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The Computational Complexity of Controller-Environment Co-design Using Library Selection for Distributed Construction

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Distributed Autonomous Robotic Systems

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 9))

Abstract

Creating specified structures through the coordinated efforts of teams of simple autonomous robots is a very important problem in distributed robotics. All previous effort, both empirical and theoretical, has focused on the problems of designing either controllers or environments which, in tandem with given environments or controllers, built the specified structures. In this paper, we give the results of the first computational and parameterized complexity analyses of the controller-environment co-design problem in the simple case where robot teams are designed by selecting controllers from a given library. We show that this problem cannot be solved efficiently in general or under a number of restrictions, and give the first restrictions under which this problem is efficiently solvable.

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Notes

  1. 1.

    Like the conjectures \(P \ne NP\) and \(P = BPP\) mentioned earlier, the conjecture \(FPT \ne W[1]\) is also widely believed to be true within Computer Science [8].

  2. 2.

    Note that both here and in the remaining proofs involving Clique, we have renamed the set of edges in graph G to \(E'\) to avoid confusion with the robot-team construction environment E.

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Acknowledgements

The authors would like to thank the MUN Writing Center, Rory Campbell, Caroline Strickland, and the three anonymous reviewers for comments that helped to significantly improve the presentation of this paper. MT was supported by funds from the MUN School of Graduate Studies and National Science and Engineering Research Council (NSERC) Discovery Grant 228104-2015 held by TW; TW was also supported by the latter.

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Authors and Affiliations

  1. Department of Computer Science, Memorial University of Newfoundland, St. John’s, NL, A1B 3X5, Canada

    Mesam Timmar & Todd Wareham

Authors
  1. Mesam Timmar
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  2. Todd Wareham
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Corresponding author

Correspondence to Mesam Timmar .

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Colorado Boulder, Boulder, CO, USA

    Nikolaus Correll

  2. Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA

    Mac Schwager

  3. Department of Aerospace Engineering, University of Maryland, College Park, MD, USA

    Michael Otte

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Timmar, M., Wareham, T. (2019). The Computational Complexity of Controller-Environment Co-design Using Library Selection for Distributed Construction. In: Correll, N., Schwager, M., Otte, M. (eds) Distributed Autonomous Robotic Systems. Springer Proceedings in Advanced Robotics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-05816-6_4

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