Optimal Control of Motion of a Robot Driven by a Movable Internal Body in a Resistive Environment

A two-body system moving along a horizontal line in a nonlinear viscous medium is considered. One of the bodies (main body) interacts with the environment and with the other body (internal body), which interacts with the main body but does not interact with the environment. A periodic optimal motion of the internal body relative to the main body, which sustains the motion of the main body with periodically changing velocity and maximizes its average speed, is defined by solving an optimal control problem.