NAMOUnc: Navigation Among Movable Obstacles with Decision Making on Uncertainty Interval

In real applications, robots take actions with partial and noisy observation on the environment, and a given action may cause unexpected effect due to uncertainties. If the robot has over confidence on the observation and action, it can lead to some subop-timal decisions, even to dangerous actions resulting in catastrophic effects, like destroying objects in the workspace. It is therefore essential for the robot to recognize the limitation of its observations and actions, and make decisions with awareness of uncertainty and risks. Recent studies on task and motion planning incorporate uncertainty and update plans based on the observation and action uncertainties. For example (Safronov et al., 2020; Pan et al., 2022) take success rate (SR) into account in a manipulation task: if a grasp action fails, the planner updates its estima-a