This paper deals with motion planning and control for an underactuated system, the hoop-pendulum, a pendulum mounted at the center of a hoop. The dynamic model for this system is derived and the local controllability around the equilibrium point is established. To transfer the system from a initial configuration to a desired final configuration in rest-to-rest mode, two controllers, the feedback and feedforward ones, are constructed. The feedback controller stabilizes the system at the origin and is based on the construction of a suitable Lyapunov function. The feedforward controller is based on the representation of the motion of the pendulum by the second derivative of Beta function. The feasibility and the performance of the proposed controllers are verified under simulations.
['Yang Bai', 'Mikhail M. Svinin', 'Motoji Yamamoto']
Motion planning for a hoop-pendulum type of underactuated systems