We propose to synthesize feasible caging grasps for a target object through computing Caging Loops, a closed curve defined in the shape embedding space of the object. Different from the traditional methods, our approach decouples caging loops from the surface geometry of target objects through working in the embedding space. This enables us to synthesize caging loops encompassing multiple topological holes, instead of always tied with one specific handle which could be too small to be graspable by the robot gripper. Our method extracts caging loops through a topological analysis of the distance field defined for the target surface in the embedding space, based on a rigorous theoretical study on the relation between caging loops and the field topology. Due to the decoupling, our method can tolerate incomplete and noisy surface geometry of an unknown target object captured on-the-fly. We implemented our method with a robotic gripper and demonstrate through extensive experiments that our method can synthesize reliable grasps for objects with complex surface geometry and topology and in various scales.
This paper formalizes qualitative test of 3D frictional form-closure grasps of n robotic fingers as a problem of linear programming (LP). It is well-known that a sufficient and necessary condition for form-closure grasps is that the origin of the wrench space lies inside the convex hull of primitive contact wrenches. We demonstrate that the problem of querying whether the origin lies inside the convex hull is equivalent to a ray-shooting problem, which is dual to a LP problem based on the duality between convex hulls and convex polytopes. Furthermore, this paper addresses a problem of minimizing the L sub 1 norm of the grasp forces balancing an external wrench, which can be also transformed to a ray-shooting problem. We have implemented the algorithms and confirmed their real-time efficiency for qualitative test and grasp force optimization. A grasped object is defined to be in equilibrium if the sum of all forces and moments acting on a body equals zero. An equilibrium grasp may be stable or unstable. Force closed grasps are a well-known subset of equilibrium grasps, and they are known to be stable. However, not all stable grasps are force closed, including many common and easily obtainable grasps. In this paper, we classify the categories of equilibrium grasps and establish a general framework for the determination of the stability of a grasp. In order to analyze the stability of grasps with multiple contacts, we first model the compliance at each contact. We develop expressions for the changes in contact forces as a function of the rigid body relative motion between the fingers and the grasped object. The stability of a grasp is shown to depend on the local curvature of the contacting bodies, as well as the magnitude and arrangement of the contact forces. We then derive results providing simple criteria to determine the stability of a grasped object, including the special but important limiting case of rigid bodies where the contact compliance is zero. Computation of grasps with form force-closure is one of the fundamental problems in the study of multifingered grasping and dexterous manipulation. Based on the geometric condition of the closure property, this paper presents a numerical test to quantify how far a grasp is from losing form force-closure. With the polyhedral approximation of the friction cone, the proposed numerical test can be formulated as a single linear program. An iterative algorithm for computing optimal force-closure grasps, which is implemented by minimizing the proposed numerical test in the grasp configuration space, is also developed. The algorithm is computationally efficient and generally applicable. It can be used for computing form force-closure grasps on 3D objects with curved surfaces, and with any number of contact points. Several simulation examples are given to show the effectiveness and computational efficiency of the proposed algorithm. The form-closure and force-closure properties of robotic grasp ing are investigated. Loosely speaking, these properties are related to the capability of the robot to inhibit motions of the workpiece in spite of externally applied forces. In this article, form-closure is considered as a purely geometric property of a set of unilateral (contact) constraints, such as those applied on a workpiece by a mechanical fixture, while force-closure is related to the capability of the particular robotic device being considered to apply forces through contacts. The concepts of partial form- and force-closure properties are introduced and discussed, and an algorithm is proposed to obtain a synthetic geometric description of partial form-closure constraints. Al though the literature abounds with form-closure tests, proposed algorithms for testing force-closure are either approximate or computationally expensive. This article proves the equiva lence of force-closure analysis with the study of the equilibria of an ordinary... We address the problem of computing optimal fingertip locations yielding n-finger form-closure grasps of polyhedral objects. Given grasping points of m fingers not in form-closure, we show that the calculation of optimal grip points for the n-m fingers can be viewed as a nonlinear programming problem. We propose a sufficient and necessary condition for the n-m fingers to achieve an n-finger form-closure grasp with the m fingers given. Based on this condition, we derive a set of nonlinear constraints for the nonlinear programming problem. Furthermore, we give a performance index serving as an objective function which measures the distance between the center of mass of the grasped object and the contact points to be determined. In addition, the algorithm proposed can be applied to the frictionless grasp. We have implemented the algorithm and verified its efficiency by two examples. A robotic grasping simulator, called Graspit!, is presented as versatile tool for the grasping community. The focus of the grasp analysis has been on force-closure grasps, which are useful for pick-and-place type tasks. This work discusses the different types of world elements and the general robot definition, and presented the robot library. The paper also describes the user interface of Graspit! and present the collision detection and contact determination system. The grasp analysis and visualization method were also presented that allow a user to evaluate a grasp and compute optimal grasping forces. A brief overview of the dynamic simulation system was provided.