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Nowadays, the multi-robot task allocation problem is one of the most challenging problems in multi-robot systems. It concerns the optimal assignment of a set of tasks to several robots while optimizing a given criterion subject to some constraints. This problem is very complex, particularly when handling large groups of robots and tasks. We propose a formal analysis of the task allocation problem in a multi-robot system, based on set theory concepts. We believe that this analysis will help researchers understand the nature of the problem, its time complexity, and consequently develop efficient solutions. Also, we used that formal analysis to formulate two well-known taxonomies of multi-robot task allocation problems. Finally, a generic solving scheme of multi-robot task allocation problems is proposed and illustrated on assigning papers to reviewers within a journal.

Towards a formal analysis of the multi-robot task allocation problem using set theory