Reduced-Effort Control Laws for Underactuated Rigid Spacecraft

Recent results show that a nonsmooth, time-invariant feedback control law can be used to rotate an axisymmetric rigid spacecraft to the zero equilibrium using only two control torques. This method, however, may require a significant amount of control effort, especially for initial conditions close to an equilibrium manifold corresponding to rotations about the unactuated principal axis. In this paper a control law is proposed which reduces the control effort required to perform rest-to-rest maneuvers for initial conditions close to this equilibrium manifold. Specifically, the phase space of the system is divided into two parts, one corresponding to initial conditions producing large control effort (the "bad" region) and the other corresponding to initial conditions producing small control signals (the "good" region). The proposed control law then renders this undesirable equilibrium manifold unstable driving the trajectories of the closed-loop system into the "good" region, where the o..