Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 31267, 20 pages
Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems
Institute of Aircraft Engineering and Applied Mechanics, Warsaw University of Technology, Nowowiejska 24 str., Warsaw 00-665, Poland
Received 28 September 2006; Revised 5 February 2007; Accepted 17 April 2007
Academic Editor: José Manoel Balthazar
Copyright © 2007 Elżbieta Jarzębowska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper addresses formulation of stabilizability and motion tracking conditions for mechanical
systems from the point of view of constraints put on them. We present a new classification of constraints,
which includes nonholonomic constraints that arise in both mechanics and control. Based on our
classification we develop kinematic and dynamic control models of systems subjected to these constraints.
We demonstrate that a property of being a “hard-to-control” nonholonomic system may
not be related to the nature of the constraints. It may result from the formulation of control
objectives for a
system. We examine two control objectives which are stabilization to the target equilibrium by a
continuous static state feedback control and motion tracking. Theory is illustrated with examples
of control objective
formulations for systems with constraints of various types.