This paper considers the problem of exploring an unknown rectangular cellular environment with a rectangular hole using a mobile robot. The robot's task is to visit each cell at least once and return to the start. The robot has limited visibility that can only detect four cells adjacent to it. And it has large amount of memory that can store a map of discovered cells. The goal of this work is to find the shortest exploration tour, that is, minimizing the total number of multiple visited cells. We consider the environment in four possible scenarios: rectangular, L-shaped, C-shaped or O-shaped grid polygon. An on-line strategy has been proposed for these scenarios. We prove that it is optimal for rectangular, L-shaped, C-shaped grid polygon, and is 4/3-competitive for O-shaped grid polygon.

本文考虑使用移动机器人探索具有矩形孔的未知矩形细胞环境的问题。机器人的任务是至少访问每个单元一次并返回起点。该机器人的能见度有限，只能检测到与其相邻的四个单元。它具有大量内存，可以存储已发现细胞的图谱。这项工作的目标是找到最短的探索之旅，即最小化多个访问单元的总数。我们考虑四种可能场景的环境：矩形、L形、C形或O形网格多边形。针对这些情况提出了在线策略。我们证明了它对于矩形、L形、C形网格多边形是最优的，对于O形网格多边形是 4/3 竞争的。