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Formation control of multi-robot systems in a fuzzy sliding mode
QIAN Dianwei
School of Control and Computer Engineering, North China Electric Power University, Beijing 102206, China
Abstract: To resolve the formation problem resulting from a swarm of robots, a control scheme is proposed based on sliding mode control and fuzzy logic. A formation dynamic model is established utilizing the leader-follower approach. The model is subject to uncertainties. If the upper bounds of these uncertainties are unknown, then a fuzzy compensator can be adopted to approximate the uncertainties. From an Lyapunov approach, not only is the sliding-mode-based formation control system asymptotically stable, but the approximate error of the fuzzy compensator is also convergent. The simulation results demonstrate that the robots can rapidly form and maintain the desired specified geometrical shapes during movement.
Key words: multi-robot     formation control     uncertainties     sliding model control     fuzzy logic

1 系统描述

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 图 1 跟随—领航者编队控制模型 Fig. 1 Leader-follower formation of multiple robots

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φikikik，各参数矩阵描述如下

I2是2×2单位矩阵；Fik=[F1 F2]T；Pik=[P1 P2]T；Δk和Δi是2×2扰动矩阵；

2 控制系统设计及稳定性分析 2.1 模糊补偿器的设计

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 图 2 模糊推理系统结构图 Fig. 2 Structure of the FIS

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FIS的输入与输出变量均模糊化为负大(NB)，负小(NS)，零(ZO)，正小(PS)和正大(PB)5个模糊子集，即Apl=Bpl={NB, NS, ZO, PS, PB}。所设计的FIS第l条模糊规则如下：

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Θ存在最优参数矩阵Θ*，且Θ*满足

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2.2 滑模控制器的设计

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2.3 稳定性证明

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3 仿真结果

 图 3 控制方法结构图 Fig. 3 Structure of control scheme

 图 4 直线编队跟踪圆形轨迹 Fig. 4 Line formation while moving in a circle

 图 5 状态轨迹 Fig. 5 State trajectories

 图 6 跟随者2的控制量 Fig. 6 Control variables of follower 2
 图 7 跟随者3的控制量 Fig. 7 Control variables of follower 3
 图 8 滑模面向量的三维图 Fig. 8 3 D plots of the sliding surfaces vector
 图 9 不确定项dik及其逼近值 Fig. 9 The uncertain term and its approximations
4 结束语

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DOI: 10.11992/tis.201510017

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#### 文章信息

QIAN Dianwei

Formation control of multi-robot systems in a fuzzy sliding mode

CAAI Transactions on Intelligent Systems, 2016, 11(5): 641-647
http://dx.doi.org/10.11992/tis.201510017