Closed-Loop Control of the Motion of a Disk–Rod System

Abstract

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 Pi, i=1, ..., N, in the horizontal plane, a set of angles ψ2i, i=1, ..., N, a finite-time interval [0, tf], and a sequence of times τ1=0<τ2<...<τN=tf. 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 ψ2 will pass through (Pi, ψ2i) at the times τi, i=1,...,N, respectively. This system serves as a model for the motion of a simple mobile robot.