# Orbital-Based Automatic Multi-Layer Multi-Pass Welding Equipment for Small Assembly Plates
## 3 Equipment Debugging and Simulation Analysis
### Debugging of the Robotic Arm
Under the world coordinate system, the robotic arm is operated to sequentially collect and record the position and posture information of the TCP relative to the calibration object. This calibration algorithm uses the J5 axis as the main control axis. In Figure 19a, the TCP  
Figure 18: Schematic of Euler angle rotation. of the robotic arm needs to be perpendicular to the calibration object when taking points. In Figure 19b-h, A and B represent the rotational directions around the X and Y axes in the robotic arm's world coordinate system, and the new posture changes are made as large as possible compared to the previous ones. After point acquisition is completed, calculate the errors. Once they are within the allowable range, operate the robotic arm under the world coordinate system to make its TCP perpendicular to the calibration object and rotate the robotic arm around the A, B, and C axes to check the degree of alignment. Upon passing the verification, the TCP calibration is completed. The smaller the calibration error, the higher the working efficiency and precision of the robotic arm, except when there are errors in the robotic arm itself. In automatic welding technology, visual sensors are an important component driving the development of intelligent welding [19]. As the \"eyes\" of robotic arms, visual sensors are also a necessary means of assisting operations [20; 21]. Next, we will complete the solution and calibration of the transformation relationship of the laser sensor to achieve precise perception of position and orientation, ensuring the accuracy and stability of scanning recognition. First, we introduce the laser sensor model and use its intrinsic and extrinsic parameter matrices for solving. Both map points from the 3D world to the 2D image plane, i.e., conversion between dimensions. The intrinsic parameters \(IP\), related to the internal characteristics of the laser sensor, can be represented as follows (14):  
\[\textbf{IP}= \begin{bmatrix}f&0&x_{0}\\ 0&f&y_{0}\\ 0&0&1\end{bmatrix}  \tag{14}\]  
The extrinsic parameters describe the position and orientation of the laser sensor in the world coordinate system, allowing for the transformation from world coordinates to laser sensor coordinates. That is, the extrinsic parameters are \(EP=H\). Based on the derivation of the relationship between intrinsic and extrinsic parameters, after performing homogenization operations on the point \(p(u_{0}\,,v_{0})\) from the 2D image plane and its spatial coordinates \(p(x_{0}\,,y_{0}\,,z_{0})\), we obtain the model of the laser sensor, represented as (15). \[\lambda \begin{bmatrix}u_{0}\\ 0\\ v_{0}\\ 1\end{bmatrix} =\textbf{IP}\cdot\textbf{EP}\cdot \begin{bmatrix}x_{0}\\ y_{0}\\ z_{0}\\ 1\end{bmatrix} \quad\textbf{or}\quad\lambda \begin{bmatrix}u_{0}\\ 0\\ v_{0}\\ 1\end{bmatrix} = \begin{bmatrix}f&0&x_{0}\\ 0&f&y_{0}\\ 0&0&1\end{bmatrix}\begin{bmatrix}r_{11}&r_{12}&r_{13}&t_{x}\\ r_{21}&r_{22}&r_{23}&t_{y}\\ r_{31}&r_{32}&r_{33}&t_{z}\\ 0&0&0&1\end{bmatrix}\begin{bmatrix}x_{0}\\ y_{0}\\ z_{0}\\ 1\end{bmatrix}  \tag{15}\]  
Figure 19: Robotic arm TCP eight-point calibration diagram. In (15), \(\lambda\) refers to degrees of freedom. During the process of moving from 3D space (laser sensor coordinates) to 2D space (captured image coordinates), one degree of freedom is reduced, particularly depth. The intrinsic parameters focal length (\(\lambda\)) and principal point \(c_{0}(x_{0},y_{0})\) are provided by the laser sensor. Subsequently, combining the above matrices to solve for the extrinsic parameters, this paper obtains \(CHT\) by utilizing the projection information of five different calibration points.