Stabilization and asymptotic path tracking of a rolling disk

In this paper, the dynamics and control of a uniform disk (a thin wheel) rolling without slipping on a horizontal plane are considered. A model of the rolling disk is derived using the Lagrangian formulation, assuming that rolling, steering and leaning torques are available as control inputs. A dynamic extension is used to achieve a well defined vector relative degree. On the basis of the dynamic extension, a feedback control law is designed to stabilize the disk from falling over, while simultaneously allowing the disk to asymptotically track a ground reference trajectory. For this class of stabilization and tracking problems, the nonholonomic rolling without slipping constraint does not preclude the existence of smooth feedback that accomplishes the control objectives.