Abstract
Rhythmic movements of walking, swimming, etc. are controlled by mutually coupled endogenous neural oscillators. These rhythms coordinate with one another to generate temporal and spatial moving patterns suitable for their environments and purposes. The walking motion of quadruped is a representative example; here, the periodic motions of each limb coordinate to generate stable gait patterns suitable for the organism's moving speeds and environments. These patterns are mainly decided by the locomotive speed; i.e. as a cat moves faster, the gait patterns change from “walk” to “trot”, and lastly to “gallop”. This moving pattern generator system can be ragarded as one of the autonomous distributed systems which generate global patterns suitable for their environments and purposes.
This paper shows an approach for constructing such a moving pattern generator system by use of the bifurcation concepts in nonlinear system. Let the total dynamic system that represents a global pattern be a gradient system with an auxiliary potential function, then the desirable patterns can be generated by specifying the potential functions. Also, the patterns are changeable by altering the potential functions. Further, using the bifurcation concepts, it is possible to construct a system that suitably changes patterns discontinuously according to continuous change of a parameter. This synthesis approach is applied to construct a gait pattern generator of a quadruped artificially. A gait pattern generator is realized to couple four oscillators in which each oscillating state is regarded as each limb's rhythmic motion. Finally, it is shown using computer simulations that the proposed system generates and changes patterns suitable for some moving speeds; i.e. “walk”, “trot” and “gallop”.
