6DLS: Modeling Nonplanar Frictional Surface Contacts for Grasping using 6D Limit Surfaces (1909.06885v4)

Abstract: Robot grasping with deformable gripper jaws results in nonplanar surface contacts if the jaws deform to the nonplanar local geometry of an object. The frictional force and torque that can be transmitted through a nonplanar surface contact are both three-dimensional, resulting in a six-dimensional frictional wrench (6DFW). Applying traditional planar contact models to such contacts leads to over-conservative results as the models do not consider the nonplanar surface geometry and only compute a three-dimensional subset of the 6DFW. To address this issue, we derive the 6DFW for nonplanar surfaces by combining concepts of differential geometry and Coulomb friction. We also propose two 6D limit surface (6DLS) models, generalized from well-known three-dimensional LS (3DLS) models, which describe the friction-motion constraints for a contact. We evaluate the 6DLS models by fitting them to the 6DFW samples obtained from six parametric surfaces and 2,932 meshed contacts from finite element method simulations of 24 rigid objects. We further present an algorithm to predict multicontact grasp success by building a grasp wrench space with the 6DLS model of each contact. To evaluate the algorithm, we collected 1,035 physical grasps of ten 3D-printed objects with a KUKA robot and a deformable parallel-jaw gripper. In our experiments, the algorithm achieves 66.8% precision, a metric inversely related to false positive predictions, and 76.9% recall, a metric inversely related to false negative predictions. The 6DLS models increase recall by up to 26.1% over 3DLS models with similar precision.