Optimization of coupling weights in a 4-cell central pattern generator network for bipedal locomotion gait generation

Locomotion regulation of a robot according to path conditions is one of the main interests in the robotics, because it enables the robot to move in unknown environments. This can be realized using inspiration from the human and animal's bio-mechanism in generating various motion patterns called central pattern generator (CPG). These motion patterns are called “gaits” and changing between the motion patterns is called “gait transition”. Many models have been proposed to model CPGs and used for trajectory generating of various mobile robots. In this paper, a type of CPG network called 4-cell CPG model is studied to generate the rhythmic signals of the ankle joints in a bipedal locomotion gaits. This model is composed of four coupled identical cells whose internal dynamics is described by the Morris-Lecar nonlinear differential equations and the couplings between the cells follow the diffusive type. The generation of various locomotion gaits depends on the adjustment of the phase differences between rhythmic signals produced by the cells. The phase differences, in-turn, are obtained via properly adjusting the coupling weights between the cells. Here, we exploit a non-dominated sorting genetic algorithm (NSGA-II) to find the best set of coupling weights for maximally approaching the desired phase differences of the primary bipedal gaits of walk, run, two-legged jump, and two-legged hop. Also, some secondary bipedal gaits, especially one that called “hesitation walkˮ, are obtained by symmetry breaking bifurcations of the primary gaits. The “hesitation walkˮ has already predicted in [28], however the authers could not generate it.