Efficiency and Optimality of Two-Period Limit Cycle Walking

This paper investigates the efficiency of a 2-period gait from the kinetic energy view-point. First, we formulate a steady 2-period gait for a compass-like bipedal robot by using a simple recurrence formula for the kinetic energy of an asymmetric rimless wheel. Second, we theoretically show that, in the case that the mean value of the hip angle is constant, the generated 2-period steady gait is less efficient than a 1-period symmetric one in terms of kinetic energy. We also show that the symmetric gait is not always optimal from another viewpoint. We then extend the analysis to biped walking and investigate the validity of the derived method through numerical simulations of virtual passive dynamic walking. keywords: Limit cycle walking, 2-period gait, kinetic energy, efficiency, rimless wheel