Simple controllable walking mechanisms which exhibit bifurcations

We revisit the semi-passive, torso-driven biped model proposed by McGeer (1993) and remark upon the discovery of additional gait behaviors when driven in its simplest locomotion strategy. The two-dimensional model we study utilizes the simplifying mass-distribution assumptions of Garcia et al. for a slope-driven, passive-dynamic biped (1998). It is found that the torso-driven biped model exhibits the same richness of gait behaviors as slope-driven biped models. A homotopy method is used to locate the torso-driven biped gaits from the equilibrium gait behavior of the slope-driven biped. The method is also used to find previously missing gaits for slope-driven bipeds, including a stable period-3 gait. Control of these simple walking mechanisms is accomplished by careful choice of parameter settings. The knowledge of additional gaits is useful in prescribing these settings.