This paper digs into the relationship between cages and grasps of a rigid body. In particular, it considers the use of cages as waypoints to grasp an object. We introduce the concept of pregrasping cages, caging configurations from which an object can be grasped without first breaking the cage. For two-fingered manipulators, all cages are pregrasping cages and, consequently, useful waypoints to grasp an object. A contribution of this paper is to show that the same does not hold for more than two fingers. A second contribution is to show how to overcome that limitation. We explore the natural generalization of the well-understood squeezing/stretching characterization of two-finger cages to arbitrary workspace dimension, arbitrary object shapes without holes, and arbitrary number of point fingers, and exploit it to give sufficient conditions for a cage to be a pregrasping cage. As a product of that generalization, we introduce grasping functions: scalar functions defined on the finger formation that control the process of going from a cage to a grasp. We finish the paper by establishing an analogy between the role of grasping functions in grasping and that of Lyapunov functions in stability theory.

/pdf/from-caging-to-grasping-1hczu2nkb4.pdf

From caging to grasping

High-precision manipulation is very important for a variety of tasks in manufacturing. In general, high-precision manipulation is usually achieved by the guidance of high-precision sensors; however, sensorless methods, for some special cases, are more reliable and effective. There are many important works in this aspect [1] – [3] . The concept of “attractive region in environment” (ARIE), which was proposed in our previous works [4] – [6] , provides a prospective approach for low-precision systems to achieve high-precision manipulation. It has been used in various industrial applications, such as robotic assembly [7] , grasping [8] , and localization [9] . ARIE is a region from any point of which the uncertainty of the system can be eliminated by a state-independent input. The utilization of attractive region can be easily understood by the case of a bean in a bowl. For a bean in a bowl, no matter where the initial position of the bean is, it will move to and finally stay at the bottom of the bowl under gravity. Thus, the uncertainty of the bean is eliminated by gravity without any sensor feedback. Inspired by the above case, the general concept of ARIE is proposed and is applied to industry. In this paper, we review the application of ARIE and give its formal definition. Furthermore, we establish conditions for the existence of ARIE in the generalized configuration space, which is complex and nonideal. The relationship between the high-dimensional attractive region and the low-dimensional one is also discussed, which is helpful to make feasible and reliable manipulation strategies in the low-dimensional configuration space. The main contribution of this paper is the generalization of the concept of ARIE, which provides a theoretical foundation for applications including the high-precision manipulation with low-precision system. The experimental simulations on different kinds of complex manipulations show the effectiveness of the proposed method for industrial applications.

The Concept of “Attractive Region in Environment” and its Application in High-Precision Tasks With Low-Precision Systems

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 the construction of a collision-free path for a modified form of the object, and 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

/pdf/motion-planning-for-disc-shaped-robots-pushing-a-polygonal-5d1x7btbnz.pdf

Motion planning for disc-shaped robots pushing a polygonal object in the plane

We present algorithms for computing all placements of two and three fingers that cage a given polygonal object with n edges in the plane. A polygon is caged when it is impossible to take the polygon to infinity without penetrating one of the fingers. Using a classification into squeezing and stretching cagings, we provide an algorithm that reports all caging placements of two disc fingers in O(n 2logn) time. Our result extends and improves a recent solution for point fingers. In addition, we construct a data structure requiring O(n 2) storage that can answer in O(logn) whether two fingers in a query placement cage the polygon. We also study caging with three point fingers. Given the placements of two so-called base fingers, we report all placements of the third finger so that the three fingers jointly cage the polygon. Using the fact that the boundary of the set of placements for the third finger consists of equilibrium grasps, we present an algorithm that reports all placements of the third finger in O(n 6log2 n) deterministic time and O(n 6logn(loglogn)3) expected time. Our results extend previous solutions that only apply to convex polygons.

/pdf/caging-polygons-with-two-and-three-fingers-481gd3lkra.pdf

Caging Polygons with Two and Three Fingers

The task of fitting parametric curve models to the boundaries of perceptually meaningful image regions is a key problem in computer vision with numerous applications, such as image segmentation, pose estimation, object tracking, and 3-D reconstruction. In this article, we propose the Contracting Curve Density (CCD) algorithm as a solution to the curve-fitting problem.

The CCD algorithm extends the state-of-the-art in two important ways. First, it applies a novel likelihood function for the assessment of a fit between the curve model and the image data. This likelihood function can cope with highly inhomogeneous image regions, because it is formulated in terms of local image statistics. The local image statistics are learned on the fly from the vicinity of the expected curve. They provide therefore locally adapted criteria for separating the adjacent image regions. These local criteria replace often used predefined fixed criteria that rely on homogeneous image regions or specific edge properties. The second contribution is the use of blurred curve models as efficient means for iteratively optimizing the posterior density over possible model parameters. These blurred curve models enable the algorithm to trade-off two conflicting objectives, namely heaving a large area of convergence and achieving high accuracy.

We apply the CCD algorithm to several challenging image segmentation and 3-D pose estimation problems. Our experiments with RGB images show that the CCD algorithm achieves a high level of robustness and sub-pixel accuracy even in the presence of severe texture, shading, clutter, partial occlusion, and strong changes of illumination.

The Contracting Curve Density Algorithm: Fitting Parametric Curve Models to Images Using Local Self-Adapting Separation Criteria

This paper extends the caging theory of Rimon and Blake (1996) for one-parameter two-finger grippers to one-parameter three-finger grippers. The caging theory describes how the fingers of a robot gripper can be placed around an object so that it cannot escape. As the fingers close from such a configuration, the freedom of the object to move is gradually restricted, until, in the absence of friction, it is completely immobilized by the fingers at an immobilizing grasp. The extension of the caging theory to three-fingered grippers is important because convex objects cannot be caged by two-finger grippers. The computation of the set of caging formations requires the identification of both the two- and three-finger frictionless grasps. These grasps correspond to critical points of the opening parameter in the gripper's configuration space. There are two main problems here. Firstly, a method is needed to compute the critical points of the opening parameter in the three-finger contact space. This is complicated by the fact that this space may have more that one connected component. The second problem is how to associate the immobilizing grasps with punctures. In this paper we solve both these problems, presenting efficient algorithmic solutions.

Caging planar objects with a three-finger one-parameter gripper

This paper describes an efficient method to calculate, from an image of an object, configurations of a two-fingered robot gripper that form a "cage" to contain that object. Closing the fingers on the object from these configurations is guaranteed to reach a given desired grasp. This builds on the visual grasping theory of A. Blake et al. (1993), which describes how to find optimal grasps. It extends the results of E. Rimon and A. Blake (1996) which show how to construct such cages, in two ways. First, a more efficient algorithm for computing the cage is described. Second, a further development deals with occlusion by solving the caging problem within a restricted image window. The new methods greatly reduce the complexity of the visual caging problem, making it feasible in a real time computer vision system.

Error-tolerant visual planning of planar grasp

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Caging planar objects with a three-finger one-parameter gripper

Error-tolerant visual planning of planar grasp