Stability Analysis of Passive Monopedal Dynamic Hopping

Passive dynamic locomotion occurs through the interaction of an object’s dynamics and the ground, using no actuators, sensors, or controls. Passive dynamics is important for exploring the principles of human and animal locomotion. An important characteristic is that there might be a stable limit cycle for passive dynamic locomotion. Expression of stable limit cycles in passive bipedal walking, bipedal running, and quadrupedal running has been confirmed. However, studies conducted to date have characterized passive monopedal hopping as unstable. We investigated the dynamic stability of the passive monopedal hopping without torso pitch. Numerical simulation revealed that the passive monopedal hopping examined in this study has a stable limit cycle. Moreover, both theoretical analysis and simulation results suggest that asymptotically stable fixed points of the 1-PDH model are related closely to the leg spring damping ratio and the hopping period. Results show that the 1-PDH model has high stability with respect to steps. Additionally, findings indicate that changes in leg spring stiffness cause changes in forward velocity during stable hopping with no feedback control.