Abstract
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.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
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
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)
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)
Duan, J.: The transitive clousure, convegence of powers and adjoint of generalized fuzzy matrices. Fuzzy Sets Syst. 145, 301–311 (2004)
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)
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
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
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
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht (2000)
Navarro, I., Matía, F.: An introduction to swarm robotics. ISRN Robotics (2013)
Zadeh, L.: Fuzzy sets as a basis for a theory of possibility. FSS 1, 3–28 (1978)
Acknowledgement
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
Editor information
Editors and Affiliations
Rights 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. https://doi.org/10.1007/978-3-319-66805-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-66805-5_1
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)