Exponential stability of an attitude tracking control system on SO(3) for large-angle rotational maneuvers

This paper studies a tracking control system for the attitude dynamics of a rigid body. By selecting an attitude error function carefully, we show that the proposed control system guarantees a desirable tracking performance uniformly for rotational maneuvers involving a large initial attitude error. A strict Lyapunov analysis is presented to show exponential stability, and a sufficient condition to avoid non-differentiable points of the attitude error function is also shown. The proposed control system is directly developed on the special orthogonal group to avoid complexities and ambiguities associated with other attitude representations such as Euler angles or quaternions. These are illustrated by numerical examples.