Stabilization and guidance of the motion of a rolling disk by using two rotors fixed along its axis

This work deals with the stabilization and guidance of a system which is composed of a disk rolling on a plane, a slender rod that is fixed along the diskʹs axis with its middle point fixed in the diskʹs center, and two identical rotors fixed in the rod equally spaced along both sides of the disk. Each of the rotors is rotating in a plane that is perpendicular to the plane of the disk. In addition, these planes are perpendicular to each other (see Figure 1). By using a kind of inverse control transformation and the concept of path controllability, control laws are derived under which the motion of the disk is stabilized and the diskʹs motion is steered from a point p1 to a point P2, both of them in the plane, during a given time interval [0,tƒ].