Sagittal gait of a biped robot during the single support phase. Part 2: optimal motion

Abstract

The paper is aimed at generating optimal swing motions during the single-support phase of sagittal gait. Unlike the previous Part 1 which deals with passive motions, all joints of the biped are assumed to be active in the present Part 2. The final conditions specify an impactless heel-touch in order to avoid a destabilizing effect on the biped motion. As the biped is essentially submitted to gravity forces, the motion is generated by minimizing the joint actuating torques. Feasible motions are defined by state inequality constraints limiting joint motions, and defining foot clearance and obstacle avoidance during the swing. The optimization problem is dealt with using Pontryagin's Maximum Principle. A final two-point boundary value problem is solved by implementing a shooting method. The approach presented is illustrated by various numerical simulations applying to a seven-body planar biped which has four or five active joints during the swing phase.