In this paper, we consider the problem of covering all regions of interests (targets) by relocating a set of mobile sensors such that total movement made by them is minimized. This problem itself is a challenging one and addressed recently by some researchers under free mobility model. We consider a more restricted version of the problem where sensors can move only in two mutually perpendicular directions. We first show that the optimal point to which a sensor must move to cover a specific target is different under this model from the one where sensors can move freely, and characterize such a point. On the basis of this observation, we have developed heuristics to solve the problem. The heuristics run in two phases; the first phase ensures coverage and the second phase, connectivity. In both the phases, the sensors can move only with restricted mobility. We have run a set of experiments to evaluate the performance of the proposed algorithm and found that the total movement made in the first phase is comparable to the solution given by an IPP (Integer Programming Problem). For the second phase, we have presented two heuristics MinCon and MinConm. The algorithm MinCon works by finding connected components of the graph consisting of sensor nodes. It then identifies destination locations where some sensors must be placed so that all necessary components become connected. Once the destinations are known, the problem is solved by mapping it to an LSAP (Linear Sum Assignment Problem). The other heuristic MinConm improves over MinCon by moving only a subset of sensors to their destinations using the solution of LSAP. It then finds the movement of the remaining sensors applying a technique used in the first phase. © 2013 IEEE.