Synthesis of Energy-Bounded Planar Caging Grasps Using Persistent Homology
Jeffrey Mahler, Florian T. Pokorny, Sherdil Niyaz, Ken Goldberg · IEEE Transactions on Automation Science and Engineering · 2018
For applications such as manufacturing, caging grasps restrict object motion without requiring complete immobilization, providing a robust alternative to forceand form-closure grasps. Energy-bounded cages are a new class of caging grasps that relax the requirement of complete caging in the presence of external forces such as gravity or constant velocity pushing in the horizontal plane with Coulomb friction. We address the problem of synthesizing planar energy-bounded cages by identifying gripper and force-direction configurations that maximize the energy required for the object to escape. We present Energy-BoundedCage-Synthesis-2-D (EBCS-2-D), a sampling-based algorithm that uses persistent homology, a recently-developed multiscale approach for topological analysis, to efficiently compute candidate rigid configurations of obstacles that form energy-bounded cages of an object from an α-shape approximation to the configuration space. If a synthesized configuration has infinite escape energy then the object is completely caged. EBCS-2-D runs in O(s3+ sn2) time, where s is the number of samples and n is the number of object and obstacle vertices, where typically n ≪ s. We observe runtimes closer to O(s) for fixed n. We implement EBCS-2-D using the persistent homology algorithms toolbox and study performance on a set of seven planar objects and four gripper types. Experiments suggest that EBCS-2-D takes 2-3 min on a 6 core processor with 200000 pose samples. We also confirm that an rapidly-exploring random tree* motion planner is unable to find escape paths with lower energy. Physical experiments on a five degree of freedom Zymark Zymate and ABB YuMi suggest that push grasps synthesized by EBCS-2-D are robust to perturbations. Data and code are available at http://berkeleyautomation.github.io/caging/.