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

Abstract

This work deals with the stabilization and guidance of a system which is composed of a disk rolling on a plane, a peddaling mechanism located at the center of the disk, an upright controlled slender rod that is pivoted through its center of mass about the disk's center and two overhead rotors with their axes fixed in the upper part of the rod (see Figs. 1 and 2). By using a kind of inverse dynamics control and the concept of path controllability, control laws for the peddaling mechanism and the rotors are derived, under which the motion of the disk is stabilized and the disk's motion is steered in such a manner that the point of contact between the disk and the horizontal plane will move from one given point to another given point during a given time interval.