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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 3-D, resulting in a 6-D frictional wrench (6DFW). Applying traditional planar contact models to such contacts leads to overconservative results as the models do not consider the nonplanar surface geometry and only compute a 3-D 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 6-D limit surface (6DLS) models, generalized from well-known 3-D 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 2932 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 1035 physical grasps of ten 3-D-printed objects with a KUKA robot and a deformable parallel-jaw gripper. In our experiments, the algorithm achieves 66.8&#x0025; precision, a metric inversely related to false positive predictions, and 76.9&#x0025; recall, a metric inversely related to false negative predictions. The 6DLS models increase recall by up to 26.1&#x0025; over 3DLS models with similar precision.<xref ref-type="fn" rid="fn1"><sup>1</sup></xref>

6DLS: Modeling Nonplanar Frictional Surface Contacts for Grasping Using 6-D Limit Surfaces