Global Stabilization of an Inverted 3D Pendulum including Control Saturation Effects

This paper continues the development of asymptotic stabilization results for a 3D pendulum. The main results provide almost global asymptotic stabilization of the inverted equilibrium of the 3D pendulum, taking into account saturation of the control moment vector. Control saturation is accommodated by a novel feedback structure that is based on the special geometric features of the 3D pendulum, namely that the attitude representation lies in a compact manifold. The analysis is based on construction of a Lyapunov function for the closed-loop that explicitly involves the saturation. Several different controller forms are presented and evaluated through simulation examples