Optimal control of the multi-module vibration-driven locomotion robot

Abstract

The vibration-driven robot utilizes the periodic inertia force from the oscillator to realize locomotion. Because its movement does not rely on wheels or legs, the robot's body can be designed very neatly for working in restricted circumstances such as pipeline inspection and post-disaster rescue. Because high mobility is essential in these applications, the issue of actuation design to maximize the robot's average locomotion velocity emerges. Distinct from parameter optimization at given actuation patterns, the present paper represents the actuation design as the problem of optimal control and constructs an evolutionary algorithm to solve it. First, taking advantage of the periodicity, the internal actuation is represented as the Fourier series with the unknown period, harmonic coefficients, and phase shifts. Then, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is employed to optimize the unknown multi-parameters. Numerical results show that the optimal actuation of the one-module robot with isotropic friction is consistent with existing theoretical solutions, which verifies the correctness and practicability of our general scheme. Further explorations of the multi-module robot reveal that the optimal actuation continuously degenerates from the three-phase pattern to the two-phase when the friction ratio gradually attenuates to zero. Most importantly, although the optimal actuation phase shift between adjacent robot modules has been commonly accepted as half of the actuation period, the proposed scheme finds that the average velocity indeed maintains the maximum within a certain phase margin. As can be expected, this robustness will relax the burden of sophisticated actuation tuning in practice.