Multi-Agent Coverage Control in Non-Convex Annulus Region with Conformal Mapping

TL;DR

This paper presents a novel approach using conformal mapping to enable multi-agent systems to efficiently cover non-convex, non-star-shaped annulus regions by transforming them into topologically equivalent convex regions, optimizing coverage and load balancing.

Contribution

It introduces a sectorial coverage formulation with conformal mapping, a decentralized control law, and an iterative algorithm for optimal deployment in complex non-convex regions.

Findings

The control law guarantees exponential convergence to desired configurations.

The iterative algorithm effectively finds near-optimal multi-agent deployment.

Simulations validate the approach's practicality and effectiveness.

Abstract

Efficiently fulfilling coverage tasks in non-convex regions has long been a significant challenge for multi-agent systems (MASs). By leveraging conformal mapping, this paper introduces a novel sectorial coverage formulation to transform a non-convex annulus region into a topologically equivalent one. This approach enables the deployment of MASs in a non-star-shaped region while optimizing coverage performance and achieving load balance among sub-regions. It provides a unique perspective on the partitioned sub-regions to highlight the geodesic convex property of the non-star-shaped region. By utilizing the sectorial partition mechanism and the diffeomorphism property of conformal mapping, a decentralized control law is designed to drive MASs towards a desired configuration, which not only optimizes the global coverage cost but also ensures exponential convergence of equitable workload. Moreover, an iterative search algorithm is developed to identify the optimal approximation of multi-agent deployment in the non-star-shaped region. Theoretical analysis is conducted to confirm the asymptotic stability and global convergence with arbitrary small tolerance of the closed-loop system. Finally, numerical simulations demonstrate the practicality of the proposed coverage formulation with conformal mapping.