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Optimal Trajectories for Planar Rigid Bodies with Switching Costs

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Algorithmic Foundations of Robotics XI

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 107))

Abstract

The optimal trajectory with respect to some metric may require very many switches between controls, or even infinitely many, a phenomenon called chattering; this can be problematic for existing motion planning algorithms that plan using a finite set of motion primitives. One remedy is to add some penalty for switching between controls. This paper explores the implications of this switching cost for optimal trajectories, using rigid bodies in the plane (which have been studied extensively in the cost-free-switch model) as an example system. Blatt’s Indifference Principle (BIP) is used to derive necessary conditions on optimal trajectories; Lipschitzian optimization techniques together with an A* search yield an algorithm for finding trajectories that can arbitrarily approximate the optimal trajectories.

This work was supported in part by NSF grant IIS-0643476.

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Authors and Affiliations

  1. Department of Computer Science, Dartmouth College, Hanover, NH, 03755, USA

    Yu-Han Lyu & Devin Balkcom

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  1. Yu-Han Lyu
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  2. Devin Balkcom
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Correspondence to Yu-Han Lyu .

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Editors and Affiliations

  1. Department of Computer Engineering, Bogazici University, Istanbul, Turkey

    H. Levent Akin

  2. Department of Computer Science and Engineering, Texas A&M University, College Station, Texas, USA

    Nancy M. Amato

  3. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota, USA

    Volkan Isler

  4. Department of Information and Computing Sciences, Utrecht University, Utrecht, Utrecht, The Netherlands

    A. Frank van der Stappen

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Lyu, YH., Balkcom, D. (2015). Optimal Trajectories for Planar Rigid Bodies with Switching Costs. In: Akin, H., Amato, N., Isler, V., van der Stappen, A. (eds) Algorithmic Foundations of Robotics XI. Springer Tracts in Advanced Robotics, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-16595-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-16595-0_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16594-3

  • Online ISBN: 978-3-319-16595-0

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