Stability characteristics in walking behavior with two different oscillatory elements: Roles of arc foot and internal oscillator

Simple models with circular arc feet rigidly mounted to the shank of the leg are widely used to investigate bipedal walking behavior. We use a simple walking model with arc feet, whose swing leg is driven by a rhythmic signal from an internal oscillator. The dynamical effects of the arc feet resemble flat feet mounted on ankles with a torsional spring, where the circular arc radius of the arc feet has similar dynamical characteristics to the spring stiffness in the ankle torque. Walking behavior generally consists of the falling motion of the body relative to the stance and the swinging motion of the swing leg. However, when the circular radius exceeds a certain threshold, the body motion changes from such divergent behavior to oscillatory behavior due to the dynamical influence inherent in the arc feet, and the mechanism to create walking behavior greatly changes. Since our model is driven by a rhythmic signal from the oscillator, the walking behavior is driven by two different oscillatory elements and the relationship between them plays an important role. In this paper, we clarify the dynamical effect of the relationship on walking stability.