  We study a mobile wireless sensor network (MWSN) consisting of multiple
mobile sensors or robots. Three key factors in MWSNs, sensing quality, energy
consumption, and connectivity, have attracted plenty of attention, but the
interaction of these factors is not well studied. To take all the three factors
into consideration, we model the sensor deployment problem as a constrained
source coding problem. %, which can be applied to different coverage tasks,
such as area coverage, target coverage, and barrier coverage. Our goal is to
find an optimal sensor deployment (or relocation) to optimize the sensing
quality with a limited communication range and a specific network lifetime
constraint. We derive necessary conditions for the optimal sensor deployment in
both homogeneous and heterogeneous MWSNs. According to our derivation, some
sensors are idle in the optimal deployment of heterogeneous MWSNs. Using these
necessary conditions, we design both centralized and distributed algorithms to
provide a flexible and explicit trade-off between sensing uncertainty and
network lifetime. The proposed algorithms are successfully extended to more
applications, such as area coverage and target coverage, via properly selected
density functions. Simulation results show that our algorithms outperform the
existing relocation algorithms.
