Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 31267, 20 pages
Research Article

Stabilizability and Motion Tracking Conditions for Mechanical Nonholonomic Control Systems

Elżbieta Jarzębowska

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.