Stabilization and control of the motion of a rolling disk by using two overhead rotors

This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, a controlled slender rod that is pivoted through its center of mass about the diskʹs center and two overhead rotors with their axes fixed in the upper part of the rod (see Figures 1 and 2). The rod is controlled in such a manner that it is always aligned along the line passing through the points O and C, where O denotes the center of the disk and C denotes the point of contact between the disk and the plane. The upper rotor rotates in a plane that passes through the diskʹs axis and the rod, whereas the lower rotor rotates in a plane that is perpendicular to the rod (see Figures 1 and 2). By using a kind of inverse dynamics control a control strategy is proposed under which the diskʹs inclination is stabilized about its vertical position and the diskʹs motion is able asymptotically to track any given smooth ground trajectory.