A reduced-effort control law for underactuated rigid bodies

Recent results show that a nonsmooth, time-invariant feedback control law can be used to stabilize an axisymmetric rigid body using only two control torques to the zero equilibrium. This method, however, may require a significant amountofcontrol e ort, especially for initial conditions close to an equilibrium manifold. In this paper we propose a modi cation of the previous control law which reduces the control e ort required. The new control law renders the equilibrium manifold unstable and drives the trajectories of the closed-loop system into a "safe" region where the original control law can be subsequently used