Target-density formation in swarms with stochastic sensing and dynamics

TL;DR

This paper develops a stochastic model for swarm agents to achieve a desired density distribution through local sensing and interactions, analyzing how various factors influence the accuracy and speed of formation.

Contribution

It introduces a statistical physics-based model for swarm density formation, incorporating stochastic sensing and dynamics, with analytical insights into performance dependencies.

Findings

Quantifies the impact of sensing uncertainty on density accuracy.

Analyzes how agent number affects convergence speed.

Provides bounds on swarm density error based on model parameters.

Abstract

An important goal for swarming research is to create methods for predicting, controlling and designing swarms, which produce collective dynamics that solve a problem through emergent and stable pattern formation, without the need for constant intervention, and with a minimal number of parameters and controls. One such problem involves a swarm collectively producing a desired (target) density through local sensing, motion, and interactions in a domain. Here, we take a statistical physics perspective and develop and analyze a model wherein agents move in a stochastic walk over a networked domain, so as to reduce the error between the swarm density and the target, based on local, random, and uncertain measurements of the current density by the swarming agents. Using a combination of mean-field, small-fluctuation, and finite-number analysis, we are able to quantify how close and how fast a swarm comes to producing a target as a function of sensing uncertainty, stochastic collision rates, numbers of agents, and spatial variation of the target.