On a horizontal version of the inverse pendulum problem Original Research Article

This work deals with the guidance and control of a system which is composed of a rolling disk and a slender rod that is freely pivoted, through its middle point, about the diskʹs center. The motion of the disk-rod system is subjected to state and control constraints, of which one of them serves as a generalized, horizontal version, of the inverse pendulum problem. In this work two concepts are introduced. First the concept of feasible command strategies is introduced and their applicability is demonstrated by solving a guidance and control problem concerning the above-mentioned system. Second, the concept of path controllability is introduced 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 systemsʹs motion.