Arc Feet Effects on Stability Based on a Simple Oscillator-Driven Walking Model

Lower-extremity movement in bipedal walking is characterized by a foot-rolling motion that includes heel-strike and toe-off. We investigated the dynamical influence of this movement on walking stability using a simple walking model that has a circular arc at the end of each leg. The leg is driven by a rhythmic signal from an internal oscillator to generate walking. We focused on stability characteristics due to the arc foot based on (1) the stability region for parameters such as mass distribution and walking speed, in which the circular arc radius is optimal when it is almost the same length as the leg to maximize the stable region and (2) the rate of convergence to stable walking, which is maximized by a circular arc radius of zero. These two conflicting results imply that the optimal radius of a circular arc for local stability is a trade-off between the two criteria, reflecting a dynamic feature of bipedal walking that should be considered in biped robot design.