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With such advantages as nonphysical cell contact and a relatively high efficiency, the application of optical tweezers for the manipulation of biological cells has received increasing attention in recent years. The use of optical tweezers to transfer cells to user-defined goal positions is useful in many biomedical applications. In this paper, we investigate how to automatically transport biological cells using robotically controlled optical tweezers. We characterize the forces applied to a trapped cell by a dynamic viscous drag force method, which provides us insight into information on optimal motion parameters. To prevent the cell from escaping the optical trap and to ensure high efficiency in cell movement, a proportional-integral (PI) scheme, designed based on calibrated dynamic parameters, is used to determine the ideal movement velocity of the cell. The PI scheme utilizes a feedback of the actual cell displacement from the laser focus. Finally, a modified A* algorithm is adopted for path planning during automated cell transportation. Experiments are finally performed to verify the proposed approach.