Trend formation with sparse global sampling
Abstract
Achieving global coordination without a central controller or dense global communication is a defining challenge for both biological collectives and engineered swarms. We introduce and analyze a minimal model in which self-propelled agents in a bounded domain periodically reorient their motions toward the centroid of a small, randomly chosen subset of their peers, with no direct sensing of any individual neighbor's position or heading. We show that this sparse, non-local sampling rule reliably drives an initially disordered population to a globally aligned, nematic state, and that shrinking the sampled subset -- down to the minimum of two agents -- accelerates ordering rather than impeding it: the resulting estimation noise, filtered through a geometric turning rule, is itself the engine of symmetry breaking. We derive an analytical criterion, in quantitative agreement with simulation, that predicts when this ordering succeeds as a function of the sampling size and sampling frequency. We confirm the mechanism experimentally in a swarm of up to fifteen differential-drive robots. These results identify sparse random sampling as an information-efficient route to collective coordination, with implications for understanding animal collectives and for designing communication-limited robotic swarms.
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BibTeX
@misc{sankar2026trend,
title = {{Trend formation with sparse global sampling}},
author = {Sarath Sankar and Abhijit Sinha and Shankar Ghosh and Vikram Tripathi and Amitava Bhattacharya},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10521},
eprint = {2610.10521},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10521},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Trend formation with sparse global sampling
AU - Sarath Sankar
AU - Abhijit Sinha
AU - Shankar Ghosh
AU - Vikram Tripathi
AU - Amitava Bhattacharya
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10521
UR - https://arxiv.org/abs/2610.10521
AB - Achieving global coordination without a central controller or dense global communication is a defining challenge for both biological collectives and engineered swarms. We introduce and analyze a minimal model in which self-propelled agents in a bounded domain periodically reorient their motions toward the centroid of a small, randomly chosen subset of their peers, with no direct sensing of any individual neighbor's position or heading. We show that this sparse, non-local sampling rule reliably drives an initially disordered population to a globally aligned, nematic state, and that shrinking the sampled subset -- down to the minimum of two agents -- accelerates ordering rather than impeding it: the resulting estimation noise, filtered through a geometric turning rule, is itself the engine of symmetry breaking. We derive an analytical criterion, in quantitative agreement with simulation, that predicts when this ordering succeeds as a function of the sampling size and sampling frequency. We confirm the mechanism experimentally in a swarm of up to fifteen differential-drive robots. These results identify sparse random sampling as an information-efficient route to collective coordination, with implications for understanding animal collectives and for designing communication-limited robotic swarms.
ER -