Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems
This addresses the problem of efficient area coverage for multi-agent systems in missions with spatial priorities, offering a rigorous solution with convergence guarantees, though it is incremental as it builds on density-based methods.
The paper tackles the decentralized non-uniform area coverage problem for multi-agent systems by proposing Stochastic Density-Driven Optimal Control (D^2OC), a Lagrangian framework that ensures the time-averaged empirical distribution converges to a target density with bounded tracking error under stochastic LTI dynamics, outperforming previous heuristic methods in optimality and consistency.
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.