The objective of this study is to obtain optimal cyclic gaits for a biped robot without actuated ankles. Two types of motion are studied: walking and running. For walking, the gait is composed uniquely of successive single support phases and instantaneous double support phases that are modelled by passive impact equations. The legs swap their roles from one single support phase to the next one. For running, the gait is composed of stance phases and flight phases. A passive impact with the ground exists at the end of flight. During each phase the evolution of m joints variables is assumed to be polynomial functions, m is the number of actuators. The evolution of the other variables is deduced from the dynamic model of the biped. The coefficients of the polynomial functions are chosen to optimise criteria and to insure cyclic motion of the biped. The chosen criteria are: maximal advance velocity, minimal torque, and minimal energy. Furthermore, the optimal gait is defined with respect to given performances of actuators: The torques and velocities at the output of the gear box are bounded. For this study, the physical parameters of a prototype, which is under construction, are used. Optimal walking and running are defined. The running is more efficient for high velocities than the walking with respect to the studied criteria.

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International audienceFast humanwalking 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 current humanoid robots. The objective of this study is to determine whether the introduction of this phase for a 3-D bipedal 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 a flat stance foot on the ground, and the stance foot does not rotate. The second cyclic motion is composed of single-support phases that include a subphase of rotation of the supporting foot about the toe. The single-support phases are separated by a double-support phase. For simplicity, this double-support phase is considered as instantaneous (passive impact). For these two gaits, optimal motions are designed by minimizing the torques cost. The given performances of actuators are taken into account. It is shown that, for a fast motion, a foot-rotation subphase is useful to reduce the cost criterion. These gaits are illustrated with simulation results

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 this phase is useful to reduce the energy consumed in the walking. In order to study the efficiency of this phase, six cyclic gaits are presented for a planar biped robot. The simplest cyclic motion is composed of successive single support phases with flat stance foot on the ground. The most complex cyclic motion is composed of single support phases that include a subphase of rotation of the stance foot about the toe and of finite time double support phase. For the synthesis of these walking gaits, optimal motions with respect to the torque cost, are defined by taking into account 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), fullyactuated phase (flat foot phase) and over-actuated phase (double support phase) are considered.