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Optical tweezers utilize highly focused laser beam to produce optical forces on the object, and can be used for trapping, orienting and moving micro-/nano-scaled particles, ideally for biological cells. At present time, the majority of tasks with optical tweezers are carried out manually. Increasing demands for both accuracy and efficiency in cell manipulation highlight the need for automation process that integrates robotics and optical tweezer technologies. In this paper, we propose to use a robot-tweezer manipulation system to automatically transport cells. We calibrate the forces applied to the trapped cell by a dynamic viscous-drag-force method to determine the optimal motion parameters, and adopt a modified A-star algorithm for path planning during automated transportation. Experiments are performed on manipulating living cells to demonstrate the effectiveness of the proposed approach.