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Human in-hand dexterity can be highly fluid and unstructured, with multiple phalanxes breaking and re-establishing contact during any given task. In contrast, prevailing research in robotic manipulation has focused on highly structured well-controlled motions, where contact points are carefully characterized. Maintaining grasp stability by satisfying traditional closure conditions during complex within-hand manipulation motions can be difficult, even with highly articulated end effectors. However, simple grippers can still achieve an effective range of in-hand manipulation tasks without strict closure conditions, as long as the object can be bounded locally relative to the hand frame. The end effector can be considered as a tool to limit the range of possible object poses. In particular, the energy of the hand-object system can be used to determine an attractor region toward which the hand drives the object. This can be combined with a sparse sampling of the configuration space to find a set of manipulation primitives that can reliably constrain the object inside the hand workspace even without feedback, a strategy proposed as whole-hand caging manipulation. In this paper, experimental results with a planar underactuated gripper are presented to validate this manipulation strategy, and it is shown that even though contacts are regularly broken and reformed, the object can be reliably manipulated within the hand workspace without ejection, and challenging movements such as sliding and gaiting can be reliably performed. [ABSTRACT FROM AUTHOR]

Multifinger caging offers a robust object grasping approach. However, while efficient computation of two-finger caging grasps is well developed, the computation of three-finger caging grasps has remained a challenge. This paper considers the caging of polygonal objects with three-finger hands which maintain an equilateral triangle formation during the grasping process. While the c-space of such hands is 4-D, their contact space that represents all two and three finger contacts along the grasped object’s boundary forms a 2-D stratified manifold. The paper describes a caging graph that can be constructed in the hand’s relatively simple contact space. Starting from a desired immobilizing grasp of the polygonal object, the caging graph can be readily searched for the largest finger opening that maintains a three-finger cage about the object to be grasped. Any equilateral finger placement within the corresponding caging regions guarantees robust object grasping. Note to Practitioners—A commonly used industrial gripper is the parallel gripper. While it is well suited for grasping objects that have parallel edges, it is less suited for objects with more complicated geometries, and it relies on high coefficients of friction. This paper considers the robust grasping of polygonal objects using equilateral three-finger robot hands. Such hands are mechanically simple, and enable grasping objects with complicated shapes without relying on contact friction. To safely grasp an object, the hand is first brought to a caging configuration around the object. Once the object is caged, it cannot be accidentally ejected from the hand, and the fingers can be closed safely until an immobilizing grasp is reached. To reach a specific immobilizing grasp, the fingers are placed in the three caging regions associated with that grasp. This paper proposes a method that is both physically intuitive and computationally simple, to compute these caging regions. Although this paper considers grasping polygonal objects using frictionless point fingers, the proposed method can be used for grasping nonpolygonal objects using identical disc fingers, by expanding the object by the finger radius, and then approximating the expanded object by a polygon. Finger’s center can then be treated as a point finger. Frictional jamming of the fingers can overcome using rotating fingers or slightly vibrating the hand. [ABSTRACT FROM AUTHOR]

This paper presents an efficient algorithm to test whether a planar object can be caged by a formation of point agents (point fingertips or point mobile robots). The algorithm is based on a space mapping between the 2-D work space ( \mathcal W space) and the 3-D configuration space ( \mathcal C space) of the given agent formation. When performing caging test on a planar object, the algorithm looks up the space mapping to recover the \mathcal C space of the given agent formation, labels the recovered \mathcal C space, and counts the number of labeled surfaces to judge the success of caging. The algorithm is able to work with various planar shapes, including objects with convex boundaries, concave boundaries, or holes. It can also respond quickly to varying agent formations and different object shapes. Experiments and analysis on different objects and fingertip formations demonstrate the completeness, robustness, and efficiency of our proposal.

Note to Practitioners—This paper proposes an algorithm to solve a geometric problem—find whether a given formation of planar points can constrain (or cage) a planar shape. Users can use the proposed algorithm to actuate a formation of robotic fingertips to perform caging-based grasping tasks or use the proposed algorithm to actuate a formation of mobile robots to perform cooperative transportation tasks. The algorithm inherits the merits of caging and helps users to avoid explicit force analysis. It offers robustness to avoid uncertainty in the tasks. The code of our work is in the supplementary material. [ABSTRACT FROM AUTHOR]

An object is caged by a formation of fingers when it is blocked by the fingers from moving arbitrarily far away. Although some objects such as those with opposing concave sections can be caged by only two fingers, many other objects require at least three. Rectangles and 3-D convex objects without a supporting plane, for example, require at least four. This paper focuses on multifinger squeezing caging in which the positions of fingers obey dispersion constraints. In particular, we present an algorithm for computing all initial finger placements at which the object can be caged in an aforementioned manner. An implementation of the proposed algorithm is described along with implementation results both in 2-D and 3-D. [ABSTRACT FROM PUBLISHER]

In general, any object can be restricted or caged within a bounded region if we evenly place a sufficient number of fingers around the object. This naive approach often leads to inefficient utilization of fingers because only two fingers are sufficient to cage most nonconvex objects. In this paper, we propose an algorithm that identifies all the caging sets, i.e., set of two-finger placements that cage a given polytope representing the object. Whether a finger placement could cage the object can be queried efficiently from a structure generated by the algorithm. We implemented and tested the algorithm in the case of 2-D and 3-D objects. [ABSTRACT FROM PUBLISHER]

This paper addresses the problem of capturing an arbitrary convex object P in the plane with three congruent disc-shaped robots. Given two stationary robots in contact with P, we characterize the set of positions of a third robot, the so-called capture region, that prevent P from escaping to infinity via continuous rigid motion. We show that the computation of the capture region reduces to a visibility problem. We present two algorithms for solving this problem, and for computing the capture region when P is a polygon and the robots are points (zero-radius discs). The first algorithm is exact and has polynomial time complexity. The second one uses simple hidden surface removal techniques from computer graphics to output an arbitrarily accurate approximation of the capture region; it has been implemented, and examples are presented. [ABSTRACT FROM AUTHOR]