Canonical Approach to Stabilization of Rigid Body Dynamics

Abstract

This paper develops a new paradigm for stabilization of rigid body dynamics. The state-space model is formulated using canonical elements, known as the Serret-Andoyer (SA) variables, thus far scarcely used for engineering applications. The main feature of the SA formalism is the reduction of the dynamics via the underlying symmetry stemming from conservation of angular momentum and rotational kinetic energy. We use the Hamiltonian as a natural Lyapunov function for the closed-loop dynamics. It is shown that the Hamiltonian controller is both passive and inverse optimal with respect to a meaningful performance index