On the Convergence of Density-Based Predictive Control for Multi-Agent Non-Uniform Area Coverage

Abstract This paper investigates the convergence conditions of Density-based Predictive Control (DPC) for nonuniform area coverage. In large-scale real-world scenarios, such as search and rescue (SAR) or environmental monitoring missions, efficient nonuniform multi-agent area coverage is essential, as uniform coverage fails to account for varying regional priorities and operational constraints. To address this, we propose a novel multi-agent density-based predictive control strategy, DPC, grounded in optimal transport (OT) theory. Given a preconstructed reference distribution representing priority regions, DPC ensures that agents allocate their coverage efforts by spending more time in high-priority or densely sampled areas, achieving effective nonuniform coverage. We analyze the convergence conditions of DPC by formulating the contraction mapping problem in terms of the Wasserstein distance. Additionally, we derive the analytic optimal control law for the unconstrained case and propose a numerical optimization method for determining the optimal control law under input constraints. Comprehensive simulations were conducted on both first-order dynamic systems and a linearized quadrotor model under constrained and unconstrained conditions. The results demonstrate that when the proposed conditions are satisfied, the Wasserstein distance locally converges, and the agent trajectories closely match the nonuniform reference distribution. Furthermore, the comparison with the existing coverage method demonstrated the superiority of the DPC method in nonuniform area coverage.