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On the Topology of Plans

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Book cover Algorithmic Foundation of Robotics VIII

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 57))

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Abstract

This paper explores a topological perspective of planning. A series of examples and theorems establishes a fundamental coupling between tasks on graphs and simplicial complexes. Planning under uncertainty is one application. The paper introduces strategy and loopback complexes. The paper’s main theorem shows that tasks specified by goal states in nondeterministic graphs have guaranteed solutions if and only if their loopback complexes are homotopic to spheres.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213

    Michael Erdmann

Authors
  1. Michael Erdmann
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, The Johns Hopkins University, 21218, Baltimore, Maryland, USA

    Gregory S. Chirikjian

  2. Carnegie Mellon University, 5000 Forbes Ave., Newell-Simon Hall 3211, 15213, Pittsburgh, PA, USA

    Howie Choset

  3. Sistemas Digitales, Instituto Tecnológico, Autónomo de México, Rio Hondo 1, Progreso Tizapán, 01080, México, D.F., México

    Marco Morales

  4. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, 60208, Evanston, IL, USA

    Todd Murphey

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© 2009 Springer-Verlag Berlin Heidelberg

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Erdmann, M. (2009). On the Topology of Plans. In: Chirikjian, G.S., Choset, H., Morales, M., Murphey, T. (eds) Algorithmic Foundation of Robotics VIII. Springer Tracts in Advanced Robotics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00312-7_17

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  • DOI: https://doi.org/10.1007/978-3-642-00312-7_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00311-0

  • Online ISBN: 978-3-642-00312-7

  • eBook Packages: EngineeringEngineering (R0)

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