# An Improved NSGA-II-Based Method for Cutting Trajectory Planning of Boom-Type Roadheader
## 5 Conclusions  
(1) A kinematic model of the boom-type roadheader was established to achieve coordinate transformation among the roadheader, target section, and roadway. By simplifying the cutting head model using segmented curves and establishing a section constraint model, a cutting space driven by the body pose was designed. Within this space, cutting trajectory points that meet the requirements for sectional forming cutting were obtained.  
(2) A bi-objective optimization function was designed for the total length and total turning angle of the cutting trajectory, and an improved NSGA-II algorithm was used to solve for executable cutting trajectories. A simulation and experimental validation platform was built to verify the superiority of the improved algorithm. Additionally, a virtual simulation platform for trajectory tracking was used to verify the effectiveness of the cutting trajectories under different body poses, ensuring high forming quality.  
(3) A trajectory-tracking experimental platform was built. The experimental results show that the cutting trajectory tracking is effective, with a maximum deviation of 23.879 mm, which can effectively support autonomous cutting control. This method not only provides effective cutting trajectories for autonomous cutting but also avoids frequent inverse kinematics solutions during the control process, improving computational efficiency and laying a foundation for autonomous control of sectional forming cutting.  
(4) Future work will focus on enhancing the adaptability of the proposed method to more complex roadway conditions, including variable cross-sections and irregular geological environments. Additionally, the trajectory-planning approach will be further optimized to improve computational efficiency and real-time performance for practical applications.  
Figure 23: Comparative analysis and error of tracking paths in various directions. (**a**) Trajectory comparison and deviation in \(x\)-axis. (**b**) Trajectory comparison and deviation in \(y\)-axis. (**c**) Trajectory comparison and deviation in \(z\)-axis.  
**Author Contributions:** Conceptualization, C.Z. and X.Z.; Methodology, C.Z. and X.Z.; Software, W.Y. and J.W.; Validation, S.T. and Z.W.; Formal analysis, G.Z.; Investigation, C.Z.; Resources, C.Z.; Data curation, C.Z. and Y.D.; Writing--original draft, C.Z.; Writing--review & editing, X.Z.; Project administration, X.Z.; Funding acquisition, W.Y. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 52104166), the Natural Science Foundation of Shaanxi Province (Grant No. 2021 JLM-03), the China Postdoctoral Science Foundation funded project (No. 2022 MD723826) and Key R & D project in Shaanxi (No. 2023-YBGY-063).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.