Thermodynamics-inspired Macroscopic States of Bounded Swarms

TL;DR

This paper introduces a thermodynamics-inspired framework to characterize and predict the collective behavior of robotic swarms using macroscopic properties analogous to pressure, temperature, and density, bridging fluid dynamics and swarm systems.

Contribution

It proposes a novel set of macroscopic properties for swarms, modeled after thermodynamic variables, and demonstrates their applicability in describing swarm behaviors governed by simple interactions.

Findings

Macroscopic properties analogous to pressure, temperature, and density are defined for swarms.

These properties satisfy an ideal gas law-like equation and a virial equation for real gases.

Swarm density and velocity significantly influence the macrostate.

Abstract

The collective behavior of swarms is extremely difficult to estimate or predict, even when the local agent rules are known and simple. The presented work seeks to leverage the similarities between fluids and swarm systems to generate a thermodynamics-inspired characterization of the collective behavior of robotic swarms. While prior works have borrowed tools from fluid dynamics to design swarming behaviors, they have usually avoided the task of generating a fluids-inspired macroscopic state (or macrostate) description of the swarm. This work will bridge the gap by seeking to answer the following question: is it possible to generate a small set of thermodynamics-inspired macroscopic properties that may later be used to quantify all possible collective behaviors of swarm systems? In this paper, we present three macroscopic properties analogous to pressure, temperature, and density of a gas, to describe the behavior of a swarm that is governed by only attractive and repulsive agent interactions. These properties are made to satisfy an equation similar to the ideal gas law, and also generalized to satisfy the virial equation of state for real gases. Finally, we investigate how swarm specifications such as density and average agent velocity affect the system macrostate.