Skip to main content

New Results on Possibilistic Cooperative Multi-robot Systems

Part of the Lecture Notes in Computer Science book series (LNISA,volume 10451)


This paper addresses one of the main problems to solve in a multi-robot system, allocating tasks to a set of robots (multi-robot task allocation-MRTA). Among all the approaches proposed in the literature to face up MRTA problem, this paper is focused on swarm-like methods called response threshold algorithms. The task allocation algorithms inspired on response threshold are based on probabilistic Markov chains. In the MRTA problem literature, possibilistic Markov chains have proved to outperform the probabilistic Markov chains when a Max-Min algebra is considered for matrix composition. In this paper we analyze the system behavior when a more general algebra than the Max-Min one is taken for matrix composition. Concretely, we consider the algebra \(([0,1], S_{M},T)\), where \(S_{M}\) denotes the maximum t-conorm and T stands for any t-norm. The performed experiments show how only some well-known t-norms are suitable to allocate tasks and how the possibility transition function parameters are related to the used t-norm.


  • Multi-robot
  • Possibility theory
  • Swarm intelligence
  • Task allocation
  • Triangular conorm
  • Triangular norm

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-66805-5_1
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   59.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-66805-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   79.99
Price excludes VAT (USA)
Fig. 1.
Fig. 2.
Fig. 3.


  1. Agassounon, W., Martinoli, A.: Efficiency and robustness of threshold-based distributed allocation algorithms in multi-agent systems. In: AAMAS 2012, Bolonia, Italy, pp. 1090–1097, July 2002

    Google Scholar 

  2. Bonabeau, E., Theraulaz, G., Deneubourg, J.: Fixed response threshold threshold and the regulation of division labour in insect societes. Bull. Math. Biol. 4, 753–807 (1998)

    CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  4. Duan, J.: The transitive clousure, convegence of powers and adjoint of generalized fuzzy matrices. Fuzzy Sets Syst. 145, 301–311 (2004)

    CrossRef  Google Scholar 

  5. Gerkey, B.P., Mataric, M.: A formal analysis and taxonomy of task allocation in multi-robot systems. Int. J. Robot. Res. 23(9), 939–954 (2004)

    CrossRef  Google Scholar 

  6. 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

    CrossRef  Google Scholar 

  7. Heap, B., Pagnucco, M.: Repeated sequential single-cluster auctions with dynamic tasks for multi-robot task allocation with pickup and delivery. In: Klusch, M., Thimm, M., Paprzycki, M. (eds.) MATES 2013. LNCS, vol. 8076, pp. 87–100. Springer, Heidelberg (2013). doi:10.1007/978-3-642-40776-5_10

    CrossRef  Google Scholar 

  8. Kalra, N., Martinoli, A.: A comparative study of market-based and threshold-based task allocation. In: Gini, M., Voyles, R. (eds.) DARS, pp. 91–102. Springer, Tokyo (2006). doi:10.1007/4-431-35881-1_10

    CrossRef  Google Scholar 

  9. Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)

    CrossRef  MATH  Google Scholar 

  10. Navarro, I., Matía, F.: An introduction to swarm robotics. ISRN Robotics (2013)

    Google Scholar 

  11. Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. FSS 1, 3–28 (1978)

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references


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 (LODISCO II) and AEI/FEDER, UE funds.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Pilar Fuster-Parra .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Fuster-Parra, P., Guerrero, J., Martín, J., Valero, Ó. (2017). New Results on Possibilistic Cooperative Multi-robot Systems. In: Luo, Y. (eds) Cooperative Design, Visualization, and Engineering. CDVE 2017. Lecture Notes in Computer Science(), vol 10451. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66804-8

  • Online ISBN: 978-3-319-66805-5

  • eBook Packages: Computer ScienceComputer Science (R0)