Two-stage optimization for energy-efficient bipedal walking

This paper proposes a two-stage optimization strategy for energy-efficient gait generation. At the first stage, by tracking the reference zero moment point (ZMP) trajectory, the optimal center of mass (CoM) trajectory, which contributes to the minimal unit energetic cost (UEC) of one step, is solved analytically by using an unconstrained optimization method. At the second stage, to minimize the multi-joint mechanical work, the ZMP reference during the single support phase is optimized by a constrained optimization method. As a result, by considering the feasibility constraints such as the limitation on ZMP movement, the energy-efficient walking patterns can be generated in real-time. Furthermore, the energetic performances under different step parameter configurations, which consist of step length, step duration, and time ratio of double support, are discussed. Simulations and hardware experiments have demonstrated the energetic benefits of the proposed strategy when compared with other state-of-the-art works.