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In numerous cellular applications, cells are transported to specific positions or extracted from complex cell solutions. Therefore, an efficient cell transportation path planner for these applications is important for avoiding collisions with other cells or obstacles. In this paper, a path planning approach to transporting cells using a robot-aided optical manipulation system is presented. Optical tweezers functions as a special end-effector in transporting a target cell to the desired position along the generated path. The path planner is designed based on the rapidly exploring random trees (RRT) algorithm for calculating a collision-free path for cell transportation. Both static and dynamic path planners are developed. For the dynamic path planner, an online monitoring strategy is employed to dynamically avoid collisions with randomly appeared obstacles caused by environmental influence such as the Brownian movement of microparticles. Experiments of transporting yeast cells are performed to demonstrate the effectiveness of the proposed approach. Note to Practitioners - Manipulations of cells and other microparticles represent an essential process for most cell-based bioengineering applications, such as cytopathology, cell sociology, and cytotaxonomy. Cell transportation, which is treated as a typical cell manipulation task, has recently received considerable attention because of its wide applications. This paper presents a novel approach to applying RRT-based path planner to cell transportation with a robot-aided optical manipulation system. The research outcome provides a unique solution to achieving cell transportation automatically and efficiently.