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A grasping force control strategy is proposed in order to complete various fine manipulations by using anthropomorphic prosthetic hand.The position-based impedance control and force-tracking impedance control are used in free and constraint spaces,respectively.The fuzzy observer is adopted in transition in order to switch control mode.Two control modes use one position-based impedance controller.In order to achieve grasping force track,reference force is added to the impedance controller in the constraint space.Trajectory tracking in free space and torque tracking in constrained space are realized,and reliability of mode switch and stability of system are achieved.An adaptive sliding mode friction compensation method is proposed.This method makes use of terminal sliding mode idea to design sliding mode function,which makes the tracking error converge to zero in finite time and avoids the problem of conventional sliding surface that tracking error cannot converge to zero.Based on the characteristic of the exponential form friction,the sliding mode control law including the estimation of friction parameter is obtained through terminal sliding mode idea,and the online parameter update laws are obtained based on Lyapunov stability theorem.The experiments on the HIT Prosthetic Hand Ⅳ are carried out to evaluate the grasping force control strategy,and the experiment results verify the effectiveness of this control strategy.