Mobile robots controlled by the motion of internal bodies

Control problems for mobile robotic systems able to move in resistive media due to the motion of internal bodies that interact with the main body of the robot but do not interact with the medium are considered. The optimal periodic motions of the internal bodies that sustain a velocity-periodic motion of the main body relative to the medium and maximize the average speed are searched for. Three types of resistance to the motion of the robot's main body in the medium are considered: piecewise-linear friction, quadratic-law friction, and Coulomb's dry friction.