Stabilization of rotational motion with application to spacecraft attitude control

The objective of this paper is to develop a control scheme for stabilization of a hamiltonian system. The method generalizes the results available in the literature on motion control in the Euclidean space to an arbitrary differrential manifol equipped with a metric. This modification is essencial for global stabilization of a rotary motion. Along with a model of the system formulated in the Hamilton's canonical from the algorithm uses information about a required potential energy and a dissipation term. The control action is the sum of the gradient of the potential energy and the dissipation force. It is shown that this control law makes the system uniformly asymptotically stable to the desired reference point. The concepet is very straightforward in the Euclidean space however a global rotation control cannot be tackled.An additional modification is made to address a system which flow lies on a Riemannian manifold. The Lyapnov stability theory is adapted and reformulated to fit to the new framework of Riemannian manifolds. Toillustrate the results a spacecraft attitude control problem is considered. Firstly, a global canonical representation for the spacecraft motion is found, then three spacecraft control problems are addressed: stabilization in the inertial frame, magnetic libration damping for the gravity gradient stabilization and a slew maneuver with obstacle avoidance