## 1 Introduction  
Power transmission lines play a vital role in the transmission of electrical energy, which is essential for economic development and the functioning of human life. However, these lines are susceptible to corrosion and wear and tear damage. Regular inspections are required to avoid potential hazards. As power grids develop, the length of transmission lines is rapidly increasing [1, 2]. To improve efficiency and safety, intelligent and automated inspection robots are replacing traditional manual inspections [3]. Currently, these robots can be classified into three categories: flight-mode inspection robots [4, 5, 6], crawling-mode inspection robots [7, 8, 9, 10], and hybrid-mode inspection robots [11, 12, 13, 14]. Flight-mode inspection robots offer greater flexibility and faster mission completion but have shorter endurance due to higher energy consumption [15]. Crawling-mode inspection robots move along the power lines, providing better stability and lower energy consumption. However, they require manual assistance to land on and off power lines [16]. Hybrid-mode inspection robots incorporate the combined capabilities of flight and crawling to perform inspections that are durable, energy-saving, safe, and autonomous [17, 18]. By switching between flight and crawling modes, the robots can achieve longer endurance and perform more effective inspections. These inspection robots rely on built-in lithium-ion batteries for limited power. The growing range of robot functions and the increasing number of inspection tasks have resulted in higher energy requirements during missions. Therefore, overcoming the energy challenge Is crucial for enabling these robotic systems to perform large-scale, long-distance inspections [19]. To improve the endurance and inspection efficiency of the inspection robot, a comprehensive analysis and optimization of its energy demand is crucial. The main focus of this paper is to analyze the energy consumption of the FPTLIR during its flight missions since their energy consumption is higher compared to that of travelling missions, which can be compared to that of rotary-wing unmanned aerial vehicles (UAVs). There are currently two methods to achieve this. The first method involves constructing a model of the UAV's energy consumption and optimizing its relevant parameters to minimize energy consumption during flight. These models typically include various aspects such as flight speed, attitude control, sensors, and communication systems [20, 21, 22]. The second method involves reducing energy consumption and extending the mission time of the UAV through rational trajectory planning and movement strategies within the defined trajectory [23, 24]. Previous studies have classified the energy consumption modeling of UAVs into two types: the black-box method and the white-box method [25]. Regarding the black-box method, [PERSON] et al. [26] proposed a technique that uses machine learning algorithms to construct a UAV energy consumption model based on test data obtained under different payloads, thereby improving the accuracy of energy consumption prediction. This approach eliminates the need to analyze the intricate design principles of UAVs, thereby reducing model complexity. However, it requires extensive data support and high precision in experimental measurements. [PERSON] et al. [27] analyzed the effects of UAV ground power consumption, communication, hovering, and vertical and horizontal motion on energy consumption by quantifying these factors and proposed a more comprehensive UAV energy consumption model based on battery performance parameters. The proposed model can be more easily used for energy-efficient planning of UAV missions, but its lack of transparency makes it difficult to identify errors and flaws, hindering debugging and improvement. [PERSON] et al. [28] proposed a black-box model to predict the energy consumption of UAVs based on their missions. The model automatically collects motion data and uses regression analysis to estimate the energy consumption of the UAVs.