Paper Detail
Kooktae Lee
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.
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@article{lee2026density,
title = {Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems},
author = {Kooktae Lee},
year = {2026},
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\$\textasciicircum{}2\$OC). This is a rigorous Lagrangian framework that bridges the gap between individual agent dynamics and collective distribution matching. By form},
url = {https://arxiv.org/abs/2604.08495},
keywords = {math.OC, cs.MA, cs.RO, eess.SY},
eprint = {2604.08495},
archiveprefix = {arXiv},
}
{}