Characterizing The Limits of Linear Modeling of Non-Linear Swarm Behaviors

TL;DR

This paper investigates the effectiveness and limitations of linear models in capturing swarm behaviors, especially as behaviors become non-linear, using large-scale robot swarm simulations and mean-field approximations.

Contribution

It introduces a linear modeling approach based on first principles for swarm behavior and characterizes its accuracy limits in non-linear regimes.

Findings

Linear models accurately predict swarm dynamics within mean-field regimes.

Finite-size effects cause deviations from linear predictions in smaller swarms.

Linear models can still provide useful predictions for some non-linear behaviors.

Abstract

We study the limits of linear modeling of swarm behavior by characterizing the inflection point beyond which linear models of swarm collective behavior break down. The problem we consider is a central place object gathering task. We design a linear model which strives to capture the underlying dynamics of object gathering in robot swarms from first principles, rather than extensively relying on post-hoc model fitting. We evaluate our model with swarms of up to 8,000 robots in simulation, demonstrating that it accurately captures underlying swarm behavioral dynamics when the swarm can be approximated using the mean-field model, and when it cannot, and finite-size effects are present. We further apply our model to swarms exhibiting non-linear behaviors, and show that it still provides accurate predictions in some scenarios, thereby establishing better practical limits on linear modeling of swarm behaviors.