Phase coordination and phase–velocity relationship in metameric robot locomotion

This research proposes a new approach for the control of metameric robot locomotion via phase coordination. Unlike previous studies where global wave-like rules were pre-specified to construct the actuation sequence of segments, this phase coordination method generates robot locomotion by assigning the actuation phase differences between adjacent segments without any global prerequisite rules. To effectively coordinate the phase differences, different symmetry properties are introduced. Optimization is then carried out on various symmetrically coordinated phase-difference patterns to maximize the average steady-state velocity of the robot. It is shown that the maximum average velocity is always achieved when the reflectional symmetry is included in the phase-difference pattern, and the identical-phase-difference (IPD) pattern is preferred for implementation because it reduces the number of independent phase variables to only one without significant loss in locomotion performance. Extensive analytical investigations on the IPD pattern reveal the relationship between the average locomotion velocity and some important parameters. Theoretical findings on the relationship between the average velocity and the phase difference in the IPD pattern are verified via experimental investigations on an 8-segment earthworm-like metameric robot prototype. Finally, this paper reveals an interesting result that the optimized phase-difference pattern can naturally generate peristalsis waves in metameric robot locomotion without global prerequisite wave-like rules.