A ballistic walking gait is designed for a planar biped with two identical two-link legs, a trunk and two one-link arms. This seven-link biped is controlled via impulsive torques at the instantaneous double support to obtain a cyclic gait. These impulsive torques are applied in six inter-link joints. Then infinity of solutions exists to find the impulsive torques. An energy cost functional of these impulsive torques is calculated to choose a unique solution by its minimization. Numerical results show that for a given time period of the walking gait step and a length of the step, there exists an optimal swinging amplitude of arms. For this optimal motion of the arms, mentioned above cost functional is minimum.

A bicycle with a gyroscopic stabilisation capable of autonomous motion along a straight line as well as along a curve is described. The stabilisation unit consists of two coupled gyroscopes spinning in opposite directions. It makes use of a gyroscopic torque due to the precession of gyroscopes. This torque counteracts the destabilising torque due to gravity forces. The control law of the actuator drive making the gyroscopes to process is described.

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.