Deform Closure: a Framework for Holding Deformable Parts
نویسنده
چکیده
We extend the well-known form closure framework for rigid parts to holding a class of deformable parts. We consider 2D deformable parts modeled as polygons with a triangular FEM mesh and given stiffness matrix that models linear elasticity and the potential energy associated with deformations of the mesh. We define the D-space (deformation-space) of a part E as the C-space of all nodes in the FEM mesh M representing E. The free space Dfree is defined as the intersection of the set of topology preserving mesh configurations with the complement of the union of all D-obstacles that represent collisions of the part with finger bodies. Given mesh M of part E, FEM stiffness matrix K, and A, the set of finger bodies in frictionless point contact with E, UA is the minimum work required to release the part. We say A holds E in deform closure if UA > 0. We present a numerical example and prove two results: (1) If contact set A holds a rigid part in form closure, A will hold the equivalent deformable part in deform closure and (2) Deform closure is frame invariant.
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