Optimal dynamics of constrained multibody systems. Application to bipedal walking synthesis

Optimal motion synthesis of closed-loop multibody systems is carried out using a penalty technique designed in order to avoid dealing with dynamic models described by differential algebraic equations. This approach allows for both implementing Pontryagin´s maximum principle as an optimization tool, and using the same state equation to describe the dynamics of structure-varying kinematic chains. The method presented is especially suitable to deal with unilateral mechanical constraints. We take advantage of this possibility to generate an optimal complete step of a planar biped.