C.A. Pinto and M. Golubitsky
Central pattern generators for bipedal locomotion
J. Math. Biol.
53 (2006) 474-489.
We use symmetry to study two central pattern generator
(CPG) models for biped locomotion. The first one is a coupled
four-cell network, proposed by Golubitsky, Stewart, Buono, and
Collins, that models rhythms associated to legs. A classification
based on symmetry shows that this network can produce periodic
solutions with rhythms corresponding to the standard bipedal
gaits of run, walk, hop, gallop, and skip, among others.
Moreover, the four-cell model can produce two types of hop,
two types of gallop, and three additional symmetry types of
periodic solutions that have yet to be identified with the rhythms
of known bipedal gaits. The second locomotor CPG network models interlimb
coordination in bipeds (arms+legs). It is obtained by breaking the
symmetry between fore and hind legs in an eight-cell CPG network for quadruped
gaits, also proposed by Golubitsky et al. We match the rhythms of
perturbed periodic solutions found in this eight-cell network with legs rhythms
produced by the four-cell CPG model. We also compare patterns of oscillation
of gaits of the eight-cell model with results on bipedal interlimb coordination
in the literature, showing that the eight-cell model is a plausible network
for modeling human interlimb coordination.
We show numerical simulations of periodic solutions corresponding
to the bipedal gaits in the two CPG models. These simulations
use clamped Hodgkin-Huxley equations to model cell internal
dynamics and partial linear coupling (where only the electrical
potentials of different cells are coupled). We use synaptic
coupling in the four-cell model and diffusive coupling in the
eight-cell model.