## 6 Simulation and Test Results
### Energy Consumption Model Validation Tests
Figure 18a,b shows the instantaneous power measurements during both the acceleration and deceleration phases, as well as the average power values for all five trials and the corresponding prediction curves based on the energy consumption model of the flight systems. For power prediction during the acceleration phase, there is an average error of 0.2114 \(\times\) 10\({}^{3}\) W with an average relative error of 3.24%. For power  
Figure 16: Schematic diagram of the test sites and test equipment. (**a**) Test sites; (**b**) flying–walking power transmission line inspection robot; (**c**) upper computer. prediction during the deceleration phase, there is an average error of 0.0988 \(\times\) 10\({}^{3}\) W with an average relative error of 2.03%. The third flight test involved several vertical constant velocity flights, where the FPTLIR ascended at a steady rate of 1 m/s, 2 m/s, 3 m/s, and 4 m/s within the height range of 4 m to 16 m. Each velocity was repeated five times for testing purposes. Figure 19 shows the instantaneous power measurements at different vertical velocities, together with the average power value obtained from five trials and the corresponding prediction curves based on the energy consumption model of the flight systems. The initial phase from ground level to 4 m altitude served as an acceleration and deceleration stage for ensuring appropriate test velocities and safe landing speeds for the FPTLIR. For power prediction at uniform ascent velocities of 1 m/s, 2 m/s, 3 m/s, and 4 m/s, the average errors are found to be 0.0879 \(\times\) 10\({}^{3}\) W, 0.0831 \(\times\) 10\({}^{3}\) W, 0.0551 \(\times\) 10\({}^{3}\) W, and 0.0971 \(\times\) 10\({}^{3}\) W respectively. The corresponding average relative errors are found to be approximately at levels of 1.08%, 1.11%, 0.76%, and 1.41%. The fourth flight test involved several vertical variable velocity flights, where the FPTLIR's velocity was gradually increased from 0 m/s (hovering state) to 10 m/s with an acceleration of 1 m/s\({}^{2}\). Subsequently, the velocity was gradually reduced with a deceleration of 1 m/s\({}^{2}\) and repeated for five trials. Figure 20a,b shows the instantaneous power measurements during both the acceleration and deceleration states, together with the average power value obtained from five trials and the corresponding prediction curves based on the energy consumption model of the flight system. For power prediction during acceleration, there is an average error of 0.1914 \(\times\) 10\({}^{3}\) W with an average relative error of 2.43%. Similarly, for power prediction during deceleration, there is an average error of 0.0774 \(\times\) 10\({}^{3}\) W with an average relative error of 1.83%. Figure 17: The power of FPTLIR flying at different constant velocities horizontally. Figure 18: The power of FPTLIR flying at uniform variable velocity horizontally. **(a)** At uniform acceleration; **(b)** at uniform deceleration. The model shows satisfactory performance in predicting the power of the FPTLIR over different flight paths and operational states. It is observed that the model has a higher prediction bias during horizontal flight when compared to vertical flight. This is due to the air disturbance caused by the forward motion and mutual interference of the airflow between the rotors, which affects the accuracy of the momentum theory when applied to horizontal flight. Figure 19: The power of FPTLIR flying at different constant velocities vertically. (**a**) 1 m/s; (**b**) 2 m/s\({}_{2}\) (**c**) 3 m/s; (**d**) 4 m/s. Figure 20: The power of FPTLIR flying at uniform variable velocity vertically. (**a**) At uniform acceleration; (**b**) at uniform deceleration.