In this paper, we address the problem of optimization of trajectories for a new class of biped robot. The knees of this biped are similar as the anthropomorphic one and have a rolling contact between the femur and the tibia. The robot has seven mechanical links and six actuators. The walking gait considered is a succession of single support phase (SSP) and impact of the mobile foot with the ground. Cubic uniform spline functions defined on a time interval express the gait for one step. An energy consumption function and a torques quadratic function are used to compare the new robot with anthropomorphic knees to a conventional robot with revolute joint knees. The minimization of the criteria is made with simplex algorithm. The physical constraints concerning the ZMP and the mobile foot behavior are respectively checked to make a step. Simulation results show that the energy consumption of the new biped with rolling knee contact is less than that of the robot with revolute joint knees

The purpose is to define the range of feasible speeds for two walking motions for a particular planar biped robot, which differ in the definition of their finite-time double support phases. For each speed, these two walking motions are numerically obtained by using a parametric optimization algorithm, regarding a sthenic criterion. Results allow us to define the range of allowable speeds for each walking. One result is that the first gait is less consuming in energy for moderate to fast velocity with respect to the second one, while the second gait is more efficient for low walking velocity.