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Asymptotically Optimal Stochastic Motion Planning with Temporal Goals

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Book cover Algorithmic Foundations of Robotics XI

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

Abstract

This work presents a planning framework that allows a robot with stochastic action uncertainty to achieve a high-level task given in the form of a temporal logic formula. The objective is to quickly compute a feedback control policy to satisfy the task specification with maximum probability. A top-down framework is proposed that abstracts the motion of a continuous stochastic system to a discrete, bounded-parameter Markov decision process (bmdp), and then computes a control policy over the product of the bmdp abstraction and a dfa representing the temporal logic specification. Analysis of the framework reveals that as the resolution of the bmdp abstraction becomes finer, the policy obtained converges to optimal. Simulations show that high-quality policies to satisfy complex temporal logic specifications can be obtained in seconds, orders of magnitude faster than existing methods.

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Acknowledgments

Work by Ryan Luna is supported by a NASA Space Technology Research Fellowship. Work by Morteza Lahijanian, Mark Moll, and Lydia Kavraki is supported in part by NSF NRI 1317849, NSF 1139011, and NSF CCF 1018798. Computing resources supported in part by NSF CNS 0821727.

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Authors and Affiliations

  1. Department of Computer Science, Rice University, Houston, TX, USA

    Ryan Luna, Morteza Lahijanian, Mark Moll & Lydia E. Kavraki

Authors
  1. Ryan Luna
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  2. Morteza Lahijanian
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  3. Mark Moll
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  4. Lydia E. Kavraki
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Corresponding author

Correspondence to Lydia E. Kavraki .

Editor information

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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Luna, R., Lahijanian, M., Moll, M., Kavraki, L.E. (2015). Asymptotically Optimal Stochastic Motion Planning with Temporal Goals. 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_20

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  • DOI: https://doi.org/10.1007/978-3-319-16595-0_20

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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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