Impulsive control for a thirteen-link biped

A thirteen-link biped with twelve actuated joints in three dimensional space is considered in this paper. The objective is to design a ballistic motion numerically for this biped. A first dynamical model of the biped is calculated in single support only. A second dynamical model tacking into account the wrench reaction from the ground is calculated for the single support phase and the double support phase. These two models are founded on the Newton Euler algorithm, considering that the reference frame is connected to a stance foot. At the impact the biped loses energy, the ballistic motion cannot be cyclic. Then impulsive controls around the impact are designed to overcome this lost energy and to obtain a cyclic motion. The initial and final configurations of the biped for the ballistic motion and the energy are calculated using an optimization process. Constraints such no take off, no sliding, and position of the center of pression are considered for these optimizations algorithms