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The increasing need for real time robotic systems capable of performing tasks in changing and constrained environments demands the development of reliable and adaptable motion planning and control algorithms. This paper considers a mobile robot whose performance is measured by the completion of temporal logic tasks within a certain period of time. In addition to such time constraints, the planning algorithm must also deal with changes in the robot's workspace during task execution. In our case, the robot is deployed in a partitioned environment subjected to structural changes in which doors shift from open to closed and vice-versa. The motion of the robot is modeled as a Continuous Time Markov Decision Process and the robot's mission is expressed as a Continuous Stochastic Logic (CSL) temporal logic specification. An approximate solution to find a control strategy that satisfies such specifications is derived for a subset of probabilistic CSL formulae. Simulation and experimental results are provided to illustrate the method.