Decentralized kinematic control of a class of collaborative redundant
manipulators via recurrent neural networks
Shuai Li
a
, Sanfeng Chen
b
, Bo Liu
c,
n
, Yangming Li
d
, Yongsheng Liang
b
a
Department of Electrical and Computer Engineering, Stevens Institute of Technology, Hoboken, NJ 07030, USA
b
Key Lab of Visual Media Processing and Transmission, Shenzhen Institute of Information Technology, Shenzhen, Guangdong 518029, China
c
Department of Computer Science, University of Massachusetts, Amherst, MA 01003, USA
d
Institute of Intelligent Machines, Chinese Academy of Sciences, Hefei, Anhui 07309, China
article info
Article history:
Received 16 October 2011
Received in revised form
22 January 2012
Accepted 22 January 2012
Communicated by H.R. Karimi
Available online 30 March 2012
Keywords:
Recurrent neural network
Quadratic programming
Cooperative task execution
Redundant manipulator
Decentralized kinematic control
abstract
This paper studies the decentralized kinematic control of multiple redundant manipulators for the
cooperative task execution problem. The problem is formulated as a constrained quadratic program-
ming problem and then a recurrent neural network with independent modules is proposed to solve the
problem in a distributed manner. Each module in the neural network controls a single manipulator in
real time without explicit communication with others and all the modules together collectively solve
the common task. The global stability of the proposed neural network and the optimality of the neural
solution are proven in theory. Application orientated simulations demonstrate the effectiveness of the
proposed method.
& 2012 Elsevier B.V. All rights reserved.
1. Introduction
With the development of mechanics, electronics, computer
engineering, etc., using a collection of manipulators to perform a
common task, such as load transport [1], cooperative assembly [2],
dextrous grasping [3], coordinate welding [4], etc., is becoming
increasingly popular and has received considerable studies. The
solution of executing the task using redundant manipulators, which
have more degree-of-freedom (DOF) than required, normally is not
unique. The extra design degrees can be exploited for obstacle
avoidance, performance optimization and so on to improve the
performance.
A fundamental issue in multiple redundant manipulator con-
trol is the redundancy resolution problem, which provides fea-
sible solutions in the joint space to a task in the Cartesian space.
Conventionally, the general solution of redundancy resolution is
obtained by solving a set of redundant time-varying linear [5,6].
However, as pointed in [7,8], this type of method cannot generate
a repeatable solution and the drift of joint angles is unavoidable.
Authors in [9] formulate the problem of single redundant manip-
ulator kinematic control as a constrained optimization problem
and opened an avenue to study the redundancy resolution
problem using optimization based methods [10,11]. In [12],
a penalty term is introduced into the objective function to restrict
the solution inside a physically feasible range. This method
enables direct monitoring and control of the magnitudes of the
individual joint torques. However, the solution is merely an
approximate solution of the problem and the approximation error
strongly depends on the coefficient of the penalty term. To fix this
problem, in [13], the optimization problem is studied in the dual
space and dual neural networks are developed to solve the
problem in real time. Further performance improvements of the
dual neural network approach, such as convergence time, archi-
tecture complexity, etc., are obtained in the successive studies
[14–16]. In [17], a local optimization approach is proposed to
resolve the kinematic control problem of redundant manipula-
tors. This approach is applicable to either serial manipulators or
parallel manipulators but the result is a locally optimal one
instead of globally. In [18], an optimal real-time redundancy
resolution scheme is proposed to solve the problem. The optimal
control law can be derived in real-time using adaptive critic
framework after a period of off-line training. An analytic-iterative
solution is presented in [19] to solve the redundancy resolution
problem formulated as an inequality constrained convex optimi-
zation problem. The optimization based formulation framework
also allows us to analyze the multiple redundant manipulator
cooperative task execution problem. However, the framework
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journal homepage: www.elsevier.com/locate/neucom
Neurocomputing
0925-2312/$ - see front matter & 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.neucom.2012.01.034
n
Corresponding author.
E-mail addresses: lshuai@stevens.edu (S. Li), chensanf@sziit.com.cn (S. Chen),
boliu@cs.umass.edu (B. Liu), ymli@iim.ac.cn (Y. Li), liangys@sziit.com.cn (Y. Liang).
Neurocomputing 91 (2012) 1–10