## 4 Discussion
Based on the value of the objective function, the Particle Swarm Optimization algorithm was used to update the parameters. Accurate measurement of the robot's joint angles is essential for this process, which necessitates reliable measurement tools. Therefore, we introduced the vision-based joint angle measurement technique in Section 2.5. The maximum discrepancy between the visual measurements and IC Measure software readings was 0.96\({}^{\circ}\), indicating that the accuracy of our algorithm is comparable to that of IC Measure. However, unlike IC Measure, our method offers the advantage of automating multi-joint measurements. Furthermore, the decoupling of multiple joints relies on high accuracy in single-joint motion. Therefore, we conducted a single-joint accuracy experiment as described in Section 3.1.1. The maximum absolute error in the motion of shoulder joint 1 was 0.79\({}^{\circ}\), with an average error of 0.51\({}^{\circ}\). Based on the above work on single-joint accuracy, multi-joint decoupling, and the validation of the measurement system's accuracy, we performed parameter identification for the robot prototype and conducted a repetitive positioning accuracy verification experiment. The results indicated that, after parameter identification, the robot's repetitive positioning accuracy improved by an average of 1.97 mm, with a percentage improvement of approximately 37.74%. During the accuracy measurement, we measured the accuracy of four target points. For points P2, P3, and P4, the accuracy before and after parameter identification was 3.03 mm, 3.93 mm, and 1.32 mm, respectively, and 2.14 mm, 2.45 mm, and 0.91 mm, respectively, after identification. The accuracy of target point P1 was 9.62 mm before and 4.53 mm after parameter identification. The larger error for target point P1 may be attributed to several factors: (1) Target point P1 may be located at the robot's motion range limits or in a complex position where kinematic model predictions, particularly in regions with strong nonlinearity and coupling effects, struggle to predict movement accurately. (2) The robot arm or end-effector may experience higher mechanical loads or structural elastic deformation in certain positions, leading to a decrease in accuracy. Target point P1 may be located in a high-load position, resulting in more significant elastic deformation or system instability, which contributes to larger positional errors. (3) If the joint position or orientation for target point 1 is influenced by a high degree of joint coupling, the decoupling effects may be limited, leading to lower accuracy even after parameter identification. Whilethe accuracy for point P1 did not improve to below 3 mm after parameter identification, the 52% improvement highlights the effectiveness of parameter identification in enhancing the robot's accuracy. This also indicates that further refinement of the kinematic model is necessary. In [35], a compensation method for continuum robots considering nonlinear friction was proposed. After compensation, the robot's motion control accuracy significantly improved, with the average position error reduced from 5.94 mm to 3.15 mm, achieving a compensation rate of 46.97%. Incorporating cable friction and joint friction into the robot's control model is an area we plan to explore in future research. In addition, to enable the robot to be used for clinical applications, we proposed a force feedback master-slave control strategy based on safety zone constraints. A simulation verification of the force feedback constraint was conducted in the Gazebo simulation environment, and the robot completed a ring-grasping experiment on a surgical training platform (physical model) to validate the effectiveness of the proposed incremental master-slave control method in Cartesian space.