On the Convergence of Density-Based Predictive Control for Multi-Agent Non-Uniform Area Coverage

TL;DR

This paper introduces Density-based Predictive Control (DPC), a new multi-agent control method using optimal transport theory to achieve efficient non-uniform area coverage aligned with regional priorities.

Contribution

The paper develops DPC, a novel control strategy that leverages optimal transport for non-uniform coverage, including convergence analysis and practical control laws.

Findings

DPC effectively matches non-uniform reference distributions in simulations.

DPC outperforms existing coverage methods in efficiency and accuracy.

Convergence conditions are established using Wasserstein distance.

Abstract

This paper presents Density-based Predictive Control (DPC), a novel multi-agent control strategy for efficient non-uniform area coverage, grounded in optimal transport theory. In large-scale scenarios such as search and rescue or environmental monitoring, traditional uniform coverage fails to account for varying regional priorities. DPC leverages a pre-constructed reference distribution to allocate agents' coverage efforts, spending more time in high-priority or densely sampled regions. We analyze convergence conditions using the Wasserstein distance, derive an analytic optimal control law for unconstrained cases, and propose a numerical method for constrained scenarios. Simulations on first-order dynamics and linearized quadrotor models demonstrate that DPC achieves trajectories closely matching the non-uniform reference distribution, outperforming existing coverage methods.