AlgoTime-Varying Formation-Containment Tracking Control for Unmanned Aerial Vehicle Swarm Systems with Switching Topologies and a Non-Cooperative Target

doi:10.1007/s12204-024-2728-x

Abstract

Abstract: This paper studies the time-varying formation-containment tracking control problems for unmanned aerial vehicle (UAV) swarm systems with switching topologies and a non-cooperative target, where the UAV swarm systems consist of one tracking-leader, several formation-leaders, and followers. The formation-leaders are required to accomplish a predefined time-varying formation and track the desired trajectory of the tracking-leader, and the states of the followers should converge to the convex hull spanned by those of the formation-leaders. First, a formation-containment tracking protocol is proposed with the neighboring relative information, and the feasibilit condition for formation-containment tracking and the algebraic Riccati equation are given. Then, the stability of the control system with the designed control protocol is proved by constructing a reasonable Lyapunov function. Finally, the simulation examples are applied to verify the effectiveness of the theoretical results. The simulation results show that both the formation tracking error and the containment error are convergent, so the system can complete the formation containment tracking control well. In the actual battlefield, combat UAVs need to chase and attack hostile UAVs, but sometimes when multiple UAVs work together for military interception, formationcontainment tracking control will occur.

Key words: formation-containment tracking control, switching topology, unmanned aerial vehicle (UAV)

摘要： 本文研究了具有切换拓扑和非合作目标的无人机集群系统的时变编队合围跟踪控制问题，其中无人机集群系统由一个跟踪领导者、多个编队领导者和跟随者组成。编队领导者需要去完成预定的时变编队并追踪上跟踪领导者期望的轨迹，并且跟随者的状态收敛到编队领导者的状态所形成的凸包内。首先，提出了一种包含相邻相对信息的编队合围跟踪协议，且给出了编队跟踪的可行性条件和代数黎卡提方程；然后，通过构造合理的李雅普诺夫函数，证明了所设计控制协议下控制系统的稳定性。最后，通过仿真算例验证了理论结果的有效性。仿真结果表明，编队跟踪误差和合围误差都是收敛的，从而系统可以很好地完成编队合围跟踪控制。实际战场上，战斗无人机需要追逐和攻击敌对无人机，但有时多无人机协同作战进行军事拦截时，就会出现编队合围跟踪控制。

关键词: 编队合围跟踪控制, 切换拓扑，无人机

CLC Number:

TP273

WU Xiaojing^∗(武晓晶), CAO Tongyao (曹童瑶), ZHEN Ran (甄然), LI Zhijie (李志杰). AlgoTime-Varying Formation-Containment Tracking Control for Unmanned Aerial Vehicle Swarm Systems with Switching Topologies and a Non-Cooperative Target[J]. J Shanghai Jiaotong Univ Sci, 2024, 29(4): 689-701.

References

[1] HE W, ZHANG S. Control design for nonlinear flexible wings of a robotic aircraft [J]. IEEE Transactions on Control Systems Technology, 2017, 25(1): 351-357. [2] HAN J L, CHEN Y Q. Multiple UAV formations for cooperative source seeking and contour mapping of a radiative signal field [J]. Journal of Intelligent & Robotic Systems, 2014, 74(1): 323-332. [3] WILLIAMSON W R, ABDEL-HAFEZ M F, RHEE I, et al. An instrumentation system applied to formation flight [J]. IEEE Transactions on Control Systems Technology, 2007, 15(1): 75-85. [4] MAZA I, KONDAK K, BERNARD M, et al. MultiUAV cooperation and control for load transportation and deployment [J]. Journal of Intelligent and Robotic Systems, 2010, 57(1): 417-449. [5] SUH J, YOU S, CHOI S, et al. Vision-based coordinated localization for mobile sensor networks [J]. IEEE Transactions on Automation Science and Engineering, 2016, 13(2): 611-620. [6] YUN B, CHEN B M, LUM K Y, et al. Design and implementation of a leader-follower cooperative control system for unmanned helicopters [J]. Journal of Control Theory and Applications, 2010, 8(1): 61-68. [7] LI N H M, LIU H H T. Formation UAV flight control using virtual structure and motion synchronization [C]//2008 American Control Conference. Seattle: IEEE, 2008: 1782-1787. [8] QIU H X, DUAN H B, FAN Y M. Multiple unmanned aerial vehicle autonomous formation based on the behavior mechanism in pigeon flocks [J]. Control Theory & Applications, 2015, 32(10): 1298-1304 (in Chinese). [9] KURIKI Y, NAMERIKAWA T. Consensus-based cooperative formation control with collision avoidance for a multi-UAV system [C]//2014 American Control Conference. Portland: IEEE, 2014: 2077-2082. [10] WANG P, ZHANG Z F, CAO M C, et al. Research status and development of multi-UAVs formation based on consensus [J]. Ship Electronic Engineering, 2017, 37(9): 1-9 (in Chinese). [11] ABDESSAMEUD A, TAYEBI A. Formation control of VTOL Unmanned Aerial Vehicles with communication delays [J]. Automatica, 2011, 47(11): 2383-2394. [12] WANG D D, ZONG Q, ZHANG B Y. Distributed adaptive finite-time formation control of multiple UAV helicopter system [C]//2018 37th Chinese ControlConference. Wuhan: IEEE, 2018: 2631-2636. [13] HUA Y Z, DONG X W, LI Q D, et al. Fault-tolerant time-varying formation control for second-order multiagent systems with directed topologies [C]//2017 13th IEEE International Conference on Control & Automation. Ohrid: IEEE, 2017: 467-472. [14] ZHENG Y S, ZHAO Q, MA J Y, et al. Second-order consensus of hybrid multi-agent systems [J]. Systems & Control Letters, 2019, 125: 51-58. [15] HOSSEINZADEH YAMCHI M, MAHBOOBI ESFANJANI R. Distributed predictive formation control of networked mobile robots subject to communication delay [J]. Robotics and Autonomous Systems, 2017, 91: 194-207. [16] JI X K, HAI J T, LUO W G, et al. Obstacle avoidance in multi-agent formation process based on deep reinforcement learning [J]. Journal of Shanghai Jiao Tong University (Science), 2021, 26(5): 680-685. [17] WANG J, SHI L R. Semi-global consensus problems of discrete-time multi-agent systems in the presence of input constraints [J]. Journal of Shanghai Jiao Tong University (Science), 2020, 25(3): 288-298. [18] WANG P, JIA Y M. Distributed containment control of second-order multi-agent systems with inherent nonlinear dynamics [J]. IET Control Theory & Applications, 2014, 8(4): 277-287. [19] LI T, LI Z P, FEI S M, et al. Second-order eventtriggered adaptive containment control for a class of multi-agent systems [J]. ISA Transactions, 2020, 96: 132-142. [20] LI Z K, REN W, LIU X D, et al. Distributed containment control of multi-agent systems with general linear dynamics in the presence of multiple leaders [J]. International Journal of Robust and Nonlinear Control, 2013, 23(5): 534-547. [21] LI P Y, JABBARI F, SUN X M. Containment control of multi-agent systems with input saturation and unknown leader inputs [J]. Automatica, 2021, 130: 109677. [22] WANG Y Q, WU Q H, WANG Y. Containment control for multiple quadrotors with stationary leaders under directed graphs [C]//2012 IEEE 51st IEEE Conference on Decision and Control. Maui: IEEE, 2012: 2781-2786. [23] DONG X W, HUA Y Z, ZHOU Y, et al. Theory and experiment on formation-containment control of multiple multirotor unmanned aerial vehicle systems [J]. IEEE Transactions on Automation Science and Engineering, 2019, 16(1): 229-240. [24] CHEN L M, LI C J, GUO Y N, et al. Formationcontainment control of multi-agent systems with communication delays [J]. ISA Transactions, 2022, 128(Pt A): 32-43. [25] DONG X W, SHI Z Y, LU G, et al. Formationcontainment analysis and design for high-order linear time-invariant swarm systems [J]. International Journal of Robust and Nonlinear Control, 2015, 25(17): 3439-3456. [26] ZHANG J X, SU H S. Formation-containment control for multi-agent systems with sampled data and time delays [J]. Neurocomputing, 2021, 424: 125-131. [27] GAO Z Y, ZHANG H G, WANG Y C, et al. Timevarying output formation-containment control for homogeneous/heterogeneous descriptor fractional-order multi-agent systems [J]. Information Sciences, 2021, 567: 146-166. [28] CAI Y L, ZHANG H G, WANG Y C, et al. Adaptive bipartite fixed-time time-varying output formationcontainment tracking of heterogeneous linear multiagent systems [J]. IEEE Transactions on Neural Networks and Learning Systems, 2022, 33(9): 4688-4698. [29] XU B, WANG Z Y, LI W H, et al. Distributed robust model predictive control-based formation-containment tracking control for autonomous underwater vehicles [J]. Ocean Engineering, 2023, 283: 115210. [30] HUA Y Z, DONG X W, HAN L, et al. Formationcontainment tracking for general linear multi-agent systems with a tracking-leader of unknown control input [J]. Systems & Control Letters, 2018, 122: 67-76. [31] LIAO R W, HAN L, DONG X W, et al. Finitetime formation-containment tracking for second-order multi-agent systems with a virtual leader of fully unknown input [J]. Neurocomputing, 2020, 415: 234-246. [32] LU Y Z, DONG X W, LI Q D, et al. Time-varying group formation-containment tracking control for general linear multiagent systems with unknown inputs [J]. IEEE Transactions on Cybernetics, 2022, 52(10): 11055-11067. [33] ZHANG X Y, WU J, ZHAN X S, et al. Observer-based adaptive time-varying formation-containment tracking for multiagent system with bounded unknown input [J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2023, 53(3): 1479-1491. [34] CHEN L J, HAN T, XIAO B, et al. Predefined-time hierarchical controller-estimator time-varying formationcontainment tracking for multiple Euler-Lagrange systems with two-layer leaders [J]. Journal of the Franklin Institute, 2023, 360(7): 5242-5266. [35] WEI Z Q, WENG Z M, HUA Y Z, et al. Formationcontainment tracking control for heterogeneous unmanned swarm systems with switching topologies [J]. Acta Aeronautica ET Astronautica Sinica, 2021, 44(2): 252-267 (in Chinese). [36] NI W, CHENG D Z. Leader-following consensus of multi-agent systems under fixed and switching topologies [J]. Systems & Control Letters, 2010, 59(3/4): 209-217. [37] ZHENG R H, LIU Y H, SUN D. Enclosing a target by nonholonomic mobile robots with bearing-only measurements [J]. Automatica, 2015, 53: 400-407.