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 under-actuated 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 biped robot is useful to reduce the energy consumed in the walking. For simplicity only a planar biped is considered. In order to study the efficiency of this phase, four cyclic gaits are presented. For these gaits optimal motions with respect to the torque cost are defined for given performances of actuators. It is shown that for fast motions a foot rotation sub-phase is useful to reduce the criteria cost. In the optimization process, under-actuated phase (foot rotation phase), fully-actuated phase (flat foot phase) and over-actuated phase (double support phase) are considered.

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