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Adaptive stabilization of uncertain nonholonomic mechanical systems

Published online by Cambridge University Press:  05 April 2001

R. Colbaugh ,
E. Barany  and
K. Glass
R. Colbaugh
Affiliation:
Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88003, USA
E. Barany
Affiliation:
Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA
K. Glass
Affiliation:
Department of Mechanical Engineering, New Mexico State University, Las Cruces, NM 88003, USA
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Abstract

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This paper presents a new adaptive controller as a solution to the problem of stabilizing nonholonomic mechanical systems in the presence of incomplete information concerning the system dynamic model. The proposed control system consists of two su bsystems: a slightly modified version of the kinematic stabilization strategy of M'Closkey and Murray which generates a desired velocity trajectory for the nonholonomic system, and an adaptive control scheme which ensures that this velocity trajector y is accurately tracked. This approach is shown to provide arbitrarily accurate stabilization to any desired configuration and can be implemented with no knowledge of the system dynamic model. The efficacy of the proposed stabilization strategy is illustr ated through extensive computer simulations with nonholonomic mechanical systems arising from explicit constraints on the system kinematics and from symmetries of the system dynamics.

Keywords

Nonholonomic systemsAdaptive controlDynamic modelRobot controlLyapunov methods
Type
Research Article
Information
Robotica , Volume 16 , Issue 2 , March 1998 , pp. 181 - 192
Copyright
1998 Cambridge University Press