A central pattern generator network for simple control of gait transitions in hexapod robots based on phase reduction

Abstract

Abstract We present a model of the central pattern generator (CPG) network that can control gait transitions in hexapod robots in a simple manner based on phase reduction theory. Our CPG network consists of six weakly coupled limit-cycle oscillators as the CPG units, where arbitrary smooth limit-cycle oscillators can be employed as the CPG unit. The synchronization dynamics of the six multidimensional limit-cycle oscillators can be described by six one-dimensional phase equations through phase reduction. Utilizing the symmetries in the specific hexapod gaits, the six phase equations of the CPG network can further be reduced to two independent equations for the phase differences, which enables us to analyze the gait transition dynamics easily. By choosing appropriate coupling functions for the CPG network, we can achieve desired synchronization dynamics regardless of the detailed properties of the limit-cycle oscillator used for the CPG unit. The effectiveness of our CPG network is demonstrated by numerical and physical simulations of gait transitions between the wave, tetrapod, and tripod gaits, using the FitzHugh-Nagumo oscillator as the CPG unit.