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

The paper is aimed at generating optimal swing motions during the single-su pport phase of sagittal gait. Unlike the previous Part 1 which deals with p assive motions, all joints of the biped are assumed to be active in the pre sent 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 essen tially submitted to gravity forces, the motion is generated by minimizing t he joint actuating torques. Feasible motions are defined by state inequalit y constraints limiting joint motions, and defining foot clearance and obsta cle avoidance during the swing. The optimization problem is dealt with usin g Pontryagin's Maximum Principle. A final two-point boundary value problem is solved by implementing a shooting method. The approach presented is illu strated by various numerical simulations applying to a seven-body planar bi ped which has four or five active joints during the swing phase.