Investigation of the Effects on Stability of Foot Rolling Motion Based on a Simple Walking Model

The motion of the lower limbs in bipedal walking is characterized by a foot-rolling motion, including heel-strike and toe-off. In this paper, the dynamical influence of this motion on walking stability is examined using a simple walking model driven by a rhythmic signal from an internal oscillator. In order to model the rolling motion, a circular arc is attached to the tip of the legs. In particular, we obtained approximate periodic solutions and analyzed the dependence of the local stability on the circular arc radius using a Poincaré map, which revealed that the circular arc radius is optimal when it is similar in size to the leg length, to maximize the stable region for such characteristic parameters as mass ratio and walking speed. On the other hand, it is also found that a circular arc radius of zero maximizes the rate of convergence to the stable walking motion. These conflicting results imply that the optimal radius of a circular arc with respect to local stability exists from a tradeoff between these different criteria, which should be considered in designing a biped robot.