基于SO(3)的多四旋翼无人机编队协同控制
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摘要
针对多四旋翼无人机系统的编队飞行问题,提出了基于特殊正交群SO(3)的协同控制设计方法.在给出编队空间队形和通信拓扑描述后,建立了多四旋翼无人机系统SO(3)控制模型.由于SO(3)与传统俯仰/偏航/滚转三通道模型具有不同的结构,文中进一步研究了SO(3)中无人机之间相对误差的表示方法,设计了适用于多飞行器的SO(3)控制器实现对编队和姿态的协同控制.推力控制器用于调节无人机的位置与速度,并在此基础上构造旋转矩阵形式的姿态协同指令.文中相应设计了SO(3)姿态控制器用于实现指令跟踪,最后从理论上对协同稳定性进行了分析.提出的控制方法能够使得多四旋翼无人机形成期望的队形,并且保持姿态一致进行稳定飞行.仿真结果验证了本文方法的有效性.
This paper is concerned with the formation control for multiple quadrotors, and a coordinated control strategy on SO(3) is proposed. Based on the descriptions of flight formation and communication topology, the control model of multiple quadrotors system on SO(3) is first presented. Because of the difference from the conventional model described by pitch/yaw/roll angles, this paper further studies the structure of relative error between quadrotors to formulate the thrust and attitude controllers on SO(3). The thrust controller is designed to coordinate position and velocity, and it is also employed to construct the coordinated attitude commands in the form of rotation matrix. Then, the SO(3) attitude controller is designed for command tracking, and the stability of the closed-loop system is analyzed by Lyapunov theory. It is proved that by applying the proposed control strategy, the multiple quadrotors could achieve the desired formation with stable attitude consensus. Simulation results show the effectiveness of our method.
This paper is concerned with the formation control for multiple quadrotors, and a coordinated control strategy on SO(3) is proposed. Based on the descriptions of flight formation and communication topology, the control model of multiple quadrotors system on SO(3) is first presented. Because of the difference from the conventional model described by pitch/yaw/roll angles, this paper further studies the structure of relative error between quadrotors to formulate the thrust and attitude controllers on SO(3). The thrust controller is designed to coordinate position and velocity, and it is also employed to construct the coordinated attitude commands in the form of rotation matrix. Then, the SO(3) attitude controller is designed for command tracking, and the stability of the closed-loop system is analyzed by Lyapunov theory. It is proved that by applying the proposed control strategy, the multiple quadrotors could achieve the desired formation with stable attitude consensus. Simulation results show the effectiveness of our method.
引文
[1] FAN Qiongjian, YANG Zhong, FANG Ting, et al. Research status of coordinated formation flight control for multi-UAVs[J]. Acta Aeronautica et Astronautica Sinica, 2009, 30(4):683–691.(樊琼剑,杨忠,方挺,等.多无人机协同编队飞行控制的研究现状[J].航空学报, 2009, 30(4):683–691.)
[2] DONG X, ZHOU Y, REN Z, et al. Time-varying formation tracking for second-order multi-agent systems subjected to switching topologies with application to quadrotor formation flying[J]. IEEE Transactions on Industrial Electronics, 2017, 64(6):5014–5024.
[3] LUO Delin, ZHANG Haiyang, XIE Rongzeng, et al. Unmanned aerial vehicles swarm conflict based on multi-agent system[J]. Control Theory&Applications, 2015, 32(11):1498–1504.(罗德林,张海洋,谢荣增,等.基于多agent系统的大规模无人机集群对抗[J].控制理论与应用, 2015, 32(11):1498–1504.)
[4] ZONG Qun, WANG Dandan, SHAO Shikai, et al. Research status and development of multi UAV coordinated formation flight control[J]. Journal of Harbin Institute of Technology, 2017, 49(3):1–13.(宗群,王丹丹,邵士凯,等.多无人机协同编队飞行控制研究现状及发展[J].哈尔滨工业大学学报, 2017, 49(3):1–13.)
[5] WU Chen, SU Jianbo. Trajectory tracking of quadrotor based on disturbance rejection control[J]. Control Theory&Applications, 2016,33(11):1422–1430.(吴琛,苏剑波.四旋翼飞行器的轨迹跟踪抗干扰控制[J].控制理论与应用, 2016, 33(11):1422–1430.)
[6] DU H, ZHU W, WEN G, et al. Finite-time formation control for a group of quadrotor aircraft[J]. Aerospace Science and Technology,2017, 69:609–616.
[7] SUN Miaoping, LIU Jingjing, NIAN Xiaohong, et al. Robust tracking control of a quad-rotor unmanned aerial vehicle via interval matrix[J]. Control Theory&Applications, 2017, 34(2):168–178.(孙妙平,刘静静,年晓红,等.基于区间矩阵的四旋翼无人机鲁棒跟踪控制[J].控制理论与应用, 2017, 34(2):168–178.)
[8] WANG R, LIU J. Adaptive formation control of quadrotor unmanned aerial vehicles with bounded control thrust[J]. Chinese Journal of Aeronautics, 2017, 30(2):807–817.
[9] GARCIA-DELGADO L, DZUL A, SANTIBANEZ V, et al. Quadrotors formation based on potential functions with obstacle avoidance[J]. IET Control Theory and Applications, 2012, 6(12):1787–1802.
[10] MA Siqian, DONG Chaoyang, MA Mingyu, et al. Formation reconfiguration control of quadrotor UAVs based on adaptive switchting topology[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(4):841–850.(马思迁,董朝阳,马鸣宇,等.基于自适应通讯拓扑四旋翼编队重构控制[J].北京航空航天大学学报, 2018, 44(4):841–850.)
[11] WANG Ning, WANG Yong, ER Meng-joo. Adaptive dynamic surface trajectory tracking control of a quadrotor unmanned aerial vehicle[J]. Control Theory&Applications, 2017, 34(9):1185–1194.(王宁,王永,余明裕.四旋翼飞行器自适应动态面轨迹跟踪控制[J].控制理论与应用, 2017, 34(9):1185–1194.)
[12] LIU Chao, TANG Shengjing, GUO Jie, et al. Design and application of intrinsic sliding-mode observer on SO(3)[J]. Systems Engineering and Electronics, 2017, 39(3):606–611.(刘超,唐胜景,郭杰,等. SO(3)上的内蕴滑模观测器设计与应用[J].系统工程与电子技术, 2017, 39(3):606–611.)
[13] ZHENG Zhong, SONG Shenmin. Rotation matrix based passive attitude tracking control of spacecraft without angular velocity measurements[J]. Control and Decision, 2014, 29(9):1628–1632.(郑重,宋申民.基于旋转矩阵描述的航天器无角速度测量姿态跟踪无源控制[J].控制与决策, 2014, 29(9):1628–1632.)
[14] LEE T, LEOKY M, MCCLAMROCH N H. Geometric tracking control of a quadrotor UAV on SE(3)[C]//The 49th IEEE Conference on Decision and Control(CDC). Atlanta, GA, USA:IEEE, 2010:5420–5425.
[15] LIU Jintao, WU Wenhai, LI Jing, et al. Sliding mode variable structure attitude controller design of quadrotor UAVs on SO(3)[J]. Control and Decision, 2016, 31(6):1057–1064.(刘锦涛,吴文海,李静,等.四旋翼无人机SO(3)滑模变结构姿态控制器设计[J].控制与决策, 2016, 31(6):1057–1064.)
[16] LIU Jintao, WU Wenhai, LI Jing, et al. Trajectory controller design for quadrotor UAVs on wind field disturbance[J]. Flight Dynamics,2016, 34(2):47–54.(刘锦涛,吴文海,李静,等.四旋翼无人机风场扰动轨迹控制器设计[J].飞行力学, 2016, 34(2):47–54.)
[17] KULUMANI S, POOLE C, LEE T, et al. Geometric adaptive control of attitude dynamics on SO(3)with state inequality constraints[C]//2016 American Control Conference(ACC). Boston, MA, USA:IEEE, 2016:4936–4941.
[18] OH K K, PARK M C, AHN H S. A survey of multi-agent formation control[J]. Automatica, 2015, 53:424–440.
[19] ZHU Xu, ZHANG Xunxun, YOU Jinyu, et al. Swarm control of UAV close formation based on information consensus[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(12):3919–3929.(朱旭,张逊逊,尤谨语,等.基于信息一致性的无人机紧密编队集结控制[J].航空学报, 2015, 36(12):3919–3929.)
[20] GENG Zhiyong. Finite time formation control for multiple vehicles based on pontryagin’s minimum principle[J]. Acta Automatica Sinica, 2017, 43(1):40–59.(耿志勇.基于庞特里亚金极小值原理的多运载体有限时间编队控制[J].自动化学报, 2017, 43(1):40–59.)
[21] PEREIRA P O, CUNHA R, CABECINHAS D, et al. Leader following trajectory planning:A trailer-like approach[J]. Automatica, 2017,75:77–87.
[22] RAN D, CHEN X, MISRA A K. Finite time coordinated formation control for spacecraft formation flying under directed communication topology[J]. Acta Astronautica, 2017, 136:125–136.
[23] QIU Huaxin, DUAN Haibin, FAN Yanming. Multiple unmanned aerial vehicle autonomous formation based on the behavior mechanism in pigeon flocks[J]. Control Theory&Applications, 2015, 32(10):1298–1304.(邱华鑫,段海滨,范彦铭.基于鸽群行为机制的多无人机自主编队[J].控制理论与应用, 2015, 32(10):1298–1304.)
[24] WANG Y, WU Q, WANG Y. Distributed cooperative control for multiple quadrotor systems via dynamic surface control[J]. Nonlinear Dynamics, 2014, 75(3):513–527.
[25] QIN J, YU C, ANDERSON B D O. On leaderless and leaderfollowing consensus for interacting clusters of second-order multiagent systems[J]. Automatica, 2016, 74:214–221.
[26] LIU Wei, ZHOU Shaolei, QI Yahui, et al. Distributed formation control for multiple unmanned aerial vehicles with directed switching communication topologies[J]. Control Theory&Applications, 2015,32(10):1422–1427.(刘伟,周绍磊,祁亚辉,等.有向切换通信拓扑下多无人机分布式编队控制[J].控制理论与应用, 2015, 32(10):1422–1427.)
[27] XUE Ruibin, SONG Jianmei, ZHANG Minqiang. Research on distributed multi-vehicle coordinated formation flight control with coupling time-delay and jointly-connected topologies[J]. Acta Armamentarii, 2015, 36(3):492–502.(薛瑞彬,宋建梅,张民强.具有时延及联合连通拓扑的多飞行器分布式协同编队飞行控制研究[J].兵工学报, 2015, 36(3):492–502.)
[28] DONG X, YU B, SHI Z, et al. Time-varying formation control for unmanned aerial vehicles:Theories and applications[J]. IEEE Transactions on Control Systems Technology, 2015, 23(1):340–348.
[29] LIU W, HUANG J. Event-triggered cooperative robust practical output regulation for a class of linear multi-agent systems[J]. Automatica, 2017, 85:158–164.
[30] ZHOU Shaolei, KANG Yuhang, SHI Xianjun, et al. Autonomous reconfiguration control method for multi-UAVs formation based on RQPSO-DMPC[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(10):1960–1971.(周绍磊,康宇航,史贤俊,等.基于RQPSO–DMPC的多无人机编队自主重构控制方法[J].北京航空航天大学学报, 2017, 43(10):1960–1971.)
[31] WENG S X, DONG Y, YANG T C. Coordinated attitude motion control of multiple rigid bodies on manifold SO(3)[J]. IET Control Theory and Applications, 2013, 7(16):1984–1991.
[2] DONG X, ZHOU Y, REN Z, et al. Time-varying formation tracking for second-order multi-agent systems subjected to switching topologies with application to quadrotor formation flying[J]. IEEE Transactions on Industrial Electronics, 2017, 64(6):5014–5024.
[3] LUO Delin, ZHANG Haiyang, XIE Rongzeng, et al. Unmanned aerial vehicles swarm conflict based on multi-agent system[J]. Control Theory&Applications, 2015, 32(11):1498–1504.(罗德林,张海洋,谢荣增,等.基于多agent系统的大规模无人机集群对抗[J].控制理论与应用, 2015, 32(11):1498–1504.)
[4] ZONG Qun, WANG Dandan, SHAO Shikai, et al. Research status and development of multi UAV coordinated formation flight control[J]. Journal of Harbin Institute of Technology, 2017, 49(3):1–13.(宗群,王丹丹,邵士凯,等.多无人机协同编队飞行控制研究现状及发展[J].哈尔滨工业大学学报, 2017, 49(3):1–13.)
[5] WU Chen, SU Jianbo. Trajectory tracking of quadrotor based on disturbance rejection control[J]. Control Theory&Applications, 2016,33(11):1422–1430.(吴琛,苏剑波.四旋翼飞行器的轨迹跟踪抗干扰控制[J].控制理论与应用, 2016, 33(11):1422–1430.)
[6] DU H, ZHU W, WEN G, et al. Finite-time formation control for a group of quadrotor aircraft[J]. Aerospace Science and Technology,2017, 69:609–616.
[7] SUN Miaoping, LIU Jingjing, NIAN Xiaohong, et al. Robust tracking control of a quad-rotor unmanned aerial vehicle via interval matrix[J]. Control Theory&Applications, 2017, 34(2):168–178.(孙妙平,刘静静,年晓红,等.基于区间矩阵的四旋翼无人机鲁棒跟踪控制[J].控制理论与应用, 2017, 34(2):168–178.)
[8] WANG R, LIU J. Adaptive formation control of quadrotor unmanned aerial vehicles with bounded control thrust[J]. Chinese Journal of Aeronautics, 2017, 30(2):807–817.
[9] GARCIA-DELGADO L, DZUL A, SANTIBANEZ V, et al. Quadrotors formation based on potential functions with obstacle avoidance[J]. IET Control Theory and Applications, 2012, 6(12):1787–1802.
[10] MA Siqian, DONG Chaoyang, MA Mingyu, et al. Formation reconfiguration control of quadrotor UAVs based on adaptive switchting topology[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44(4):841–850.(马思迁,董朝阳,马鸣宇,等.基于自适应通讯拓扑四旋翼编队重构控制[J].北京航空航天大学学报, 2018, 44(4):841–850.)
[11] WANG Ning, WANG Yong, ER Meng-joo. Adaptive dynamic surface trajectory tracking control of a quadrotor unmanned aerial vehicle[J]. Control Theory&Applications, 2017, 34(9):1185–1194.(王宁,王永,余明裕.四旋翼飞行器自适应动态面轨迹跟踪控制[J].控制理论与应用, 2017, 34(9):1185–1194.)
[12] LIU Chao, TANG Shengjing, GUO Jie, et al. Design and application of intrinsic sliding-mode observer on SO(3)[J]. Systems Engineering and Electronics, 2017, 39(3):606–611.(刘超,唐胜景,郭杰,等. SO(3)上的内蕴滑模观测器设计与应用[J].系统工程与电子技术, 2017, 39(3):606–611.)
[13] ZHENG Zhong, SONG Shenmin. Rotation matrix based passive attitude tracking control of spacecraft without angular velocity measurements[J]. Control and Decision, 2014, 29(9):1628–1632.(郑重,宋申民.基于旋转矩阵描述的航天器无角速度测量姿态跟踪无源控制[J].控制与决策, 2014, 29(9):1628–1632.)
[14] LEE T, LEOKY M, MCCLAMROCH N H. Geometric tracking control of a quadrotor UAV on SE(3)[C]//The 49th IEEE Conference on Decision and Control(CDC). Atlanta, GA, USA:IEEE, 2010:5420–5425.
[15] LIU Jintao, WU Wenhai, LI Jing, et al. Sliding mode variable structure attitude controller design of quadrotor UAVs on SO(3)[J]. Control and Decision, 2016, 31(6):1057–1064.(刘锦涛,吴文海,李静,等.四旋翼无人机SO(3)滑模变结构姿态控制器设计[J].控制与决策, 2016, 31(6):1057–1064.)
[16] LIU Jintao, WU Wenhai, LI Jing, et al. Trajectory controller design for quadrotor UAVs on wind field disturbance[J]. Flight Dynamics,2016, 34(2):47–54.(刘锦涛,吴文海,李静,等.四旋翼无人机风场扰动轨迹控制器设计[J].飞行力学, 2016, 34(2):47–54.)
[17] KULUMANI S, POOLE C, LEE T, et al. Geometric adaptive control of attitude dynamics on SO(3)with state inequality constraints[C]//2016 American Control Conference(ACC). Boston, MA, USA:IEEE, 2016:4936–4941.
[18] OH K K, PARK M C, AHN H S. A survey of multi-agent formation control[J]. Automatica, 2015, 53:424–440.
[19] ZHU Xu, ZHANG Xunxun, YOU Jinyu, et al. Swarm control of UAV close formation based on information consensus[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(12):3919–3929.(朱旭,张逊逊,尤谨语,等.基于信息一致性的无人机紧密编队集结控制[J].航空学报, 2015, 36(12):3919–3929.)
[20] GENG Zhiyong. Finite time formation control for multiple vehicles based on pontryagin’s minimum principle[J]. Acta Automatica Sinica, 2017, 43(1):40–59.(耿志勇.基于庞特里亚金极小值原理的多运载体有限时间编队控制[J].自动化学报, 2017, 43(1):40–59.)
[21] PEREIRA P O, CUNHA R, CABECINHAS D, et al. Leader following trajectory planning:A trailer-like approach[J]. Automatica, 2017,75:77–87.
[22] RAN D, CHEN X, MISRA A K. Finite time coordinated formation control for spacecraft formation flying under directed communication topology[J]. Acta Astronautica, 2017, 136:125–136.
[23] QIU Huaxin, DUAN Haibin, FAN Yanming. Multiple unmanned aerial vehicle autonomous formation based on the behavior mechanism in pigeon flocks[J]. Control Theory&Applications, 2015, 32(10):1298–1304.(邱华鑫,段海滨,范彦铭.基于鸽群行为机制的多无人机自主编队[J].控制理论与应用, 2015, 32(10):1298–1304.)
[24] WANG Y, WU Q, WANG Y. Distributed cooperative control for multiple quadrotor systems via dynamic surface control[J]. Nonlinear Dynamics, 2014, 75(3):513–527.
[25] QIN J, YU C, ANDERSON B D O. On leaderless and leaderfollowing consensus for interacting clusters of second-order multiagent systems[J]. Automatica, 2016, 74:214–221.
[26] LIU Wei, ZHOU Shaolei, QI Yahui, et al. Distributed formation control for multiple unmanned aerial vehicles with directed switching communication topologies[J]. Control Theory&Applications, 2015,32(10):1422–1427.(刘伟,周绍磊,祁亚辉,等.有向切换通信拓扑下多无人机分布式编队控制[J].控制理论与应用, 2015, 32(10):1422–1427.)
[27] XUE Ruibin, SONG Jianmei, ZHANG Minqiang. Research on distributed multi-vehicle coordinated formation flight control with coupling time-delay and jointly-connected topologies[J]. Acta Armamentarii, 2015, 36(3):492–502.(薛瑞彬,宋建梅,张民强.具有时延及联合连通拓扑的多飞行器分布式协同编队飞行控制研究[J].兵工学报, 2015, 36(3):492–502.)
[28] DONG X, YU B, SHI Z, et al. Time-varying formation control for unmanned aerial vehicles:Theories and applications[J]. IEEE Transactions on Control Systems Technology, 2015, 23(1):340–348.
[29] LIU W, HUANG J. Event-triggered cooperative robust practical output regulation for a class of linear multi-agent systems[J]. Automatica, 2017, 85:158–164.
[30] ZHOU Shaolei, KANG Yuhang, SHI Xianjun, et al. Autonomous reconfiguration control method for multi-UAVs formation based on RQPSO-DMPC[J]. Journal of Beijing University of Aeronautics and Astronautics, 2017, 43(10):1960–1971.(周绍磊,康宇航,史贤俊,等.基于RQPSO–DMPC的多无人机编队自主重构控制方法[J].北京航空航天大学学报, 2017, 43(10):1960–1971.)
[31] WENG S X, DONG Y, YANG T C. Coordinated attitude motion control of multiple rigid bodies on manifold SO(3)[J]. IET Control Theory and Applications, 2013, 7(16):1984–1991.
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