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The Kinematics of Containment

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Advances in Robot Kinematics

Abstract

This chapter is concerned with two problems related to what we call the kinematics of containment: (1) Given a small convex body in \(n\)-dimensional Euclidean space, such as an ellipsoid, that is contained inside of a large convex body, characterize the range of allowable motions for which the boundaries of the bodies do not collide, and calculate the corresponding volume of this motion in the group of rigid-body motions, \(SE(n)\); (2) If the smaller body is almost the size of the larger one, and can only execute small collision-free motions, analyze the range of these motions. Both of these problems are addressed fully here. The first uses methods of the fields of Integral Geometry and Geometric Probability and derives an expression similar to the so-called Principal Kinematic Formula. The second uses the kinematics of infinitesimal motions and properties of ellipsoids.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Johns Hopkins University, Baltimore, USA

    Gregory S. Chirikjian & Yan Yan

Authors
  1. Gregory S. Chirikjian
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  2. Yan Yan
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Correspondence to Gregory S. Chirikjian .

Editor information

Editors and Affiliations

  1. J. Stefan Institute, Ljubljana-Vic-Rudnik, Slovenia

    Jadran Lenarčič

  2. Department of Computer Science Artificial Intelligence Laboratory, Stanford University, Stanford, California, USA

    Oussama Khatib

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Chirikjian, G.S., Yan, Y. (2014). The Kinematics of Containment. In: Lenarčič, J., Khatib, O. (eds) Advances in Robot Kinematics. Springer, Cham. https://doi.org/10.1007/978-3-319-06698-1_37

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  • DOI: https://doi.org/10.1007/978-3-319-06698-1_37

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06697-4

  • Online ISBN: 978-3-319-06698-1

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