Density-Driven Optimal Control for Non-Uniform Area Coverage in Decentralized Multi-Agent Systems Using Optimal Transport

TL;DR

This paper introduces Density-Driven Optimal Control (D2OC), a novel framework that combines optimal transport theory with multi-agent coverage control to achieve efficient non-uniform area coverage respecting real-world constraints.

Contribution

The paper presents a new decentralized control framework integrating optimal transport with coverage control, providing optimal solutions under physical and operational constraints.

Findings

D2OC outperforms existing methods in non-uniform coverage tasks.

The control solutions are analytically derived for linear systems.

Simulation results confirm scalability and effectiveness of D2OC.

Abstract

This paper addresses the fundamental problem of non-uniform area coverage in multi-agent systems, where different regions require varying levels of attention due to mission-dependent priorities. Existing uniform coverage strategies are insufficient for realistic applications, and many non-uniform approaches either lack optimality guarantees or fail to incorporate crucial real-world constraints such as agent dynamics, limited operation time, the number of agents, and decentralized execution. To resolve these limitations, we propose a novel framework called Density-Driven Optimal Control (D2OC). The central idea of D2OC is the integration of optimal transport theory with multi-agent coverage control, enabling each agent to continuously adjust its trajectory to match a mission-specific reference density map. The proposed formulation establishes optimality by solving a constrained optimization problem that explicitly incorporates physical and operational constraints. The resulting control input is analytically derived from the Lagrangian of the objective function, yielding closed-form optimal solutions for linear systems and a generalizable structure for nonlinear systems. Furthermore, a decentralized data-sharing mechanism is developed to coordinate agents without reliance on global information. Comprehensive simulation studies demonstrate that D2OC achieves significantly improved non-uniform area coverage performance compared to existing methods, while maintaining scalability and decentralized implementability.