Optimal control of a two-body limbless crawler along a rough horizontal straight line

Abstract

An optimal control problem is solved for a two-body limbless locomotor crawling along a straight line on a horizontal rough plane. Coulomb’s dry friction acts between the locomotor’s bodies and the underlying plane. The control is performed by the force of interaction between the bodies. The system should be moved from the state of rest by a given distance in a minimal time, provided that the relative positions of the bodies in the initial and terminal states coincide and the velocities of the bodies at the terminal instant are equal to zero. A particular attention is given to the case where the bodies are prohibited to change the direction of their motion.