Quantitative Assessment of Robotic Swarm Coverage

TL;DR

This paper introduces a new error metric for evaluating robotic swarm coverage, backed by theoretical analysis, benchmarks, and practical MATLAB tools, improving upon existing discretization-based methods.

Contribution

It proposes a novel, continuous coverage error metric inspired by vortex blob methods, with rigorous theoretical foundations and practical benchmarking tools.

Findings

The error metric obeys a central limit theorem.

Provided bounds and probability density functions for the error metric.

MATLAB code implementation available for practitioners.

Abstract

This paper studies a generally applicable, sensitive, and intuitive error metric for the assessment of robotic swarm density controller performance. Inspired by vortex blob numerical methods, it overcomes the shortcomings of a common strategy based on discretization, and unifies other continuous notions of coverage. We present two benchmarks against which to compare the error metric value of a given swarm configuration: non-trivial bounds on the error metric, and the probability density function of the error metric when robot positions are sampled at random from the target swarm distribution. We give rigorous results that this probability density function of the error metric obeys a central limit theorem, allowing for more efficient numerical approximation. For both of these benchmarks, we present supporting theory, computation methodology, examples, and MATLAB implementation code.