## 2 UAV Dynamics Model
### Climbing Performance Analysis and Leap Control Strategy Design  
To meet the requirements of the mission scenario, the MY-UAV drone chooses to complete the takeoff mission by jumping up at a large stopping angle. The entire takeoff process of the drone will be divided into two stages: jumping acceleration and stable climbing. The acceleration process of the drone jumping up will be designed to achieve the fastest acceleration with the maximum throttle, which accounts for a very small proportion of the entire takeoff mission time. Therefore, the focus of the jumping up process is to find the most favorable climbing flight state. Figure 15: Real flight data during takeoff climb phase. (**a**) Taxing takeoff actual flight—altitude; (**b**) taxing takeoff actual flight—airspeed; (**c**) taxiing takeoff actual flight—climb rate; (**d**) taxiing takeoff actual flight—pitch angle. (1) Performance Analysis of UAV Climbing  
In order to seek a better strategy for unmanned aerial vehicle jumping and climbing, the force during the climbing process of the distributed-propeller fixed-wing unmanned aerial vehicle is first analyzed. Figure 16 is a schematic diagram of the force during the climbing state of the unmanned aerial vehicle. Without considering wind interference, the drone's flight altitude is set to 500 m, and climb balancing is performed on the drone:  
\[\left\{ \begin{array}{l}-L\sin\gamma-D\cos\gamma+\\ \sum\limits_{i=1}^{8}T_{xi}\cos(\alpha+\gamma)+\sum\limits_{i=1}^{8}T_{zi} \sin(\alpha+\gamma)=0\\ m+\sum\limits_{i=1}^{8}m_{Ti}=0\\ -L\cos\gamma+D\sin\gamma-\\ \sum\limits_{i=1}^{8}T_{xi}\sin(\alpha+\gamma)+\sum\limits_{i=1}^{8}T_{zi} \cos(\alpha+\gamma)+G=0\end{array} \right. \tag{16}\]  
where \(m_{Ti}=T_{xi}\cdot l_{zi}-T_{zi}\cdot l_{xi}\), \(T_{xi}=T_{i}\cos\theta_{td}\), \(T_{zi}=-T_{i}\sin\theta_{td}\). The relationship between each state quantity, flight speed, and climb angle is obtained as shown in Figure 17:  
Figure 16: Force diagram of MY-UAV drone climbing state. By combining the curve of the angle of attack with speed and the curve of the pitch angle with speed, it can be concluded that in order for the drone to meet the requirements of a small climb angle and low-speed climb tasks, it needs to maintain a high-angle-of-attack flight state. At this time, the drone's balance state is very sensitive to changes in flight speed and climb angle, which is not conducive to the stable climb of the drone. When the drone climbs at a larger climb angle or speed, its balance state is relatively sluggish due to changes in flight speed and climb angle, which is beneficial for the stable climb of the drone. Combining the curve of balancing thrust with speed and the curve of balancing throttle opening with speed, it can be concluded that as the climbing angle of the drone increases, the required thrust and throttle for drone climbing also increase accordingly. As the climbing speed of the drone increases, the required thrust and throttle do not increase  
Figure 17: The variation curve of MY-UAV climb trim state variables with flight speed. monotonically, and there is a minimum required thrust and minimum required throttle during this process. Therefore, when considering the stable climb of drones, their designed flight speed should be as close as possible to the flight speed corresponding to the minimum required thrust and minimum required throttle, in order to achieve a more energy-efficient steady climb. Overall, the analysis of drone climb and balance states shows that although drones have the ability to climb slowly at low speeds and high pitch angles, their various balance states are very sensitive to changes in flight speed and climb angle. When the drone flies in this state, it is highly susceptible to external environmental interference, which requires high stability, maneuverability, and robustness of the controller.