Robust global exponential attitude tracking controls on SO(3)

Four types of attitude control systems are developed for the rotational dynamics of a rigid body on the special orthogonal group. 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 problems on the special orthogonal group is the unique contribution of this paper. These are illustrated by numerical examples.