In this work we present an algorithm for covering continuous connected domains by ant-like robots with very limited capabilities. The robots can mark visited places with pheromone marks and sense the level of the pheromone in their local neighborhood. In case of multiple robots these pheromone marks can be sensed by all robots and provide the only way of (indirect) communication between the robots. The robots are assumed to be memoryless, and to have no global information such as the domain map, their own position (either absolute or relative), total marked area percentage, maximal pheromone level, etc.. Despite the robots simplicity, we show that they are able, by running a very simple rule of behavior, to ensure efficient covering of arbitrary connected domains, including non-planar and multidimensional ones. The novelty of our algorithm lies in the fact that, unlike previously proposed methods, our algorithm works on continuous domains without relying on some induced underlying graph, that effectively reduces the problem to a discrete case of graph covering. The algorithm guarantees complete coverage of any connected domain. We also prove that the algorithm is noise immune, i.e., it is able to cope with any initial pheromone profile (noise). In addition the algorithm provides a bounded constant time between two successive visits of the robot, and thus, is suitable for patrolling or surveillance applications.
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