A Sufficient Condition For Computing N-Finger Force-Closure Grasps of 3D Objects

Abstract—We address the problem of computing n-finger force-closure grasps of 3D objects. As 3D force-closure grasps involve 6D wrench space, we use Plücker coordinates and Grassmann algebra, to demonstrate that wrenches associated to any three non-aligned contact points of 3D objects form a basis of the 6D wrench space. Thus, given non-aligned locations of n − 1 fingers, a 6D basis can be extracted form their wrenches. This permits the formulation of a fast and simple sufficient force-closure test. The problem is transformed to searching for a set of locations of the nth finger which wrenches can be uniquely expressed as a strictly negative linear combination of the 6D basis. We have implemented the algorithm and confirmed its efficiency by comparing it to the classical convex-hull method [21]. Index Terms—Force-closure grasps, Grassmann algebra. I