# End-Effectors Developed for Citrus and Other Spherical Crops
## 3 Picking Performance Tests
### Multi-Factor Tests  
Considering the mutual influence of each parameter, multi-factor orthogonal tests were conducted for stepper motor speed, end-effector speed, and picking angle based on the results of single-factor tests, and the results were averaged five times for each group of tests. The experimental design is shown in Table 2.  
In order to find the best combination of end-effector structures, the level factors of the orthogonal test were determined based on the comprehensive analysis of the single-factor test results, and the orthogonal test of picking performance was carried out [53]. The test results are presented in Table 3.  
The regression coefficients and equations between picking success rate Q, single fruit picking time T, stepper motor speed \(X_{1}\), end-effector speed \(X_{2}\), and picking angle \(X_{3}\) were obtained by using Design-Expert 8.0 software (Stat-Ease, Minneapolis, MN, USA).  
Picking success rate \(Q\):  
\[\begin{array}{c}Q=33.2+0.32X_{1}+1.35X_{2}-0.85X_{3}-0.85X_{1}X_{2}+0.15X_{2} X_{3}-1.62X_{1}X_{3}\\ +0.32X_{1}^{2}+0.62X_{2}^{2}-1.62X_{3}^{2}\end{array}\]  
Single-fruit picking time \(T\):  
\[\begin{array}{c}T=15.32+1.23X_{1}-2.23X_{2}+1.52X_{3}+1.62X_{1}X_{2}-2.33X_{ 2}X_{3}+1.82X_{1}X_{3}\\ -0.1X_{1}^{2}+2.85X_{2}^{2}-5.88X_{3}^{2}\end{array}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{3}{c}{**Factor**} \\ \cline{2-5}  & \(X_{1}\)**/(r/min)** & \(X_{2}\)**/(mm/min)** & \(X_{3}\)**/(\({}^{\circ}\))** & **Rate Q**/**\%** & **Picking Time T/s** \\ \hline
1 & \(-1\) & \(-1\) & \(-1\) & 92.38 & 4.95 \\
2 & \(1\) & \(-1\) & \(-1\) & 90.05 & 4.88 \\
3 & \(-1\) & \(1\) & \(-1\) & 93.61 & 4.65 \\
4 & \(1\) & \(1\) & \(-1\) & 92.64 & 4.84 \\
5 & \(-1\) & \(-1\) & \(1\) & 91.88 & 4.54 \\
6 & \(1\) & \(1\) & \(1\) & 90.38 & 4.68 \\
7 & \(1\) & \(1\) & \(1\) & 91.35 & 4.62 \\
8 & \(1.682\) & \(0\) & \(0\) & 93.21 & 4.85 \\
9 & \(1.682\) & \(0\) & \(0\) & 94.22 & 4.74 \\
10 & \(0\) & \(1.682\) & \(0\) & 92.56 & 4.68 \\
11 & \(0\) & \(-1.682\) & \(0\) & 91.62 & 4.69 \\
12 & \(0\) & \(0\) & \(1.682\) & 91.46 & 4.66 \\
13 & \(0\) & \(0\) & \(1.682\) & 91.20 & 4.82 \\
14 & \(0\) & \(0\) & \(0\) & 93.25 & 4.86 \\
15 & \(0\) & \(0\) & \(0\) & 92.88 & 4.69 \\
16 & \(0\) & \(0\) & \(0\) & 91.95 & 4.73 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Picking performance orthogonal test results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{3}{c}{**Factor**} \\ \cline{2-4}  & \(X_{1}\)**/(r/min)** & \(X_{2}\)**/(mm/min)** & \(X_{3}\)**/(\({}^{\circ}\))** \\ \hline
1.682 & 200 & 80 & \(-15\) \\
1 & 225 & 120 & 0 \\
0 & 250 & 160 & 15 \\ \(-1\) & 275 & 200 & 30 \\ \(-1.682\) & 300 & 240 & 45 \\ \hline \hline \end{tabular}
\end{table}
Table 2: End-effector picking performance test factor level coding table.  
In summary, the magnitude of factors affecting the picking success was \(X_{2}\), \(X_{1}\), and \(X_{3}\), in order; the magnitude of factors affecting single fruit picking time was \(X_{2}\), \(X_{1}\), and \(X_{3}\), in order.  
To verify the effectiveness of the citrus picking end-effector designed in this paper, we compared the common three-finger under-driven end-effector and suction cup end-effector in the market for the test and the results of the grasping test are shown in Table 4.  
According to the comparison test results (Table 4), it can be seen that the end-effector designed in this paper has the best picking performance, with the highest picking success rate of 93.33%, the lowest damage rate of 1.11%, and a single fruit picking time of 4.05 s, which is slightly lower than that of the suction cup end-effector.