Dynamic Stability of a Simple Biped Walking System with Swing Leg Retraction

In human walking, the swing leg moves backward just prior to ground contact, i.e. the relative angle between the thighs is decreasing. We hypothesize that this swing leg retraction may have a positive effect on gait stability, because similar effects have been reported in passive dynamic walking models, in running models, and in robot juggling. For this study, we use a simple inverted pendulum model for the stance leg. The swing leg is assumed to accurately follow a time-based trajectory. The model walks down a shallow slope for energy input which is balanced by the impact losses at heel strike. With this model we show that a mild retraction speed indeed improves stability, while gaits without a retraction phase (the swing leg keeps moving forward) are consistently unstable. By walking with shorter steps or on a steeper slope, the range of stable retraction speeds increases, suggesting a better robustness. An optimization of the swing leg trajectory of a more realistic model also consistently comes up with a retraction phase, and indeed our prototype demonstrates a retraction phase as well. The conclusions of this paper are twofold; (1) use a mild swing leg retraction speed for better stability, and (2) walking faster is easier.