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In this paper, we consider a robotic surveillance problem where a fixed remote station deploys a team of mobile robots to spatially explore a given workspace, detect an unknown number of static targets, and inform the remote station of their findings. We are interested in designing trajectories (local motion decisions) for the robots that minimize the probability of target detection error at the remote station, while satisfying the requirements on the connectivity of the robots to the remote station. We show how such a design is possible by co-optimization of sensing (information gathering) and communication (information exchange) when motion planning. We start by considering the case where the robots need to constantly update the remote station on the locations of the targets as they learn about the environment. For this case, we propose a communication-constrained motion planning approach for the robots. We next consider the case where the remote station only needs to be informed of the locations of the targets at the end of a given operation time. By building on our communication-constrained results, we propose a hybrid motion planning approach for this case. We consider realistic communication channels that experience path loss, shadowing and multipath fading in the paper. Then, our proposed communication-aware motion planning approaches evaluate the probability of connectivity at unvisited locations and integrate it with the sensing objectives of the robots. We mathematically characterize the asymptotic behavior of our motion planning approaches and discuss the underlying tradeoffs. We finally devise strategies to increase their robustness to multipath fading and other channel estimation uncertainties.