Algorithms for Constructing Immobilizing Fixtures and Grasps of Three-Dimensional Objects.

A. Sudsang, J. Ponce and N. Srinivasa.

Algorithmic Foundations of Robotics II, AK Peters, Ltd., 1997.


We address the problem of computing immobilizing fixtures and grasps of three-dimensional objects, using simple fixturing devices and grippers with both discrete and continuous degrees of freedom. The proposed approach is based on the notion of second-order immobility introduced by Rimon and Burdick \cite{rimon&burdick.icra93,RiBur95a,RiBur95}, which is used here to derive simple sufficient conditions for immobility and stability in the case of contacts between spherical locators and polyhedral objects. In turn, these conditions are the basis for efficient geometric algorithms that enumerate all of the stable immobilizing fixtures and grasps of polyhedra that can be achieved by various types of fixturing devices and grippers. Preliminary implementations of the proposed algorithms have been constructed, and examples are presented.