Low-speed Limit Cycle Walking of Planar X-shaped Bipedal Robot with Special Properties

Abstract

This paper proposes a novel planar semicircular-footed X-shaped bipedal robot in which the center of mass of each leg link is at the same position as the hip joint, and discusses a method for generating a stable limit cycle gait on level ground. First, we outline the assumptions of the robot model with four degrees of freedom, and develop the mathematical equations of motion and collision. Second, we set the relative hip-joint angle as a control output and design a control system to follow it to the desired trajectory specified as a fifth-order function of time. Third, we mathematically show that there are special properties: the angular velocity of the swing leg does not change before and after the collision, and the time-integral of the control input becomes zero in a steady gait. We also mathematically show that the model has the feature that approximate linearization is effective and the antigravity effect of semicircular feet can be utilized. Through numerical simulations, we verify the validity of the theoretical results, and analyze some fundamental gait properties such as convergence speed and mechanical energy restoration.