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

TL;DR

The paper tackles non-uniform area coverage by multi-agent systems using Density-based Predictive Control (DPC), rooted in optimal transport. It formulates a Wasserstein-distance objective between the agent-trajectory distribution $\mu$ and a precomputed reference distribution $\nu$, and derives both unconstrained and constrained control laws within a three-stage framework (Optimal Control, Weight Update, Weight Sharing). The authors prove convergence properties via the local Wasserstein distance and validate the approach with first-order and LTI quadrotor simulations, showing improved coverage over the Spectral Multiscale Coverage (SMC) baseline and favorable scalability. The work offers principled, dynamics-aware, decentralized coordination for high-priority-region coverage in large-scale SAR and environmental monitoring tasks.

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.

Figures (8)

• Figure 1: Conceptual illustration of prioritized search coverage using a multi-agent system.
• Figure 2: Description of the function $\Delta \mathcal{W}^k$.
• Figure 3: Conceptual illustration of the weight update stage. Green circles represent the sample-points, while the dashed circles represent sample-points with no weight after transportation.
• Figure 4: Reference distribution.
• Figure 5: Agent trajectories generated using the DPC method under first-order dynamics.

Theorems & Definitions (11)

• Remark 1: Notation Conventions for Variable Indices
• Remark 2
• Example 1
• Remark 3: Interpretation of the mass center, $\bar{q}^{k}$
• Proposition 1: Simplification of $\Delta \mathcal{W}^k$
• proof
• Theorem 1: The convergence condition and the optimality of DPC -- Unconstrained case
• proof
• Remark 4: Physical interpretation of the convergence range
• Remark 5