Authors:
Brendon G. Anderson
1
;
Eva Loeser
2
;
Marissa Gee
3
;
Fei Ren
1
;
Swagata Biswas
1
;
Olga Turanova
1
;
Matt Haberland
1
and
Andrea L. Bertozzi
1
Affiliations:
1
UCLA, Dept. of Mathematics, Los Angeles, CA 90095 and U.S.A.
;
2
Brown University, Mathematics Department, Providence, RI 02912 and U.S.A.
;
3
Harvey Mudd College, Dept. of Mathematics, Claremont, CA 91711 and U.S.A.
Keyword(s):
Swarm Robotics, Multi-agent Systems, Coverage, Optimization, Central Limit Theorem.
Related
Ontology
Subjects/Areas/Topics:
Autonomous Agents
;
Distributed Control Systems
;
Informatics in Control, Automation and Robotics
;
Intelligent Control Systems and Optimization
;
Mobile Robots and Autonomous Systems
;
Robotics and Automation
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: nontrivial 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.