Efficient Inspection of Underground Galleries Using k Robots with Limited Energy

Abstract

We study the problem of optimally inspecting an underground (underwater) gallery with k agents. We consider a gallery with a single opening and with a tree topology rooted at the opening. Due to the small diameter of the pipes (caves), the agents are small robots with limited autonomy and there is a supply station at the gallery’s opening. Therefore, they are initially placed at the root and periodically need to return to the supply station. Our goal is to design off-line strategies to efficiently cover the tree with k small robots. We consider two objective functions: the covering time (maximum collective time) and the covering distance (total traveled distance). The maximum collective time is the maximum time spent by a robot needs to finish its assigned task (assuming that all the robots start at the same time); the total traveled distance is the sum of the lengths of all the covering walks. Since the problems are intractable for big trees, we propose approximation algorithms. Both efficiency and accuracy of the suboptimal solutions are empirically showed for random trees through intensive numerical experiments.

The problem studied in this paper is in the framework of the project “Algorithms for autonomous navigation of underground systems” funded by the Company SPT (Stockholm Precision Tools, http://www.stockholmprecisiontools.com/). This research has also received funding from (a) the project GALGO (Spanish Ministry of Economy and Competitiveness, MTM2016-76272-R AEI/FEDER,UE) and (b) the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922.