Gaits generation of quadruped locomotion for the CPG controller by the delay-coupled VDP oscillators

Generating locomotive gaits is a very important work for bioinspired robots and has received wide attentions among scientists and engineers. The central pattern generator (CPG) neural system located in spinal cord is a very important imitating object to produce rhythm patterns and control locomotion of animals. This paper proposes a theoretical method to construct a novel style CPG controller for the quadruped locomotive gait based on the delay-coupled VDP oscillators. The controller system consists of four VDP oscillators scheduled with unidirectional ring structure. By using the Hopf bifurcation analysis, we obtain parameter conditions for rhythm generation and present dynamical classification of periodic rhythm with different spatiotemporal patterns, which corresponds to the gait of the quadruped locomotion. Assisting with switching network structure, the delayed VDP-CPG controller presents six types of classical locomotive gaits, i.e., pronk, lateral-sequence (L-S) walk, diagonal-sequence (D-S) walk, bound, pace, and trot, in a wide range of parameter areas. The numerical simulations are illustrated to agree with theoretical analysis. The presented approach herein provides a frame of dynamical analysis to build the CPG controller producing rhythm controlling signals of the quadruped locomotion gaits.