# Non-Uniform Robot Densities in Vibration Driven Swarms Using Phase Separation Theory

## TL;DR

This paper explores how vibration-driven robot swarms can naturally form high-density clusters and low-density regions through phase separation, using theoretical insights from statistical mechanics and experimental validation.

## Contribution

It introduces a novel application of phase separation theory to robot swarms, linking collective behavior to equilibrium thermodynamics for the first time in robotics.

## Key findings

- Robots form high-density aggregates through collisions.
- Theoretical models predict density segregation.
- Experiments confirm non-uniform distributions in bounded areas.

## Abstract

In robot swarms operating under highly restrictive sensing and communication constraints, individuals may need to use direct physical proximity to facilitate information exchange. However, in certain task-related scenarios, this requirement might conflict with the need for robots to spread out in the environment, e.g., for distributed sensing or surveillance applications. This paper demonstrates how a swarm of minimally-equipped robots can form high-density robot aggregates which coexist with lower robot densities in the domain. We envision a scenario where a swarm of vibration-driven robots---which sit atop bristles and achieve directed motion by vibrating them---move somewhat randomly in an environment while colliding with each other. Theoretical techniques from the study of far-from-equilibrium collectives and statistical mechanics clarify the mechanisms underlying the formation of these high and low density regions. Specifically, we capitalize on a transformation that connects the collective properties of a system of self-propelled particles with that of a well-studied molecular fluid system, thereby inheriting the rich theory of equilibrium thermodynamics. This connection is a formal one and is a relatively recent result in studies of motility induced phase separation; it is previously unexplored in the context of robotics. Real robot experiments as well as simulations illustrate how inter-robot collisions can precipitate the formation of non-uniform robot densities in a closed and bounded region.