文章快速检索 高级检索

1. 南开大学津南校区 计算机与控制工程学院, 天津 300353;
2. 天津市智能机器人技术重点实验室, 天津 300353

A distributed formation control method formultiple nonholonomic mobile robots
LI Miao1,2, LIU Zhongxin1,2, CHEN Zengqiang1,2
1. College of Computer and Control Engineer, Jinnan Campus, Nankai University, Tianjin 300353, China;
2. Tianjin Key Laboratory of Intelligent Robotics, Tianjin 300353, China
Abstract: This paper addresses the algorithm of formation control for multiple nonholonomic mobile robots. The reference trajectory was represented by a virtual leader whose states were available to a subset of the following mobile robots and the robots only interacted with each other locally. Coordinate transformation was proposed to convert the formation control problem for multiple nonholonomic mobile robots into a state consensus problem. Under the restriction of persistent excitation on reference trajectories, distributed control laws were proposed for achieving the formation control objectives. Using the Lyapunov function and graph theory, rigorous proofs show that the group of mobile robots can exponentially converge to a desired geometric formation pattern and its centroid can move along the reference trajectory. The validity of the proposed control method is verified by numerical simulation.
Key words: nonholonomic mobile robots     formation control     consensus     distributed control

1 问题的提出

 图 1 移动机器人示意图 Fig. 1 The sketch of mobile robot
 (1)

 (2)

 (3)

 (4)
 (5)
 (6)
 (7)

2 分布式控制算法 2.1 控制器的设计

 (8)

 (9)

 (10)

 (11)

 (12)
 (13)
 (14)

 (15)
 (16)

 图 2 移动机器人1控制原理框图 Fig. 2 The control principle block diagram of mobile robot 1
2.2 稳定性分析

 (17)

，把式 (17) 整理成矩阵形式，那么就得到了一阶子系统式 (12) 所对应的闭环系统的表达式：

 (18)

V1求导可得

tT1时，V1(x)=0。因为L+B>0，由V1定义可得x1i=x10(1≤in)，此时有u1i=u10(1≤in)。

 (19)

1) 证明当tT1时，是有界的。

 (20)

 (21)

V2沿着轨迹式 (19) 求导可得

 (22)

 (23)

 (24)

2) 证明当t>T1时，指数收敛于零。

 (25)

 (26)

3 仿真结果分析

 图 3 移动机器人编队运动轨迹 Fig. 3 Trajectory of tracking of mobile robots formation
 图 4 移动机器人控制输入ω Fig. 4 The control input ω of the mobile robots
 图 5 移动机器人控制输入v Fig. 5 control input v of the mobile robots
 图 6 航角误差θe Fig. 6 Heading errors θe
 图 7 X轴方向的位置误差xe Fig. 7 Position errors in X coordinates
 图 8 Y轴方向的位置误差ye Fig. 8 Position errors in Y coordinates
4 结束语

 [1] BALCH T, ARKIN R C. Behavior-based formation control for multirobot teams[J]. IEEE transactions on robotics and automation, 1998, 14(6): 926-939. DOI:10.1109/70.736776. [2] SHAO J, XIE G M, WANG L. Leader-following formation control of multiple mobile vehicles[J]. IET control theory & applications, 2007, 1(2): 545-552. [3] DESAI J P, OSTROWSKI J P, KUMAR V. Modeling and control of formations of nonholonomic mobile robots[J]. IEEE transactions on robotics and automation, 2001, 17(6): 905-908. DOI:10.1109/70.976023. [4] TAN K H, LEWIS M A. Virtual structures for high-precision cooperative mobile robotic control[C]//Proceedings of the 1996 IEEE/RSJ International Conference Intelligent Robots and Systems'96. Osaka, Japan, 1996: 132-139. [5] KHATIB O. Real-time obstacle avoidance for manipulators and mobile robots[J]. International journal of robotics research, 1986, 5(1): 90-98. DOI:10.1177/027836498600500106. [6] ZHAI G, TAKEDA J, IMAE J, et al. Towards consensus in networked non-holonomic systems[J]. IET control theory & applications, 2010, 4(10): 2212-2218. [7] YUAN Z P, WANG Z P, CHEN Q J. Trajectory tracking control of a nonholonomic mobile robot[C]//Proceedings of the 8th IEEE International Conference on Control and Automation. Xiamen, China, 2010: 2207-2211. [8] 袁健, 唐功友. 采用一致性算法与虚拟结构的多自主水下航行器编队控制[J]. 智能系统学报, 2011, 6 (3): 248-253. YUAN Jian, TANG Gongyou. Formation control of autonomous underwater vehicles with consensus algorithms and virtual structure[J]. CAAI transactions on intelligent systems, 2011, 6(3): 248-253. [9] CHEN Lei, MA Baoli. A nonlinear formation control of wheeled mobile robots with virtual structure approach[C]//Proceedings of the 34th Chinese Control Conference. Hangzhou, China, 2015: 1080-1085. [10] 王中林, 刘忠信, 陈增强, 等. 一种多智能体领航跟随编队新型控制器的设计[J]. 智能系统学报, 2014, 9 (3): 298-306. WANG Zhonglin, LIU Zhongxin, CHEN Zengqiang, et al. A kind of new type controller for multi-agent leader-follower formation[J]. CAAI transactions on intelligent systems, 2014, 9(3): 298-306. [11] DONG Wenjie, FARRELL J A. Decentralized cooperative control of multiple nonholonomic dynamic systems with uncertainty[J]. Automatica, 2009, 45(3): 706-710. DOI:10.1016/j.automatica.2008.09.015. [12] CAO Kecai, YANG Hao, JIANG Bin. Formation tracking control of nonholonomic chained form systems[C]//Proceedings of the 10th IEEE International Conference on Control and Automation (ICCA). Hangzhou, China, 2013: 846-851. [13] CAO Kecai, JIANG Bin, CHEN Yangquan. Cooperative control design for non-holonomic chained-form systems[J]. International journal of systems science, 2015, 46(9): 1525-1539. DOI:10.1080/00207721.2013.809615. [14] PENG Zhaoxia, WEN Guoguang, Rahmani A, et al. Distributed consensus-based formation control for multiple nonholonomic mobile robots with a specified reference trajectory[J]. International journal of systems science, 2015, 46(8): 1447-1457. [15] 方勇纯, 卢桂章. 非线性系统理论[M]. 北京: 清华大学出版社, 2009: 1-151. [16] HONG Yiguang, HU Jiangping, GAO Linxin. Tracking control for multi-agent consensus with an active leader and variable topology[J]. Automatica, 2006, 42(7): 1177-1182. DOI:10.1016/j.automatica.2006.02.013.
DOI: . 10.11992/tis.201512021

0

#### 文章信息

LI Miao, LIU Zhongxin, CHEN Zengqiang

A distributed formation control method formultiple nonholonomic mobile robots

CAAI Transactions on Intelligent Systems, 2017, 12(1): 88-94
. http://dx.doi.org/10.11992/tis.201512021