This article addresses the problem of computing stable grasps of three-dimensional polyhedral objects. We consider the case of a hand equipped with four hard fingers and assume point contact with friction. We prove new necessary and sufficient conditions for equilibrium and force closure, and present a geometric characterization of all possible types of four-finger equilibrium grasps. We then focus on concurrent grasps, for which the lines of action of the four contact forces all intersect in a point. In this case, the equilibrium conditions are linear in the unknown grasp parameters, which reduces the problem of computing the stable grasp regions in configuration space to the problem of constructing the eight-dimensional projec tion of an ll-dimensinnal polytope. We present two projection methods: the first one uses a simple Gaussian elimination ap proach, while the second one relies on a novel output-sensitive contour-tracking algorithm. Finally, we use linear optimization within the valid configuration space regions to compute the maximal object regions where fingers can be positioned inde pendently while ensuring force closure. We have implemented the proposed approach and present several examples.

Abstract-We consider the task of grasping novel objects and cleaning fairly cluttered tables with many novel objects. Recent successful approaches employ machine learning algorithms to identify points on the scene that the robot should grasp. In this paper, we show that the task can be significantly simplified by using segmentation, especially with depth information. A supervised localization method is employed to select graspable segments. We also propose a shape completion and grasp planner method which takes partial 3D information and plans the most stable grasping strategy. Extensive experiments on our robot demonstrate the effectiveness of our approach.

This paper addresses the problem of using three disc-shaped robots to manipulate a polygonal object in the plane in the presence of obstacles. The proposed approach is based on the computation of maximal discs (dubbed maximum independent capture discs, or MICaDs) where the robots can move independently while preventing the object from escaping their grasp. It is shown that, in the absence of obstacles, it is always possible to bring a polygonal object from any configuration to any other one with robot motions constrained to lie in a set of overlapping MICaDs. This approach is generalized to the case where obstacles are present by decomposing the corresponding motion planning task into (1) the construction of a collision-free path for a modified form of the object, and (2) the execution of this path by a sequence of simultaneous and independent robot motions within overlapping MICaDs. The proposed algorithm is guaranteed to generate a valid plan provided a collision-free path exists for the modified form of the object. It has been implemented and experiments with Nomadic Scout mobile robots are presented.

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This paper addresses the problem of using three disc-shaped robots to manipulate a polygonal object in the plane in the presence of obstacles. The proposed approach is based on the characterization of the maximal discs (dubbed maximum independent capture discs, or MICaDs) where the robots can move independently while preventing the object from escaping their grasp. It is shown that, in the absence of obstacles, it is always possible to bring a polygonal object from any configuration to any other one with robot motions constrained to lie in a set of overlapping MICaDs. A strategy for computing these motions is used in conjunction with an exact motion planner to devise an algorithm guaranteed to find a motion plan avoiding collisions with obstacles as long as a collisionfree path exists for the object grown by the diameter of the robots plus some arbitrary positive number E.