3D walking biped: optimal swing of the arms

A ballistic walking gait is designed for a 3D biped with two identical two-link legs, a torso, and two identical one-link arms. In the single support phase, the biped moves due to the existence of a momentum, produced mechanically, without applying active torques in the interlink joints. This biped is controlled with impulsive torques at the instantaneous double support to obtain a cyclic gait. The impulsive torques are applied in the seven interlink joints. Then an infinity of solutions exists to find the impulsive torques. An effort cost functional of these impulsive torques is minimized to determine a unique solution. Numerical results show that for a given time period and a given length of the walking gait step, there is an optimal swinging amplitude of the arms. For this optimal motion of the arms, the cost functional is minimum.