## 2 Materials and Methods
### Experiment of Multi-Factor Optimization  
It was intended at the beginning of the study to concentrate maximum efforts on making the function of the robotic transplanting system more accurate and applicable. Under the standard seedling-raising conditions, the growth of plug seedlings is relatively uniform. So, the mechanical factors have a significant effect on the percentage of successfully transplanting seedlings from their growth cells [8; 14]. This paper will test and evaluate the adaptability of relevant mechanical operations in the Key Laboratory of Modern Agriculture Equipment and Technology, Ministry of Education, Jiangsu University, Zhenjiang, China. The test objects were the conventional cultivated tomato grohole seedlings used in the mechanism design. According to the previous design, the pick-up pins were made of 304 stainless steel wire with a diameter of 1.6 mm [8]. Their spacing was kept at 3 mm less than the cell wall width as slanting into the root soil of the seedling. The gripper grasps the root system to lift the seedling in a vertical direction out of the cell. So, this lifting motion would affect the extraction rate, which was closely related to the transplanting efficiency. Thus, the slow, medium, and high speeds were set for transplanting operation at which the transplanting frequencies were 15 plants/min, 20 plants/min and 25 plants/min from the source try to the growth pot. The spring tightening force of the pick-up pins was theoretically deduced in design. The grasping forces at 0.9 N, 1.2 N, and 1.5 N were tested to compare seedling extraction. According to the 72-cell dimension, the maximum penetration depth was 45 mm. The penetration depth with minus 2 mm coverage was divided into three levels of 30 mm, 35 mm, and 40 mm. As shown in Table 2, the multifactor orthogonal tests of several factors and levels were conducted according to the above design analysis.  
Low damage to the seedling's root lump during the transplanting process is the key to ensuring growth and development in the later stage (7,8,14). So, the integrity rate of root lumps in automatic transplanting was chosen as the index of transplanting experiments. It was defined as follows.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factors** & **A: Transplanting Frequency** & **B: Grasping Force** & **C: Penetration Depth** \\ (Levels) & **(plant/min)** & **(N)** & **(mm)** \\ \hline
1 & 15 & 0.9 & 30 \\
2 & 20 & 1.2 & 35 \\
3 & 25 & 1.5 & 40 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Factors and levels of the orthogonal experimental design.  
Figure 10: Performance tests of the simplified greenhouse robotic transplanting workcell.  
\[IR_{AT}=[W_{1}/(W_{1}+W_{2})]\times 100 \tag{8}\]  
where \(IR_{AT}\) is the integrity rate of automatic transplanting, %; \(W_{1}\) is the residual weight of a plug seedling after transplanting, g; \(W_{2}\) is the damage weight during automatic transplanting and dropping, g.  
To facilitate the statistics of the root lump damage, plug seedlings were transplanted one by one into the same plug trays, as shown in Supplementary Video S1. Based on these factors and levels, the L\({}_{9}\) (3\({}^{4}\)) type orthogonal table was used for the multi-factor optimization. There were nine testing groups, and the unused column was used as the error. In each test, the whole-tray seedlings were continuously transplanted, and the process was repeated three times. The corresponding results were recorded on-site, and the statistical analysis was conducted using the SPSS 18.0 software package (SPSS Inc., Chicago, IL, USA). Analysis of variance (ANOVA) was carried out with the least significant difference method (LSD).