## 1 Introduction  
Regular inspection of power transmission lines is crucial for ensuring the stable operation and reliability of power systems. Currently, intelligent inspection of overhead high-voltage transmission lines is primarily conducted using arm robots, wheeled robots, and unmanned aerial vehicles (UAVs) domestically and internationally. Existing inspection methods are limited by weather conditions, endurance, and equipment adaptability, making it difficult to meet the demands in complex environments. Researchers, drawing inspiration from the movement patterns of snakes, such as undulation, crawling, and coiling, have designed snake-like robots to enhance their degrees of freedom and adaptability to various environments [1, 2, 3]. With the in-depth research on biological snake gaits, Central Pattern Generator (CPG)-based control methods have emerged. These methods mimic the nervous systems of vertebrates, adjusting the connection weights and parameters of control signals to enable robots to adapt to a variety of complex movements [4; 5; 6]. In recent years, research in the field of CPG control has flourished. [PERSON] et al. [7] designed a closed-loop central pattern generator (Generator-CPG) based on distance information to achieve stable and rapid regulation of the rotary angle of a fish-like robot, enabling it to turn within concave obstacles and escape smoothly. [PERSON] et al. [8] proposed a two-tier CPG control system, modeling with Kuramoto oscillators, clarifying the hierarchical structure and coupling topology of the CPG network to achieve multiple movement modes in snake-like robots. [PERSON] [9] successfully implemented various gait movements in modular snake-like robots, including lateral undulation and two-step creasing, accumulating experience in multimodal movement of snake-like robots. The aforementioned studies have successfully generated and regulated various gaits in robots but lack an analysis of the serpentine robot's crawling and rolling gait along power transmission cables. [PERSON] et al. [10] used dual-chain Hopf oscillators to generate spiral wrapping gaits, combined with simulated annealing to optimize step length, and improved the crawling speed of snake-like robots along cables. [PERSON] et al. [11] used IMU inertial navigation sensor feedback compensation, incorporated virtual signal calculation of the head navigation angle in the CPG network, and combined with the VICON motion capture system to solve the head stability problem in the movement of snake-like robots. References [10; 11], respectively, improved the motion efficiency and head control performance of snake-like robots in wrapping and crawling from the perspectives of gait optimization and navigation stability. However, facing complex hardware on power lines, a single gait mode, large joint angle signal noise, and susceptibility to electromagnetic interference affecting IMU signals in high-electromagnetic-interference environments, navigation angle calculation accuracy decreases, limiting the application effect of the system in power line scenarios. [PERSON] et al. [12] improved the stability of the spiral wrapping gait of snake-like robots by predicting and updating external disturbances, viscous friction, and time-varying parameters, compensating system control inputs, using Lyapunov functions to analyze subsequent errors, accelerating error convergence speed, and reducing fluctuation peaks. [PERSON] et al. [13] proposed a robust model-based radius estimation method for the spiral climbing problem of snake-like robots, using multi-step calculation and curve fitting, and feedback estimation of the winding radius from joint angle measurements to achieve variable-diameter spiral climbing motion. References [12; 13] performed well in improving the stability and robustness of snake-like robots, but due to strong sensor dependence and high computational complexity, they may be insufficient in response speed in power line obstacle-crossing scenarios, thus affecting operational efficiency. [PERSON] et al.