  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.
