Geometry and Inverse Optimality in Global Attitude Stabilization

The problem of globally stabilizing the attitude of a rigid body is considered. Topological and geometric properties of the space of rotations relevant to the stabilization problem, are discussed. Chevalley's exponential coordinates for a Lie group are used to represent points in this space. An appropriate attitude error is formulated and used for control design. A control Lyapunov function approach is used to design globally stabilizing feedbacklaws that have desirable optimality properties. Their performance is compared to the performance of previously developed proportional-derivativetype control laws. The new control laws achieve the same or greater stabilization rate with less control e#ort. Special issues in the Lyapunov stability proofs due to the topology of the space of rotations are identi#ed and resolved. The simpler problem of stabilization # Graduate Student; Student Member AIAA y Postdoctoral Researcher z Associate Professor; Associate Fellow of AIAA x C...