  Submodular maximization has been widely used in many multi-robot task
planning problems including information gathering, exploration, and target
tracking. However, the interplay between submodular maximization and
communication is rarely explored in the multi-robot setting. In many cases,
maximizing the submodular objective may drive the robots in a way so as to
disconnect the communication network. Driven by such observations, in this
paper, we consider the problem of maximizing submodular function with
connectivity constraints. Specifically, we propose a problem called
Communication-aware Submodular Maximization (CSM), in which communication
maintenance and submodular maximization are jointly considered in the
decision-making process. One heuristic algorithm that consists of two stages,
i.e. \textit{topology generation} and \textit{deviation minimization} is
proposed. We validate the formulation and algorithm through numerical
simulation. We find that our algorithm on average suffers only slightly
performance decrease compared to the pure greedy strategy.
