Form-closure Grasps Research Articles

An Improved Four-Pin Gripper for Robust 2.5-D Form-Closure Grasp

The four-pin gripper is an ideal end-effector to achieve form-closure grasps, which is especially useful in scenarios where a stable grasp is necessary. In this article, we propose an improved parallel four-pin gripper design. Compared with the previous designs, the new design achieves more planar configurations while introducing only one more actuator, thus enlarging the possibility of the gripper to stably grasp. Based on the improved design, we extend the environment constraint-based form-closure grasping point search algorithm to find the optimal parameters for the improved four-pin gripper. Furthermore, we apply an inverse kinematics-based planning method to drive the gripper from any initial state to a form-closure state. The simulation and experiment demonstrate that, compared with the previous designs, the improved design can achieve stable grasping for a wider range of planar objects.

Fundamental Study on the Feasibility of Alignment of Parts for 2nd-order Form Closure Grasps by Two Circular Fingers

Fundamental Study on the Feasibility of Alignment of Parts for 2nd-order Form Closure Grasps by Two Circular Fingers

KNTU hand and application of MAG index for form closure grasp

This paper presents a novel hand, consisting of both rigid link and continuum mechanisms, and the application of a newly proposed Multi-Aspect Grasp (MAG) index in Form Closure Grasp (FCG) constraint for holding objects, by the presented robotic hand. The KNTU hand, exploits the characteristics of both, rigid-link fingers and continuum fingers, in order to achieve a better grasp. This hand can hold any symmetrical or unsymmetrical object with FCG constraint. First, as a case study, the application of MAG index to Staubli TX40 manipulator is presented. Then, to grasp objects with KNTU hand based on the MAG index, two sets of candidate points with the form closure property are evaluated and the better set is determined. Using MAG index, the grasp by this novel robotic hand is analyzed and the obtained results of such system are introduced.

Synthesis of Energy-Bounded Planar Caging Grasps Using Persistent Homology

For applications such as manufacturing, caging grasps restrict object motion without requiring complete immobilization, providing a robust alternative to force- and form-closure grasps. Energy-bounded cages are a new class of caging grasps that relax the requirement of complete caging in the presence of external forces such as gravity or constant velocity pushing in the horizontal plane with Coulomb friction. We address the problem of synthesizing planar energy-bounded cages by identifying gripper and force-direction configurations that maximize the energy required for the object to escape. We present Energy-Bounded-Cage-Synthesis-2-D (EBCS-2-D), a sampling-based algorithm that uses persistent homology, a recently-developed multiscale approach for topological analysis, to efficiently compute candidate rigid configurations of obstacles that form energy-bounded cages of an object from an $\alpha $ -shape approximation to the configuration space. If a synthesized configuration has infinite escape energy then the object is completely caged. EBCS-2-D runs in $O(s^{3} + s n^{2})$ time, where $s$ is the number of samples and $n$ is the number of object and obstacle vertices, where typically $n \ll s$ . We observe runtimes closer to $O(s)$ for fixed $n$ . We implement EBCS-2-D using the persistent homology algorithms toolbox and study performance on a set of seven planar objects and four gripper types. Experiments suggest that EBCS-2-D takes 2–3 min on a 6 core processor with 200 000 pose samples. We also confirm that an rapidly-exploring random tree* motion planner is unable to find escape paths with lower energy. Physical experiments on a five degree of freedom Zymark Zymate and ABB YuMi suggest that push grasps synthesized by EBCS-2-D are robust to perturbations. Data and code are available at http://berkeleyautomation.github.io/caging/ . Note to Practitioners —For automation applications in manufacturing where object models are precisely known, “energy-bounded cages” are a robust approach to robot grasping in the presence of gravity or friction. This paper presents a synthesis algorithm for planar instances, where the object can be modeled as a planar extrusion and the motion occurs in the vertical or horizontal plane. We also present experiments with robots and a website with code and data.

Grasping Objects: The Relationship Between the Cage and the Form-Closure Grasp

In various industries, there is a need for low-cost, flexible robotic grasping systems that handle and classify different items, which usually involve low-cost grippers and reliable manipulations. One-degree-offreedom (1-DoF) two-pin or three-pin grippers are widely used in the automation of manufacturing processes because of their low cost and high reliability. However, some uncertainties introduced by the object and the gripper may affect the robustness of the grasp. The principle of caging enables us to deal with these uncertainties, and it is therefore important to study caging as a practical solution to improve the grasps of 1-DoF industrial grippers.

Mathematical Studying in Control of Grasping

The main purpose of developing of mechanical hands is to give robots the knack in order to grasp objects of varying geometric and physical properties. The complete model is a coupling of models which describe contact behavior with generally using the models of rigid-body kinematics and dynamics. The contact model fundamentally come down to the choice of components of contact force and moment which are transmitted through each contact. Mathematical properties of the complete model obviously bring about two primary grasp types whose physical interpretations provide insight for grasping and manipulation planning. A grasp with complete restraint avoids loss of contact and therefore is so secure. As will be mentioned, two primary limitation properties are force closure and form closure. A form closure grasp assurances the maintenance of contact as long as the links of the hand and the proposed object are also well verged on as rigid and as long as the joint actuators are sturdy enough. It should be noted that the main difference between force closure and also form closure grasps is the latter’s reliance on contact friction.

Immobilizing 2-D Serial Chains in Form-Closure Grasps

The immobilization of nonrigid objects is a relatively unexplored area in grasp mechanics. In this paper, we consider the immobilization of freely moving serial chains of n hinged polygons using frictionless point fingers. We first set this problem in the context of classical grasping theory by showing that chain immobilization can only be achieved with equilibrium grasps. Then, we describe two immobilization approaches based on first- and second-order geometric effects. Based on curvature effects, chains of n ≠ 3 hinged polygons with nonparallel edges can be immobilized by n + 2 frictionless point fingers. Serial chains of three hinged polygons form an exception to this rule. Based on first-order geometric effects, we describe how to immobilize any chain of n hinged polygons with only one extra contact for the entire chain, using a total of n + 3 frictionless point fingers. Moreover, the immobilizing grasps are robust with respect to small contact placement errors. The results are illustrated with examples and described as readily implementable procedures.

Efficient Procedures for Form-Closure Grasp Planning and Fixture Layout Design

This paper presents an algorithm for optimal grasp planning and fixture synthesis. The object surface is depicted by a number of discrete points, which are used as the candidate contact points. This algorithm consists of two procedures. The first procedure selects a minimal subset of contacts from the candidates so as to construct a form-closure grasp or fixture, which is to determine a minimal subset of contact wrenches such that their convex hull forms a simplex containing the origin of the wrench space as an interior point. The second procedure adjusts the contact positions or alters the selected contact wrenches to maximize the minimum distance from the origin to the facets of the simplex, which enhances the capability of the grasp or fixture to immobilize and balance the object. As this algorithm does not employ any general optimization techniques and utilizes recursive formulas for most computations, it runs very fast. Its effectiveness and efficiency are demonstrated with illustrative examples.

A Complete and Efficient Algorithm for Searching 3-D Form-Closure Grasps in the Discrete Domain

A complete and efficient algorithm is proposed for searching form-closure grasps of n hard fingers on the surface of a three-dimensional object represented by discrete points. Both frictional and frictionless cases are considered. This algorithm starts to search a form-closure grasp from a randomly selected grasp using an efficient local search procedure until encountering a local minimum. The local search procedure employs the powerful ray-shooting technique to search in the direction of reducing the distance between the convex hull corresponding to the grasp and the origin of the wrench space. When the distance reaches a local minimum in the local search procedure, the algorithm decomposes the problem into a few subproblems in subsets of the points according to the existence conditions of form-closure grasps. A search tree whose root represents the original problem is employed to perform the searching process. The subproblems are represented as children of the root node and the same procedure is recursively applied to the children. It is proved that the search tree generates O(KlnK/n) nodes in case a from-closure grasp exists, where K is the number of the local minimum points of the distance in the grasp space and n is the number of fingers. Compared to the exhaustive search, this algorithm is more efficient, and, compared to other heuristic algorithms, the proposed algorithm is complete in the discrete domain. The efficiency of this algorithm is demonstrated by numerical examples.

Computation of 3-D form-closure grasps

We address the problems of computing form-closure regions as well as computing optimal fingertip locations yielding n-finger form-closure grasps of three-dimensional (3-D) objects. Given grip points of k fingers not in form-closure, we propose a sufficient and necessary condition for the n-k fingers to achieve an n-finger form-closure grasp. Based on the condition, it is demonstrated that the problem of computing form-closure regions can be formulated as an existence problem of a solution for a set of inequalities. A sufficient condition is also proposed to simplify the computation of form-closure regions. As to searching for optimal fingertip locations, we transform the problem to a nonlinear programming problem subject to a set of constraints arising from that sufficient and necessary condition. Furthermore, a performance index is defined by measuring the distance between the center of mass of the grasped object and the center of the contact points. Finally, we have implemented the approach proposed and verified its efficiency by several numerical examples.

The synthesis of 3-D form-closure grasps

This paper presents a new formulation of computing three-dimensional (3-D) frictional form-closure grasps of n robotic fingers. As 3-D form-closure grasps involve 6-D wrench space, we first propose a recursive reduction technique to transform the complicated problem in the 6-D space into a simpler 3-D one. Next, we rewrite the sufficient and necessary condition for form-closure grasps into its equivalent form of two sets of linear inequalities. Then, according to the linear inequality theory, the problem is transformed to searching for a set of points which ensure the inconsistency of each of the two linear inequality systems. To search for such points, we proposed two methods: The first one is based on testing whether the convex region formed by each linear inequality system is empty, while the second one relies on the potential field method. We have implemented the algorithm and confirmed their efficiency for the synthesis of 3-D form-closure grasps.

Qualitative test and force optimization of 3-D frictional form-closure grasps using linear programming

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.

凸多面錐理論を用いたマニピュレーションの運動学とその把握および組立作業への応用

A new approach to the kinematic analysis of object motion constrained by mechanical contacts is presented. In robotic manipulation, such as grasping and assembly, robots manipulate objects through mechanical contacts with the grasped object and with the environment. We need to understand the kinematic behavior of the object motion under the constraints by the mechanical contacts in order to find appropriate strategies for manipulation tasks. In this paper, we first show that the constraints by mechanical contacts are generally described by a set of homogeneous linear inequalities. In task planning, it is often necessary for the planner to treat the complex inequalities. Thus, we develop an efficient mathematical tool based on the theory of polyhedral convex cones in order to treat the inequalities in a simple and systematic manner. Furthermore, we develop computation algorithms of the polyhedral convex cones in order to treat the inequalities on a computer. We apply the method to the planning of form-closure grasps, workpiece fixturing, and hybrid position/force control. Several examples demonstrate the usefulness of the algorithms.