On the Stabilization of Nonholonomic Mechanical Systems via Immersion and Invariance

Abstract

AbstractThis work presents some results on the application of the Immersion & Invariance (I&I) approach proposed for stabilization of nonlinear systems to the case of mechanical systems with kinematic constraints. We consider only smooth state–feedback control laws and thus, by Brockett's necessary condition, restrict our attention to deriving an I&I controller that achieves smooth stabilization of an equilibrium manifold. As is well–known, the design of I&I controllers requires the solution of some partial differential equations. A second contribution of our work is to obviate this obstacle, giving explicit control laws for a class of nonholonomic mechanical systems, which include the knife-edge and the rolling wheel. The approach is illustrated with the well-known knife-edge example.