A Comparative Analysis of Indistinguishability Operators Applied to Swarm Multi-Robot Task Allocation Problem

  • José GuerreroEmail author
  • Juan-José Miñana
  • Oscar Valero
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10451)


One of the main problems to solve in multi-robot systems is to select the best robot to execute each task (task allocation). Several ways to address this problem have been proposed in the literature. This paper focuses on one of them, the so-called response threshold methods. In a recent previous work, it was proved that the possibilistic Markov chains outperform the classical probabilistic using a celebrated possibility transition function. In this paper we use a new possibility transition function and we make several experiments in order to compare both, the new one and the tested before. The experiments show that the number of steps that a possibilistic Markov chain needs to converge does not depend on the response function used. This paper also emphasizes that these possibility transition functions are indistinguishably operators.


Indistinguishability operator Markov chain Multi-robot Possibility theory Swarm intelligence Task allocation 



This research was funded by the Spanish Ministry of Economy and Competitiveness under Grants DPI2014-57746-C03-2-R, TIN2014-53772-R, TIN2014-56381-REDT (LODISCO), TIN2016-81731-REDT and AEI/FEDER, UE funds.


  1. 1.
    Agassounon, W., Martinoli, A.: Efficiency and robustness of threshold-based distributed allocation algorithms in multi-agent systems. In: 1st International Joint Conference on Autonomous Agents and Multi-agents Systems, Bolonia, Italy, pp. 1090–1097, July 2002Google Scholar
  2. 2.
    Avrachenkov, K., Sanchez, E.: Fuzzy Markov chains and decision making. Fuzzy Optim. Decis. Making 1, 143–159 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Castello, E., Yamamoto, T., Libera, F.D., Liu, W., Winfield, A.F.T., Nakamura, Y., Ishiguro, H.: Adaptive foraging for simulated and real robotic swarms: the dynamical response threshold approach. Swarm Intell. 10(1), 1–31 (2016)CrossRefGoogle Scholar
  4. 4.
    Duan, J.: The transitive clousure, convegence of powers and adjoint of generalized fuzzy matrices. Fuzzy Sets Syst. 145, 301–311 (2004)CrossRefGoogle Scholar
  5. 5.
    Guerrero, J., Valero, Ó., Oliver, G.: A first step toward a possibilistic swarm multi-robot task allocation. In: Rojas, I., Joya, G., Catala, A. (eds.) IWANN 2015. LNCS, vol. 9094, pp. 147–158. Springer, Cham (2015). doi: 10.1007/978-3-319-19258-1_13 CrossRefGoogle Scholar
  6. 6.
    Guerrero, J., Oliver, G., Valero, O.: Multi-robot coalitions formation with deadlines: complexity analysis and solutions. PLoS ONE 12(1), 1–26 (2017)Google Scholar
  7. 7.
    Kalra, N., Martinoli, A.: A comparative study of market-based and threshold-based task allocation. In: 8th International Symposium on Distributed Autonomous Robotic Systems, Minneapolis, USA, pp. 91–102 (2006)Google Scholar
  8. 8.
    Recasens, J.: Indistinguishability Operators: Modelling Fuzzy Equalities and Fuzzy Equivalence Relations. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  9. 9.
    Vajargah, B.F., Gharehdaghi, M.: Ergodicity of fuzzy markov chains based on simulation using sequences. Int. J. Appl. Math. Comput. Sci. 11(2), 159–165 (2014)Google Scholar
  10. 10.
    Yang, Y., Zhou, C., Tin, Y.: Swarm robots task allocation based on response threshold model. In: 4th International Conference on Autonomous Robots and Agents, Wellington, New Zealand, pp. 171–176 (2009)Google Scholar
  11. 11.
    Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1, 3–28 (1978)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • José Guerrero
    • 1
    Email author
  • Juan-José Miñana
    • 1
  • Oscar Valero
    • 1
  1. 1.Mathematics and Computer Science DepartmentUniversitat de les Illes BalearsPalma de MallorcaSpain

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