A sufficient condition for computing n-finger force-closure grasps of 3D objects

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 Pl¨ucker 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 forceclosure 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.