Geometric approach to tracking and stabilization for a spherical robot actuated by internal rotors

The paper adopts a geometric approach to stabilization and tracking of a spherical robot actuated by three internal rotors mounted on three mutually orthogonal axes inside the robot. The system is underactuated and subject to nonholonomic constraints. Initially, the equations of motion are derived through Euler-Poincaré reduction. Then two feedback control laws are synthesized: the first control law addresses orientation of the robot alone, keeping the contact point arbitrary; the second control law is a tracking law that addresses the contact position and angular velocity tracking.