning Systems, 3711, PP(99):1-11.
[9] ZHANG W Q, DONG C Y, RAN M P, et al. Fully distributed time-varying formation tracking control for multiple quadrotor vehicles via finite-time convergent extended state observer[J]. Chinese Journal of Aeronautics, 2020, 33(11):2907-2920.
[10] SONG Y D, HE L, ZHANG D, et al. Neuroadaptive fault-tolerant control of quadrotor UAVs:A more affordable solution[J]. IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(7):1975-1983.
[11] YU Z Q, LIU Z X, ZHANG Y M, et al. Decentralized fault-tolerant cooperative control of multiple UAVs with prescribed attitude synchronization tracking performance under directed communication topology[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(5):685-700.
[12] LIANG Y Q, DONG Q, ZHAO Y J. Adaptive leader-follower formation control for swarms of unmanned aerial vehicles with motion constraints and unknown disturbances[J]. Chinese Journal of Aeronautics, 2020, 33(11):2972-2988.
[13] WANG R, LIU J K. Adaptive formation control of quadrotor unmanned aerial vehicles with bounded control thrust[J]. Chinese Journal of Aeronautics, 2017, 30(2):807-817.
[14] HUANG Y F, LIU W, LI B, et al. Finite-time formation tracking control with collision avoidance for quadrotor UAVs[J]. Journal of the Franklin Institute, 2020, 357(7):4034-4058.
[15] JIA Z Y, WANG L L, YU J Q, et al. Distributed adaptive neural networks leader-following formation control for quadrotors with directed switching topologies[J]. ISA Transactions, 2019, 93:93-107.
[16] ZHANG W Q, DONG C Y, RAN M P, et al. Fully distributed time-varying formation tracking control for multiple quadrotor vehicles via finite-time convergent extended state observer[J]. Chinese Journal of Aeronautics, 2020, 33(11):2907-2920.
[17] GARCÍA-DELGADO L, DZUL A, SANTIBÁÑEZ V, et al. Quadrotors formation based on potential functions with obstacle avoidance[J]. IET Control Theory & Applications, 2012, 6(12):1787-1802.
[18] ARUL S H, MANOCHA D. DCAD:Decentralized collision avoidance with dynamics constraints for agile quadrotor swarms[J]. IEEE Robotics and Automation Letters, 2020, 5(2):1191-1198.
[19] DONG X W, HU G Q. Time-varying formation tracking for linear multiagent systems with multiple leaders[J]. IEEE Transactions on Automatic Control, 2017, 62(7):3658-3664.
[20] REKABI F, SHIRAZI F A, SADIGH M J. Distributed nonlinear H∞ control algorithm for multi-agent quadrotor formation flying[J]. ISA Transactions, 2020, 96:81-94.
[21] CHEN M, SHI P, LIM C C. Adaptive neural fault-tolerant control of a 3-DOF model helicopter system[J]. IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2016, 46(2):260-270.
[22] CHEN M, GE S S, REN B B. Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints[J]. Automatica, 2011, 47(3):452-465.
[23] LEI X S, LU P. The adaptive radial basis function neural network for small rotary-wing unmanned aircraft[J]. IEEE Transactions on Industrial Electronics, 2014, 61(9):4808-4815.
[24] BECHLIOULIS C P, ROVITHAKIS G A. Prescribed performance adaptive control for multi-input multi-output affine in the control nonlinear systems[J]. IEEE Transactions on Automatic Control, 2010, 55(5):1220-1226.
[25] CHEN M. Disturbance attenuation tracking control for wheeled mobile robots with skidding and slipping[J]. IEEE Transactions on Industrial Electronics, 2017, 64(4):3359-3368.
[26] VAMVOUDAKIS K G, LEWIS F L. Online actorcritic algorithm to solve the continuous-time infinite horizon optimal control problem[J]. Automatica, 2010, 46(5):878-888.
[27] ZHANG C, MA G F, SUN Y C, et al. Simple model-free attitude control design for flexible spacecraft with prescribed performance[J]. Proceedings of the Institution of Mechanical Engineers, Part G:Journal of Aerospace Engineering, 2019, 233(8):2760-2771.
[28] 刘金琨. 滑模变结构控制MATLAB仿真[M]. 2版. 北京:清华大学出版社, 2012. LIU J K. Sliding mode control design and matlab simulation[M]. 2nd ed. Beijing:Tsinghua University Press, 2012(in Chinese).
[29] YANG H L, JIANG B, YANG H, et al. Synchronization of multiple 3-DOF helicopters under actuator faults and saturations with prescribed performance[J]. ISA Transactions, 2018, 75:118-126.
CJA