Low energy cost reference trajectories for a biped robot

The impulsive torque at the beginning and end of the ballistic motion between these two instants give energetically optimal motion for a pendulum. Many authors assume that in human walking, muscle activities alternate with some periods of relaxation. From these two arguments, we assume that a motion defined by ballistic motion and impulsive control at dual support instances will lead to an energetically economical trajectory. Optimal configurations are defined, and smooth changes on the reference trajectory are proposed to obtain a trajectory which can be followed with finite torques. The physical constraints on the reaction forces to avoid take off or sliding of the biped walking robot, and saturation on the torques produced by the actuators are explicitly taken into account