On the Use of Fuzzy Preorders in Multi-robot Task Allocation Problem
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This paper addresses the multi-robot task allocation problem. In particular, given a collection of tasks and robots, we focus on how to select the best robot to execute each task by means of the so-called response threshold method. In the aforesaid method, each robot decides to leave a task and to perform another one (decides to transit) following a probability (response functions) that depends mainly of a stimulus and the current task. The probabilistic approaches used to model the transitions present several handicaps. To solve these problems, in a previous work, we introduced the use of indistinguishability operators to model response functions and possibility theory instead of probability. In this paper we extend the previous work in order to be able to model response functions when the stimulus under consideration depends on the distance between tasks and the utility of them. Thus, the resulting response functions that model transitions in the Markov chains must be asymmetric. In the light of this asymmetry, it seems natural to use fuzzy preorders in order to model the system’s behaviour. The results of the simulations executed in Matlab validate our approach and they show again how the possibilistic Markov chains outperform their probabilistic counterpart.
KeywordsFuzzy preorders Markov chain Multi-robot Possibility Swarm Intelligence Task allocation Asymmetric distance
This research was funded by the Spanish Ministry of Economy and Competitiveness under Grants DPI2014-57746-C03-2-R, TIN2014-53772-R, TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds, by the Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project ref. PROCOE/4/2017 (Direccio General d’Innovacio i Recerca, Govern de les Illes Balears), and by project ROBINS. The latter has received research funding from the EU H2020 framework under GA 779776. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.
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