This paper presents two new approaches to planning with uncertainty in position that achieve better performance than existing techniques and that are able to incorporate changes in the environment in near real-time. Both approaches reuse previous searches and replan when changes in the environment are detected. The first approach, called replanning with prior map updates, assumes that changes in the prior map originate from the same source as the original prior map. Therefore, the updates are registered with the existing map, but not with the position of the robot. The resulting path after applying the updates is the same as if the updates had been present in the original prior map. The second approach, called replanning with sensor updates, assumes that changes in the prior map originate from on-board sensors. Therefore, the updates are registered with the robot, but not with the existing map. The resulting path after applying the updates is not the same path that would be found if the updates had taken place in the original prior map. Replanning with prior map updates achieves a speed-up to one order of magnitude with respect to forward planning from scratch, while replanning with sensor updates achieves a speedup of almost two orders of magnitude.