基于共形映射的非凸环形区域多智能体覆盖控制
Multi-Agent Coverage Control in Non-Convex Annulus Region with Conformal Mapping
AI总结：
本文针对非凸环形区域的多智能体覆盖问题，提出基于共形映射的扇形覆盖公式和分散控制律，实现负载均衡与指数收敛，并通过迭代搜索算法和仿真验证其有效性。
摘要：
在非凸区域中高效完成覆盖任务长期以来是多智能体系统（MASs）面临的重大挑战。本文利用共形映射，提出了一种新颖的扇形覆盖公式，将非凸环形区域转换为拓扑等价区域。该方法能够在非星形区域中部署多智能体系统，同时优化覆盖性能并实现子区域间的负载均衡。它为划分后的子区域提供了独特视角，以突出非星形区域的测地凸性质。通过利用扇形划分机制和共形映射的微分同胚性质，设计了一种分散控制律，驱动多智能体系统趋向期望构型，该控制律不仅优化全局覆盖代价，还确保公平工作负载的指数收敛。此外，开发了一种迭代搜索算法，用于识别非星形区域中多智能体部署的最优近似。理论分析证实了闭环系统的渐近稳定性和具有任意小容差的全局收敛性。最后，数值仿真验证了所提出的基于共形映射的覆盖公式的实用性。
英文摘要：
Efficiently fulfilling coverage tasks in non-convex regions has long been a significant challenge for multi-agent systems (MASs). By leveraging conformal mapping, this paper introduces a novel sectorial coverage formulation to transform a non-convex annulus region into a topologically equivalent one. This approach enables the deployment of MASs in a non-star-shaped region while optimizing coverage performance and achieving load balance among sub-regions. It provides a unique perspective on the partitioned sub-regions to highlight the geodesic convex property of the non-star-shaped region. By utilizing the sectorial partition mechanism and the diffeomorphism property of conformal mapping, a decentralized control law is designed to drive MASs towards a desired configuration, which not only optimizes the global coverage cost but also ensures exponential convergence of equitable workload. Moreover, an iterative search algorithm is developed to identify the optimal approximation of multi-agent deployment in the non-star-shaped region. Theoretical analysis is conducted to confirm the asymptotic stability and global convergence with arbitrary small tolerance of the closed-loop system. Finally, numerical simulations demonstrate the practicality of the proposed coverage formulation with conformal mapping.
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