Synthesis of Energy-Bounded Planar Caging Grasps Using Persistent Homology

For applications such as manufacturing, caging grasps restrict object motion without requiring complete immobilization, providing a robust alternative to force- and 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-Bounded-Cage-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 <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">$O(s^{3} + s n^{2})$ </tex-math></inline-formula> time, where <inline-formula> <tex-math notation="LaTeX">$s$ </tex-math></inline-formula> is the number of samples and <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is the number of object and obstacle vertices, where typically <inline-formula> <tex-math notation="LaTeX">$n \ll s$ </tex-math></inline-formula>. We observe runtimes closer to <inline-formula> <tex-math notation="LaTeX">$O(s)$ </tex-math></inline-formula> for fixed <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>. 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 200 000 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 <uri>http://berkeleyautomation.github.io/caging/</uri>. <italic>Note to Practitioners</italic>—For automation applications in manufacturing where object models are precisely known, “energy-bounded cages” are a robust approach to robot grasping in the presence of gravity or friction. This paper presents a synthesis algorithm for planar instances, where the object can be modeled as a planar extrusion and the motion occurs in the vertical or horizontal plane. We also present experiments with robots and a website with code and data.