Energy Optimal Trajectory Planning of Biped Walking Motion

Abstract

This paper describes an optimal trajectory planning of walking locomotion for a planar biped walking mechanism which has thighs, shanks and small feet. The biped mechanism was modeled to be a 3-degree-of-freedom (dof) link system composed of a stance leg and a 2-dof swing leg. The one step walking locomotion is divided into two phases, i.e., the swing motion of 2-dof swing until knee collision and the swing motion of the straight leg until toe collision. It is assumed that the knee collision of the swing leg and the toe collision at the foot exchange are plastic and occur instantly. The motion of the swing and stance legs in the first phase is solved by the optimal trajectory planning based on the function approximation method. Under the full-actuated condition at the hip, knee and ankle joints, we obtained the optimal trajectory solution with a minimum square integral of input torque. We also obtained a sub-optimal walking locomotion for an under-actuated system whose ankle is a passive joint. The validity of the optimal trajectory solution is confirmed by a forward dynamic simulation. The optimal trajectory solution for the human body parameter values exhibits a natural and stable walking locomotion with the step length of 0.33 m and a step period of 0.62 s.