Bifurcations and chaos in passive walking of a compass-gait biped with asymmetries

In this paper we study the problem of passive walking for a compass-gait biped with gait asymmetry. In particular, we identify and classify bifurcations leading to chaos caused by gait asymmetries due to unequal leg masses. We present bifurcation diagrams showing step period versus the ratio of leg masses at various walking slopes. The cell mapping method is used to find stable limit cycles as the parameters are varied. It is found that a variety of bifurcation diagrams can be grouped into six stages that consist of three expanding and three contracting stages. The analysis of each stage shows that passive dynamic walking has multiple attractors depending on initial conditions, and marginally stable limit cycles exhibit not only period doubling, but also period remerging, disconnecting, and disappearing. We also show that the rate of convergence of period doubling sequences is in good agreement with the Feigenbaum constant.