Closure and Quality Equivalence for Efficient Synthesis of Grasps from Examples

One goal of grasp selection for robotics is to choose contact points that guarantee properties such as force- or form-closure. Many efficient algorithms have been developed to address this problem, but most of these algorithms focus on grasps having a minimal number of contact points. Increasing the number of contacts can dramatically improve the quality and flexibility of grasps that are constructed. However, computation time becomes a problem, as grasp synthesis algorithms that can be generalized to an arbitrary number of contacts typically require time exponential in the number of contacts. This paper presents an efficient algorithm for synthesis of many-contact grasps. The key idea is to geometrically construct families of grasps around a single example such that all grasps within a family meet user-specified design goals. We show that our construction technique can be used to form force-closure grasps, partial force-closure grasps, and grasps above a quality threshold. Our approach requires time polynomial in the number of contacts, making it feasible to handle grasps with relatively large numbers of contacts. Results are shown for three-dimensional grasps with friction having five to twelve contacts and specialized for a variety of tasks. We have used this approach to design grasps for a robot hand and quasi-static manipulation plans for a humanoid robot.