15,586 research outputs found

    A stiffness-based quality measure for compliant grasps and fixtures

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    This paper presents a systematic approach to quantifying the effectiveness of compliant grasps and fixtures of an object. The approach is physically motivated and applies to the grasping of two- and three-dimensional objects by any number of fingers. The approach is based on a characterization of the frame-invariant features of a grasp or fixture stiffness matrix. In particular, we define a set of frame-invariant characteristic stiffness parameters, and provide physical and geometric interpretation for these parameters. Using a physically meaningful scheme to make the rotational and translational stiffness parameters comparable, we define a frame-invariant quality measure, which we call the stiffness quality measure. An example of a frictional grasp illustrates the effectiveness of the quality measure. We then consider the optimal grasping of frictionless polygonal objects by three and four fingers. Such frictionless grasps are useful in high-load fixturing applications, and their relative simplicity allows an efficient computation of the globally optimal finger arrangement. We compute the optimal finger arrangement in several examples, and use these examples to discuss properties that characterize the stiffness quality measure

    Discrete spherical means of directional derivatives and Veronese maps

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    We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a general construction for obtaining discrete spherical means of directional derivatives. The construction is based on using the Minkowski's existence theorem and Veronese maps. Approximating the directional derivatives by appropriate finite differences allows one to obtain finite difference operators with good rotation invariance properties. In particular, we use discrete circular and spherical means to derive discrete approximations of various linear and nonlinear first- and second-order differential operators, including discrete Laplacians. A practical potential of our approach is demonstrated by considering applications to nonlinear filtering of digital images and surface curvature estimation

    The space of essential matrices as a Riemannian quotient manifold

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    The essential matrix, which encodes the epipolar constraint between points in two projective views, is a cornerstone of modern computer vision. Previous works have proposed different characterizations of the space of essential matrices as a Riemannian manifold. However, they either do not consider the symmetric role played by the two views, or do not fully take into account the geometric peculiarities of the epipolar constraint. We address these limitations with a characterization as a quotient manifold which can be easily interpreted in terms of camera poses. While our main focus in on theoretical aspects, we include applications to optimization problems in computer vision.This work was supported by grants NSF-IIP-0742304, NSF-OIA-1028009, ARL MAST-CTA W911NF-08-2-0004, and ARL RCTA W911NF-10-2-0016, NSF-DGE-0966142, and NSF-IIS-1317788

    Robust and Efficient Recovery of Rigid Motion from Subspace Constraints Solved using Recursive Identification of Nonlinear Implicit Systems

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    The problem of estimating rigid motion from projections may be characterized using a nonlinear dynamical system, composed of the rigid motion transformation and the perspective map. The time derivative of the output of such a system, which is also called the "motion field", is bilinear in the motion parameters, and may be used to specify a subspace constraint on either the direction of translation or the inverse depth of the observed points. Estimating motion may then be formulated as an optimization task constrained on such a subspace. Heeger and Jepson [5], who first introduced this constraint, solve the optimization task using an extensive search over the possible directions of translation. We reformulate the optimization problem in a systems theoretic framework as the the identification of a dynamic system in exterior differential form with parameters on a differentiable manifold, and use techniques which pertain to nonlinear estimation and identification theory to perform the optimization task in a principled manner. The general technique for addressing such identification problems [14] has been used successfully in addressing other problems in computational vision [13, 12]. The application of the general method [14] results in a recursive and pseudo-optimal solution of the motion problem, which has robustness properties far superior to other existing techniques we have implemented. By releasing the constraint that the visible points lie in front of the observer, we may explain some psychophysical effects on the nonrigid percept of rigidly moving shapes. Experiments on real and synthetic image sequences show very promising results in terms of robustness, accuracy and computational efficiency
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