A robot welding trajectory correction method based on optical low-coherence technology

Abstract

The present invention relates to the technical field of industrial robot welding, and in particular to a robot welding trajectory correction method based on optical low-coherence technology, comprising the following steps: step one, static path finding, the robot completes the extraction of weld trajectory and the optimization of weld trajectory; step two, dynamic deviation correction, the robot completes the real-time deviation correction of weld trajectory; the entire weld trajectory extraction and optimization process has higher accuracy and robustness, and the three-dimensional coordinate information of the weld is obtained by optical low-coherence measurement technology, and the real-time measurement of the weld contour is realized according to the characteristics of the weld contour line. The entire deviation correction process can achieve a cycle of 4ms, and a single deviation correction is controlled within 0.5mm, which meets the real-time nature of the deviation correction and the accuracy of welding, and improves the fitting degree between the welding trajectory and the actual weld trajectory.

Description

Technical Field

[0001] The invention relates to the technical field of industrial robot welding, and in particular to a robot welding trajectory correction method based on optical low-coherence technology. Background Art

[0002] Robot welding is one of the main material processing technologies in the modern industrial field and is widely used in industrial production such as aerospace, transportation, machinery, electronics, energy and chemical industry. However, at present, the robot's weld trajectory planning is mainly completed through the "teaching-reproduction" operation mode, which requires re-planning for different test pieces, and the teaching effect is mainly determined by the experience of the instructor, and it is impossible to make real-time feedback adjustments according to changes in the type, size and position of the workpiece. How to achieve autonomous weld identification, autonomous planning of welding trajectories and real-time correction is the main direction of current research.

[0003] Optical low-coherence measurement technology is based on the principle of optical coherence tomography technology. It has the characteristics of non-destructive, non-contact, and high resolution. It has discovered great application potential in medical testing, material testing and other work. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide an efficient robot welding trajectory correction method based on optical low-coherence technology, which controls an industrial robot to achieve precise static guidance and real-time dynamic deviation correction of the welding trajectory.

[0005] In order to solve the above technical problems, the technical solution of the present invention is: a robot welding trajectory correction method based on optical low coherence technology, comprising the following steps:

[0006] Step 1: Static path finding: the robot statically guides the extraction and optimization of the weld trajectory:

[0007] After the robot carries the optical low-coherence measurement module and moves to the position above the workpiece to be welded, it obtains the three-dimensional coordinate information of the weld with the support and guidance of the optical low-coherence measurement technology, and completes the extraction of the weld trajectory through real-time measurement of the weld contour;

[0008] The host optimizes the weld trajectory obtained by the robot to obtain a proposed welding trajectory;

[0009] Step 2: Dynamic deviation correction: the robot completes the real-time deviation correction of the weld trajectory:

[0010] During the movement of the robot according to the planned welding trajectory, the robot's movement trajectory is corrected in real time according to the deviation between the weld trajectory synchronously extracted by the optical low-coherence measurement module and the planned welding trajectory.

[0011] As a preferred technical solution, the optical low-coherence measurement module includes a broadband light source. The light beam emitted by the broadband light source is divided into two beams after passing through a fiber optic coupler, one beam enters a reference arm, and the other beam enters a sample arm and is focused on the workpiece to be welded. The light beam reflected from the surface and interior of the workpiece to be welded returns to the fiber optic coupler and is reintegrated into a light beam with the light beam returned from the reference arm. The integrated light beam then enters a spectrometer for analysis. The spectrometer transmits the analyzed data to a computer, and the computer obtains the profile information of the weld surface after calculation.

[0012] As a preferred technical solution, in step 1, the extraction of the weld trajectory includes the following steps:

[0013] Step 11: Establish TCP / IP communication between the host and the robot;

[0014] Step 12: Roughly teach the placement of the workpiece to be welded;

[0015] Step 13: After the robot moves to the teaching point according to the result of the rough teaching, it returns to the current tool posture;

[0016] Step 14: the host receives the current tool posture and calls the optical low-coherence measurement module to obtain the weld trajectory in the camera coordinate system;

[0017] Step 15: According to the current tool posture of the robot and the hand-eye calibration matrix, the weld coordinates in the robot coordinate system, i.e., the weld trajectory, are converted;

[0018] In the step 1, the optimization of the weld trajectory includes the following steps:

[0019] Step 16: The host side optimizes the weld trajectory using a cubic spline interpolation algorithm to obtain the proposed welding trajectory;

[0020] Step 17: Send the proposed welding trajectory to the robot for trajectory verification.

[0021] As a preferred technical solution, in step 12, the role of the rough teaching is only to determine the placement space of the workpieces to be welded.

[0022] As a preferred technical solution, in the step 1, the optimization of the weld trajectory aims to reduce the excessive change in the movement speed of the robot caused by the excessive curvature of a certain trajectory point, thereby adversely affecting the welding effect;

[0023] In step 16, the specific implementation steps of the cubic spline interpolation algorithm are:

[0024] Assume that there are n+1 data nodes (x0, y0), (x1, y1), …, (x n ,y n )

[0025] Step 161: Calculate step length h i =x i+1 -x i

[0026] Step 162: Substitute the data into the matrix equation under natural boundary conditions

[0027]

[0028] Step 163: Solve the matrix equation to obtain m i , use Gaussian elimination method to perform LU decomposition on the coefficient matrix, that is

[0029] B=Ax=(LU)x=L(Ux)=Ly;

[0030] Step 164: Calculate spline coefficients

[0031] a i =y i

[0032]

[0033]

[0034]

[0035] Step 165: In each subinterval x i ≤x≤x i+1 , create the equation

[0036] g i (x) = a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 ;

[0037] Step 166: extracting a suitable number of interpolation points on the curve of each sub-interval;

[0038] Step 167: Integrate the information of the interpolation points extracted in three dimensions to obtain the proposed welding trajectory in three-dimensional space:

[0039] [X,Y,Z] track=[CS(x),CS(y),CS(z)].

[0040] As a preferred technical solution, in step 2, the purpose of dynamic deviation correction is to correct the deviation between the proposed welding trajectory and the actual weld trajectory; specifically, the following steps are included:

[0041] Step 21: Complete the construction that meets the requirements of the weld correction task;

[0042] Step 22: the robot starts welding according to the welding planned trajectory in step 167;

[0043] Step 23: Starting from the starting point of the proposed welding trajectory, the robot periodically returns the current tool posture and timestamp;

[0044] Step 24: the host receives the current tool posture and timestamp of the robot, and calls the optical low-coherence measurement module to synchronously collect the deviation of the next unwelded trajectory position point from the proposed welding trajectory;

[0045] Step 25: Perform the same coordinate conversion operation as in step 14 and step 15, and send the deviation in the converted robot coordinate system to the robot for real-time correction until it moves to the end point of the planned welding trajectory.

[0046] Due to the adoption of the above technical solution, a robot welding trajectory correction method based on optical low-coherence technology includes the following steps:

[0047] Step 1: static path finding. The robot statically guides the extraction and optimization of the weld trajectory: after the robot carries the optical low-coherence measurement module and moves above the placement position of the workpiece to be welded, it obtains the three-dimensional coordinate information of the weld under the support and guidance of the optical low-coherence measurement technology, and completes the extraction of the weld trajectory by real-time measurement of the weld contour; the host optimizes the weld trajectory obtained by the robot to obtain the proposed welding trajectory;

[0048] Step 2: Dynamic deviation correction: the robot completes the real-time deviation correction of the weld trajectory:

[0049] During the movement of the robot according to the proposed welding trajectory, the robot's running trajectory is corrected in real time according to the deviation between the weld trajectory synchronously extracted by the optical low-coherence measurement module and the proposed welding trajectory; the beneficial effect of the present invention is: with the support of optical low-coherence technology, an efficient weld tracking method is designed to control the industrial robot to achieve accurate static path finding and real-time dynamic deviation correction of the weld trajectory. The weld tracking method consists of two stages, the first stage is static path finding before welding, and the second stage is dynamic deviation correction during welding. The entire static path finding before welding can be regarded as a precise teaching process. Unlike traditional teaching, although the rough teaching step also requires manual intervention, its role is only to determine the placement space of the workpiece to be welded, and it does not need to be repeated many times. The extraction of the proposed welding trajectory is automatically completed with the support of optical low-coherence technology, and can be completed adaptively in the face of changes in the type, size and welding environment of the workpiece to be welded. The entire precise teaching process has higher accuracy and robustness than traditional teaching. The three-dimensional coordinate information of the weld is obtained by using optical low-coherence measurement technology, and the real-time measurement of the weld contour can be achieved according to the characteristics of the weld contour line. The entire dynamic correction process can be achieved in a cycle of 4ms, and the single correction is controlled within 0.5mm, which can fully meet the real-time correction and the accuracy of laser welding, and further improve the fitting degree between the welding trajectory and the actual weld trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] The following drawings are intended only to illustrate and explain the present invention, and do not limit the scope of the present invention.

[0051] Figure 1 is a schematic structural diagram of an optical low-coherence measurement module according to an embodiment of the present invention;

[0052] Figure 2 This is a flow chart of the robot statically guiding the extraction of weld seam trajectories and the optimization of weld seam trajectories in step 1 of an embodiment of the present invention;

[0053] Figure 3 3. It is a comparison diagram of the weld trajectory optimization effect before and after the optimization obtained by the two-dimensional cubic spline interpolation algorithm of the embodiment of the present invention;

[0054] Figure 4 This is a partial enlarged diagram comparing the effects before and after the optimization of the weld trajectory obtained by the two-dimensional cubic spline interpolation algorithm in the embodiment of the present invention;

[0055] Figure 5 3. It is a comparison diagram of the weld trajectory optimization effect before and after obtained by the three-dimensional cubic spline interpolation algorithm of the embodiment of the present invention;

[0056] Figure 6 This is a partial enlarged diagram comparing the effects before and after the optimization of the weld trajectory obtained by the three-dimensional cubic spline interpolation algorithm in the embodiment of the present invention;

[0057] Figure 7 This is a flowchart of the real-time deviation correction of the welding seam trajectory by the robot in step 2 of the embodiment of the present invention;

[0058] Figure 8 It is a schematic diagram of RSI context construction required by the weld deviation correction task in an embodiment of the present invention;

[0059] Fig. 9 It is a schematic diagram of the overall process of a robot welding trajectory correction method based on optical low-coherence technology of the present invention.

[0060] In the figure: 1- broadband light source; 2- spectrometer; 3- fiber coupler; 4- computer; 5- sample arm; 6- reference arm; 7- collimator; 8- confocal mirror; 9- galvanometer; 10- plane mirror; 11- processing laser; 12- workpiece to be welded. DETAILED DESCRIPTION

[0061] The present invention is further described below in conjunction with the accompanying drawings and examples. In the following detailed description, certain exemplary embodiments of the present invention are described only by way of illustration. Needless to say, those of ordinary skill in the art will recognize that the described embodiments may be modified in various ways without departing from the spirit and scope of the present invention. Therefore, the drawings and description are illustrative in nature and are not intended to limit the scope of protection of the claims.

[0062] like Figures 1 to 9 As shown in the figure, a robot welding trajectory correction method based on optical low coherence technology includes the following steps:

[0063] Step 1: Static path finding: the robot statically guides the extraction and optimization of the weld trajectory:

[0064] After the robot carries the optical low-coherence measurement module and moves to the position above the workpiece 12 to be welded, the robot obtains the three-dimensional coordinate information of the weld under the support and guidance of the optical low-coherence measurement technology, and completes the extraction of the weld trajectory through real-time measurement of the weld contour;

[0065] The host optimizes the weld trajectory obtained by the robot to obtain a proposed welding trajectory;

[0066] Step 2: Dynamic correction, real-time correction of the robot’s weld trajectory: During the robot’s movement along the planned welding trajectory, the robot performs real-time correction based on the deviation synchronously extracted by the optical low-coherence measurement module.

[0067] The present invention aims to design an efficient weld tracking method under the support of optical low-coherence technology, and control the industrial robot to realize accurate static path finding and real-time dynamic deviation correction of the weld trajectory. In the process of the robot moving according to the proposed welding trajectory, the robot's running trajectory is corrected in real time according to the deviation between the weld trajectory synchronously extracted by the optical low-coherence measurement module and the proposed welding trajectory; the weld tracking method consists of two stages, the first stage is static path finding before welding, and the second stage is dynamic deviation correction during welding. The entire static path finding before welding can be regarded as a precise teaching process. Unlike traditional teaching, although the rough teaching step also requires manual intervention, its role is only to determine the placement space of the workpiece 12 to be welded, and it does not need to be repeated many times. The extraction of the proposed welding trajectory is automatically completed with the support of optical low-coherence technology, and can be completed adaptively in the face of changes in the type, size and welding environment of the workpiece 12 to be welded. The entire precise teaching process has higher accuracy and robustness than traditional teaching. The three-dimensional coordinate information of the weld is obtained by using optical low-coherence measurement technology, and the real-time measurement of the weld contour can be achieved according to the characteristics of the weld contour line. The entire dynamic correction process can be achieved in a cycle of 4ms, and the single correction is controlled within 0.5mm, which can fully meet the real-time correction and the accuracy of laser welding, and further improve the fitting degree between the welding trajectory and the actual weld trajectory.

[0068] like Figure 1 As shown, the optical low coherence measurement module includes a broadband light source 1. The light beam emitted by the broadband light source 1 is divided into two beams after passing through the fiber coupler 3. One beam enters the reference arm 6, passes through the collimator 7 and the plane mirror 10 in sequence, and then is reflected back. The other beam enters the sample arm 5, passes through the confocal mirror 8 and the collimator 7 in sequence, and is focused to the workpiece 12 to be welded under the reflection of the galvanometer 9. The light beam reflected from the surface and the interior of the workpiece 12 to be welded returns to the fiber coupler 3, and is re-integrated into a light beam with the light beam returned from the reference arm 6. Then the integrated light beam enters the spectrometer 2 for analysis. When the two returning light beams have the same frequency, the same vibration direction, and the phase difference is within a certain range, a low coherence phenomenon will occur. The spectrometer 2 transmits the analyzed data to the computer 4. The computer 4 obtains the profile information of the weld surface after calculation, and the processing laser 11 performs welding work on the workpiece 12 to be welded according to the instructions. The optical low-coherence measurement module is used to extract the weld trajectory, and the three-dimensional coordinate information of the weld is obtained by using the optical low-coherence measurement technology. According to the characteristics of the weld contour line, the real-time measurement of the weld contour can be realized.

[0069] like Figures 2 to 6 As shown together, in the step 1, the extraction of the weld trajectory includes the following steps:

[0070] Step 11: Establishing TCP / IP communication between the host and the robot; in this embodiment, the TCP / IP communication between the host and the robot is established through Ethernet KRL;

[0071] Step 12: roughly teach the placement position of the workpiece 12 to be welded;

[0072] Step 13: After the robot moves to the teaching point according to the result of the rough teaching, it returns to the current tool posture;

[0073] Step 14: the host receives the current tool posture and calls the optical low-coherence measurement module to obtain the weld trajectory in the camera coordinate system;

[0074] Step 15: According to the current tool posture of the robot and the hand-eye calibration matrix, a weld trajectory in the robot coordinate system is converted, that is, a weld trajectory;

[0075] The robot is preferably a KUKA robot. The KUKA.EthernetKRL software package provides a function of bidirectional communication with the robot controller through the network. The TCP / IP protocol is used to communicate through the server and client. The network transmission is configured through XML, and the transmission content is also in XML format. The communication delay is less than 2ms. Therefore, tasks with relatively high real-time requirements can be performed.

[0076] In the step 1, the optimization of the weld trajectory includes the following steps:

[0077] Step 16: The host side optimizes the weld trajectory using a cubic spline interpolation algorithm to obtain the proposed welding trajectory;

[0078] Step 17: Send the proposed welding trajectory to the robot for trajectory verification.

[0079] The weld trajectory extracted by the optical low-coherence measurement module from the preliminary measurement is composed of straight lines connecting the trajectory points. In order to reduce the impact on the welding effect caused by excessive changes in the robot's movement speed due to excessive curvature of a certain trajectory point, the present invention uses a cubic spline interpolation algorithm to optimize the proposed trajectory to make it more suitable for the robot's movement mode and improve the welding quality.

[0080] like Figure 2 As shown, in step 12, the role of the coarse teaching is only to determine the placement space of the workpiece 12 to be welded. It does not need to be repeated multiple times. The extraction of the weld trajectory is automatically completed with the support of optical low-coherence technology, and can be completed adaptively in the face of changes in the type, size and welding environment of the workpiece. The whole process has higher accuracy and robustness than traditional coarse teaching.

[0081] In the step 1, the purpose of optimizing the weld trajectory is to reduce the excessive change in the movement speed of the robot caused by the excessive curvature of a certain trajectory point, thereby reducing the adverse effect on the welding effect; the optimized weld trajectory is more in line with the movement mode of the robot, thereby improving the welding quality.

[0082] In step 16, the specific implementation steps of the cubic spline interpolation algorithm are:

[0083] Assume that there are n+1 data nodes (x0, y0), (x1, y1), …, (x n ,y n )

[0084] Step 161: Calculate step length h i =x i+1 -x i

[0085] Step 162: Substitute the data into the matrix equation under natural boundary conditions

[0086]

[0087] Step 163: Solve the matrix equation to obtain m i , use Gaussian elimination method to perform LU decomposition on the coefficient matrix, that is

[0088] B=Ax=(LU)x=L(Ux)=Ly;

[0089] Step 164: Calculate spline coefficients

[0090] a i =y i

[0091]

[0092]

[0093]

[0094] Step 165: In each subinterval x i ≤x≤x i+1 , create the equation

[0095] g i (x) = a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3;

[0096] Step 166: extracting a suitable number of interpolation points on the curve of each sub-interval;

[0097] Step 167: Integrate the information of the interpolation points extracted in the three dimensions to obtain the proposed welding trajectory in the three-dimensional space: for the interpolation of the three-dimensional trajectory, the parameters of the three dimensions are separated in equal steps according to the point order, and after performing cubic spline interpolation respectively, the interpolation point information extracted in the three dimensions is integrated to obtain the optimized proposed trajectory in the three-dimensional space.

[0098] [X,Y,Z] track =[CS(x),CS(y),CS(z)].

[0099] from Figures 3 to 6 It can be seen that the trajectory after optimization by the cubic spline interpolation algorithm is smoother and more reasonable, and more suitable for the robot to perform welding movements.

[0100] like Figure 2 , Figure 7 , Figure 8 and Fig. 9 As shown in the figure, in step 2, the purpose of dynamic correction is to correct the deviation between the proposed welding trajectory and the actual weld trajectory; specifically, the following steps are included:

[0101] Step 21: Complete the construction that meets the requirements of the weld correction task; mainly includes the construction of the RSI context, such as Figure 8 shown.

[0102] Step 22: the robot starts welding according to the welding planned trajectory in step 167;

[0103] Step 23: Starting from the starting point of the proposed welding trajectory, the robot periodically returns the current tool posture and timestamp;

[0104] Step 24: the host receives the current tool posture and timestamp of the robot, and calls the optical low-coherence measurement module to synchronously collect the deviation of the next unwelded trajectory position point from the proposed welding trajectory;

[0105] Step 25: Perform the same coordinate conversion operation as in step 14 and step 15, and send the deviation in the converted robot coordinate system to the robot for real-time correction until it moves to the end point of the welding planned welding trajectory.

[0106] The entire correction process can be completed in a cycle of 4ms, and a single correction is controlled within 0.5mm, which can fully meet the real-time correction and welding accuracy. In this embodiment, laser welding is taken as an example for explanation. Other welding methods are also within the protection scope of the present invention, which further improves the fit between the welding trajectory and the actual weld trajectory.

[0107] The technical features of the software and circuit programs involved in this application belong to the prior art in terms of the implementation of their functions. The essence of the technical solution of this application is the improvement of the composition and connection relationship of the hardware part, and does not involve improvements to the software program or circuit structure itself.

[0108] In the description of the present invention, it is necessary to understand that the terms "upper", "lower", "front", "back", "left", "right", "top", "bottom", "inside", "outside", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention.

[0109] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A robot welding trajectory correction method based on optical low-coherence technology, characterized in that: The steps include: Step 1: Static path finding: the robot statically guides the extraction and optimization of the weld trajectory: After the robot carries the optical low-coherence measurement module and moves to a position above the workpiece (12) to be welded, the robot obtains the three-dimensional coordinate information of the weld under the support and guidance of the optical low-coherence measurement technology, and completes the extraction of the weld trajectory by real-time measurement of the weld contour; The host optimizes the weld trajectory obtained by the robot to obtain a proposed welding trajectory; Step 2: Dynamic deviation correction: the robot completes the real-time deviation correction of the weld trajectory: During the movement of the robot according to the planned welding trajectory, the robot's running trajectory is corrected in real time according to the deviation between the weld trajectory synchronously extracted by the optical low-coherence measurement module and the planned welding trajectory; In the step 1, the extraction of the weld trajectory includes the following steps: Step 11: Establish TCP / IP communication between the host and the robot; Step 12: roughly teach the placement position of the workpiece (12) to be welded; Step 13: After the robot moves to the teaching point according to the result of the rough teaching, it returns to the current tool posture; Step 14: the host receives the current tool posture and calls the optical low-coherence measurement module to obtain the weld trajectory in the camera coordinate system; Step 15: According to the current tool posture of the robot and the hand-eye calibration matrix, the weld coordinates in the robot coordinate system, i.e., the weld trajectory, are converted; In the step 1, the optimization of the weld trajectory includes the following steps: Step 16: The host side optimizes the weld trajectory using a cubic spline interpolation algorithm to obtain the proposed welding trajectory; Step 17: Sending the proposed welding trajectory to the robot for trajectory verification; In the step 2, the purpose of dynamic deviation correction is to correct the deviation between the proposed welding trajectory and the actual weld trajectory; The specific steps include: Step 21: Complete the construction that meets the requirements of the weld correction task; Step 22: the robot starts welding according to the corrected welding planned trajectory; Step 23: Starting from the starting point of the proposed welding trajectory, the robot periodically returns the current tool posture and timestamp; Step 24: the host receives the current tool posture and timestamp of the robot, and calls the optical low-coherence measurement module to synchronously collect the deviation of the next unwelded trajectory position point from the proposed welding trajectory; Step 25: Perform the same coordinate conversion operation as in step 14 and step 15, and send the deviation in the converted robot coordinate system to the robot for real-time correction until it moves to the end point of the planned welding trajectory.

2. The robot welding trajectory correction method based on optical low-coherence technology as claimed in claim 1, characterized in that: The optical low-coherence measurement module comprises a broadband light source (1). The light beam emitted by the broadband light source (1) is divided into two beams after passing through a fiber coupler (3), one beam entering a reference arm (6), and the other beam entering a sample arm (5) and focused onto a workpiece to be welded (12). The light beam reflected from the surface and the interior of the workpiece to be welded (12) returns to the fiber coupler (3) and is re-integrated with the light beam returned from the reference arm (6) into a light beam. The integrated light beam then enters a spectrometer (2) for analysis. The spectrometer (2) transmits the analyzed data to a computer (4). The computer (4) obtains the profile information of the weld surface after calculation.

3. The robot welding trajectory correction method based on optical low-coherence technology as claimed in claim 1, characterized in that: In the step 12, the role of the rough teaching is only to determine the placement space of the workpiece (12) to be welded.

4. The robot welding trajectory correction method based on optical low-coherence technology as claimed in claim 1, characterized in that: In the step 1, the optimization of the weld trajectory aims to reduce the excessive change in the movement speed of the robot caused by the excessive curvature of a certain trajectory point, thereby adversely affecting the welding effect; In step 16, the specific implementation steps of the cubic spline interpolation algorithm are: Assume that there are n+1 data nodes (x0, y0), (x1, y1), …, (x n ,y n ) Step 161: Calculate step length h i =x i+1 -x i Step 162: Substitute the data into the matrix equation under natural boundary conditions Step 163: Solve the matrix equation to obtain m i , use Gaussian elimination method to perform LU decomposition on the coefficient matrix, that is B=Ax=(LU)x=L(Ux)=Ly; Step 164: Calculate spline coefficients to i =and i Step 165: In each subinterval x i ≤x≤x i+1 , create the equation g i (x)=a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 ; Step 166: extracting a suitable number of interpolation points on the curve of each sub-interval; Step 167: Integrate the information of the interpolation points extracted in three dimensions to obtain the proposed welding trajectory in three-dimensional space: [X,Y,Z] track =[CS(x),CS(y),CS(z)]。

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