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In this paper, we propose a visual-servo-control approach and a two-stage grasping strategy and, then, develop control software to perform micrograsping tasks, i.e., to control a passive microgripper to automatically grasp a micropart, in a 2-D plane with high accuracy. In the proposed control scheme, we employ closed-loop control with the use of two position feedback signals: relative positions of the micropart with respect to the microgripper measured by the vision-control system and absolute displacements of the micropart measured by linear encoders. To improve the grasping efficiency and success rate, a two-stage grasping strategy is employed: (1) the bonded microgripper is controlled to directly reach a specific position adjacent to the mating edge of a designated micropart with the same y coordinate, by matching the patterns of the microgripper and the micropart only once, and (2) finely align the micropart with the microgripper along the x and y translation axes of the microassembly robot in the horizontal plane by employing the proposed visual servo control, until the micropart is completely grasped. Experiments conducted with a 6-DOF microassembly robot demonstrate the efficiency and validity of the proposed control approach and grasping strategy.