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 (D2OC). 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 D2OC achieves robust, decentralized coverage while outperforming previous heuristic methods in optimality and consistency.
Figures & tables
Figure 1: Comparison of 3D quadrotor trajectories under (a) Conventional D 2 C and (b) Proposed Stochastic D 2 OC. Solid lines represent agent paths, while ‘ × ’ and ‘ ∘ ’ markers denote initial and final positions, respectively.
Figure 2: Performance analysis of the proposed Stochastic D 2 OC. (a) Communication events between agents. (b) Empirical mean (solid line) and standard deviation (shaded region) of W22 over 100 simulation runs.
Multi-agent control coordinates interacting autonomous agents to achieve shared goals while respecting safety, communication, and resource constraints.