群机器人系统基于最优输运的覆盖控制：Voronoi网格方法的推广
Optimal Transport-based Coverage Control for Swarm Robot Systems: Generalization of the Voronoi Tessellation-based Method
摘要：
群机器人系统是由多个移动机器人组成的协作机器人系统，具有环境适应性和容错性等优点，受到了广泛的关注。这种系统的最重要的任务之一是覆盖控制，其中机器人自主部署，以近似给定的空间分布。在这项研究中，我们制定了一个覆盖控制范例使用的概念，最优输运，并提出了一种新的控制技术，我们称之为最优输运为基础的覆盖控制（OTCC）方法。建议的OTCC，通过梯度流的费用函数在Kantorovich对偶问题，所示出的覆盖广泛使用的现有控制方法作为一个特例。我们还进行了控制系统的李雅普诺夫稳定性分析，并提供数值计算表明，OTCC再现目标分布具有更好的性能比现有的控制方法。
英文摘要：
Swarm robot systems, which consist of many cooperating mobile robots, have attracted attention for their environmental adaptability and fault tolerance advantages. One of the most important tasks for such systems is coverage control, in which robots autonomously deploy to approximate a given spatial distribution. In this study, we formulate a coverage control paradigm using the concept of optimal transport and propose a novel control technique, which we have termed the optimal transport-based coverage control (OTCC) method. The proposed OTCC, derived via the gradient flow of the cost function in the Kantorovich dual problem, is shown to covers a widely used existing control method as a special case. We also perform a Lyapunov stability analysis of the controlled system, and provide numerical calculations to show that the OTCC reproduces target distributions with better performance than the existing control method.
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