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Most coordinated tasks performed by teams of mobile robots, require reliable communications between the members of the team. Therefore, task accomplishment requires that robots navigate their environment with their collective movement restricted to formations that guarantee integrity of the communication network. Maintaining this communication capability induces physical constraints on trajectories but also requires determination of communication variables like routes and transmitted powers. In this paper, we address this problem using a distributed hybrid approach, where continuous motion controllers based on potential fields interact with discrete distributed optimization of the communication variables to result in a muti-robot network that ensures integrity of communications. Our definition of network integrity is defined as the ability of a network to support desired communication rates.