Finding antipodal point grasps on irregularly shaped objects

Two-finger antipodal point grasping of arbitrarily shaped smooth 2-D and 3-D objects is considered. An object function is introduced that maps a finger contact space to the object surface. Conditions are developed to identify the feasible grasping region, F, in the finger contact space. A “grasping energy function”, E , is introduced which is proportional to the distance between two grasping points. The antipodal points correspond to critical points of E in F. Optimization and/or continuation techniques are used to find these critical points. In particular, global optimization techniques are applied to find the “maximal” or “minimal” grasp. Further, modeling techniques are introduced for representing 2-D and 3-D objects using B-spline curves and spherical product surfaces

Independent contact regions for discretized 3D objects with frictionless contacts

This paper deals with the problem of determining independent contact regions on a 3D object boundary such that a seven finger frictionless grasp with a contact point in each region assures a force-closure grasp on the object, independently of the exact position of the contact points. These regions provide robustness in front of finger positioning errors in grasp and fixturing applications. The object’s structure is discretized in a cloud of points, so the procedure is applicable to objects of any arbitrary shape. The procedure finds an initial form-closure grasp that is iteratively improved through an oriented search procedure: once a locally optimum grasp has been reached, the independent contact regions are computed. The procedure has been implemented, and application examples are included in the paper

Searching force-closure optimal grasps of articulated 2D objects with n links

This paper proposes a method that finds a locally optimal grasp of an articulated 2D object with n links considering frictionless contacts. The surface of each link of the object is represented by a finite set of points, thus it may have any shape. The proposed approach finds, first, an initial force-closure grasp and from it starts an iterative search of a local optimum grasp. The quality measure considered in this work is the largest perturbation wrench that a grasp can resist with independence of the direction of the perturbation. The approach has been implemented and some illustrative examples are included in the article.Postprint (published version

Modeling and grasping of thin deformable objects

Deformable modeling of thin shell-like and other objects have potential application in robot grasping, medical robotics, home robots, and so on. The ability to manipulate electrical and optical cables, rubber toys, plastic bottles, ropes, biological tissues, and organs is an important feature of robot intelligence. However, grasping of deformable objects has remained an underdeveloped research area. When a robot hand applies force to grasp a soft object, deformation will result in the enlarging of the finger contact regions and the rotation of the contact normals, which in turn will result in a changing wrench space. The varying geometry can be determined by either solving a high order differential equation or minimizing potential energy. Efficient and accurate modeling of deformations is crucial for grasp analysis. It helps us predict whether a grasp will be successful from its finger placement and exerted force, and subsequently helps us design a grasping strategy. The first part of this thesis extends the linear and nonlinear shell theories to describe extensional, shearing, and bending strains in terms of geometric invariants including the principal curvatures and vectors, and the related directional and covariant derivatives. To our knowledge, this is the first non-parametric formulation of thin shell strains. A computational procedure for the strain energy is then offered for general parametric shells. In practice, a shell deformation is conveniently represented by a subdivision surface. We compare the results via potential energy minimization over a couple of benchmark problems with their analytical solutions and the results generated by two commercial softwares ABAQUS and ANSYS. Our method achieves a convergence rate an order of magnitude higher. Experimental validation involves regular and freeform shell-like objects (of various materials) grasped by a robot hand, with the results compared against scanned 3-D data (accuracy 0.127mm). Grasped objects often undergo sizable shape changes, for which a much higher modeling accuracy can be achieved using the nonlinear elasticity theory than its linear counterpart. The second part numerically studies two-finger grasping of deformable curve-like objects under frictional contacts. The action is like squeezing. Deformation is modeled by a degenerate version of the thin shell theory. Several differences from rigid body grasping are shown. First, under a squeeze, the friction cone at each finger contact rotates in a direction that depends on the deformable object\u27s global geometry, which implies that modeling is necessary for grasp prediction. Second, the magnitude of the grasping force has to be above certain threshold to achieve equilibrium. Third, the set of feasible finger placements may increase significantly compared to that for a rigid object of the same shape. Finally, the ability to resist disturbance is bounded in the sense that increasing the magnitude of an external force may result in the breaking of the grasp

Frictionless grasp with 7 fingers on discretized 3D objects

This paper presents an algorithm to plain locally frictionless grasp on 3D objects. The objects can be of any arbitrary shape, since the surface is discretized in a cloud of points. The planning algorithm finds an initial force-closure grasp that is iteratively improved through an oriented search procedure. The grasp quality is measured with the “largest ball” criterion, and a force-closure test based on geometric considerations is used. The efficiency of the algorithm is illustrated through numerical example

Examples of 3D grasp quality computations

Previous grasp quality research is mainly theoretical, and has assumed that contact types and positions are given, in order to preserve the generality of the proposed quality measures. The example results provided by these works either ignore hand geometry and kinematics entirely or involve only the simplest of grippers. We present a unique grasp analysis system that, when given a 3D object, hand, and pose for the hand, can accurately determine the types of contacts that will occur between the links of the hand and the object, and compute two measures of quality for the grasp. Using models of two articulated robotic hands, we analyze several grasps of a polyhedral model of a telephone handset, and we use a novel technique to visualize the 6D space used in these computations. In addition, we demonstrate the possibility of using this system for synthesizing high quality grasps by performing a search over a subset of possible hand configurations