# Design and Control of an Ultra-Low-Cost Logistic Delivery Fixed-Wing UAV
## 3 Overview of Image Recognition Technology
### Target Identification Applications
#### 3.3.4 Target's Throwing Test  
When the target is detected, the vertical projection distance of the target relative to the UAV is obtained, and the UAV starts to adjust its attitude to be colinear with the target. Then, the onboard computer releases the dropping command to control the switch of the dropping bin so that the 500 mL water bottle makes a free-fall motion to hit the target. In this study, we set the distance of the target from the vertical ground projection of the UAV as S, the height of the UAV drop as U, the cruising speed of the UAV as V, and X is the distance between the drop's ground-landing point and the target. The formulae are as follows:  
\[\left\{ \begin{aligned} & U=\frac{1}{2}gt^{2}\\ & S=Vt\end{aligned} \right. \tag{25}\]  
where \(g\) is the acceleration of gravity, and t is the falling time. To find the best throwing height and cruising speed, this study carried out a throwing test many times because the positioning error of the GPS is around 5 m. It also takes into account the wind resistance and the wind direction influences to ensure the smooth flight of the UAV. Thus, this study limits the throwing height to 8-12 m, and the speed is limited to 11-12 m/s. The test results are shown in Table 9. In Table 9, frequencies 1-9 indicate that we conducted nine rounds of experiments, and in each round, dozens of experiments were carried out at speeds of 11 m/s and 12 m/s. The simple random sampling method was adopted to extract five pieces of data and calculate the average value. Two sets of data, including the delivery distance and landing error, were obtained for each round, corresponding to speeds of 11 m/s and 12 m/s, respectively. As shown in Figure 28, when the UAV's throwing height is 10 m, the error in the target point is 2.66 m when throwing/dropping the 500 mL water bottle at 12 m/s. Figure 28 shows the simulated drop point of the 500 mL water bottle; we can see that when the UAV's throwing height is 10 m, the drop point falls within the effective throwing range of 3 m when throwing/dropping the 500 mL bottle of water at 12 m/s. The requirement of this study is thus satisfied. In Figure 28, we can see that most of the landing points reach a relatively accurate distance, but there are still some landing points beyond the effective range of 5 m, which is mainly affected by the weather; the wind is too strong, and the landing point is offset, but compared with the overall landing point, such similar errors can be ignored. According to the analysis of nearly one hundred kinds of data from our previous nine rounds of experiments, we established a multiple linear regression model for the analysis, and the multiple linear regression model is as follows:  
\[e_{i}=\beta_{0}+\beta_{1}h_{i}+\beta_{2}s_{i}+\epsilon_{i} \tag{26}\]  
where \(h_{i}\) represents the throwing height (height) of the ith experiment; \(s_{i}\) represents the throwing speed (speed) of the ith experiment; \(e_{i}\) represents the corresponding landing error; \(\beta_{0}\) is the intercept of the model and represents the baseline value of the landing error when both the height and speed are zero; \(\beta_{1}\) represents the coefficient of the height, which represents the expected amount of change in the landing error for each unit of change in the height; \(\beta_{2}\) represents the coefficient of the velocity, which represents the expected amount of change in the drop point error for each unit of change in the velocity; and \(\epsilon_{i}\) represents the error term, which represents the random error that the model fails to account for. The requirements of this study are met, as the drop point falls within the effective drop range of 3 m when throwing/throwing the 500 mL bottle at a UAV drop height of 10 m. The water velocity is 12 m/s, and the error term is minimized.