Density-Driven Optimal Control: Convergence Guarantees for Stochastic LTI Multi-Agent Systems
TLDR
Stochastic D$^2$OC provides a rigorous Lagrangian framework for decentralized multi-agent area coverage, ensuring convergence with formal guarantees.
Key contributions
- Introduces Stochastic D$^2$OC, a Lagrangian framework for decentralized non-uniform multi-agent area coverage.
- Formulates a stochastic MPC problem minimizing Wasserstein distance for collective distribution matching.
- Provides formal convergence guarantees via reachability analysis, ensuring bounded tracking error under noise.
- Achieves robust, decentralized coverage, outperforming prior heuristic methods in optimality and consistency.
Why it matters
This paper offers a rigorous solution to decentralized multi-agent area coverage, overcoming limitations of computationally heavy or heuristic methods. Its formal convergence guarantees ensure robust performance, making it crucial for missions with high spatial priority.
Original 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.
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