Global stabilization of a fully actuated mechanical system on a Riemannian manifold: controller structure

Abstract

We present a general intrinsic controller for stabilization of an arbitrary configuration of a fully actuated simple mechanical control system, evolving on a Riemannian manifold. We explicitly determine conditions for an error function on the configuration manifold and present a family of controllers. We show that under certain assumptions the controllers achieve stabilization with an almost global domain of attraction. The controllers do not cancel benign nonlinearities and can accommodate control saturation effects. Being intrinsic, we do not assume any coordinates. Finally, we illustrate our technique by explicitly deriving a control law that almost globally asymptotically stabilizes the inverted position of a spherical pendulum. Continuing this work by N. A. Chaturvedi, et al., we explicitly present error functions for many configuration manifolds encountered in engineering examples, and show how to design almost globally stabilizing controllers, under saturation effects. In this paper, we present the structure of such a controller and establish the properties of the resulting closed-loop