Density-aware decentralised multi-agent exploration with energy constraint based on optimal transport theory

This paper addresses a density-aware multi-agent exploration problem based on an Optimal Transport (OT) theory while considering energy constraints of a multi-agent system. The density-aware exploration means how a team of agents (robots) cover a given domain, reflecting a priority of areas of interest represented by a density distribution, rather than simply following a preset of uniform patterns. To achieve the density-aware multi-agent exploration, the optimal transport theory that quantifies a distance between two density distributions is employed as a tool, which also serves as a means of similarity measure. Energy constraints for a multi-agent system are then incorporated into the OT-based density-aware multi-agent exploration scheme. The proposed method is developed targeting a decentralised control to cope with more realistic scenarios such as communication range limits between agents. To measure the exploration efficiency, the upper bound of the similarity measure is proposed, which is computationally tractable. The developed multi-agent exploration scheme is applicable to a time-varying distribution as well, where a spatio-temporal evolution of the given reference distribution is desired. To validate the proposed method, multiple simulation results are provided.