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This paper tackles the problem of constructing a communication map of a known environment using multiple robots. A communication map encodes information on whether two robots can communicate when they are at two arbitrary locations and plays a fundamental role for a multi-robot system deployment to reliably and effectively achieve a variety of tasks, such as environmental monitoring and exploration. Previous work on communication map building typically considered only scenarios with a fixed base station and designed offline methods, which did not exploit data collected online by the robots. This paper proposes Gaussian Process-based online methods to efficiently build a communication map with multiple robots. Such robots form a mesh network, where there is no fixed base station. Specifically, we provide two leader-follower online sensing strategies to coordinate and guide the robots while collecting data. Furthermore, we improve the performance and computational efficiency by exploiting prior communication models that can be built from the physical map of the environment. Extensive experimen

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