Page 280 - Autonomous Mobile Robots

7 Adaptive Control of

Mobile Robots

Including Actuator

Dynamics

Zhuping Wang, Chun-Yi Su, and
Shuzhi Sam Ge

CONTENTS

7.1 Introduction ............................................................ 267
7.2 Dynamic Modeling and Properties.................................... 269
7.3 Control System Design ................................................ 277
7.3.1 Kinematic and Dynamic Subsystems ........................ 277
7.3.2 Control Design at the Actuator Level ........................ 279
7.4 Simulation.............................................................. 285
7.5 Conclusion ............................................................. 289
References .................................................................... 290
Biographies ................................................................... 292

7.1 INTRODUCTION
A number of typical mobile robots can be described by the chained form or
more general nonholonomic systems. Due to Brockett’s theorem [1], it is
well known that nonholonomic systems with restricted mobility cannot be
stabilized to a desired configuration (or posture) via differentiable, or even
continuous, pure-state feedback [2]. The design of stabilizing control laws for
these systems is a challenging problem which has attracted much attention in
the control community. A number of approaches have been proposed for the
problem, which can be classified as (i) discontinuous time-invariant stabiliza-
tion [3], (ii) time-varying stabilization [4], and (iii) hybrid stabilization [5,6].
In References 7 and 8, an elegant approach to constructing piecewise continu-
ous controllers has been developed. A nonsmooth state transformation is used

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© 2006 by Taylor & Francis Group, LLC

FRANKL: “dk6033_c007” — 2006/3/31 — 16:43 — page 267 — #1