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Complex manipulation tasks require careful integration of symbolic reasoning and motion planning. This problem, commonly referred to as Task and Motion Planning (TAMP), is even more challenging if the workspace is non-static, e.g. due to human interventions and perceived with noisy non-ideal sensors. This work proposes an online approximated TAMP method that combines a geometric reasoning module and a motion planner with a standard task planner in a receding horizon fashion. Our approach iteratively solves a reduced planning problem over a receding window of a limited number of future actions during the implementation of the actions. Thus, only the first action of the horizon is actually scheduled at each iteration, then the window is moved forward, and the problem is solved again. This procedure allows to naturally take into account potential changes in the scene while ensuring good runtime performance. We validate our approach within extensive experiments in a simulated environment. We showed that our approach is able to deal with unexpected changes in the environment while ensuring comparable performance with respect to other recent TAMP approaches in solving traditional static benchmarks. We release with this paper the open-source implementation of our method.