## 4 Verification and Analysis
### Validation of Optimization Methods for Applications  
According to the non-inferior solution set constructed by the optimal system in the above section, two sets of mobile robot systems were constructed based on the existing equipment and accuracy to verify the correctness and effectiveness of the optimization method. According to Figures 5 and 6, System 1 and System 2 were constructed, and the corresponding data were obtained. The specific selection is shown in Table 2.  
As can be seen from the data in Table 2, the constructed System 1 has two working schemes by changing the working space of the manipulator. Scheme 1: the omnidirectional mobile platform carries the manipulator to one position for installation face milling, and then the omnidirectional mobile platform carries the manipulator to another position for installation face milling. Scheme 2: The omnidirectional mobile platform carries the robot to one position and completes the milling of two mounting surfaces in turn. Compared with the two schemes, it can be seen that the larger working space of the manipulator leads to the reduction in accuracy. Although it can process two more mounting surfaces in one position, and the cost is reduced and the efficiency is improved, the final milling error is increased. Similarly, the same conclusion exists for construction System 2. By comparing the constructed System 1 and System 2, it can be concluded that by selecting an end-effector with different precision and manipulator with different workspace, the combination can select appropriate programs of milling error, total cost and milling time. Figure 7 shows Scheme 1 of the actual construction System 1 and Scheme 2 of the constructed System 2. According to the actual system composition, the flexible positioning tool is changed into a fixed tool, the vision measurement system is changed into a laser tracker, and the cost is still calculated as before. The length of the large cabin body is 1.5 m, and only two mounting surfaces are processed, with a spacing of 0.3 m between the mounting surfaces. The machining accuracy of the mounting surface of the large cabin is required to be 0.04 mm. The milling end-effector in the constructed System 1 has two degrees of freedom of linear motion, and the milling end-effector in the constructed System 2 is an integrated spindle with higher accuracy. The accuracy and cost of the two are shown in Figure 8.  
By using scheme 1 of System 1, and Scheme 2 of System 2 constructed in Table 2 to milling multiple mounting surfaces, the error transmission route is shortened due to the difference in actual system combination, and the accuracy of each link is partially coupled, so there is deviation between the actual results and the calculated results, as shown in Table 3 below. The trend of the two constructed systems is the same as that of the optimized system. The milling error, total costs are similar, and the proportion of milling time between Scheme 1 and Scheme 2 is consistent between the predicted results and the actual results, so the correctness and effectiveness of the method are verified. The final milling error\(f_{1}\) is expressed as the maximum error in the \(Z\)-axis direction of the milled mounting surface in the local reference coordinate system. The laser tracker is used to measure the \(Z\)-axis