Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base Using Feedback

This paper treats the problem of a spherical robot with an axisymmetric pendulum drive rolling without slipping on a vibrating plane. The main purpose of the paper is to investigate the stabilization of the upper vertical rotations of the pendulum using feedback (additional control action). For the chosen type of feedback, regions of asymptotic stability of the upper vertical rotations of the pendulum are constructed and possible bifurcations are analyzed. Special attention is also given to the question of the stability of periodic solutions arising as the vertical rotations lose stability.