Desingularization by minimum projection method and its application to rigid body control

Stabilization on a non-contractible manifold is a difficult control problem. We have proposed the minimum projection method for asymptotic stabilization of nonlinear systems on manifolds. The minimum projection method requires the strict condition for a control Lyapunov function (CLF) on another manifold. In this paper, we relax the condition by desingularization of the function on the other manifold. We consider a rigid body control problem as an application of desingularization based control method. S³ is a double covering space of SO(3). Stabilization on SO(3) is a difficult problem; however, the strong CLF design on S³ is not difficult. Then, we design a strict CLF from the CLF on S³ by desingularization. Finally, we confirm the effectiveness of the desingularization based control method by computer simulation.