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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

Formation control of leader-following type multi-robotbased on fuzzy control method
WU Yin1,2, LIU Zhongxin1,2 , CHEN Zengqiang1,2, SUN Qinglin1,2
1. College of Computer and Control Engineering, Nankai University, Tianjin 300071, China;
2. Key Laboratory of Intelligent Robotics of Tianjin, Tianjin 300071, China
Abstract: The leader-following method is adopted in this paper to achieve formation control of multi-robot. In order to overcome the complexity and uncertainty of mobile robot model, fuzzy control which is independent of system model is chosen as the path tracking strategy for the leader robot. The velocity and angular velocity of the leader are adjusted in real time by the output of fuzzy controller, guaranteeing that the leader can reach and move along the desired path. At the same time, the appropriate control law is designed to make the relative distance and angle between the leader and each follower converge to the given value, so as to achieve the desired formation control. Numerical simulations and actual field experiments are provided in this paper, showing the effectiveness of the control strategy in path tracking and the formation control of multiple mobile robots.
Key words: fuzzy control     path following     mobile robot     kinematic model     leader     follower     SBC control     formation control

1 机器人模型

1.1 领导者运动学模型

 图 1 机器人运动学模型 Fig. 1 Kinematic model of the robot

1.2 跟随者运动学模型

 图 2 跟随者保持队形模型 Fig. 2 Formation keeping model of followers

γ=θ2-θ1+φ，在对跟随者的运动状态进行数学描述时，文中采用SBC控制(separation-bearing control,SBC)方法建立跟随者模型[15]。因此对跟随者进行建模时，由跟随者与领导者的相对位置和角度表示的跟随者的运动学方程为

2 控制算法

2.1 基于模糊控制的路径跟踪

 图 3 领导者向目标点移动 Fig. 3 The leader move to the target

β即为机器人运动方向与目标点的偏离角，则β=θ-α。选取D与β作为模糊控制器的输入量，机器人的线速度v(t)和角速度w(t)作为模糊控制器的输出量。通过设计合理的模糊控制规则，来保证移动机器人在轨迹跟踪的过程总能达到目标点P，即变量D与β总是趋于零，即可达到机器人实时跟踪给定轨迹的目的。下面由模糊语言变量分别对2个输入输出变量进行模糊子集的划分，如表 1表 2所示。

 距离D 角度β ZE 零 NL 负大 VN 非常近 NM 负中 NE 近 NS 负小 ME 中等 ZE 零 FA 远 PS 正小 VF 非常远 PM 正中 EF 格外远 PL 正大

 速度v 角速度w ZE 零 NL 负大 VS 非常小 NM 负中 SM 小 NS 负小 ME 中等 ZE 零 LA 大 PS 正小 VL 非常大 PM 正中 EL 极大 PL 正大

 图 4 D隶属度函数 Fig. 4 subordinate degree function of D
 图 5 β隶属度函数 Fig. 5 subordinate degree function of β
 图 6 v隶属度函数 Fig. 6 subordinate degree function of v
 图 7 w隶属度函数 Fig. 7 subordinate degree function of w

2.2 跟随者编队保持

α1α2>0可知，≤0当且仅当el=0、eφ=0时等号成立。则系统渐近稳定。证毕。

3 仿真研究 3.1 基于MATLAB的数值仿真

 图 8 领导者给定路径为直线y=0时的编队运动轨迹 Fig. 8 Formation trajectory when the given path of leader is the straight line y=0
 图 9 领导者给定路径为斜线y=x时的编队运动轨迹 Fig. 9 Formation trajectory when the given path of leader is the diagonal line y=x
 图 10 领导者给定路径为圆x2+y2=4时的编队运动轨迹 Fig. 10 Formation trajectory when the given path of leader is the circle x2+y2=4
3.2 基于轮式机器人的相关实验

 图 11 程序流程图 Fig. 11 The program flow chart

 图 12 领导者跟踪直线时的不同时刻t的编队运动情况 Fig. 12 The formation situation when the leader tracking the straight line in different time t
 图 13 领导者跟踪圆时的不同时刻t的编队运动情况 Fig. 13 The formation situation when the leader tracking the circle in different time t
 图 14 领导者跟踪直线时的实际输出的运动曲线 Fig. 14 The actual output curves when the leader tracking the straight line
 图 15 领导者跟踪圆时的实际输出的运动曲线 Fig. 15 The actual output curves when the leader tracking the circle
5 总结与展望

 [1] WANG F, GAO L X, WANG L Y. Tracking Control for Multi-agent Consensus for Discrete-time Case[C]//2011 Chinese Control and Decision Conference. Mianyang, China: IEEE, 2011: 923-928. [2] JADBABAIE A, LIN J, MORSE A S. Coordination of groups of mobile autonomous agents using nearest neighbor rules[J]. IEEE Transactions on Automatic Control, 2003, 48(6): 988-1001. [3] 苗国英, 马倩.多智能体系统的协调控制研究综述[J].南京信息工程大学学报: 自然科学版, 2013, 5(5): 385-369. MIAO Guoying, MA Qian.A survey of developments on coordinated control of multi-agent systems[J]. Journal of Nanjing University of Information Science and Technology: Natural Science Edition, 2013, 5(5): 385-369. [4] PENG Z X, WEN GG, RAHMANI A. Leader-follower formation control of multiple nonholonomic robots based on backstepping[C]//Proceedings of the 28th Annual ACM Symposium on Applied Computing. New York, NY, USA: SAC, 2013: 211-216. [5] HONG Y G, HU J P, GAO L X. Tracking control for multi-agent consensus with an active leader and variable topology[J]. Automatica, 2006, 42(7): 1177-1182. [6] HERNANDEZ-MENDOZA DE, PEÑ ALOZA-MENDOZA G R, ARANDA-BRICAIRE E. Discrete-Time Formation and Marching Control of Multi-Agent Robots Systems[C]//2011 8th International Conference on Electrical Engineering Computing Science and Automatic Control (CCE). Merida City: IEEE, 2011: 1-6. [7] ARAI T, PAGELLO E, PARKER L E. Guest editorial advances in multirobotsystems[J]. IEEE Transactions on Robotics and Automation, 2002, 18(5): 655-661. [8] 刘曙光, 魏俊民, 竺志超. 模糊控制技术[M]. 北京: 中国纺织出版社, 2001: 1-8. LIU Shuguang, WEI Junmin, ZHU Zhichao. Fuzzy control technology[M]. Beijing: China Textile Press, 2001: 1-8. [9] 孙德丰. MATLAB模糊系统设计[M].北京: 国防工业出版社, 2009.SUN DefengThe design of Fuzzy Systems[M]. Beijing: National Defence Industry Press, 2009. [10] HSU Y -C, CHEN G R, LI H X. A Fuzzy adaptive variable structure controller with application to robot manipulators[J]. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 2001, 31(3): 331-340. [11] 骆德渊, 刘荣, 李纪文. 采用模糊逻辑的移动机器人轨迹跟踪[J].电子科技大学学报, 2008, 37(6): 943-947. LUO Deyuan, LIU Rong, LI Jiwen. Path tracking of mobile robots using fuzzy logic[J].Journal of University of Electronic Science and Technology of China, 2008, 37(6): 943-947. [12] 陈杨杨, 田玉平.多智能体沿多条给定路径编队运动的有向协同控制[J].自动化学报, 2009, 35(12): 1541-1549.CHEN Yangyang, TIAN Yuping. Directed coordinated control for multi-agent formation motion on a set of given curves[J]. ActaAutomaticaSinica, 2009, 37(12): 1541-1549. [13] 徐国焯.多UUV编队路径跟踪控制研究[D].哈尔滨:哈尔滨工程大学, 2012:12-54. XUGuozhuo. Research on path following control for Multi-UUV formation[D]. Harbin: Harbin Engineering University, 2012: 12-54. [14] FIERRO R, SONG P, DAS Aet al. Cooperative Control of Robot Formations[M]. Philadelphia, US: Springer, 2002, 66: 73-93. [15] CROWLEY J L. Asynchronous control of orientation and displacement in a robot vehicle[C]//Proceeding of 1989 IEEE International Conference on Robotics and Automation. Scottsdale, AZ: IEEE, 1989: 1277-1282. [16] 吴瑾斐, 秦东兴, 刘俊.四轮式移动机器人非完整运动控制[J]. 电子科技大学学报, 2007, 36(2): 301-304. WU Jinfei, QIN Dongxing, LIU Jun. Nonholonomic motion control of four-wheeled mobile robot[J]. Journal of University of Electronic Science and Technology of China, 2007, 36(2): 301-304. [17] 汪超, 唐勇奇. 基于独立C代码的模糊控制器应用程序设计[J].计算机技术与发展, 2009, 19(5): 242-244. WANG Chao, TANG Yongqi. Programmer of fuzzy controller based on stand-alone C-Code[J]. Computer Technology and Development, 2009, 19(5): 242-244.
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DOI: 10.3969/j.issn.1673-4785.201407014

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#### 文章信息

WU Yin, LIU Zhongxin, CHEN Zengqiang, SUN Qinglin

Formation control of leader-following type multi-robotbased on fuzzy control method

CAAI Transactions on Intelligent Systems, 2015, 10(04): 533-540.
DOI: 10.3969/j.issn.1673-4785.201407014