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Computation on Parametric Curves with Applications in Localization and Grasping

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Algorithmic Foundations of Robotics V

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 7))

Summary

This paper investigates efficient curve processing that originates from the localization and grasping of 2D curved objects.

The first algorithm locates the boundary section of an object traced out by a rolling finger based on the length and total curvature information obtained with the finger’s tactile sensor. The algorithm slides an imaginary segment along the object boundary by alternatively marching its two endpoints forward, stretching or contracting the segment if necessary.

The second algorithm computes all pairs of antipodal points on an object. Two fingers placed at such a pair of points can achieve a force-closure grasp in the presence of friction. Dissecting the boundary into segments everywhere convex or everywhere concave, the algorithm marches simultaneously on every two segments with opposing normals and alternates marching with numerical bisection recursively. It builds on a procedure that constructs common tangents of two curves with quadratic local convergence.

Completeness (up to numerical resolution) of the above algorithms is established by applying curvature-based analyses. Dissection and the coupling of marching with bisection introduced in this paper are potentially applicable to optimization problems involving curves and curved surfaces.

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Author information

Authors and Affiliations

  1. Iowa State University, Ames, IA, 50011-1040, USA

    Yan-Bin Jia

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  1. Yan-Bin Jia
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Editor information

Editors and Affiliations

  1. INRIA, 2004 Route des Lucioles, 06902, Sophia-Antipolis, France

    Jean-Daniel Boissonnat

  2. Dept. of Mechanical Engineering, California Inst. of Technology, East California Boulevard 12000, 91125, Pasadena, CA, USA

    Joel Burdick

  3. Dept. of Mechanical Engineering, University of California at Berkeley, 4189 Etcheverry Hall, 94720, Berkeley, CA, USA

    Ken Goldberg

  4. Beckman Inst., University of Illinois, North Matthews Avenue 405, 61801, Urbana, IL, USA

    Seth Hutchinson

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Jia, YB. (2004). Computation on Parametric Curves with Applications in Localization and Grasping. In: Boissonnat, JD., Burdick, J., Goldberg, K., Hutchinson, S. (eds) Algorithmic Foundations of Robotics V. Springer Tracts in Advanced Robotics, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45058-0_20

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  • DOI: https://doi.org/10.1007/978-3-540-45058-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07341-0

  • Online ISBN: 978-3-540-45058-0

  • eBook Packages: Springer Book Archive

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