Optimal reference walking with rotation of the stance feet in single support for a 3D biped

Fast human walking includes a phase where the stance heel rises from the ground and the stance foot rotates about the stance toe. This phase where the biped becomes underactuated is not present during the walk of humanoid robots. The objective of this study is to determine if the introduction of this phase for a 3D biped robot is useful to reduce the energy consumed in the walking. In order to study the efficiency of this new gait, two cyclic gaits are presented. The first cyclic motion is composed of successive single support phases with flat stance foot on the ground. The second cyclic motion includes a sub-phase of rotation of the supporting foot about the toe. For these two gaits, optimal motions are designed by minimizing a functional torques cost. It is shown that for fast motion a foot rotation sub-phase is useful to reduce the functional cost.