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Task and motion planning (TAMP) integrates the generation of high-level tasks in a discrete space and the execution of low-level actions in a continuous space. Such planning integration is susceptible to uncertainties and computationally challenging as low-level actions should be verified for high-level tasks. Therefore, this paper presents a hierarchical task and motion planning method under uncertainties. We utilize Markov Decision Processes (MDPs) to model task and motion planning in a stochastic environment. The motion planner handles motion uncertainty and leverages physical constraints to synthesize an optimal low-level control policy for a single robot to generate motions in continuous action and state spaces. Given the optimal control policy for multiple homogeneous robots, the task planner synthesizes an optimal high-level tasking policy in discrete task and state spaces addressing both task and …