Mean Field Behaviour of Collaborative Multi-Agent Foragers

TL;DR

This paper applies mean field techniques to analyze a biologically-inspired multi-agent foraging system, transforming stochastic dynamics into deterministic models to study limit behaviors and performance implications of finite agents.

Contribution

It introduces a mean field reformulation for multi-agent foraging, enabling analysis of limit behaviors and finite-agent effects in collaborative robotic systems.

Findings

Mean field models approximate finite-agent performance effectively.

Deterministic analysis simplifies understanding of complex multi-agent dynamics.

Finite agents' performance deviates from the mean field limit, impacting system design.

Abstract

Collaborative multi-agent robotic systems where agents coordinate by modifying a shared environment often result in undesired dynamical couplings that complicate the analysis and experiments when solving a specific problem or task. Simultaneously, biologically-inspired robotics rely on simplifying agents and increasing their number to obtain more efficient solutions to such problems, drawing similarities with natural processes. In this work we focus on the problem of a biologically-inspired multi-agent system solving collaborative foraging. We show how mean field techniques can be used to re-formulate such a stochastic multi-agent problem into a deterministic autonomous system. This de-couples agent dynamics, enabling the computation of limit behaviours and the analysis of optimality guarantees. Furthermore, we analyse how having finite number of agents affects the performance when compared to the mean field limit and we discuss the implications of such limit approximations in this multi-agent system, which have impact on more general collaborative stochastic problems.