Stability of non-holonomic systems

Nonholonomic constraints characterize robot systems in rolling contact with the environment as well as space manipulators. In this paper, the authors address the issue of stability of nonholonomic systems. In the past, it has been shown (Neimark and Fufaev, 1972) that an equilibrium manifold, rather than an isolated equilibrium point, exists for these systems. It is shown that Lyapunov´s second method and La Salle´s theorem of invariance can be adapted to study the stability of this manifold. Specifically, the Lyapunov function must be positive definite with respect to the equilibrium manifold and its derivative must vanish identically only thereupon. The example of the rolling vertical disc is used to illustrate the analysis