  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. The CPG network consists of six weakly coupled limit-cycle
oscillators, whose synchronization dynamics can be described by six phase
equations through phase reduction. Focusing on the transitions between the
hexapod gaits with specific symmetries, the six phase equations of the CPG
network can further be reduced to two independent equations for the phase
differences. By choosing appropriate coupling functions for the network, we can
achieve desired synchronization dynamics regardless of the detailed properties
of the limit-cycle oscillators used for the CPG. The effectiveness of our CPG
network is demonstrated by numerical simulations of gait transitions between
the wave, tetrapod, and tripod gaits, using the FitzHugh-Nagumo oscillator as
the CPG unit.
