## 4 Verification and Analysis  
### Application of the Multi-Objective Optimization Method in Optimal System Construction  
Based on the above analysis, the measured data was first collected and summarized, and the component set was initialized as shown in Figure 6. The precision, efficiency and cost of omni-directional mobile platform, manipulator, milling end actuator, visual measurement system and flexible displacement system are related. The manuscript directly gives the results of the relationship among precision, efficiency and cost through the existing data, without detailed analysis.  
According to the optimization method proposed in the previous section and the data in Figure 5, 300 iterations of the algorithm were performed on 100 populations after the convergence of the algorithm. The non-inferior solution set of 89 optimal sampling points was finally obtained, as shown in Figure 7.  
Figure 6: Initialized data.  
In Figure 6a, the \(x\)-coordinate is the cumulative error of the constructed mobile robot system and represents the fitness value of the objective function \(f_{1}\). The \(y\)-coordinate is the sum of the cost of the constructed mobile robot system and represents the fitness value of the objective function \(f_{2}\). In Figure 6b, the \(x\)-coordinate represents the fitness value of the cumulative error objective function \(f_{1}\). The \(y\)-coordinate is the time spent in milling all the multi-mounting surfaces of the large cabin of the constructed mobile robot system and represents the fitness value of the objective function \(f_{3}\). In Figure 6c, the \(x\)-coordinate represents the fitness value of the objective function \(f_{2}\) of the sum of costs; The \(y\)-coordinate is the fitness value of the milling time objective function \(f_{3}\). In Figure 6d, the coordinates represent the fitness value of cumulative error objective function \(f_{1}\), the fitness value of cost sum objective function \(f_{2}\), and the fitness value of milling time objective function \(f_{3}\).  
By analyzing the multi-objective optimization results of the optimal system construction, the following information can be obtained:  
1. There is a significant negative correlation between the cumulative error and the sum of costs in Figure 6a, a significant negative correlation between the cumulative error and the milling time in Figure 6b, and a positive correlation between the sum of costs and the milling time in Figure 6c, indicating that the three objective functions are contradictory to each other;
2. Considering the actual design requirements, existing equipment status and subsequent support funds and other factors, the non-inferior solution set in Figure 6d can select the appropriate mobile robot system and determine the component requirements according to the corresponding code, which can ensure that the accuracy, cost and time of the system meet the construction requirements.  
Figure 7: The non-inferior solution set for optimal system construction. (**a**) Construction of error and cost optimal system; (**b**) Construction of optimal error and time-consuming system; (**c**) Construction of cost and time-consuming system; (**d**) Optimal system construction for error, cost and time.