Exploring a polygon with a robot, when the robot does not have a map of its surroundings can be viewed as an online problem. Typical for online problems is that you must make decisions based on past events without complete information about the future. In our case the robot does not have complete information about the environment. Competitive analysis can be used to measure the performance of methods solving online problems. The competitive ratio of such a method is the ratio between the method’s performance and the performance of the best method having full knowledge of the future. We are interested in obtaining good upper bounds on the competitive ratio of exploring polygons and prove a 3/2-competitive strategy for exploring a simple rectilinear polygon in the L 1 metric.