On robust, global stabilization of the attitude of an underactuated rigid body using hybrid feedback

A hybrid feedback is developed for robust, global stabilization of the attitude of an underactuated rigid body. For the case where two angular velocities are considered as controls, this objective is achieved. For the case where the two controls are torques, the objective is achieved in a "practical" sense, i.e., robust, global asymptotic stability of some arbitrarily small neighborhood of the desired attitude is achieved. To assist with the exposition, a robustly, globally stabilizing hybrid controller is also developed for the case where three angular velocities are considered as controls. This solution provides an alternative to one that has appeared recently in the literature.