Quantitative Assessment of Robotic Swarm Coverage

Abstract

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