Analysis of rectilinear motion of a three-segment snake robot under action of dry friction

Snakes and worms are capable of travelling along a straight line on a resistance medium using rectilinear locomotion. To apply this kind of gait in snake-inspired robots, some fundamental properties remain elusive. In this paper, we study the directional migration of a three-segment self-propelled system on a rough horizontal surface with Coulomb´s dry friction. We elucidate the possibility that the system achieves directional migration through the propagation of extension and contraction wave. The necessary and sufficient conditions are certified to insure that the system is able to start from the state of rest. To analyze the approximately steady-state motion of the system, we provide explicit formulas for the mean velocity of the whole system by method of averaging. It is confirmed that for isotropic friction, the average speed and direction of the motion can be excited controlled.