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

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... rchers 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.