OPTIMAL CONTROL OF PERIODIC MOTIONS OF VIBRATION-DRIVEN SYSTEMS

An optimal control problem is solved for a rigid body that moves along a straight line on a rough horizontal plane due to the motion of two internal masses. One of the masses moves horizontally parallel to the line of motion of the system's main body and the other mass moves vertically. Such a mechanical system models a vibration-driven robot able to move in a resistive medium without special propelling devices (wheels, legs or caterpillars). A periodic motion of the internal masses is constructed to ensure a velocity-periodic motion of the main body with a maximum average velocity, provided that the period is fixed and the accelerations of the internal masses relative to the main body lie within prescribed limits. This statement does not constrain the amplitude of vibrations of the internal masses. Based on the solution of the problem, a suboptimal control that takes this constraint into account is constructed.