The success rates of manually performed embryo biopsies in Preimplantation Genetic Diagnosis (PGD) are low due to human errors, excessive embryo damage and prolonged surgery times. To increase the procedure the success rate, a robotic system for the biopsy of early-stage 2-cell embryos is proposed. The system consists of robotic manipulators, a camera, sensors, a laser, and set of end-effector tools to perform different procedures on the embryo. The system is comprised of six continuous phases, implemented successively, with neither manual intervention nor software interruption. All six phases are under image-based feedback control and use linear and nonlinear controllers to move micromanipulators with high precision, reject external disturbances, and follow reference trajectories accurately. Significantly, this leads to very rapid processing of embryos. Experimental results on 2-cell and 4-cell cleavage stage embryos validate the effectiveness of the methods proposed.