An application of fuzzy sets to optimal task-allocation problem

Abstract

[eng] When dealing with multi-robot systems, one of the main challenges is assigning to each robot the best-possible task to perform at any given time, which is known as the optimal task-allocation problem. Furthermore, in numerous real-world scenarios, it is also crucial to consider time deadlines associated with the tasks. In this paper, we draw inspiration from response-threshold methods (a type of swarm-like methods), which have proven to be effective in addressing the aforesaid optimal task-allocation problem. In such methods, each robot processes a collection of stimuli to evaluate the suitability of a given task. We model the aforementioned stimuli using appropriate fuzzy sets in such a way that each robot determines the most suitable task to perform at every moment of time via the so-called Bellman-Zadeh fuzzy optimization technique which involves aggregation functions. In order to assess the efficiency of the new mathematical approach, we have conducted an extensive set of simulation experiments testing different aggregation functions. The obtained results demonstrate that the proposed approach effectively models the evolution of a swarm-like system when considering tasks with deadlines and that the most effective task allocation is achieved when OWA operators are taken into account.