To solve the problems of poor follow-up in the gripping task of the manipulator under the condition of human-computer interaction, resulting in low operation fluency and unsatisfactory trajectory tracking, a human-computer interaction follow-up control method based on surface electromyography (sEMG) is proposed. Firstly, the angle of shoulder and elbow joints are obtained by using the IMU data of dual gForcePro+ arm rings. By combining this data with the feature extraction of sEMG signals, the angle of wrist joints is estimated by the PSO-GRNN model, establishing a mapping relationship between the human arm and the robotic arm to realize the follow-up control. Experimental results show that the Root Mean Square Error (RMSE) of the PSO-GRNN model in wrist joint angle estimation is reduced by 62-39%and 55-18%, respectively, compared with the traditional GRNN method, effectively improving the control accuracy. To further enhance the control accuracy in the grasping task, a gesture recognition method based on a CNN-LSTM network is proposed to realize the real-time control of the gripper. At the same time, a stiffness estimation algorithm for the human upper limb is constructed by leveraging the mapping relationship between sEMG signals and actual stiffness. The stiffness adjustment information is then introduced into the adaptive RBF-NFTSMC controller to realize the compliant control of the robotic arm. Experimental results show that the optimized RBF-NFTSMC method reduces the trajectory tracking error by about 30.2% compared with the traditional NFTSMC method, enhancing the anti-interference ability of the system. In addition, in order to verify the effectiveness of the sEMG variable stiffness control strategy, an experimental platform based on dual gForcePro+ arm rings and UR3e robotic arms was built. Experimental results show that the end trajectory of the manipulator based on sEMG variable stiffness control was closer to the target trajectory, with trajectory tracking error reduced by 24.6% compared with the fixed stiffness control method. Furthermore, the flexibility of the manipulator in object interactions was improved, leading to improved stability and adaptability.