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.