Global Exponential Attitude Tracking Controls on SO(3)

This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is extended to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this paper, and these are developed directly on the special orthogonal group to avoid singularities of local coordinates, or ambiguities associated with quaternions. The desirable features are illustrated by numerical examples.