Dynamic model and control of a rolling disk

Aim of the paper is the control of a disk, which is rolling without slipping on an unknown curve. After the determination of the dynamic model of the rolling disk, on which an external torque is applied, a control algorithm is proposed for the regulation of the position of the disk, i.e, of its distance along the curve from the `initial point´, to a desired value. The effectiveness of the algorithm, which does not require the complete knowledge of the dynamic model of the system (i.e, of the analytic expression of the curve), is confirmed by the reported simulation results.