On computing immobilizing grasps of 3-D curved objects

We propose an algorithm for searching a form-closure grasp on a 3-D discretized curved object. The algorithm first randomly selects an initial set of seven contacts from the large collection of candidate contacts and check its form-closure property by the test algorithm developed in our early work. For the non-form-closure grasp, the candidate contacts are classified into set S where the contact wrenches lie on the same side of the separating facet as the initial wrenches and set D where the contact wrenches lie on the different side. The separating facet can be calculated through the test algorithm. Then the initial seven contacts are iteratively improved by exchanging with the candidate contacts in set D. The best-first motion together with random motion are used in the exchange procedure to ensure the convex hull of the seven contact wrenches will approach the origin step by step until the origin is completely contained. Finally, the algorithm has been implemented and its efficiency has been ascertained by three examples.