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In order to improve the productivity of processes involving contact between robotic manipulator and workpiece, it is necessary to shorten the time for the contact force to reach the desired value. In doing so, however, the contact force may experience overshoot which could damage the workpiece. In this paper, we propose a nonlinear damping control scheme which can reduce the force overshoot without compromising on the reaction speed. The controller design and the tuning of its parameters are relatively straightforward because the parameters possess clear physical meanings. Finally, experiments are carried out to verify the effectiveness of the proposed controller.