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Path Planning on Manifolds Using Randomized Higher-Dimensional Continuation

  • Chapter
Algorithmic Foundations of Robotics IX

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 68))

Abstract

Despite the significant advances in path planning methods, problems involving highly constrained spaces are still challenging. In particular, in many situations the configuration space is a non-parametrizable variety implicitly defined by constraints, which complicates the successful generalization of sampling-based path planners. In this paper, we present a new path planning algorithm specially tailored for highly constrained systems. It builds on recently developed tools for Higher-dimensional Continuation, which provide numerical procedures to describe an implicitly defined variety using a set of local charts. We propose to extend these methods to obtain an efficient path planner on varieties, handling highly constrained problems. The advantage of this planner comes from that it directly operates into the configuration space and not into the higher-dimensional ambient space, as most of the existing methods do.

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Authors and Affiliations

  1. Institut de Robòtica i Informàtica Industrial, CSIC-UPC,  

    Josep M. Porta & Léonard Jaillet

Authors
  1. Josep M. Porta
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  2. Léonard Jaillet
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Editors and Affiliations

  1. School of Computing, National University of Singapore, 13 Computing Drive, 117417, Singapore

    David Hsu

  2. Department of Computer Science, University of Minnesota, 200 Union Street SE, 55455, Minneapolis, MN, USA

    Volkan Isler

  3. Computer Science Department, Stanford University, 94305-9010, Stanford, CA, USA

    Jean-Claude Latombe

  4. Department of Computer Science, University of North Carolina, Chapel Hill, 254 Brooks Building, 27599, Chapel Hill, NC, USA

    Ming C. Lin

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Porta, J.M., Jaillet, L. (2010). Path Planning on Manifolds Using Randomized Higher-Dimensional Continuation. In: Hsu, D., Isler, V., Latombe, JC., Lin, M.C. (eds) Algorithmic Foundations of Robotics IX. Springer Tracts in Advanced Robotics, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17452-0_20

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  • DOI: https://doi.org/10.1007/978-3-642-17452-0_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17451-3

  • Online ISBN: 978-3-642-17452-0

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