Indirect Swarm Control: Characterization and Analysis of Emergent Swarm Behaviors

TL;DR

This work addresses how to predict and engineer emergent swarm macrostates without exhaustive simulation by reframing swarms as a chemistry-like system guided by environmental conditions. It introduces a framework that maps microstate interactions to macrostates via macroscopic properties and phase-diagram reasoning, and derives closed-form results for milling, including the milling radius $R_m = \tfrac{\gamma}{2\sin(\pi/N)}$ and a sufficient-condition set ${\mathcal{P}}^* = \{P \in \mathcal{P} | \phi = \tfrac{2\pi}{N}, \tfrac{v}{\omega} \le \tfrac{\gamma}{2\sin(\pi/N)}\}$. The authors validate the approach with simulations and real robot experiments, showing milling emerges in a constrained region of the parameter space and that milling radius can be prescribed, providing a practical route to indirect swarm control. By mapping environmental and interaction parameters to predictable macrostates, this framework offers a path toward scalable, real-world swarm deployment with reduced reliance on trial-and-error tuning.

Abstract

Emergence and emergent behaviors are often defined as cases where changes in local interactions between agents at a lower level effectively changes what occurs in the higher level of the system (i.e., the whole swarm) and its properties. However, the manner in which these collective emergent behaviors self-organize is less understood. The focus of this paper is in presenting a new framework for characterizing the conditions that lead to different macrostates and how to predict/analyze their macroscopic properties, allowing us to indirectly engineer the same behaviors from the bottom up by tuning their environmental conditions rather than local interaction rules. We then apply this framework to a simple system of binary sensing and acting agents as an example to see if a re-framing of this swarms problem can help us push the state of the art forward. By first creating some working definitions of macrostates in a particular swarm system, we show how agent-based modeling may be combined with control theory to enable a generalized understanding of controllable emergent processes without needing to simulate everything. Whereas phase diagrams can generally only be created through Monte Carlo simulations or sweeping through ranges of parameters in a simulator, we develop closed-form functions that can immediately produce them revealing an infinite set of swarm parameter combinations that can lead to a specifically chosen self-organized behavior. While the exact methods are still under development, we believe simply laying out a potential path towards solutions that have evaded our traditional methods using a novel method is worth considering. Our results are characterized through both simulations and real experiments on ground robots.

Figures (13)

• Figure 1: Phase diagrams of the macrostates of matter of $H_20$ molecules wiki_phase.
• Figure 2: Different local interaction rules leading to different emergent group behaviors (under certain conditions).
• Figure 3: Examples of different values of $\overline{c}$.
• Figure 4: Simulation showing (a) when the system has broken apart into multiple groups, and (b) zooming in on the 3 agents at the top right to view them as a single sub-swarm.
• Figure 5: Multiple phase diagrams showing how various conditions can lead to different behaviors. This shows that how these diagrams are only 2D slices of a much more complicated and higher dimensional space.

Theorems & Definitions (3)

• Lemma III.1
• Example III.2: Connection between ${\mathcal{G}}_\text{disk}$ and ${\mathcal{G}}_\text{vis-disk}$
• Proposition IV.1