Review of Mean-Field Theory for the Robotic Swarms Common Target Problem

Yuri Tavares dos Passos; João Victor Neves de Souza Nunes

doi:10.5433/1679-0375.2025.v46.53577

Review of Mean-Field Theory for the Robotic Swarms Common Target Problem

Authors

Yuri Tavares dos Passos Universidade Federal do Recôncavo da Bahia https://orcid.org/0000-0002-9334-1490
João Victor Neves de Souza Nunes Universidade Federal do Recôncavo da Bahia https://orcid.org/0009-0001-4416-2242

DOI:

https://doi.org/10.5433/1679-0375.2025.v46.53577

Keywords:

robotic swarms, mean-field theory, common target problem, differential equations

Abstract

This review provides a literature overview of the usage of Mean-Field Theory (MFT) for modelling the performance estimation of algorithms solving the common target problem in robotic swarm navigation. This problem involves coordinating multiple robots to converge simultaneously towards a single target, which can result in congestion and degraded performance. Its main objective is to minimise the maximum time required for all robots to reach and then depart from the target. The challenge lies in ensuring effective coordination among the robots to prevent conflicts and optimise resource utilisation. MFT may accurately predict navigation metrics, such as agent arrival and departure times, target location density, and system throughput under congestion, and it may enable control strategies based on distributed feedback. This literature overview illustrates that MFT is an effective and promising mathematical tool to mitigate the issues of high dimensionality and complexity of interactions present in systems consisting of a large number of agents.

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Author Biographies

Yuri Tavares dos Passos, Universidade Federal do Recôncavo da Bahia

Prof. Dr. at the Center for Exact and Technological Sciences (CCET) of the Federal University of Recôncavo of Bahia (UFRB), Cruz das Almas, Bahia, Brazil.

João Victor Neves de Souza Nunes, Universidade Federal do Recôncavo da Bahia

Graduate Student at the Center for Exact and Technological Sciences (CCET) of the Federal University of Recôncavo of Bahia (UFRB), Cruz das Almas, Bahia, Brazil.

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