Density-Driven Optimal Control for Efficient and Collaborative Multiagent Nonuniform Coverage

This article addresses the critical challenge of nonuniform area coverage in multiagent 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 nonuniform 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 (D²OC) is proposed. The key innovation of D²OC lies in the integration of optimal transport (OT) theory with multiagent 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 OT 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. In addition, 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.