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On the Computational Power of Energy-Constrained Mobile Robots: Algorithms and Cross-Model Analysis

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Structural Information and Communication Complexity (SIROCCO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13298))

Abstract

We consider distributed systems of identical autonomous computational entities, called robots, moving and operating in the plane in synchronous \( Look \)-\( Compute \)-\( Move \) (\( LCM \)) cycles. The algorithmic capabilities of these systems have been extensively investigated in the literature under four distinct models (\(\mathcal {OBLOT} \), \(\mathcal {FST\!A} \), \(\mathcal {FCOM} \), \(\mathcal {LUMI} \)), each identifying different levels of memory persistence and communication capabilities of the robots. Despite their differences, they all always assume that robots have unlimited amounts of energy.

In this paper, we remove this assumption and start the study of the computational capabilities of robots whose energy is limited, albeit renewable. We first study the impact that memory persistence and communication capabilities have on the computational power of such energy-constrained systems of robots; we do so by analyzing the computational relationship between the four models under this energy constraint. We provide a complete characterization of this relationship.

We then study the difference in computational power caused by the energy restriction and provide a complete characterization of the relationship between energy-constrained and unrestricted robots in each model. We prove that within \(\mathcal {LUMI} \) there is no difference; an integral part of the proof is the design and analysis of an algorithm that in \(\mathcal {LUMI} \) allows energy-constrained robots to execute correctly any protocol for robots with unlimited energy. We then show the (apparently counterintuitive) result that in all other models, the energy constraint actually provides the robots with a computational advantage.

This work was supported in part by JSPS KAKENHI No. 20K11685 and 21K11748, Israel & Japan Science and Technology Agency (JST) SICORP (Grant#JPMJSC1806), and by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Discovery Grants A2415 and 203254.

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Notes

  1. 1.

    OSP is Oscillating Points and CGE* is Perpetual Center of Gravity Expansion.

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Author information

Authors and Affiliations

  1. TU Dortmund, Dortmund, Germany

    Kevin Buchin

  2. University of Ottawa, Ottawa, Canada

    Paola Flocchini

  3. TU Eindhoven, Eindhoven, The Netherlands

    Irina Kostitsyna & Tom Peters

  4. Carleton University, Ottawa, Canada

    Nicola Santoro

  5. Hosei University, Tokyo, Japan

    Koichi Wada

Authors
  1. Kevin Buchin
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  2. Paola Flocchini
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  3. Irina Kostitsyna
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  4. Tom Peters
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  5. Nicola Santoro
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  6. Koichi Wada
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Corresponding author

Correspondence to Koichi Wada .

Editor information

Editors and Affiliations

  1. Weizmann Institute, Rehovot, Israel

    Merav Parter

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Buchin, K., Flocchini, P., Kostitsyna, I., Peters, T., Santoro, N., Wada, K. (2022). On the Computational Power of Energy-Constrained Mobile Robots: Algorithms and Cross-Model Analysis. In: Parter, M. (eds) Structural Information and Communication Complexity. SIROCCO 2022. Lecture Notes in Computer Science, vol 13298. Springer, Cham. https://doi.org/10.1007/978-3-031-09993-9_3

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  • DOI: https://doi.org/10.1007/978-3-031-09993-9_3

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