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On the robustness of a synchronized multi-robot system

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Abstract

Area coverage and communication are fundamental concerns in networks of cooperating robots. The goal is to address the issue of how well a group of collaborating robots having a limited communication range is able to monitor a given geographical space. Typically, an area of interest is partitioned into smaller subareas, with each robot in charge of a given subarea. This gives rise to a communication network that allows robots to exchange information when they are sufficiently close to each other. To be effective, the system must be resilient, i.e., be able to recover from robot failures. In a recent paper Bereg et al. (J Comb Optim 36(2):365–391, 2018), the concept of k-resilience of a synchronized system was introduced as the cardinality of a smallest set of robots whose failure suffices to cause that at least k surviving robots operate without communication, thus entering a state of starvation. It was proven that the problem of computing the k-resilience is NP-hard in general. In this paper, we study several problems related to the resilience of a synchronized system with respect to coverage and communication on realistic topologies including grid and cycle configurations. The broadcasting resilience is the minimum number of robots whose removal may disconnect the network. The coverage resilience is the minimum number of robots whose removal may result in a non-covered subarea. We prove that the three resilience measures can be efficiently computed for these configurations.

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Notes

  1. An illustration of this phenomenon is at https://www.youtube.com/watch?v=64gKnefnXew.

References

  • Abdulla AEAA, Fadlullah ZMd, Nishiyama H, Kato N, Ono F, Miura R (2014) An optimal data collection technique for improved utility in uas-aided networks. In: 2014 IEEE conference on computer communications, INFOCOM 2014, pp 736–744

  • Alena O, Niels A, James C, Bruce G, Erwin P (2018) Optimization approaches for civil applications of unmanned aerial vehicles (UAVs) or aerial drones: a survey. Networks, to appear

  • Almeida A, Ramalho G, Santana H, Tedesco P, Menezes T, Corruble V, Chevaleyre Y (2004) Recent advances on multi-agent patrolling. In: Brazilian symposium on artificial intelligence. Springer, pp 474–483

  • Bereg S, Caraballo L-E, Díaz-Báñez J-M, Lopez MA (2018) Computing the \(k\)-resilience of a synchronized multi-robot system. J Comb Optim 36(2):365–391

    Article  MathSciNet  Google Scholar 

  • Boesch F, Tindell R (1984) Circulants and their connectivities. J Graph Theory 8(4):487–499

    Article  MathSciNet  Google Scholar 

  • Choset H (2001) Coverage for robotics-a survey of recent results. Ann Math Artif Intell 31(1–4):113–126

    Article  Google Scholar 

  • Clark CM, Rock SM, Latombe J-C (2003) Motion planning for multiple mobile robots using dynamic networks. In: Proceedings of the 2003 IEEE international conference on robotics and automation, ICRA’03, vol 3. IEEE, pp 4222–4227

  • Collins A, Czyzowicz J, Gasieniec L, Kosowski A, Kranakis E, Krizanc D, Martin R, Ponce OM (2013) Optimal patrolling of fragmented boundaries. In: Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures. ACM, pp 241–250

  • Czyzowicz J, Gasieniec L, Kosowski A, Kranakis E (2011) Boundary patrolling by mobile agents with distinct maximal speeds. In: European symposium on algorithms. Springer, pp 701–712

  • Czyzowicz J, Kosowski A, Kranakis E, Taleb N (2016) Patrolling trees with mobile robots. In: International symposium on foundations and practice of security. Springer, pp 331–344

  • Díaz-Báñez J-M, Caraballo L-E, Lopez M, Bereg S, Maza I, Ollero A (2015) The synchronization problem for information exchange between aerial robots under communication constraints. In: 2015 International conference on robotics and automation (ICRA). IEEE

  • Díaz-Báñez J-M, Caraballo L-E, Lopez M, Bereg S, Maza I, Ollero A (2017) A general framework for synchronizing a team of robots under communication constraints. IEEE Trans Robotics 33(4):748–755

    Article  Google Scholar 

  • Flocchini P, Santoro N, Viglietta G, Yamashita M (2016) Rendezvous with constant memory. Theor. Comput. Sci. 621:57–72

    Article  MathSciNet  Google Scholar 

  • Galceran E, Carreras M (2013) A survey on coverage path planning for robotics. Robotics Auton Syst 61(12):1258–1276

    Article  Google Scholar 

  • Hamacher HW (1992) Combinatorial optimization models motivated by robotic assembly problems. In: Combinatorial optimization. Springer, pp 187–198

  • Hazon N, Kaminka GA (2008) On redundancy, efficiency, and robustness in coverage for multiple robots. Robotics Auton Syst 56(12):1102–1114

    Article  Google Scholar 

  • Henzinger MR, Rao S, Gabow HN (2000) Computing vertex connectivity: new bounds from old techniques. J Algorithms 34(2):222–250

    Article  MathSciNet  Google Scholar 

  • Hsieh MA, Cowley A, Kumar V, Taylor CJ (2008) Maintaining network connectivity and performance in robot teams. J Field Robotics 25(1–2):111–131

    Article  Google Scholar 

  • Hwang S-I, Cheng S-T (2001) Combinatorial optimization in real-time scheduling: theory and algorithms. J Comb Optim 5(3):345–375

    Article  MathSciNet  Google Scholar 

  • Kranakis E, Krizanc D (2015) Optimization problems in infrastructure security. In: International symposium on foundations and practice of security. Springer, pp 3–13

  • Lovász L (1993) Random walks on graphs. Comb Paul Erdos Eighty 2(1–46):4

    Google Scholar 

  • Mazayev A, Correia N, Schütz G (2016) Data gathering in wireless sensor networks using unmanned aerial vehicles. Int J Wireless Inf Netw 23(4):297–309

    Article  Google Scholar 

  • Meijer PT (1991) Connectivities and diameters of circulant graphs. Master’s thesis, Simon Fraser University, 12

  • Patel R, Carron A, Bullo F (2016) The hitting time of multiple random walks. SIAM J Matrix Anal Appl 37(3):933–954

    Article  MathSciNet  Google Scholar 

  • Roy N, Dudek G (2001) Collaborative robot exploration and rendezvous: algorithms, performance bounds and observations. Auton Robots 11(2):117–136

    Article  Google Scholar 

  • Tabachnikov S (2005) Geometry and billiards. Amer. Math. Soc, Providence

    Book  Google Scholar 

  • Tetali P, Winkler P (1991) On a random walk problem arising in self-stabilizing token management. In: Proceedings of the tenth annual ACM symposium on principles of distributed computing. ACM, pp 273–280

  • Winfield AFT (2000) Distributed sensing and data collection via broken ad hoc wireless connected networks of mobile robots. In: Distributed autonomous robotic systems, vol 4. Springer, pp 273–282

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Authors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 800 West Campbell Road, Richardson, TX, 75080, USA

    Sergey Bereg

  2. Department of Computer Science, University of Denver, 2155 E. Wesley Avenue, Denver, CO, 80208, USA

    Andrew Brunner & Mario A. Lopez

  3. Higher Technical School of Engineering, University of Seville, Camino de los Descubrimientos, No number, 41092, Seville, Spain

    Luis-Evaristo Caraballo & José-Miguel Díaz-Báñez

Authors
  1. Sergey Bereg
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  2. Andrew Brunner
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  3. Luis-Evaristo Caraballo
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  4. José-Miguel Díaz-Báñez
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  5. Mario A. Lopez
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Corresponding author

Correspondence to Luis-Evaristo Caraballo.

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

L. E. Caraballo: Funded by Spanish Government under Grant Agreement FPU14/04705.

This research has received funding from the projects GALGO (Spanish Ministry of Economy and Competitiveness, MTM2016-76272-R AEI/FEDER, UE) and CONNECT (European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 734922).

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Bereg, S., Brunner, A., Caraballo, LE. et al. On the robustness of a synchronized multi-robot system. J Comb Optim 39, 988–1016 (2020). https://doi.org/10.1007/s10878-020-00533-z

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