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Intelligent Control and Automation, 2011, 2, 396-404
doi:10.4236/ica.2011.24045 Published Online November 2011 ()

Adaptive Tracking Control of an Uncertain
Nonholonomic Robot*
Nan Hu, Chaoli Wang
School of Optical-Electrical and Computer Engineering, University of Shanghai
for Science and Technology, Shanghai, China
E-mail: hn19861215@126.com
Received September 3, 2011; revised September 24, 2011; accepted October 19, 2011

In this paper, a new controller is proposed by using backstepping method for the trajectory tracking problem
of nonholonomic dynamic mobile robots with nonholonomic constraints under the condition that there is a
distance between the mass center and the geometrical center and the distance is unknown. And an adaptive
feedback controller is also proposed for the case that some kinematic parameters and dynamic parameters are
uncertain. The asymptotical stability of the control system is proved with Lyapunov stability theory. The
simulation results show the effectiveness of the proposed controller. The comparison with the previous
methods is made to show the effectiveness of the method in this article.
Keywords: Nonholonomic Systems, Wheeled Mobile Robot, Adaptive Control, Tracking Control

1. Introduction
In recent years, the control problem of the nonholonomic
systems has been widely investigated. The wheeled mobile robots have become a practical benchmark of these
systems and the hot spot of research. However, it is proved
that such systems cannot be stabilized by use smooth pure
state feedback controllers because nonholonomic systems
don't satisfy the Brockett’s necessary condition of smooth
feedback stabilization [1]. Therefore the researchers proposed many control methods to meet the challenge, for
instance, continuous time-varying feedback control laws
[2-4]; discontinuous feedback control laws [5-7]; hybrid
feedback control laws [8]; and optimal control laws [911].
The tracking control problem of the nonholonomic
mobile robots is also an important significance in project.
Many researchers have focused on solving the motion
control problem under nonholonomic constraints by using
the kinematic model of a mobile robot [12,13]. These
methods assume that there are some kinds of dynamic
controllers that can produce perfectly the same velocity
which is necessary for the kinematic controller. However,
*This paper is supported by the National Natural Science Foundation of
China, No. 60874002, and the...
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