Control of mechanical systems with classical nonholonomic constraints

A theoretical framework for the control of mechanical systems with m⩾1 classical nonholonomic constraints is established. In particular, the authors emphasize certain control properties for mechanical systems with nonholonomic constraints that have no counterpart in systems with holonomic constraints are emphasized. Conditions for smooth stabilization, of an m-dimensional equilibrium manifold are presented, and it is demonstrated that smooth stabilization of a single equilibrium solution is not possible. The development is illustrated using two physical examples: the control of a knife edge moving on a plane surface and the control of a wheel rolling without slipping on a plane surface. The physical significance of the theoretical results is described for these examples