Numerical Simulations in Two CPG Models for Bipedal Locomotion

Abstract

Pinto and Golubitsky proposed a new model for a central pattern generator (CPG) for arm/leg coordination in bipeds, the network arm. arm is derived from a CPG quadruped model (quad) by breaking the symmetry between fore- and hind limbs. This paper explores numerically some of the solution properties of two general CPG models: arm and a CPG model for leg rhythms in bipeds (which is called leg). It is assumed that the internal dynamics of each cell is modeled by a space-clamped Hodgkin—Huxley equation and the coupling is only through the voltage term. Numerical simulations are done using XPPAUT. Secondary gaits in leg are obtained from bifurcation of the Poincaré map of a primary gait. Examples of secondary gaits are gallop, asymmetric hop, one-legged hop, and skip. In particular, the gallop is obtained by bifurcation from the primary gait two-legged jump. Numerical evidence of this is shown. Numerical simulations are given of periodic solutions in arm identified with arm/leg coordination patterns in bipeds.