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1. 北京航空航天大学 第七研究室, 北京 100191;
2. 北京航空航天大学 自动化科学与电气工程学院, 北京 100191

Distributed adaptive iterative learning control for multiple robot manipulators
SUN Jipeng1, MENG Deyuan1,2 , DU Mingjun2, ZUO Zongyu1,2
1. The Seventh Research Division, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract: A hybrid adaptive and iterative learning method was proposed to obtain distributed control protocols for multiple manipulator systems with undirected interaction topology to achieve consensus tracking of the specified desired reference trajectory. By introducing an appropriate adaptive iterative learning parameter, the proposed adaptive iterative learning control (AILC) protocol can overcome the effects of disturbances and model uncertainties of manipulators, where the AILC law of each manipulator needs only the relative information between it and its nearest neighbors. Moreover, it is shown that all manipulators can be rendered to achieve the perfect tracking of the desired reference trajectory though its information can be accessed by only a portion of manipulators, where the boundedness of both the tracking error and the control input can be simultaneously guaranteed. In addition, the Lyapunov analysis method is employed to validate the obtained results, and the effectiveness of the proposed AILC protocol is illustrated through an example.
Key words: multiple manipulator systems     consensus     distributed protocol     adaptive control     iterative learning control

1 问题描述

G=(V,E,A)为具有n个节点的网络所对应的拓扑图,其中V={vii=1,2,…,n}表示由有限个顶点或节点组成的集合;E⊆{(vi,vj)vi,vj∈V}为边的集合,eij=(vi,vj)∈E称为边;A=[aij]∈Rn×n表示权重矩阵,其中aij表示连接权重,aij>0⇔(vj,vi)∈E.若节点出现重复,则定义其连接权重为0,即aii=0,∀i=1,2,…,n.若图G存在一个节点有达到所有其他节点的有向路径,则成图G包含一棵生成树.当aij=aji,∀i,j时,图G表示无向图.若无向图G中任意两个不同节点都可以通过有向路径连接起来,则称图G为连通的.

1) G有一个以v0为根节点的生成树.

2) qr(t)、$\dot{q}$r(t)、q¨r(t)有界,不失一般性,令‖qr(t)‖≤kr,‖$\dot{q}$r(t)‖≤k′r,‖qr(t)‖≤k″r.

3) qi,k(0)=qr(0),$\dot{q}$i,k(0)=$\dot{q}$r(0),∀k∈Z+. 其中:krk′rk″r为大于0的常数.

1) M(qk(t))正定有界

kminm(i)和kmaxm(i)是未知的有界正常数.

2) xT[$\dot{M}$i(qi,k)－2Ci(qi,k,$\dot{q}$i,k)]x=0,∀x∈Rm.

3) Ci(qi,k,$\dot{q}$i,k)≤kc(i)$\dot{q}$i,k,di,k≤kd(i)

2 多机械臂系统的一致性 2.1 多机械臂分布式一致性控制律

Im为m×m的单位矩阵.

2.2 收敛性分析

W1(t)有界可知$\tilde{\theta }$Tk(T)$\tilde{\theta }$k(T)和∫0T$\tilde{\theta }$Tk(T)$\tilde{\theta }$k(T)dt是有界的.同时,式(15)可变形为

3 仿真实例

i个机械臂的干扰设为
rand(k)为0~1之间的一个随机数.设各机械臂的期望参考轨迹为

 图 1 机械臂系统的拓扑结构 Fig. 1 Topology structure of robot manipulators

 图 2 机械臂的位置 Fig. 2 Position of robot manipulators

 图 3 跟踪误差 Fig. 3 Tracking errors

4 结 论

1) 只须有限次迭代,每个机械臂能够趋近于期望轨迹.相较于已有的控制协议[17],具有更好的分布式结构.

2) 不需要精确的系统参数,克服多个运动机械臂难以精确建模的难题,便于实际应用.

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#### 文章信息

SUN Jipeng, MENG Deyuan, DU Mingjun, ZUO Zongyu

Distributed adaptive iterative learning control for multiple robot manipulators

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(12): 2384-2390.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0831