Abstract: Aiming at the problem that it is difficult to accurately control the bending angle of a finger rehabilitation robot driven by a shape memory alloy (SMA) wire, this paper proposes a fuzzy adaptive PID control algorithm. Based on the kinematics model and the alloy wire drive model of a finger rehabilitation robot, this method utilizes the bending angle feedback of resistance mapping and adopts fuzzy adaptive parameters to realize position control. An experimental test platform for finger rehabilitation robots is built, the traditional PID and fuzzy adaptive PID control methods are used to conduct position control experiments on the index finger, and position control effects of each index finger joint after stability are analyzed. The research results show that, compared with the traditional PID control algorithm, the fuzzy adaptive control algorithm takes 2～3 s longer to reach the angle steady state time, the adjustment time is shorter, the position error is 2°, and the adaptive adjustment can be completed within 3 s under external disturbance conditions. The proposed method has strong robustness and can better compensate the hysteresis in the SMA phase changing process, which proves its effectiveness.