Walking Dynamics of the 2-Link Compass Biped Robot: Further Analysis Using the First Explicit Form of the Poincaré Map

In our previous studies, we have focused on generating a new explicit form of the Poincaré Map (P Map) in order to investigate and control the passive walking dynamics of the 2 -link compass biped robot. The developed explicit form was evaluated by varying the surface slope angle and comparing the results to the original natural behavior of the biped robot. In the present paper, our objective is to explore different aspects of the biped robot's passive walking dynamics by investigating further the first explicit form of the P-Map and identifying local bifurcations for different nominal slope angles. We demonstrate that the observed results align with our earlier findings and a local bifurcation; namely the subcritical flip bifurcation is detected highlighting the period-doubling bifurcation phenomenon observed in the overall system. This research represents the first milestone in our forthcoming work which focuses on tracking and depicting unstable limit cycles and developing energy-efficient control laws.