Suppression of Period-Doubling Bifurcation in Passive Dynamic Walking With Delayed Feedback Control

This paper investigates the effect of period-doubling bifurcation on passive dynamic walking (PDW) of a compass-like biped robot which consists of three point masses and two legs. The gait pattern of the robot consists of a single-support phase and a double-support phase which occurs instantaneously. The support and swing legs are exchanged at the double-support phase. Period-doubling bifurcation of PDW occurs when the slope angle of the ground becomes large, and the robot walks with a long step and a short step, alternately. Hip torque is designed based on delayed feedback control (DFC) to suppress the bifurcation. The equation of motion for the robot is numerically integrated and the walking speed is calculated. The simulation results show an increase in walking speed after a period-two gait emerges. Then, DFC is applied to the gait and stabilizes it to a period-one gait. After a period-four gait emerges, DFC is also applied to the period-four gait and stabilize it to period-two and period-one gaits. By comparing the period-one gait with the period-four and the period-two gaits, it is shown that the period-two gait has the fastest mean walking speed. The effect of the robot parameters is investigated and it is shown that the fastest walking speed for the period-one gait can be obtained when a leg mass position is chosen to a certain value.