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The Role of Heterogeneity in Autonomous Perimeter Defense Problems

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Algorithmic Foundations of Robotics XV (WAFR 2022)

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 25))

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Abstract

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.

Supported by the Army Research Laboratory as part of the Distributed and Collaborative Intelligent Systems and Technology (DCIST) Collaborative Research Alliance (CRA) under contract W911NF-17-2-0181. G.S. Sukhatme holds concurrent appointments as a Professor at USC and as an Amazon Scholar. This paper describes work performed at USC and is not associated with Amazon.

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Notes

  1. 1.

    For instance, if \(g = 5\) and \((v_{\min }, v_{\max }] = (0,1]\), we measure \({\boldsymbol{v}}\) where \(v_i \in \{0.2, 0.4, 0.6, 0.8, 1\}\) for all i.

  2. 2.

    We consider this case because it has a number of nice symmetries, and because perimeters enclosing a simply-connected 2D area are homeomorphic to \({\mathcal {S}}^1\).

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    Aviv Adler

  2. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Oscar Mickelin

  3. Department of Computer Science, University of Southern California, Los Angeles, CA, 90089, USA

    Ragesh K. Ramachandran & Gaurav S. Sukhatme

  4. Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Sertac Karaman

Authors
  1. Aviv Adler
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  2. Oscar Mickelin
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  3. Ragesh K. Ramachandran
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  4. Gaurav S. Sukhatme
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  5. Sertac Karaman
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Corresponding author

Correspondence to Aviv Adler .

Editor information

Editors and Affiliations

  1. Center for Ubiquitous Computing, University of Oulu, Oulu, Finland

    Steven M. LaValle

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

    Jason M. O’Kane

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

    Michael Otte

  4. Gates Computer Science, Stanford University, Stanford, CA, USA

    Dorsa Sadigh

  5. Department of Computer Science, University of Maryland, College Park, MD, USA

    Pratap Tokekar

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Adler, A., Mickelin, O., Ramachandran, R.K., Sukhatme, G.S., Karaman, S. (2023). The Role of Heterogeneity in Autonomous Perimeter Defense Problems. In: LaValle, S.M., O’Kane, J.M., Otte, M., Sadigh, D., Tokekar, P. (eds) Algorithmic Foundations of Robotics XV. WAFR 2022. Springer Proceedings in Advanced Robotics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-031-21090-7_8

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