Global Exponential Attitude Tracking Controls on <tex-math notation="TeX">SO( 3)</tex-math>

This technical note presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to follow a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is generalized 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 technical note.