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In this paper we present a grasping control system based on position control. The sliding mode control, which excels in robustness, is used as the position controller. Because the position control performs the grasping, it is not necessary to change the control rule accompanying the approach/grasp phase. The control system is, therefore, stable. Grasped objects may slip from fingertips when the mass of the objects and the posture of the robot's hands change. To avoid this problem, the friction coefficient is identified in real time. We believe that objects begin to slip when the friction coefficient value exceeds the maximum coefficient of friction. Using this coefficient as a threshold value, the grasping force is increased by increasing joint compliance. Our proposed control system was applied to a multifingered hand, and its efficacy and usefulness was verified.