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Aiming at the problem of precise position control and compliance control of parallel robot in the process of operation, a compliance control strategy of parallel robot based on external force estimation was proposed. The compliance strategy can realize the high-performance dynamic interaction between position and force of parallel robot in the process of operation. In the implementation of compliance control based on external force estimation, considering the high cost of contact force sensor, a sensorless external force estimation method was proposed. Firstly, the dynamic model of parallel robot and the dynamic model of servo motion system were established, and the changes of robot joint force under external force were estimated by using the established dynamic model and the current feedback value of motor. Secondly, according to the estimated joint force of the parallel robot, the position based impedance control was designed. The position based impedance control can change the rigid contact between the end effector of the parallel robot and the environment into flexible contact, so as to ensure the operation accuracy and compliance of the parallel robot. Finally, the appropriate impedance control parameters were selected to simulate and analyze the proposed compliance control strategy, and the experimental verification was carried out on the built experimental platform. The experimental results showed that the proposed method can realize the accurate, stable and fast compliance operation of the parallel robot.