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Sampling Extremal Trajectories for Planar Rigid Bodies

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Book cover Algorithmic Foundations of Robotics X

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 86))

Abstract

This paper presents an approach to finding the time-optimal trajectories for a simple rigid-body model of a mobile robot in an obstacle-free plane. Previous work has used Pontryagin’s Principle to find strong necessary conditions on time-optimal trajectories of the rigid body; trajectories satisfying these conditions are called extremal trajectories. The main contribution of this paper is a method for sampling the extremal trajectories sufficiently densely to guarantee that for any pair of start and goal configurations, a trajectory can be found that (provably) approximately reaches the goal, approximately optimally; the quality of the approximation is only limited by the availability of computational resources.

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Author information

Authors and Affiliations

  1. Dartmouth College, Dartmouth, NH, USA

    Weifu Wang & Devin Balkcom

Authors
  1. Weifu Wang
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  2. Devin Balkcom
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Corresponding author

Correspondence to Weifu Wang .

Editor information

Editors and Affiliations

  1. Associate Professor of Aeronautics and, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Emilio Frazzoli

  2. MIT Comp. Sci. & Artificial Intel. Lab., Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Tomas Lozano-Perez

  3. Robust Robotics Group, Massachusetts Institute of Technology CSAIL, Cambridge, Massachusetts, USA

    Nicholas Roy

  4. Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    Daniela Rus

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Wang, W., Balkcom, D. (2013). Sampling Extremal Trajectories for Planar Rigid Bodies. In: Frazzoli, E., Lozano-Perez, T., Roy, N., Rus, D. (eds) Algorithmic Foundations of Robotics X. Springer Tracts in Advanced Robotics, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36279-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-36279-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36278-1

  • Online ISBN: 978-3-642-36279-8

  • eBook Packages: EngineeringEngineering (R0)

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