The motion of a cylinder-rod system on a horizontal plane: Feasible control and path controllability

This work deals with the guidance and control of a system which is composed of a rolling cylinder, and a controlled slender rod that is pivoted through its center of mass, about the cylinderʹs center. At some instant the rod has to establish contact with a smooth rigid ceiling. This instant constitutes a discontinuity in the systemʹs dynamics. The cylinder-rod system is subjected to state and control constraints, and it serves as a model for the motion of a simple mobile robot. Open-loop strategies are computed for the cylinder-rod system. In addition, the concept of path controllability is introduced for this system, and a condition is derived for the systemʹs motion path controllability. The derivation of this condition enables one to design closed-loop control laws for the systemʹs motion.