Design of convex foot for efficient dynamic bipedal walking

In this paper, we consider the effects of feet in various convex shapes on the performance of underactuated passive dynamic walking. We first derive formula for calculating virtual ankle-joint torque and a performance index of dissipated mechanical energy for a convex foot shape model with general foot shape parameterization. Secondly, using the foot shape determined by a 2nd Bezier curve with which a form can be controlled easily, we calculate a value of the virtual ankle-joint torque and the performance index of dissipated mechanical energy to verify effects of change in foot shape. Furthermore, relationship between the foot shapes and the walking speeds are clarified by a numerical simulation. Finally, we propose a method to design a convex foot shape that attains a desired virtual ankle-joint torque and verify an improvement of the walking speed by a numerical simulation with the foot shape that is designed by the proposed method. We believe that the proposed method will be applied to design effective active ankle-joint torque and/or to design a foot shape for biped robots.