Optimal Control of the Motion of a Two-Mass System

Plane motions of a two-mass system consisting of a rigid body and a point mass which can move relative to the body at a bounded velocity are considered. For the system, optimal control problems in which the initial positions of the objects are given, while their terminal positions are either fixed or partially free are stated and solved. Time optimal solutions are constructed in explicit form. The optimal trajectories of the point mass relative to the body are circular arcs. The results can find applications in mobile robotics and space vehicles.