Backstepping trajectory tracking control for a spherical rolling robot

This paper deals with a trajectory tracking problem for the ball-pendulum system, a spherical rolling robot driven by a two degree of freedom pendulum. The backstepping technique is applied and first tested on the hoop-pendulum system, a planar case of the ball-pendulum. By mimicking the backstepping process of the planar case, a feedback controller for the ball-pendulum system is then proposed, tracking motion trajectories for both the position and orientation of the spherical shell of the rolling robot. The validity of the constructed tracking controller is demonstrated by establishing the asymptotic stability of the error dynamics for the closed-loop system. The performance of the controller is verified under simulations for tracking linear and circular motions.