Displayed phenomena in the semi-passive torso-driven biped model under OGY-based control method: Birth of a torus bifurcation

We consider the displayed phenomena in the semi-passive dynamic walking of a torso-driven biped robot under the OGY control method as it descends inclined surfaces. The desired torso angle is the accessible control parameter. Analysis of the controlled steady semi-passive gaits are carried out mainly by means of bifurcations diagrams and Poincaré sections as the slope parameter varies. Based on Floquet multipliers, we show that a torus bifurcation was born leading hence to the generation of a quasi-periodic bipedal walking. Analysis of the controlled semi-passive dynamic walking is investigated also through a constrained controlled Poincaré map. We demonstrate that a such controlled map and the controlled impulsive hybrid nonlinear model of the biped display almost the same phenomena. We show also that the controlled constrained Poincaré map exhibits a discontinuous period-doubling bifurcation.