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We study the limits of linear modeling of swarm behavior by characterizingthe inflection point beyond which linear models of swarm collective behaviorbreak down. The problem we consider is a central place object gathering task.We design a linear model which strives to capture the underlying dynamics ofobject gathering in robot swarms from first principles, rather than extensivelyrelying on post-hoc model fitting. We evaluate our model with swarms of up to8,000 robots in simulation, demonstrating that it accurately capturesunderlying swarm behavioral dynamics when the swarm can be approximated usingthe 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 showthat it still provides accurate predictions in some scenarios, therebyestablishing better practical limits on linear modeling of swarm behaviors.

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