## 4 Experiments
### Rebar Crossing Point Detection and Path Planning  
To accurately identify the positions of rebar intersection points, the proposed system utilizes RGB-D images captured by the calibrated camera. The 2D pixel coordinates of each detected crossing point are first extracted using a vision-based detection module. These pixel coordinates are then transformed into 3D positions in the robot base frame using the previously obtained extrinsic parameters.  
The path planning objective is to visit each detected rebar crossing point in a collision-free grid environment, ensuring complete coverage and execution efficiency. Since the detection results are represented in pixel coordinates, the original spatial planning problem is transformed into an ordered sequencing problem over the detected pixel points. The sequence determines the order in which the robot performs tasks (e.g., tying) at each intersection.  
To ensure that the manipulator maintains stable motion while minimizing total traversal time, a greedy algorithm is employed to optimize a snake-like path. This path offers efficient area coverage with low computational complexity and high stability--qualities especially desirable in repetitive industrial tasks such as automated rebar tying.  
Figure 15 shows the output of the crossing point detection and the corresponding optimized path planning sequence. Each labeled grid cell contains a detected intersection point and its identification index, which serves as the robot's operation order.  
Table 4 summarizes the core performance metrics of the proposed rebar crossing point detection and localization system. In this experiment, a total of 30 RGB-D images were collected, covering 735 rebar crossing points under various grid configurations. The detection algorithm achieves an accuracy exceeding 99% on this dataset, demonstrating stable and reliable performance across different scenarios. The average processing time for each crossing point is below 200 ms, ensuring real-time performance suitable for robotic execution. Furthermore, the maximum observed coordinate transformation error is less than 2 mm, which fully meets the precision requirements for robotic manipulation tasks in construction environments.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Original** & **X-Axis Movement** & **Inaccuracy (mm)** & **Original** & **Y-Axis Movement** & **Inaccuracy (mm)** \\
**Coordinate (mm)** & **50 mm (mm)** & **Coordinate (mm)** & **60 mm (mm)** & **Inaccuracy (mm)** \\ \hline
324.411 & 275.142 & 0.731 & 267.476 & 209.153 & 1.677 \\
202.619 & 153.094 & 0.475 & 267.402 & 208.618 & 1.216 \\
198.508 & 148.855 & 0.347 & 144.848 & 85.973 & 1.125 \\
321.635 & 272.  
Compared to existing rebar tying solutions such as TyBOT, SkyTy, and T-iROBO, the proposed vision-guided system emphasizes cost-effectiveness, adaptability, and scalability rather than maximum binding speed. TyBOT, as a large-scale commercial solution, offers high-speed operation on standard, regular grids but lacks flexibility for confined or irregular sites. SkyTy, as a drone-based approach, provides mobile wire deployment but is limited by payload, precision, and environmental conditions. T-iROBO, as a compact mobile ground robot, is versatile in tight areas but relies on complex path planning and limited battery capacity. In contrast, our system integrates a low-cost RGB-D camera with a robotic arm and robust vision algorithms, achieving over 99% detection accuracy and millimeter-level positioning precision. Moreover, the modular design and generalizable perception pipeline make it scalable to different task sizes and diverse construction environments.