Grasping and fixturing as submodular coverage problems

Abstract

Grasping and fixturing are concerned with immobilizing objects. Most prior work in this area strives to minimize the number of contacts needed. However, for delicate objects or surfaces such as glass or bone (in medical applications), extra contacts can be used to reduce the forces needed at each contact to resist applied wrenches. We focus on the following class of problems. Given a polyhedral object model, set of candidate contacts, and a limit on the sum of applied forces at the contacts or a limit on any individual applied force, compute a set of k contact points that maximize the radius of the ball in wrench space that can be resisted. We present an algorithm, SatGrasp, that is guaranteed to find near-optimal solutions in linear time. At the core of our approach are (i) an alternate formulation of the residual radius objective, and (ii) the insight that the resulting problem is a submodular coverage problem. This allows us to exploit the submodular saturation algorithm, which has recently been derived for applications in sensor placement. Our approach is applicable in situations with or without friction.