Stabilization of the motion of a disk rolling on a horizontal plane by using a translational moving rod along its axis

This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, a translational joint attached along the disk's axis, and a controlled rod that moves along the translational joint (see Figures 1 and 2). The disk's motion is controlled by the moving rod, a “directional control” 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, 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 asymptotically to track any given smooth ground trajectory.