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Given a space where some events occur and expect to be detected, and a group of devices with limited sensing and communication capabilities moving in this space, this paper aims at developing a distributed self-deployment algorithm for each agent so that the steered sensing device network can cover and sample the space in interest. At the same time, to support the collection and further processes of extracted information, the connectivity of group need be preserved during maneuvers if it is connected at the initial time. To this goal, this paper considers coverage control subject to connectivity maintenance constraints. By designing a special potential function, coverage with connectivity maintenance is encoded by an integrated utility function minimized by the gradient descent idea, which is implemented with the restriction that each device utilizes only local information. The performance of the algorithm developed in this paper is demonstrated by both theoretical analysis and numerical simulations.