Computing All Independent Form-Closure Grasp Regions of a Rectilinear Polyhedron

Immobilization of objects is crucial to robot hand grasping and manufacturing processes, and has therefore been studied extensively. Relatively little consideration has been given to the computation of all grasps of three-dimensional objects, and grasps that are insensitive to misplacements of the fingers. This paper contributes in both directions. Like Nguyen [22] (for two-dimensional objects), we achieve insensitivity to misplacements by determining combinations of regions on the object boundary that yield a form-closure grasp, no matter where the fingers are placed in each of these regions. We call such a combination of regions independent form-closure grasp regions. In this paper, we propose an efficient algorithm for computing all combinations of predefined face patches of a rectilinear polyhedron that form independent form-closure grasp regions with seven frictionless point fingers. This is the first efficient complete algorithm for computing independent form-closure grasp regions of a three-dimensional object. Our approach is based on a decomposition of the original problem in six-dimensional (wrench space) into two problems in three-dimensional subspaces. These problems, in turn, can be transformed into two-color intersection problems in the plane, which can be tackled efficiently using concepts and techniques from the field of computational geometry. The resulting algorithm has the advantage that its running time depends largely on the number of independent form-closure grasp regions reported.