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.

翻译：本文研究了多智能体系统的分布式非均匀区域覆盖问题，该问题在高空间优先级和资源约束的使命中至关重要。现有基于密度的方法通常依赖计算量较大的欧拉偏微分方程求解器或启发式规划方法，我们提出了一种严格的拉格朗日框架——随机密度驱动优化控制（D$^2$OC），该框架弥合了个体智能体动力学与集体分布匹配之间的鸿沟。通过构建一个以Wasserstein距离作为运行代价的随机模型预测控制式优化问题，我们提出的方法确保了在随机线性时不变动力学作用下，时间平均经验分布收敛于无参数目标密度。关键贡献在于通过可达性分析建立了形式化的收敛性保障，即使在存在过程和测量噪声的情况下也能提供有界跟踪误差。数值实验验证了随机D$^2$OC能实现鲁棒、分布式的覆盖，并在最优性和一致性上优于先前的启发式方法。