Global dynamics and stabilization of rigid body attitude systems

Attitude control is fundamental to the design and operation of many large engineering systems that consist in whole or in part of rotational components, with system performance defined in terms of global attitude control objectives.; The 3D pendulum is a rigid body, freely rotating about a pivot point that is not the center-of-mass. It is acted upon by gravitational and control moments. New results are obtained for the problem of feedback stabilization of a 3D pendulum; these results exemplify attitude stabilization for a 3-DOF rigid body with potential forces. New results are first obtained for the global dynamics of the 3D pendulum. We identify integrals of its motion, and it is shown that the 3D pendulum has two disjoint equilibrium manifolds, namely the hanging equilibrium manifold and the inverted equilibrium manifold. New nonlinear controllers are shown to provide almost global stabilization of these equilibrium manifolds or almost global stabilization of any desired equilibrium in these manifolds. We identify a performance constraint, namely that there are closed-loop trajectories that can take arbitrarily long to converge to the equilibrium. We then study the problem of stabilization under input saturation effects. We show that as long as the saturation limit is greater than a certain lower bound, the inverted equilibrium manifold or any desired equilibrium in these manifolds, can be almost globally asymptotically stabilized. A new non-smooth controller is proposed that stabilizes the inverted equilibrium manifold such that the domain of attraction is almost global and is geometrically simple, and the closed-loop does not exhibit a performance constraint. We then present experimental results on stabilization of the inverted equilibrium manifold illustrating the closed-loop performance. Next, new stabilization results for an axially symmetric 3D pendulum are presented that generalize stabilization results in the literature for the planar pendulum, the spherical pendulum and the spinning top. Finally, we show how results for the 3D pendulum provide a guide to obtaining almost globally stabilizing controllers for an orbiting spacecraft with gravity-gradient effects using low authority controllers such as pulsed plasma thrusters.; All dynamics and stabilization results presented in this dissertation are based on new and novel problem formulations for attitude systems with a potential. They treat global issues in a geometric framework, and they provide substantial additions to the prior literature on stabilization of attitude systems.