# Steering a Particle Swarm Using Global Inputs and Swarm Statistics

## TL;DR

This paper explores controlling large particle swarms using only global inputs and swarm statistics, demonstrating controllability, developing controllers, and validating on kilobots for manipulation tasks.

## Contribution

It introduces controllers based on mean and variance for swarm manipulation, proves controllability, and implements these controllers on kilobots for practical tasks.

## Key findings

- Mean position is controllable in swarm systems.
- Variance can be controlled under certain conditions.
- Controllers successfully manipulated kilobots using global inputs.

## Abstract

Microrobotics has the potential to revolutionize many applications including targeted material delivery, assembly, and surgery. The same properties that promise breakthrough solutions---small size and large populations---present unique challenges for controlling motion. Robotic manipulation usually assumes intelligent agents, not particle systems manipulated by a global signal. To identify the key parameters for particle manipulation, we used a collection of online games where players steer swarms of up to 500 particles to complete manipulation challenges. We recorded statistics from over ten thousand players. Inspired by techniques where human operators performed well, we investigate controllers that use only the mean and variance of the swarm. We prove the mean position is controllable and provide conditions under which variance is controllable. We next derive automatic controllers for these and a hysteresis-based switching control to regulate the first two moments of the particle distribution. Finally, we employ these controllers as primitives for an object manipulation task and implement all controllers on 100 kilobots controlled by the direction of a global light source.