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On the stabilization of nonholonomic mechanical systems via Immersion and Invariance

par Sarras, Ioannis
Référence IFAC proceedings volumes, 18, PART 1, page (7227-7232)
Publication Publié, 2011

Article révisé par les pairs

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Résumé :

This 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. © 2011 IFAC.