Mobile sensors can move and self-deploy into a network. While focusing on the problems of coverage, existing deployment schemes mostly over-simplify the conditions for network connectivity: they either assume that the communication range is large enough for sensors in geometric neighborhoods to obtain each other's location by local communications, or assume a dense network that remains connected. At the same time, an obstacle-free field or full knowledge of the field layout is often assumed. We present new schemes that are not restricted by these assumptions, and thus adapt to a much wider range of application scenarios. While maximizing sensing coverage, our schemes can achieve connectivity for a network with arbitrary sensor communication/sensing ranges or node densities, at the cost of a small moving distance; the schemes do not need any knowledge of the field layout, which can be irregular and have obstacles/holes of arbitrary shape. Simulations results show that the proposed schemes achieve the targeted properties.