This paper presents coverage algorithms for mobile sensor networks in which agents have limited power to move. Rather than making use of a constrained optimization technique, our approach accounts for power constraints by assigning non-homogeneously time-varying regions to each robot. This leads to a novel partition of the environment into limited-range, generalized Voronoi regions. The motion control algorithms are then designed to ascend the gradient of several types of locational optimization functions. In particular, the objective functions reflect the global energy available to the group and different coverage criteria. As we discuss in the paper, this has an effect on limiting each agent's velocity to save energy and balance its expenditure across the network.