Robust and Efficient Covering of Unknown Continuous Domains with Simple, Ant-Like A(ge)nts

We propose a new `Mark-Ant-Walk' algorithm for robust and efficient covering of continuous domains by ant-like robots with very limited capabilities. The robots can mark places visited with pheromone marks and sense the level of the pheromone in their local neighborhood. In the 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 information besides that mentioned above. 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 domains. 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 effectively reducing the problem to a discrete case of graph covering. In addition, we demonstrate various benefits of our algorithm such as ability to cope with arbitrary initial pheromone profile and a bounded constant time between two successive visits of the robot at the same location, making it suitable for patrolling. Finally, we provide a new theoretical bound on covering time of a wide family of such mark and walk algorithms.