This paper gives a brief description of feedback control systems engaged in DLR's recently developed multisensory 4finger robot hand. The work is concentrated on constructing the dynamic model and the control strategy for one joint of the fingers. One goal is to make the hand follow a datagiove for fine manipulation tasks. Our proposed strategy for this task is parallel torque/position controi; sliding mode controi is realized for the robust trajectoW tracking infree space; while impedance controi is provided for compliance control in the constrained environment; and an easily-designed parallel observer is used for the switch between these two control modes during the transition from or to contact motion. Some experimental results show the effectiveness of proposed strategy for the pure position control, torque control, and the transition controi.