A Framework for Optimal Grasp Contact Planning

We consider the problem of finding grasp contacts that are optimal under a given grasp quality function on arbitrary objects. Our approach formulates a framework for contact-level grasping as a path finding problem in the space of supercontact grasps. The initial supercontact grasp contains all grasps and in each step along a path grasps are removed. For this, we introduce and formally characterize search space structure and cost functions under which minimal cost paths correspond to optimal grasps. Our formulation avoids expensive exhaustive search and reduces computational cost by several orders of magnitude. We present admissible heuristic functions and exploit approximate heuristic search to further reduce the computational cost while maintaining bounded suboptimality for resulting grasps. We exemplify our formulation with point-contact grasping for which we define domain specific heuristics and demonstrate optimality and bounded suboptimality by comparing against exhaustive and uniform cost search on example objects. Furthermore, we explain how to restrict the search graph to satisfy grasp constraints for modeling hand kinematics. We also analyze our algorithm empirically in terms of created and visited search states and resultant effective branching factor.