Multirobot systems for covering environments are increasingly used in applications like cleaning, industrial inspection, patrolling, and precision agriculture. The problem of covering a given environment using multiple robots can be naturally formulated and studied as a multi-Traveling Salesperson Problem (mTSP). In a mTSP, the environment is represented as a graph and the goal is to find tours (starting and ending at the same depot) for the robots in order to visit all the vertices with minimum global cost, namely the length of the longest tour. The mTSP is an NP-hard problem for which several approximation algorithms have been proposed. These algorithms usually assume generic environments, but tighter approximation bounds can be reached focusing on specific environments. In this paper, we address the case of environments composed of sub-parts, called modules, that can be reached from each other only through some linking structures. Examples are multi-floor buildings, in which the modules are the floors and the linking structures are the staircases or the elevators, and floors of large hotels or hospitals, in which the modules are the rooms and the linking structures are the corridors. We focus on linear modular environments, with the modules organized sequentially, presenting an efficient (with polynomial worst-case time complexity) algorithm that finds a solution for the mTSP whose cost is within a bounded distance from the cost of the optimal solution. The main idea of our algorithm is to allocate disjoint "blocks" of adjacent modules to the robots, in such a way that each module is covered by only one robot. We experimentally compare our algorithm against some state-of-the-art algorithms for solving mTSPs in generic environments and show that it is able to provide solutions with lower makespan and spending a computing time several orders of magnitude shorter.

中文翻译：

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线性模块化环境的多机器人覆盖

用于覆盖环境的多机器人系统越来越多地用于清洁、工业检查、巡逻和精准农业等应用。使用多个机器人覆盖给定环境的问题可以自然地表述为多旅行销售员问题 (mTSP) 并加以研究。在 mTSP 中，环境被表示为一个图，目标是为机器人找到旅行（在同一站点开始和结束），以便以最小的全局成本访问所有顶点，即最长旅行的长度。mTSP 是一个 NP-hard 问题，已经提出了几种近似算法。这些算法通常假设通用环境，但可以针对特定环境达到更严格的近似界限。在本文中，我们解决了由子部分组成的环境的情况，称为模块，只能通过一些链接结构相互访问。例如多层建筑，其中模块是楼层，连接结构是楼梯或电梯，以及大型酒店或医院的楼层，其中模块是房间，连接结构是走廊。我们专注于线性模块化环境，模块按顺序组织，提出了一种高效的（具有多项式最坏情况时间复杂度）算法，该算法为 mTSP 找到一个解决方案，其成本与最佳解决方案的成本在有界距离内。我们算法的主要思想是将相邻模块的不相交“块”分配给机器人，这样每个模块只被一个机器人覆盖。