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This paper describes an algorithm that considers uncertainty while solving the simultaneous task and motion planning (STAMP) problem. Information about uncertainty is transferred to the task planning level from the motion planning level using the concept of a task motion multigraph (TMM). TMMs were introduced in previous work to improve the efficiency of solving the STAMP problem for mobile manipulators. In this work, Markov Decision Processes are used in conjunction with TMMs to select sequences of actions that solve the STAMP problem such that the resulting solutions have higher probability of feasibility. Experimental evaluation indicates significantly improved probability of feasibility for solutions to the STAMP problem, compared to algorithms that ignore uncertainty information when selecting possible sequences of actions. At the same time, the efficiency due to TMMs is largely maintained.
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