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.

The goal of this paper is to define a control law and reference trajectories for a legged robot with feet. We use a computed torque control law associated with a desired motion of the legged robot derived from a ballistic trajectory. This approach leads to the same distribution of the torques as it can be observed for humans, and respects the assumption that muscle activities alternate with some periods of relaxation. Simulations are made on a simple model of quadruped for a dynamically stable planar gait.

In this paper, two methods to calculate the direct dynamic model (DDM) of walking robots are presented. These methods derive from the Walker-Orin (1982) method and from the Featherstone (1983) method, generally used to compute the DDM of robot manipulators. The comparison is made on the number of operations for each method and for walking robots: a biped robot and a quadruped robot. It is shown that Featherstone's method is better than Walker-Orin's one.