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

2025-12-02

AI Summary

In large-scale scenarios (e.g., search-and-rescue, environmental monitoring), conventional uniform coverage fails to accommodate spatially varying regional priorities. Method: This paper proposes a density-guided multi-agent non-uniform coverage framework. Its core innovation is the first integration of optimal transport theory into coverage control, establishing a convergence analysis framework grounded in the Wasserstein distance and deriving an analytical optimal control law under unconstrained conditions. The approach jointly incorporates a density-weighted reference distribution, model predictive control, and first-order/linearized quadrotor dynamics. Results: Simulations demonstrate significant improvements in sampling density and coverage accuracy over high-priority regions; agent trajectories closely match the target reference distribution, outperforming state-of-the-art methods in both fidelity and task-aware coverage efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: State Estimation
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• Develops a multi-agent control strategy for non-uniform area coverage.
• Addresses varying regional priorities in large-scale scenarios like search and rescue.
• Analyzes convergence and optimizes agent allocation using optimal transport theory.

Innovation

• Density-based Predictive Control for multi-agent coverage
• Uses Wasserstein distance for convergence analysis
• Derives analytic optimal control for unconstrained cases