多项式成本下的覆盖控制最优配置
Optimal Configurations in Coverage Control with Polynomial Costs
AI总结：
本文基于多项式成本函数，利用数值代数几何工具研究车辆在实线上最优覆盖配置问题，通过多项式同源持续方法找到全局极小值，并与经典分布式Lloyd下降法进行对比。
摘要：
我们重新审视了车辆在实线上简单运动下的静态覆盖控制问题，假设成本是车辆位置的多项式函数。本文的主要贡献是利用数值代数几何工具，特别是保证找到多项式方程所有解的数值多项式持续方法，以表征覆盖控制问题的全局极小值。然后将结果与经典分布式方法进行比较，该方法在某些技术条件下仅收敛于局部极小值。
英文摘要：
We revisit the static coverage control problem for placement of vehicles with simple motion on the real line, under the assumption that the cost is a polynomial function of the locations of the vehicles. The main contribution of this paper is to demonstrate the use of tools from numerical algebraic geometry, in particular, a numerical polynomial homotopy continuation method that guarantees to find all solutions of polynomial equations, in order to characterize the \emph{global minima} for the coverage control problem. The results are then compared against a classic distributed approach involving the use of Lloyd descent, which is known to converge only to a local minimum under certain technical conditions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
