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1. 南开大学 计算机与控制工程学院，天津 300071;
2. 天津市智能机器人技术重点实验室，天津 300071

A kind of new type controller for multi-agent leader-follower formation
WANG Zhonglin1,2 , LIU Zhongxin1,2 , CHEN Zengqiang1,2 , SUN Qinglin1,2 , WU Yin1,2 , MA Zhengguang1,2
1. College of Computer and Control Engineering, Nankai University, Tianjin 300071, China ;
2. Key Laboratory of Intelligent Robotics of Tianjin, Tianjin 300071, China
Abstract: In this paper, the algorithm of formation control concerning the Leader-Follower Multi-Agent System(MAS) based on the discrete-time model is researched. By introducing the neighbor-based local control law and the neighbor-based state estimation rules, a kind of new type controller for multi-agent leader-follower formation is designed. Arbitrary shape formations can be easily achieved by simply setting the follower and leader relative coordinates. At the same time, the coordinate rotating formula is introduced to realize the entire formation rotating accordingly with changes of the direction of the movement of the leader. This paper gives two sufficient conditions for the system's stable formation of fixed topology and switching topology, respectively. The correctness and the practical feasibility of this algorithm were verified through the MATLAB simulation and experiments were conducted using the Amigobot robot platform, respectively.
Key words: multi-agent system (MAS)     consensus     formation control     leader-follower     robots     coordinate rotating formula

1 相关的图论基础

2 控制算法设计

2.1 新型控制器设计

 (1)

 (2)

i, j=1, 2, …, nαij>0，βi>0。

 图 1 相对坐标转换对比图 Fig. 1 The comparison of Relative coordinate transformation

2.2 主要结论

 (3)

 (4)

 (5)

 (6)

 (7)

1) S < 0

2) S11 < 0, S22S12TS11－1S12 < 0

3) S22 < 0, S11S12S22－1S12T < 0

U为矩阵H的Schur转换矩阵(酉矩阵)，则

 (8)

 (9)

 (10)

V(ε)的差分为

 (11)

 (12)

3 实验结果

3.1 MATLAB仿真结果

 图 2 Matlab仿真结果 Fig. 2 The results of Matlab simulation

 图 3 箭头队形 Fig. 3 The arrow formation
 图 4 斧子队形 Fig. 4 The axe formation
 图 5 五角星队形 Fig. 5 The pentagram formation
3.2 Amigobot机器人实验结果

 图 6 Amigobot机器人实验结果 Fig. 6 The experimental result of Amigobot robots

 图 7 机器人运动轨迹图 Fig. 7 The motion track of robots
 图 8 多机器人编队的实验图 Fig. 8 The experiment of multi-robot formation
4 结束语

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DOI: 10.3969/j.issn.1673-4785

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#### 文章信息

WANG Zhonglin, LIU Zhongxin, CHEN Zengqiang, SUN Qinglin, WU Yin, MA Zhengguang

A kind of new type controller for multi-agent leader-follower formation

CAAI Transactions on Intelligent Systems, 2014, 9(3): 298-306
http://dx.doi.org/10.3969/j.issn.1673-4785