Directional control of the motion of a rolling disk by using a rotor fixed in the diskʹs plane

This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, and a circular rotor plate fixed in the diskʹs plane. The diskʹs motion is controlled by the above-mentioned rotor, a “tillting moment” and a pedalling moment. It is shown here that by applying a kind of inverse dynamics control, the motion of the disk is stabilized about a given angle, while simultaneously controlling its speed and direction in such a manner that the point of contact between the disk and the horizontal plane will be able, during a given time interval [0, tf], to move from a given point. rA to a another given point rB, both of them fixed in the plane.