Gait Generation by Coupled Oscillators with the Stuart-Landau Equation

The modeling of gait generation in quadruped animals has been studied in various areas of science and engineering. Especially, it is important for the development of quadruped robots. In this paper, we adopt a model with coupled oscillators, in which, each oscillator is described by a nonlinear differential equation which is refered to as the Stuart-Landau equation. We consider a problem that is related to convergece of the phase differences of the oscillators to the suitable values for walking. Applying phase contraction, the equilibrium points of the phase difference system are analyzed. In order to coordinate the stable equilibrium point to be the suitable values, we clarified the condition and role of the parameters of the coupled oscillators, which are related to the stability of each equilibrium point of the system.