## 1 Introduction
Related researchers have carried out a series of research on the cable tension optimization algorithm for CDPRs. [PERSON] [21] proposed a tension optimization algorithm based on the closed solution of cable tension, which is relatively simple but has a limited optimization range. [PERSON] [22] proposed to use the 2-norm method to solve the cable tension, but the tension value after the optimization was too small. [PERSON] [23] proposed P-norm method to solve the cable tension, but the continuity of force was poor after optimization. In this article, a method for solving cable tension based on the minimum variance is studied. The cable tension obtained by this method has good real-time performance and better continuity. The CDPRs are multi-input, multi-output, nonlinear and strongly coupled systems with disturbances and uncertainties, and their controller design is more difficult than general systems [24; 25; 26]. The common control strategies include PID control, fuzzy control, neural network control and sliding mode control [27; 28; 29; 30]. [PERSON] [31] adopted a fuzzy demodulator to control the cable-driven parallel rehabilitation robot, which compared the feedback position signal with the given signal to optimize the controller parameters in real time. [PERSON] et al. [32] designed a fuzzy controller with anti-interference capability, which was applied to a cable-driven manipulator. [PERSON] [33] proposed an adaptive super-twisted fractional-order non-singular terminal sliding mode (AST-FONTSM) control strategy, which ensures the system converge more quickly within a finite time. [PERSON] [34] proposed a second-order sliding mode controller, which improved the synchronous motion relationship between cables. Based on the above analysis, sliding mode control has the characteristics of fast response and strong robustness [35]. In this article, an adaptive non-singular fast terminal sliding mode controller (ANF-TSMC) is designed, which has stronger robustness and a faster convergence speed than a traditional sliding mode controller. Meanwhile, the adaptive technique is used to estimate the disturbance upper bound. By replacing the sign function of the ANF-TSMC with a saturation module, the chattering phenomenon of the controller output is effectively improved. The main contributions of this article can be summarized as follows:This article proposes a new type of ship derusting robot. The related technology of CDPRs is applied to the field of ship maintenance, which solves the problems of low degree of automation, low efficiency and limited operation range of traditional operation mode. 2. The kinematic model of CDPDR is established. On this basis, the controllable workspace of CDPDR is analyzed, and the results can provide reference for path planning. 3. Considering the influences of the ship's base motions and external disturbance on CDPDR operation, the overall dynamic model is established by the Newton-Euler method. The dynamic model takes into account the delay effect of the motor and improves the overall modeling accuracy. In addition, to tackle the problem of non-unique and discontinuous solution of cable tension, a tension optimization algorithm based on the minimum variance is proposed. 4. An adaptive non-singular fast terminal sliding mode controller is proposed, and its performance is verified in two different scenarios. The results show that the proposed control strategy has the characteristics of strong robustness, high precision and fast convergence. The rest of this article is organized as follows. The second part introduces the mechanical structure of CDPDR. The third part establishes the kinematic model and dynamic model of CDPDR; the controllable workspace and cable tension optimization algorithm are studied. The fourth part designs the ANF-TSMC controller, and its stability is proved. In the fifth part, simulation analysis is carried out for different scenarios. The sixth part draws the research conclusion and explains the future research work.