Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems

TL;DR

This paper introduces a stochastic control framework for multi-agent coverage tasks that guarantees convergence to target distributions despite noise, improving robustness and optimality over heuristic methods.

Contribution

It presents a novel Lagrangian stochastic MPC approach that ensures convergence and bounded tracking error for multi-agent systems under stochastic LTI dynamics.

Findings

The method guarantees convergence to the target density distribution.

Numerical results show improved coverage robustness and optimality.

The approach outperforms heuristic methods in simulations.

Abstract

This paper addresses the decentralized non-uniform area coverage problem for multi-agent systems, a critical task in missions with high spatial priority and resource constraints. While existing density-based methods often rely on computationally heavy Eulerian PDE solvers or heuristic planning, we propose Stochastic Density-Driven Optimal Control (D$^2$OC). This is a rigorous Lagrangian framework that bridges the gap between individual agent dynamics and collective distribution matching. By formulating a stochastic MPC-like problem that minimizes the Wasserstein distance as a running cost, our approach ensures that the time-averaged empirical distribution converges to a non-parametric target density under stochastic LTI dynamics. A key contribution is the formal convergence guarantee established via reachability analysis, providing a bounded tracking error even in the presence of process and measurement noise. Numerical results verify that Stochastic D$^2$OC achieves robust, decentralized coverage while outperforming previous heuristic methods in optimality and consistency.