Gait transition in a central pattern generator for bipeds ⋆

In this paper we study gait transition in a central pattern generator (CPG) model for bipedal locomotion. This model is proposed by Golubitsky, Stewart, Buono and Collins (14; 15) and is studied further by Pinto and Golubitsky (28). It is a network of four coupled identical cells, with D2 symmetry. Each cell is modeled by a system of ordinary differential equations. We briefly review the work done in (28). We revisite the symmetry arguments that allow us to enumerate the periodic solutions predicted by the CPG model, identified with primary and secondary gait types. Using bifurcation theory, we list the bifurcations between these two types of gaits. We compute gait transition in the 4-cell CPG model for bipeds. We use the MorrisLecar equations (26; 34) as the internal dynamics for each cell. We consider two types of coupling between the cells: diffusive and synaptic. We obtain the secondary gait skip by bifurcation of the primary gaits walk and run. The secondary gait gallop is obtained by bifurcation of the primary gait walk.