Closed-loop control of the motion of a disk-rod system

This work deals with the guidance and control of a system which is composed of a rolling disk and a controlled slender rod that is pivoted, through its center of mass, about the disk center. There are given N points P-i, i=1,..., N, in the horizontal plane, a set of angles psi(2i), i=1,..., N, a finite-time interval [0, t(f)], and a sequence of times tau(1) = 0 < tau(2) < ... < tau(N)=t(f). Using the concept of path controllability, a closed-loop control law is derived to steer the system in such a manner that the disk center and the rod angle of rotation psi(2) Will pass through (P-i, psi(2i)) at the times tau(i), i=1,..., N, respectively. This system serves as a model for the motion of a simple mobile robot.