Cyclic-fold bifurcation in passive bipedal walking of a compass-gait biped robot with leg length discrepancy

We report on the analysis of passive bipedal walking patterns generated by a compass-gait biped robot having leg length discrepancy. Such two-degrees-of-freedom biped robot but with equal leg length is known to walk passively and steadily down sloped surfaces without any source of actuation. It is known also that the passive walk exhibits only a period-doubling bifurcation leading to chaos in response to a change in some inertial or geometric parameter. In this paper, we show through bifurcation diagrams that the compass-gait biped with leg length discrepancy reveals also cyclic-fold bifurcations in its passive dynamics walking pattern. We show also that such bifurcations occur in pair giving rise to the coexistence of two distinct attractors which can be either periodic or chaotic. Furthermore, we stress that a cyclic-fold bifurcation is responsible on the fall down of the biped robot and also on the generation of another new walking patterns. In this paper, the hybrid model of the compass gait model is given. The whole dynamic model is normalized and is written with respect to a normalized parameter expressing discrepancy percentage in leg length.