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.
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