Directional control of the motion of a rollling disk by using an overhead rotor (Q2731403)

A control law is proposed for the solution of a nonlinear control problem, concerning steering a disk-rod-overhead rotor system. It is composed of a disk rolling on the horizontal \((X,Y)\) plane, a controlled slender rod that is pivoted through its center of mass about the disc's center, and a rotor with its axis fixed in the upper end of the rod. The disk has to perform, during the motion, a prescribed set of maneuvers. The path controllability formulation, introduced in the paper, separates the steering problem from the nonlinear dynamics by solving two simple control problems. The first problem concerns a linear fourth-order system with the given path requirements in \(\mathbb{R}^4\) and the second problem concerns a linear second-order system with the given path requirements in \(\mathbb{R}^2\). This separation enables one to design control strategies for the navigation of the disk's center of mass and to design control strategies for the directional control of the disk, each of them independently of the other.