Caging Grasps of Rigid and Partially Deformable 3-D Objects With Double Fork and Neck Features

Caging provides an alternative to point-contact-based rigid grasping, relying on reasoning about the global free configuration space of an object under consideration. While substantial progress has been made toward the analysis, verification, and synthesis of cages of polygonal objects in the plane, the use of caging as a tool for manipulating general complex objects in 3-D remains challenging. In this work, we introduce the problem of caging rigid and partially deformable 3-D objects, which exhibit geometric features we call double forks and necks. Our approach is based on the linking number-a classical topological invariant, allowing us to determine sufficient conditions for caging objects with these features even in the case when the object under consideration is partially deformable under a set of neck or double fork preserving deformations. We present synthesis and verification algorithms and demonstrations of applying these algorithms to cage 3-D meshes.