This paper considers an on-line exploration problem. We use a mobile robot to explore an unknown simple grid polygon. The robot is assumed to have limited sensing capability that can only detect the four basic cells adjacent to it. The robot’s task is to explore each cell and to return to the start. To explore a cell, the robot has to enter it. We ask for a short exploration tour, that is, minimizing the number of multiple-visit cells. The competitive ratio is used to measure the performance of our strategy. It is the ratio between the length of the on-line exploration path and the length of the shortest path achieved with full knowledge of the polygon. As our main result, we present a new on-line exploration strategy and prove that the robot’s path is at most 7/6 times longer than the shortest path. This matches the previously known lower bound.

本文考虑了在线探索问题。我们使用移动机器人探索未知的简单网格多边形。假定该机器人的感测能力有限，它只能检测与其相邻的四个基本单元。机器人的任务是探索每个单元并返回起点。要探索一个细胞，机器人必须进入它。我们要求进行简短的探索之旅，即最大程度地减少多次访问单元的数量。竞争率用于衡量我们策略的绩效。它是在线探索路径的长度与最充分了解多边形所获得的最短路径的长度之间的比率。作为主要结果，我们提出了一种新的在线探索策略，并证明机器人的路径最多比最短路径长7/6倍。这与先前已知的下限匹配。