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In this paper we introduce a method based on the probabilistic roadmap (PRM) planner to construct robust roadmaps for motion planning in changing environments. PRM's are usually aimed at static environments. In reality though, many environments are not static, but contain moving obstacles as well. Often the motion of these obstacles is not unconstrained, but is restricted to some confined area, e.g. a door that can be open or closed or a chair which is bounded to a room. We exploit this observation by assuming that a moving obstacle has a predefined set of potential placements. We present a variant of PRM that is robust against placement changes of obstacles. Our method creates a roadmap that is guaranteed to contain a path for any feasible query when time goes to infinity, i.e. the method is probabilistically complete. Our implementation shows that after a roadmap is created in the preprocessing phase, queries can be solved instantaneously, thus allowing for on-the-fly replanning to anticipate changes in the environment.