# An Improved NSGA-II-Based Method for Cutting Trajectory Planning of Boom-Type Roadheader
## 3 Simulations and Experiments
### Virtual Simulation of Section Cutting Verification
#### 3.2.2 Comparative Analysis of Virtual Trajectory Tracking  
Based on the cutting trajectory planning results under three poses, we conducted virtual simulations in Unity3D. A unified virtual coordinate system was established, and virtual roadheader models and virtual sections were created. The virtual models were then driven for cutting operations using the obtained joint space motion parameters. By comparing the section forming quality and cutting trajectories, the validity of the cutting trajectories constructed using the proposed method was verified. Figure 16 presents the trajectory tracking and virtual forming effects.  
Figure 18 shows that the virtual cutting trajectories are basically consistent with the planned trajectories. Under the three body poses, the virtual cutting results in good section forming effects, ensuring the quality of the section cutting and precise boundary control.  
In the three poses, deviations exist between the virtual cutting tracking trajectories and the planned trajectories. Therefore, an in-depth analysis of the trajectory tracking errors is required to verify the forming cutting performance of the planned trajectories. To quantify the cutting effect, a forming quality evaluation index, namely the cutting volume ratio, \(P_{FormQuality}\), is proposed.  
\[P_{FormQuality}=\frac{V_{Cutdone}}{V_{all}}\]  
Herein, \(V_{Cutdone}\) denotes the cut volume, and \(V_{all}\) denotes the total section volume. Figure 19 presents a comparison of the cutting quality of section forming in virtual simulations. Under the three poses, the forming quality is good; however, as the pose deviation increases, the forming quality gradually decreases.  
However, it is difficult to directly verify the effectiveness of trajectory planning solely through the forming process and quality. Therefore, it is necessary to compare the recorded virtual cutting trajectories with the planning results. Figure 20 presents comparisons of positions in various directions under three conditions, including data comparisons of cutting trajectories in the X-direction, Y-direction, and Z-direction.  
Figure 20 shows that the coordinate data in each direction are basically consistent. The trajectory tracking results for scenario 1 are: maximum deviation in the X-direction is \(-13\) mm, Y-direction is \(-4\) mm, and Z-direction is \(-6\) mm; for scenario 2: X-direction is \(6\) mm, Y-direction is \(4\) mm, and Z-direction is \(-5\) mm; for scenario 3: X-direction is \(-9\) mm, Y-direction is \(-3\) mm, and Z-direction is \(-5\) mm. In summary, regardless of the boom loader's pose, deviations exist between the virtual cutting trajectory and the planned trajectory, but their trends are consistent. From the perspective of forming quality and motion trend, the improved NSGA-II cutting trajectory planning method proposed in this paper is effective and can guide the automatic control process of the cantilever boom loader.  
Figure 19: Assessment of sectional shaping quality.  
Figure 18: Evaluation of trajectory tracking and virtual shaping quality.