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Kinodynamic RRTs with Fixed Time Step and Best-Input Extension Are Not Probabilistically Complete

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Algorithmic Foundations of Robotics XI

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

Abstract

RRTs are a popular method for kinodynamic planning that many consider to be probabilistically complete. However, different variations of the RRT algorithm exist and not all of them are probabilistically complete. The tree can be extended using a fixed or variable time step. The input can be chosen randomly or the best input can be chosen such that the new child node is as close as possible to the sampled state according to the used distance metric. It has been shown that for finite input sets an RRT using a fixed step size with a randomly selected input is probabilistically complete. However, this variant is uncommon since it is less efficient. We prove that the most common variant of choosing the best input in combination with a fixed time step is not probabilistically complete.

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Acknowledgments

This paper is dedicated to the memory of Mike Stilman. This work was supported in part by ONR grant N00014-14-1-0120.

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Authors and Affiliations

  1. Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Tobias Kunz & Mike Stilman

Authors
  1. Tobias Kunz
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  2. Mike Stilman
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Correspondence to Tobias Kunz .

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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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Kunz, T., Stilman, M. (2015). Kinodynamic RRTs with Fixed Time Step and Best-Input Extension Are Not Probabilistically Complete. 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_14

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  • DOI: https://doi.org/10.1007/978-3-319-16595-0_14

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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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