  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.
