Manipulation planning with contacts for an extensible elastic rod by sampling on the submanifold of static equilibrium configurations

We consider the manipulation planning problem of an extensible elastic rod in collision-free or contact space. We assume the rod can be handled by grippers either at both or at only one of its extremities and during the manipulation, the grasped end may change. We show that the use of both quasi-static and dynamic models can be coupled efficiently with sampling-based methods. By sampling directly on the submanifold of static equilibrium and contact-free configurations, we can take advantage of the dynamic model to improve the exploration in the state space. We show the necessity of considering contacts for this type of problems with several simulation experiments on various scenarios.