## 5 Conclusions  
This study introduces a comprehensive and practical pipeline designed for accurately detecting rebar crossing points and automating path planning for robotic operations in  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Metric** & **Value** \\ \hline Detection accuracy & \(>\)99\% \\ Detection time per crossing point & \(<\)125 ms \\ Maximum coordinate transformation error & \(<\)2 mm \\ \hline \hline \end{tabular}
\end{table}
Table 4: Performance metrics of the rebar crossing point detection and localization system.  
Figure 15: Detection and path planning results for rebar crossing points. Red labels indicate the identification index and confidence at each detected intersection. The planned sequence ensures full coverage with minimal path redundancy.  
construction settings. Through meticulous camera calibration, both intrinsic and extrinsic parameters were precisely determined, enabling reliable transformations from image coordinates to the robot's control coordinate frame. Reprojection errors were maintained at sub-pixel levels, confirming the robustness and accuracy of the calibration procedure.  
Structured probing experiments further demonstrated that the coordinate transformations achieved millimeter-level precision, with maximum errors within 2 mm.  
The proposed RGB-D vision system effectively detects intersection points within grid-structured steel reinforcements and converts the detected pixel coordinates into precise three-dimensional robot coordinates using calibrated extrinsic parameters. The path planning component redefines the problem as a sequencing optimization task and applies a greedy algorithm to generate efficient snake-like trajectories, ensuring high coverage efficiency, smooth manipulator motion, and low computational cost. Experimental results verified that the system consistently achieves detection accuracy above 99%, with average processing times below 125 ms per point and transformation errors under 2 mm, thus meeting practical requirements for robotic rebar tying tasks.  
While these results demonstrate strong feasibility and reliability in semi-controlled test scenarios, challenges remain in scaling the system for deployment on large and dynamic construction sites with varying lighting, occlusions, and environmental disturbances. To address these challenges and further advance this research, future work will focus on integrating deep learning methods to enhance the semantic understanding of complex rebar arrangements and to improve detection robustness in the presence of occlusions and clutter. Additionally, incorporating multi-sensor fusion and adaptive calibration techniques will be explored to increase system resilience and accuracy under changing on-site conditions.  
This work lays a solid foundation for the intelligent automation of rebar tying and contributes valuable insights towards broader applications of robotic systems in the construction industry.  
C.L.: Writing--original draft, Conceptualization, Methodology, Software, Validation, Investigation, Data curation. W.Z.: Writing--review and editing, Supervision, Resources, Funding acquisition. F.L.: Project administration. M.G.: Investigation, Data curation. S.F.: Visualization. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Technology and Development Joint Research Foundation of Henan Province (Grant No. 225200810070).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.