Motion of Multilink Snake-Like Mechanisms in Dynamic Mode

This chapter deals with plane multilink snake-like mobile systems the links of which are connected by cylindrical (revolute) joints in such a way that the system moves due to bending changes in its configuration. The system moves along a horizontal plane; Coulomb's dry friction acts between the links of the system and the underlying plane. The dynamic mode of motion is considered. This mode implies the alternation of slow and fast phases. In the slow phases, part of the links are moving, while the other links are kept at rest by the friction forces. The joint torques (control torques) in these phases must be comparatively small to enable the friction forces to keep part of the links at rest. During the slow phases, the system's center of mass moves relative to the plane of motion. For the displacement of the center of mass to be considerable, the slow phases must have relatively long durations. In the fast modes, vice versa, the joint torques exceed significantly the friction torques, while the duration of these phases is small. The fast phases substantially change the configuration of the system but virtually do not displace the center of mass relative to the environment. Three- and two-link mechanisms are investigated in detail. It is proved that by combining slow and fast motions one can transfer these mechanisms from any initial position to any terminal position in the plane. Appropriate gaits and control modes are constructed. Optimal design and control parameters that maximize the average velocity of the motion of the mechanisms under consideration are found. Experiments that verify theoretical conclusions are described.