Efficient parametric excitation walking with delayed feedback control

In the passive dynamic walking proposed by McGeer, mechanical energy lost by heel strike is restored by transporting potential energy to kinetic energy as walking down a slope. When energy input is large such as an angle of slope is steep, bifurcation of walking period occurs. In parametric excitation walking, which is one method to realize passive dynamic-like walking on level ground, bifurcation has also been observed when walking speed is fast. Asano et al. have shown that bifurcation exerts an adverse influence upon walking performance by using rimless wheel model. In this paper, we apply delayed feedback control (DFC) originally used in chaos control to parametric excitation walking to suppress bifurcation. We show in numerical simulation that the proposed method makes two-period walking to one-period walking, and energy efficiency is improved. The analyses using Poincare¿ map reveal that the one-period walking with DFC is unstable periodic orbit and that the robot dealt in this paper satisfies the sufficient condition of applicability of DFC.