Optimal Transport for Time-Varying Multi-Agent Coverage Control
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917232383098880 |
|---|---|
| author | Napolitano, Italo di Bernardo, Mario |
| author_facet | Napolitano, Italo di Bernardo, Mario |
| contents | Coverage control algorithms have traditionally focused on static target densities, where agents are deployed to optimally cover a fixed spatial distribution. However, many applications involve time-varying densities, including environmental monitoring, surveillance, and adaptive sensor deployment. Although time-varying coverage strategies have been studied within Voronoi-based frameworks, recent works have reformulated static coverage control as a semi-discrete optimal transport problem. Extending this optimal transport perspective to time-varying scenarios has remained an open challenge. This paper presents a rigorous optimal transport formulation for time-varying coverage control, in which agents minimize the instantaneous Wasserstein distance to a continuously evolving target density. The proposed solution relies on a coupled system of differential equations governing agent positions and the dual variables that define Laguerre regions. In one-dimensional domains, the resulting system admits a closed-form analytical solution, offering both computational benefits and theoretical insight into the structure of optimal time-varying coverage. Numerical simulations demonstrate improved tracking performance compared to quasi-static and Voronoi-based methods, validating the proposed framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Transport for Time-Varying Multi-Agent Coverage Control Napolitano, Italo di Bernardo, Mario Systems and Control Coverage control algorithms have traditionally focused on static target densities, where agents are deployed to optimally cover a fixed spatial distribution. However, many applications involve time-varying densities, including environmental monitoring, surveillance, and adaptive sensor deployment. Although time-varying coverage strategies have been studied within Voronoi-based frameworks, recent works have reformulated static coverage control as a semi-discrete optimal transport problem. Extending this optimal transport perspective to time-varying scenarios has remained an open challenge. This paper presents a rigorous optimal transport formulation for time-varying coverage control, in which agents minimize the instantaneous Wasserstein distance to a continuously evolving target density. The proposed solution relies on a coupled system of differential equations governing agent positions and the dual variables that define Laguerre regions. In one-dimensional domains, the resulting system admits a closed-form analytical solution, offering both computational benefits and theoretical insight into the structure of optimal time-varying coverage. Numerical simulations demonstrate improved tracking performance compared to quasi-static and Voronoi-based methods, validating the proposed framework. |
| title | Optimal Transport for Time-Varying Multi-Agent Coverage Control |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2601.21753 |