Computing Deform Closure Grasps

In prior work, we extended the well-known form closure grasp framework for rigid parts to a class of deformable parts, modeled as frictionless polygons with a finite element mesh and given stiffness matrix. We define the D-space (deformationspace) of a part as the C-space of all its mesh nodes and deform closure in terms of the work needed to release the part from a set of finger contacts. In the present paper, we define a measure of grasp quality for two-point deformclosure grasps. This metric is based on balancing the potential energy needed to release the part against the potential energy that would result in plastic deformation. Given two jaw contacts at the perimeter nodes, we give a numerical algorithm to determine the optimal jaw separation based on this metric. For a part with n mesh nodes and p perimeter nodes, the algorithm computes an approximation to the optimal separation in time O(n p + ( p/ε ) log p).