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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.
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This content will become publicly available on December 1, 2026
Density-Driven Optimal Control for Efficient and Collaborative Multiagent Nonuniform Coverage
This paper addresses the critical challenge of non-uniform area coverage in multi-agent systems, where certain regions require higher priority based on mission objectives. Traditional uniform coverage methods are often inadequate in many area coverage scenarios, as they may overlook real-world complexities where uniform coverage is neither feasible nor desirable. Although several non-uniform coverage methods exist, they frequently lack guarantees of optimality or fail to consider essential real-world constraints such as agent dynamics, the number of agents, available operation time, and decentralized control. To overcome these limitations, a novel control scheme called Density-Driven Optimal Control (D$^2$OC) is proposed. The key innovation of D$^2$OC lies in the integration of optimal transport theory with multi-agent control, allowing agents to dynamically adjust their coverage according to a reference density distribution that reflects the mission’s priorities. Optimality is guaranteed by solving an optimization problem that incorporates the aforementioned real-world constraints. The control law is derived from the Lagrangian associated with the objective cost, utilizing optimal transport for both linear and nonlinear systems. Guarantees for global optimality and the existence of the optimal control input for linear systems are provided through an analytic solution. Additionally, an efficient data-sharing algorithm for decentralized control among multiple agents is proposed. To evaluate the efficacy of the proposed control scheme, various simulation results are presented to compare its performance with existing methods.
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- Award ID(s):
- 2145810
- PAR ID:
- 10680136
- Publisher / Repository:
- IEEE
- Date Published:
- Journal Name:
- IEEE Transactions on Systems, Man, and Cybernetics: Systems
- Volume:
- 55
- Issue:
- 12
- ISSN:
- 2168-2216
- Page Range / eLocation ID:
- 9340 to 9354
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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