## 4 Design of a DT System for Multi-Robot Cooperative CBFMS  
### Construction and Optimization of the Robot Model  
DT models are classified into static and dynamic in this paper because the composition is extremely complex. The classification normalization process is adopted in this study; models with the same attributes and logic as higher level models are linked using a function.  
Let us take a six-degree-of-freedom robot arm as an example. To comply with the motion constraints of the robot, the subordination of the logical model needs to be established. With the pedestal of the robot as the base, the parent function is used to build the subordination from the bottom up. The first level is the child level, and the higher level is the parent level. By calling the link function, when the joints of the parent level move, the joints of the child level can also move with them. The hierarchy is constructed, as shown in Figure 18.  
Optimization of the model is a prerequisite for DT. With the volume of data increasing in the later stages of the process, if the number of points and faces in the model is too large, the memory consumption will have a burden, and the rate of operation will be affected. The basic premise of optimization is to make the number of faces and points of the model as small as possible without affecting the appearance of the model. The traditional levels of detail algorithm optimizes the model by layering the model and retaining the highest level of the model. This method does not provide sufficient model granularity when processing the model, and the finished model is still relatively crude and poorly smoothed. Therefore, an adaptive weight reduction to handle the model is used in this paper. It can reduce the number of points and surfaces of the model according to the weight size, and the model  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Time/s**} & \multicolumn{3}{c}{**Pass Rate (\%)**} \\ \cline{2-6}
**Part Name** & **Traditional** & **Optimized** & **Optimization Rate (\%)** & **Traditional** & **Optimized** \\ \hline Arc extinguishing chamber & 6.52 & 3.64 & 44.17 & 92.5 & 95.6 \\ Magnetic system & 10.57 & 3.86 & 63.48 & 91.7 & 95.3 \\ Yoke & 5.89 & 4.53 & 23.09 & 92 & 94.2 \\ Big-U rod & 7.36 & 3.27 & 55.57 & 93.4 & 93.9 \\ Handle & 5.27 & 2.62 & 50.28 & 92.2 & 94.9 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of time and success rate of grasping five parts before and after optimization.  
can be finely optimized. The model can be optimized while maintaining its smoothness of the model. The formula for the adaptive weight reduction method can be defined as  
\[\begin{array}{l}\omega=\frac{\sum_{i=0}^{n}P_{i}\mathbf{\omega}_{i}}{\sum_{i=0}^{n} P_{i}}\\ W=k_{W}\times(\omega\cdot n)+(1-k_{W})\times\left[1-\frac{\max(l_{1},l_{2},l_{3} )}{l_{1}+l_{2}+l_{3}}\right]\end{array} \tag{21}\]  
\[k_{W}=k\bigg{(}\frac{W}{W_{\max}-W_{\min}}+1\bigg{)} \tag{22}\]  
where \(P_{i}\) is the area of the triangle; \(n\) is the normal vector of the triangle; \(l_{1}\), \(l_{2}\), \(l_{3}\) is the length of the three sides of the triangle; \(W\) is the weight size; \(k_{W}\) is the dynamic weight; \(k\) is the base weight size, assuming the values \([0,1]\).  
After the calculation according to Equation (21), the triangles with larger weights are deleted, and the weights are recalculated according to Equation (22) after completion.  
The following is an example of a joint of a six-degree-of-freedom robot arm, which was optimized using this algorithm, and the test results are shown in Figure 19.  
The result of the comparison shows that the number of points and surfaces of the model is greatly reduced without changing the shape and effect of the model, and the optimization efficiency is increased by 92.51%. This proves the effectiveness of the algorithm.