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In this paper, we present a planner that plans a sequence of base positions for a mobile manipulator to efficiently and robustly collect objects stored in distinct trays. We achieve high efficiency by exploring the common areas where a mobile manipulator can grasp objects stored in multiple trays simultaneously and move the mobile manipulator to the common areas to reduce the time needed for moving the mobile base. We ensure robustness by optimizing the base position with the best clearance to positioning uncertainty so that a mobile manipulator can complete the task even if there is a certain deviation from the planned base positions. Besides, considering different styles of object placement in the tray, we analyze feasible schemes for dynamically updating the base positions based on either the remaining objects or the target objects to be picked in one round of the tasks. In the experiment part, we examine our planner on various scenarios, including different object placement: (1) Regularly placed toy objects; (2) Randomly placed industrial parts; and different schemes for online execution: (1) Apply globally static base positions; (2) Dynamically update the base positions. The experiment results demonstrate the efficiency, robustness and feasibility of the proposed method.