## 1 Introduction  
Cable-driven continuum robots are essential for achieving dexterous manipulation in minimally invasive surgical robots [1]. Minimally invasive robotic surgery systems, such as the da Vinci Surgical System [2], Versius Surgical Robotic System [3], Hugo RAS System [4], da Vinci SP Surgical System [5], SHURUI single-port robotic system [6], and Smart Endoscopic Surgical Robot System [7], are widely used in fields like gynecology [8], urology [9], hepatobilary surgery [10], and gastrointestinal surgery [11] (Figure 1). However, their application in thyroid surgery is less common. The thyroid gland, an important endocrine organ located in the head and neck region, is the site of the most common malignant tumor [12]. Its anatomical location results in a significantly smaller and more complex surgical workspace compared to laparoscopic procedures [13]. This spatial constraint demands that robotic systems achieve exceptional flexibility for navigating confined spaces while maintaining sufficient rigidity to ensure precise instrument control--a critical requirement often unmet by traditional continuum robots. To address these dual demands, this study proposes a novel cable-driven robotic system that synergistically integrates rigid and continuum robotic mechanisms, offering a tailored solution to overcome the spatial and technical challenges inherent in robotic thyroid surgery.  
Despite the potential of this hybrid design, the complex structure of the manipulator arms in minimally invasive surgical robots often incorporates several types of joints, including articulated joints, flexible continuum joints, and flexible discrete joints. This complexity results in intricate kinematic analysis. This requires sophisticated mathematical theories for theoretical analysis [14]. Commonly used kinematic analysis methods in robotics include vector analysis, Denavit-Hartenberg (D-H) parameter analysis [15], quaternion analysis [16], Lie group and Lie algebra analysis [17], and screw theory analysis [18]. However, errors inevitably occur during manufacturing and assembly processes, leading to inaccuracies in the cable-driven model parameters [19]. The accuracy of continuum robots is influenced by a variety of factors, including manufacturing errors, kinematic modeling, and the hysteresis characteristics of the tendons. However, existing research has predominantly focused on kinematic and dynamic modeling, while the exploration of the impact of manufacturing errors on the precision of continuum robots remains relatively limited [20]. This is mainly due to the difficulty in directly measuring manufacturing errors and the fact that most parameter identification methods are model-dependent, which further increases the complexity. Moreover, the coupling effects between the joints of continuum robots (as shown in Figure 2d) make parameter identification even more complex. To address this issue, this study proposes a decoupling strategy for the drive tendons between robot joints, combined with Particle Swarm Optimization (PSO) for parameter identification, to correct model errors and improve motion accuracy. Experiments have shown that this method can reduce positioning errors by 37%.  
Figure 1: Joint and drive design. (**a**) da Vinci Surgical System by Intuitive Surgical, Inc. (Sunnyvale, CA, USA); (**b**) Versus Surgical Robotic System by CMR Surgical (Cambridge, UK); (**c**) Hugo RAS System by Medtronic plc (Dublin, Ireland); (**d**) da Vinci SP Surgical System by Intuitive Surgical, Inc.; (**e**) SHURUI single-port robotic system by Beijing Surgerii Robot Company Limited (Beijing, China); (**f**) Smart Endoscopic Surgical Robot System by Shenzhen Jingfeng Medical Technology Co., Ltd. (Shenzhen, China).