Surface profile analysis method and related equipment for laser multi-axis machining

Abstract

The present invention relates to a surface contour analysis method for laser multi-axis linkage processing and related equipment, comprising the following steps: performing surface reconstruction on the target surface workpiece based on the three-dimensional point cloud data set to obtain a digital surface model; performing shape analysis on the digital surface model to obtain a surface feature descriptor, if the surface feature descriptor does not meet the expected geometric characteristic standard, performing spectral decomposition on the digital surface model based on the surface feature descriptor to obtain a contour feature spectrum; performing path planning on the contour feature spectrum based on geodesic theory to obtain a processing trajectory sequence; performing kinematics solution on the processing trajectory sequence to obtain linkage control parameters of each axis, and adjusting the linkage control parameters of each axis based on the expected geometric characteristic standard, thereby solving the technical problem that the processed surface workpiece cannot meet the expected geometric characteristic standard due to the lack of an effective surface contour analysis method.

Description

Technical Field

[0001] The present invention relates to the technical field of laser multi-axis linkage processing, and in particular to a surface profile analysis method and related equipment for laser multi-axis linkage processing. Background Art

[0002] With the continuous development of modern industrial manufacturing technology, the demand for complex-shaped parts is increasing, especially in industries such as aviation, automobiles, and mold manufacturing, where the requirements for the accuracy and surface quality of curved workpieces are getting higher and higher. Traditional processing methods often fail to meet these high-precision requirements, especially when dealing with three-dimensional surfaces with complex geometric features. As an advanced manufacturing process, laser multi-axis linkage processing technology has attracted much attention because of its ability to achieve high-precision and high-efficiency processing. However, although this technology has many advantages in theory, in practical applications, due to the lack of effective surface profile analysis methods, the processed curved workpieces cannot meet the expected geometric characteristics standards, which not only affects the performance of the product, but also limits the widespread application of laser multi-axis linkage processing technology.

[0003] A major problem that exists at present is that traditional methods often rely on limited data points and simplified mathematical models when performing surface reconstruction and feature extraction, which may lead to the reconstructed digital surface model being inaccurate and unable to truly reflect the actual shape of the workpiece. In addition, due to the lack of in-depth analysis based on differential geometry theory, it is difficult to obtain accurate surface feature descriptors, which makes the subsequent processing path planning lack of scientific basis. Even in some more advanced systems, although the contour feature map can be obtained through spectral decomposition, how to effectively plan the processing trajectory sequence based on geodesic theory is still a problem to be solved. Therefore, the kinematic solution and adjustment of the control parameters of each axis linkage in the existing processing process are often not accurate enough, which affects the final processing effect.

[0004] In order to solve the above problems, a new surface contour analysis method for laser multi-axis linkage processing is proposed, which aims to obtain a more complete three-dimensional point cloud data set through a structured light 3D scanner and obtain a more accurate digital surface model using advanced surface reconstruction technology. On this basis, the differential geometry theory is used to perform a detailed shape analysis of the model to ensure that the obtained surface feature descriptors can truly reflect the geometric characteristics of the workpiece. Then, through the geodesic path planning and dynamic constraint analysis of the contour feature map, the processing trajectory sequence and the linkage control parameters of each axis can be calculated more accurately, thereby improving the accuracy and efficiency of laser multi-axis linkage processing, so that the processed surface workpiece can better meet the design requirements. Summary of the invention

[0005] The main purpose of the present invention is to provide a surface profile analysis method and related equipment for laser multi-axis linkage processing, which solves the technical problem that the processed surface workpiece cannot meet the expected geometric characteristic standards due to the lack of an effective surface profile analysis method.

[0006] To achieve the above object, the present invention provides a surface profile analysis method for laser multi-axis linkage processing, comprising the following steps:

[0007] The target curved workpiece after laser multi-axis linkage processing is scanned by a structured light 3D scanner to obtain a 3D point cloud data set;

[0008] Reconstructing the target curved surface workpiece based on the three-dimensional point cloud data set to obtain a digital curved surface model;

[0009] Performing shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor; if the surface feature descriptor does not meet the expected geometric characteristic standard, performing spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum;

[0010] Performing path planning on the contour feature map based on geodesic theory to obtain a processing trajectory sequence;

[0011] The kinematics of the machining trajectory sequence is solved by dynamic constraint analysis to obtain the linkage control parameters of each axis, and the linkage control parameters of each axis are adjusted based on the expected geometric characteristic standard.

[0012] Furthermore, the structured light 3D scanner is used to scan the target curved workpiece after the laser multi-axis linkage processing to obtain a 3D point cloud data set, including:

[0013] The target curved surface workpiece after laser multi-axis linkage processing is scanned by a structured light 3D scanner to obtain a surface projection stripe pattern of the target curved surface workpiece;

[0014] Phase unwrapping is performed on the surface projected fringe pattern by a phase shift method to obtain phase distribution data; wherein the phase distribution data includes an absolute phase value and a relative phase difference;

[0015] By using the triangulation principle, the surface depth of the target curved workpiece is calculated based on the phase distribution data to obtain an original depth map; wherein the original depth map includes a surface height value and a depth gradient;

[0016] Performing texture enhancement on the original depth map by using bidirectional Gabor filtering to obtain an enhanced surface feature map;

[0017] Performing edge detection on the enhanced surface feature map through an adaptive threshold segmentation algorithm to obtain a contour boundary set; wherein the contour boundary set includes boundary point coordinates and boundary curvature;

[0018] Applying tensor voting technology to extract feature points from the contour boundary set to obtain a key feature point set; wherein the key feature point set includes corner point positions and curvature extreme value points;

[0019] Through the multi-view registration algorithm, the key feature point sets from different viewpoints are fused to obtain a three-dimensional point cloud data set.

[0020] Further, the target curved surface workpiece is reconstructed based on the three-dimensional point cloud data set to obtain a digital curved surface model, including:

[0021] The three-dimensional point cloud data set is hierarchically partitioned by an octree space segmentation algorithm to obtain a set of spatial sub-regions, and a density clustering analysis is performed on the set of spatial sub-regions to obtain a regional feature distribution map; wherein the regional feature distribution map includes a point cloud density gradient, a local curvature change rate, and a boundary jump point position;

[0022] Performing feature extraction on the regional feature distribution map to obtain a local geometric feature group, and performing least squares projection on the local geometric feature group to obtain a feature projection matrix;

[0023] Performing surface fitting on the set of spatial sub-regions based on the feature projection matrix to obtain a surface fitting grid framework, and performing boundary constraint optimization on the surface fitting grid framework to obtain a boundary constraint curve family;

[0024] Performing topological optimization on the surface fitting grid framework based on the boundary constraint curve family to obtain an optimized grid model;

[0025] The optimized grid model is parameterized by discrete Riemann mapping to obtain a parameter domain mapping relationship, and the parameter domain mapping relationship is isometrically transformed to obtain a standardized parameter grid;

[0026] The standardized parameter grid is subjected to NURBS surface construction based on Gregory patches to obtain a rational spline surface equation, and the target surface workpiece is subjected to geometric continuity surface reconstruction based on the rational spline surface equation to obtain a digital surface model.

[0027] Furthermore, the shape analysis of the digital surface model is performed based on differential geometry theory to obtain a surface feature descriptor, including:

[0028] The curvature tensor of the digital surface model is calculated by the Weingarten mapping algorithm to obtain a shape operator matrix, and the shape operator matrix is ​​subjected to eigenvalue decomposition to obtain a surface principal direction field; wherein the surface principal direction field includes a maximum principal curvature direction, a minimum principal curvature direction and a normal curvature distribution;

[0029] Based on the Frenet frame theory, coordinate transformation is performed on the principal direction field of the surface to obtain a parametric expression of the local surface, and geodesic curvature is calculated on the parametric expression of the local surface to obtain an intrinsic geometric feature set;

[0030] The covariant derivative of the intrinsic geometric feature set is calculated by Christoffel symbol to obtain the surface shape change rate, and the surface shape change rate is decomposed into a tensor field to obtain a set of geometric invariants; wherein the set of geometric invariants includes Gaussian curvature, mean curvature and shape factor;

[0031] Based on the Ricci flow theory, a curvature flow evolution analysis is performed on the geometric invariant set to obtain a geometric flow field distribution, and topological features are extracted from the geometric flow field distribution to obtain a singular point distribution map, wherein the singular point distribution map includes a ridge network, a valley network and critical point positions;

[0032] An exterior differential operation is performed on the singular point distribution diagram in a discrete differential form to obtain a surface feature form, and a surface feature descriptor is obtained based on the surface feature form.

[0033] Furthermore, the spectral decomposition of the digital surface model based on the surface feature descriptor to obtain a contour feature spectrum includes:

[0034] Based on the Laplace-Beltrami operator and the surface feature descriptor, the digitized surface model is subjected to spectral decomposition to obtain a feature spectrum sequence;

[0035] Performing opening and closing operations on the feature map sequence through mathematical morphology to obtain a filtered feature map, and performing edge detection on the filtered feature map to obtain a contour line set; wherein the contour line set includes a main contour line, a secondary contour line and a feature point sequence;

[0036] Performing topological reconstruction based on the contour line set to obtain a characteristic network graph; wherein the characteristic network graph includes critical point connection relationships, curvature extreme points and singular point distribution;

[0037] Based on the graph theory optimization method, feature association analysis is performed based on the feature network graph to obtain a profile feature map.

[0038] Furthermore, the path planning is performed on the contour feature map based on the geodesic theory to obtain a processing trajectory sequence, including:

[0039] Using geodesic theory to calculate the distance field of the contour feature map to obtain a geodesic distance field, and performing gradient vector calculation on the geodesic distance field to obtain a geodesic gradient vector field;

[0040] Performing a geodesic path search on the geodesic gradient vector field by a preset fast marching method to obtain an initial geodesic path, and performing path smoothing processing on the initial geodesic path to obtain a smoothed geodesic path;

[0041] The curvature of the smooth geodesic path is calculated by curvature analysis to obtain the curvature distribution of the curve, and the curvature constraint judgment is performed on the curvature distribution of the curve to obtain the curve segment that satisfies the curvature constraint;

[0042] The speed of the curve segment is distributed by a speed planning algorithm to obtain a speed curve, and the acceleration constraint is judged on the speed curve to obtain a processing trajectory segment that satisfies the acceleration constraint;

[0043] Based on a trajectory splicing algorithm, trajectory segment splicing and path planning are performed on the processing trajectory segments to obtain a processing trajectory sequence.

[0044] Furthermore, the kinematic solution of the machining trajectory sequence is performed through dynamic constraint analysis to obtain the linkage control parameters of each axis, including:

[0045] The machining trajectory sequence is subjected to variational analysis through the Hamilton-Jacobi equation to obtain the trajectory energy functional, and the trajectory energy functional is subjected to optimal control solution to obtain a group of motion state equations;

[0046] Based on the Lagrange multiplier method, the motion state equation group is constrained and optimized to obtain a multi-axis coupled dynamic equation, and the multi-axis coupled dynamic equation is numerically integrated to obtain a joint motion parameter set, wherein the joint motion parameter set includes an angular displacement sequence, an angular velocity curve, and an angular acceleration distribution;

[0047] Performing dynamic inversion on the joint motion parameter set through dynamic constraint analysis to obtain a driving torque sequence, and performing harmonic analysis on the driving torque sequence to obtain a frequency domain characteristic spectrum, wherein the frequency domain characteristic spectrum includes amplitude response, phase delay and resonance frequency;

[0048] Reconstructing the frequency domain characteristic spectrum in the time domain based on a Runge-Kutta integrator to obtain an axial motion trajectory, and interpolating and smoothing the axial motion trajectory to obtain a continuous motion curve;

[0049] The continuous motion curve is optimally time-planned by the Pontryagin minimum principle to obtain a synchronous control sequence, and error compensation is performed on the synchronous control sequence to obtain linkage control parameters of each axis.

[0050] The present invention also provides a surface profile analysis device for laser multi-axis linkage processing, comprising:

[0051] A scanning module is used to scan the target curved surface workpiece after laser multi-axis linkage processing through a structured light 3D scanner to obtain a 3D point cloud data set;

[0052] A reconstruction module, used for reconstructing the surface of the target curved workpiece based on the three-dimensional point cloud data set to obtain a digital curved surface model;

[0053] An analysis module, configured to perform shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor; if the surface feature descriptor does not meet the expected geometric characteristic standard, perform spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum;

[0054] A planning module, used for performing path planning on the contour feature map based on geodesic theory to obtain a processing trajectory sequence;

[0055] The solution module is used to perform kinematic solution on the processing trajectory sequence through dynamic constraint analysis to obtain the linkage control parameters of each axis, and adjust the linkage control parameters of each axis based on the expected geometric characteristic standard.

[0056] The present invention also provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any one of the above methods when executing the computer program.

[0057] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the computer program is executed by a processor, the steps of any of the above-mentioned methods are implemented.

[0058] The surface contour analysis method of laser multi-axis linkage processing provided by the present invention comprises the following steps: scanning the target surface workpiece after laser multi-axis linkage processing by a structured light three-dimensional scanner to obtain a three-dimensional point cloud data set; reconstructing the surface of the target surface workpiece based on the three-dimensional point cloud data set to obtain a digital surface model; performing shape analysis on the digital surface model based on differential geometry theory to obtain a surface feature descriptor, if the surface feature descriptor does not meet the expected geometric characteristic standard, performing spectral decomposition on the digital surface model based on the surface feature descriptor to obtain a contour feature spectrum; performing path planning on the contour feature spectrum based on geodesic theory to obtain a processing trajectory sequence; performing kinematics solution on the processing trajectory sequence by dynamic constraint analysis to obtain linkage control parameters of each axis, and adjusting the linkage control parameters of each axis based on the expected geometric characteristic standard. Through the above technical means, the technical problem that the surface workpiece after processing cannot meet the expected geometric characteristic standard due to the lack of an effective surface contour analysis method is solved, and it is achieved that the precise control parameters required for the linkage of each axis can be obtained by performing kinematics solution on the dynamic constraint analysis of the processing trajectory sequence. Moreover, these parameters are adjusted according to the expected geometric characteristic standards, ensuring that each step in the machining process can be executed according to the pre-set requirements, ultimately achieving the beneficial effect of high-quality surface machining effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a schematic diagram of the steps of a surface profile analysis method for laser multi-axis linkage machining in one embodiment of the present invention;

[0060] Figure 2 It is a structural block diagram of a surface profile analysis device for laser multi-axis linkage processing in one embodiment of the present invention;

[0061] Figure 3 It is a schematic block diagram of the structure of a computer device according to an embodiment of the present invention.

[0062] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0064] like Figure 1 As shown, Figure 1 It is a schematic diagram of the steps of a surface profile analysis method for laser multi-axis linkage processing in one embodiment of the present invention;

[0065] In one embodiment of the present invention, a surface profile analysis method for laser multi-axis linkage processing is provided, comprising the following steps:

[0066] Step S1, scanning the target curved surface workpiece after laser multi-axis linkage processing by using a structured light 3D scanner to obtain a 3D point cloud data set.

[0067] Specifically, when implementing the step of "scanning the target curved surface workpiece after laser multi-axis linkage processing by a structured light 3D scanner to obtain a 3D point cloud data set", it is first necessary to prepare a structured light 3D scanner with high precision and good stability. This scanner can emit a specific pattern of light to the target curved surface workpiece and construct detailed information on the surface of the object by capturing the reflected light. For example, in the field of aviation manufacturing, when a complex-shaped aircraft engine component is processed by laser multi-axis linkage, in order to ensure that it meets the design specifications and performance requirements, a structured light 3D scanner will be used to scan it in detail. In the actual operation process, the processed target curved surface workpiece is placed within the working range of the scanner, and the position is adjusted to ensure that the entire workpiece is within the effective detection area of ​​the scanner. Then the scanning program is started, and the structured light 3D scanner will quickly project a series of structured light patterns, such as stripes or spots, onto the target curved surface workpiece according to the predetermined path. As the reflection of light changes at different positions on the workpiece surface, the scanner receiving end can record the information of these changes, and then calculate the position coordinates of each reflection point relative to the scanner, thus forming a large number of discrete data points, namely a 3D point cloud data set. This process is crucial to obtaining high-quality raw data required for subsequent surface reconstruction. Since laser multi-axis machining may cause some subtle but important geometric features to appear on the workpiece, and these features often determine the performance and quality of the final product. Therefore, the 3D point cloud data set obtained by the structured light 3D scanner must have sufficient density and accuracy to truly reflect all the details of the processed surface. For example, in the automotive manufacturing industry, for streamlined parts such as car shells, any slight deviation may affect the aerodynamic performance. Therefore, using a structured light 3D scanner to accurately capture these subtle details not only helps to improve product quality, but also lays a solid foundation for the subsequent establishment of digital surface models based on the data set and deeper surface feature analysis.

[0068] Step S2, reconstructing the target curved surface workpiece based on the three-dimensional point cloud data set to obtain a digital curved surface model.

[0069] Specifically, when implementing the key step of "reconstructing the surface of the target curved workpiece based on the three-dimensional point cloud data set to obtain a digital surface model", it is first necessary to convert a large number of discrete data points, namely the three-dimensional point cloud data set, obtained by the structured light three-dimensional scanner into a continuous and smooth digital surface model. This process involves the application of complex mathematical algorithms and computer graphics technology. For example, in the field of aviation manufacturing, after completing the precise scanning of aircraft engine parts, engineers are faced with a huge database consisting of countless coordinate points. In order for these discrete data points to represent the shape of the actual object in a meaningful way, an appropriate surface reconstruction algorithm must be adopted. Specifically, methods such as radial basis function interpolation, polygon meshing or non-uniform rational B-spline (NURBS) can be used to process these point cloud data. These methods can not only ensure a high degree of consistency between the reconstructed surface and the original scan data, but also generate a smooth surface suitable for further analysis and processing planning. For example, radial basis function interpolation is a technique commonly used to reconstruct continuous surfaces from discrete data points. It can create a surface model that is both faithful to the original data and has good geometric properties by calculating the influence weight of each point on the entire surface. Polygonal meshing is another common reconstruction method, which approximates the surface morphology of the original object by connecting adjacent points to form triangles or polygonal meshes. For application scenarios that require high precision and complex geometric features, such as the design of car shells, NURBS provides a more flexible and powerful tool because they allow the definition of surfaces with arbitrary topological structures and smoothness, which is very suitable for expressing streamlined designs. Once the appropriate reconstruction method is selected, the next step is to consider how to optimize the parameter settings in the reconstruction process to ensure that the final digital surface model can accurately reflect the true geometric characteristics of the target surface workpiece and meet the requirements of subsequent processing path planning. For example, after determining the reconstruction algorithm to be used, some key parameters may need to be adjusted, such as fitting error tolerance, curvature change rate limit, etc., in order to simplify the model complexity as much as possible while ensuring the surface quality. In addition, considering some minor deformations or errors that may be introduced during the laser multi-axis machining process, the surface reconstruction stage also needs to have a certain fault tolerance, which can correct these deviations to a certain extent, so that the reconstructed digital surface model is closer to the actual state of the workpiece. In this way, whether it is a complex-shaped part inside an aircraft engine or a component that requires strict aerodynamic performance such as the outer surface of a car, a high-quality digital surface model can be obtained through this method, providing a solid foundation for subsequent shape analysis, feature extraction, and machining trajectory planning.

[0070] Step S3, performing shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor. If the surface feature descriptor does not meet the expected geometric characteristic standard, performing spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature map.

[0071] Specifically, when implementing the process of "performing shape analysis on the digital surface model based on differential geometry theory to obtain a surface feature descriptor, and if the surface feature descriptor does not meet the expected geometric characteristic standard, then performing spectral decomposition on the digital surface model based on the surface feature descriptor to obtain a contour feature spectrum", it is first necessary to use differential geometry theory to deeply understand and quantify the geometric properties of the digital surface model. For example, in the field of aviation manufacturing, after obtaining high-precision digital surface models of complex workpieces such as aircraft engine parts or car shells, engineers can use differential geometry tools such as Gaussian curvature, mean curvature, and concepts such as principal directions and principal curvatures to accurately describe the local and global morphology of these surfaces from a mathematical perspective. Specifically, by calculating the above differential geometry quantities at each point, a series of values ​​that can reflect the geometric characteristics of the surface can be obtained, and these values ​​together constitute the so-called surface feature descriptors. The surface feature descriptor not only reveals the specific morphological information of each position on the surface, such as the degree of concavity and smoothness, but also provides an important reference for subsequent processing. However, in actual applications, not all workpieces processed by laser multi-axis linkage can fully meet the initial design requirements, that is, their surface feature descriptors may not meet the expected geometric characteristics. This may be caused by subtle errors in the processing process or changes in material properties. In order to further improve the processing results and ensure that the final product has the desired performance and appearance, additional steps are needed to optimize the existing model. If it is found that the surface feature descriptors deviate from the predetermined standards, then the digital surface model should be analyzed more deeply based on these descriptors-spectral decomposition. Spectral decomposition is a powerful mathematical method that converts complex surface structures into a set of basic modes or frequency components that are easy to understand and process, thereby forming a profile feature map. This map is like a fingerprint of the surface, which records every detail of its morphology in detail, including those subtle details that are not easy to observe directly. For internal parts of aircraft engines, by performing spectral decomposition on the surface, engineers can identify which areas have potential problems, such as excessive bending or not smooth enough, and then adjust the processing parameters in a targeted manner to achieve better processing results. For streamlined designs such as car shells, spectral decomposition can help designers find the key parts that affect aerodynamic performance and make improvement suggestions accordingly to ensure that the vehicle has the best driving efficiency and aesthetics. In this way, whether facing the complex needs of the aviation or automotive industries, the quality of surface analysis can be effectively improved by combining differential geometry theory with spectral decomposition technology, thereby guiding more precise processing operations.

[0072] Step S4, performing path planning on the contour feature map based on geodesic theory to obtain a processing trajectory sequence.

[0073] Specifically, when implementing the step of "planning the path of the contour feature map based on geodesic theory to obtain a processing trajectory sequence", it is first necessary to understand the importance of geodesic theory in surface processing. A geodesic refers to the shortest path between two points on a surface. It follows the geometric characteristics of the surface and is the route with the least energy consumption when connecting any two points along the surface. In complex surface processing, planning the processing path through geodesic theory can ensure that the tool or laser head moves along the most optimized path, thereby reducing unnecessary moving distance and time, improving processing efficiency, and better maintaining the accuracy and surface quality of the workpiece. Specifically, after obtaining the contour feature map, that is, the basic patterns or frequency components describing the surface morphology have been obtained through spectral decomposition, engineers can use this information to build a mathematical model that accurately reflects the geometric characteristics of the surface. For example, in the field of aviation manufacturing, for parts with complex internal structures such as aircraft engine components, or components with extremely high requirements for appearance and aerodynamic performance such as car shells, engineers will calculate the best path from the starting point to the end point based on the subtle morphological changes contained in the contour feature map and the geodesic theory. This process involves a series of complex mathematical operations, including but not limited to solving geodesic equations, evaluating the energy consumption of different paths, and considering various constraints in the actual processing environment. Once the preliminary path plan is determined, it is necessary to refine it to generate the final processing trajectory sequence. This step requires not only that the path planning must strictly comply with the geometric restrictions of the surface, but also take into account the actual operating capabilities of the processing equipment, such as the range of motion and speed restrictions of multi-axis linkage machine tools. In order to ensure the coordinated operation of the axes during the processing process and avoid excessive acceleration or sudden stops and turns, engineers will use advanced algorithms to smooth each turning point on the path to ensure that the entire processing process is smooth and smooth. In addition, some auxiliary measures may be introduced, such as setting virtual support points or adjusting the path density to better adapt to specific processing needs. For example, when processing the car shell, since there may be multiple areas with large curvature changes on its surface, special attention needs to be paid to how to overcome these obstacles without affecting the processing quality and efficiency when planning the processing trajectory. By carefully planning the geodesic path of the contour feature map, not only can efficient processing of complex surfaces be achieved, but also accurate basic data can be provided for subsequent dynamic constraint analysis, making the adjustment of the control parameters of each axis linkage more scientific and reasonable, and ultimately ensuring that the processed surface workpiece fully meets the expected design standards.

[0074] Step S5, performing kinematics solution on the machining trajectory sequence through dynamic constraint analysis to obtain the linkage control parameters of each axis, and adjusting the linkage control parameters of each axis based on the expected geometric characteristic standard.

[0075] Specifically, when implementing the key step of "solving the kinematics of the processing trajectory sequence through dynamic constraint analysis, obtaining the linkage control parameters of each axis, and adjusting the linkage control parameters of each axis based on the expected geometric characteristic standard", we must first recognize the importance of dynamic constraint analysis in the entire laser multi-axis linkage processing. Dynamic constraint analysis is not only to ensure that the movement of the robot complies with the laws of physics, but more importantly to ensure the safety, stability and efficiency of the processing process. For example, in the field of aviation manufacturing, when it comes to the processing of complex shapes such as aircraft engine parts, or the fine processing of streamlined car shells in the automobile manufacturing industry, the motion parameters of each axis must be accurately calculated to ensure that the processing tool can move accurately along the preset path. Specifically, once the processing trajectory sequence is planned through the geodesic theory, the next step is to consider how to convert these abstract paths into actual executable instructions. This requires a deep understanding of the linkage relationship between the axes in the surface processing process and the dynamic constraints they are subject to. For example, since laser multi-axis linkage processing equipment usually contains multiple axes that can move independently, when performing kinematic solutions, not only the dynamic characteristics of the speed and acceleration of a single axis should be considered, but also the synchronization and coordination of the collaborative work between multiple axes should be paid attention to. This means that engineers need to establish a complex mathematical model to describe the motion state of the entire system, and on this basis solve the optimal control parameters so that each axis can reach the correct spatial position at the right time. In this process, dynamic constraint analysis plays a vital role. It not only helps to determine the maximum speed and acceleration limits of each axis, but also takes into account the influence of factors such as inertia and friction to ensure that mechanical failure or processing errors will not occur during the processing due to excessive inertia or inappropriate acceleration. In addition, dynamic constraint analysis can also be used to optimize path planning to avoid unnecessary emergency stops and turns, thereby reducing processing time and improving product quality. For example, when processing parts such as car shells that have extremely high requirements for appearance, any slight deviation may affect the aesthetics and performance of the final product. Therefore, strict dynamic constraint analysis must be used to fine-tune the motion parameters of each axis to ensure that each cut can be accurately placed. Finally, it is essential to further adjust the linkage control parameters of each axis according to the expected geometric characteristic standards. This is because even with the most optimized kinematic solution results, the actual processing effect may still deviate from the original design intention. In this case, it is necessary to make fine adjustments to the control parameters based on the surface feature descriptors and contour feature maps obtained in the early stage, combined with actual processing feedback. For example, if it is found that the surface finish of certain areas does not reach the ideal level, or there is a slight morphological distortion, these problems can be improved by appropriately reducing the movement speed of the axis near the area and increasing the processing time.In this way, by continuously optimizing and adjusting the control parameters of each axis linkage, it can not only ensure that the processed curved workpiece fully meets the expected design standards, but also maximize the advantages of laser multi-axis linkage processing technology to provide high-quality products for industries such as aerospace and automobile manufacturing.

[0076] In a specific embodiment, the structured light 3D scanner is used to scan the target curved workpiece after laser multi-axis linkage processing to obtain a 3D point cloud data set, including:

[0077] The target curved workpiece after laser multi-axis linkage processing is scanned by a structured light 3D scanner to obtain a surface projection stripe pattern of the curved workpiece;

[0078] Phase unwrapping is performed on the surface projected fringe pattern by a phase shift method to obtain phase distribution data; wherein the phase distribution data includes an absolute phase value and a relative phase difference;

[0079] By using the triangulation principle, the surface depth of the target curved workpiece is calculated based on the phase distribution data to obtain an original depth map; wherein the original depth map includes a surface height value and a depth gradient;

[0080] Performing texture enhancement on the original depth map by using bidirectional Gabor filtering to obtain an enhanced surface feature map;

[0081] Performing edge detection on the enhanced surface feature map through an adaptive threshold segmentation algorithm to obtain a contour boundary set; wherein the contour boundary set includes boundary point coordinates and boundary curvature;

[0082] Applying tensor voting technology to extract feature points from the contour boundary set to obtain a key feature point set; wherein the key feature point set includes corner point positions and curvature extreme value points;

[0083] Through the multi-view registration algorithm, the key feature point sets from different viewpoints are fused to obtain a three-dimensional point cloud data set.

[0084] Specifically, when implementing the process of "scanning the target curved workpiece after laser multi-axis linkage processing through a structured light 3D scanner to obtain a 3D point cloud data set", it is first necessary to understand the working principle of the structured light 3D scanner and how it is combined with technologies such as the phase shift method and the triangulation principle to ensure that every detail of the curved workpiece can be accurately captured. For example, in the field of aviation manufacturing, when a complex-shaped aircraft engine component is processed by laser multi-axis linkage, in order to ensure that it meets the design specifications and performance requirements, a structured light 3D scanner will be used to scan it carefully. This process starts with projecting a stripe pattern on the surface of the target curved workpiece, that is, the structured light 3D scanner projects a set of carefully designed stripe patterns onto the target object, which will form a specific projection effect on the surface of the object. This projection is not random, but is generated according to a pre-set algorithm to facilitate subsequent data processing. Next, the phase unwrapping is performed by applying the phase shift method to the surface projected stripe pattern to obtain the phase distribution data. The phase shift method is a technology used to calculate the phase value of each pixel point. By comparing multiple stripe patterns with different phase shifts, it can effectively remove the whole cycle component in the wrapped phase, and then obtain the absolute phase value and relative phase difference. At this stage, the phase information of each point actually reflects the positional relationship of the point relative to the light source, which is crucial for subsequent depth calculation. Taking the automobile manufacturing industry as an example, for parts with streamlined design such as automobile shells, any slight deviation may affect the aerodynamic performance. Therefore, the phase shift method is used to obtain high-precision phase distribution data, which provides a solid foundation for the next step of depth calculation. Then, based on the phase distribution data obtained above, the surface depth of the target curved workpiece is calculated by the triangulation principle to obtain the original depth map. Triangulation is to determine the position of a spatial point by the known geometric relationship between the camera and the projector and the measured phase difference. Specifically, the larger the phase difference, the farther the point is from the camera; conversely, the closer the distance is. In this way, combining the absolute phase value and relative phase difference in the phase distribution data, an original depth map containing surface height values ​​and depth gradients can be constructed. This picture intuitively shows the height information of each point on the workpiece surface relative to the reference plane, which is an important basis for further analyzing the workpiece morphology. In order to improve the quality of the original depth map, bidirectional Gabor filtering is used for texture enhancement to obtain an enhanced surface feature map. Gabor filtering is a filter commonly used in the field of image processing. It can enhance the texture features of the image while maintaining the original edge information. In this step, the application of bidirectional Gabor filtering not only enhances the detail performance of the workpiece surface, but also effectively reduces noise interference, making the subsequent edge detection more accurate and reliable.For example, when dealing with aircraft engine parts with complex internal structures, the enhanced surface feature map can help more clearly identify the boundaries between various functional areas, laying a good foundation for subsequent feature extraction. Subsequently, the enhanced surface feature map is edge detected by the adaptive threshold segmentation algorithm to obtain the contour boundary set. The adaptive threshold segmentation mentioned here refers to the method of automatically adjusting the segmentation threshold according to the local image characteristics. It can better adapt to the image changes under different lighting conditions and ensure the consistency and accuracy of the edge detection results. The contour boundary set contains the boundary point coordinates and boundary curvature, which provides important reference information for the subsequent key feature point extraction. For large workpieces such as car shells, accurate edge detection can help engineers quickly locate and analyze key parts, such as door edges or body lines, to ensure the aesthetics and functionality of the final product. Then, the tensor voting technology is applied to extract feature points from the contour boundary set to obtain the key feature point set. Tensor voting is a powerful feature extraction method that can highlight significant geometric features, such as corner positions and curvature extreme points, by aggregating information in the local neighborhood. This method can not only improve the robustness of feature point detection, but also effectively reduce the occurrence of false detection. For example, when identifying important locations such as the tip or root of an aircraft engine blade, tensor voting technology can provide very accurate results, which is of great significance for ensuring processing quality and safety. Finally, in order to fully describe the overall shape of the target curved workpiece, it is also necessary to fuse the key feature point sets from different perspectives through a multi-view registration algorithm to obtain a complete three-dimensional point cloud data set. Multi-view registration means scanning the same object from multiple different angles and integrating the data obtained from all perspectives. This process involves complex mathematical operations, including transformation operations such as rotation and translation, in order to make the data from different perspectives overlap as much as possible to form a unified and continuous three-dimensional model. For large workpieces or complex structural parts, such as aircraft engines or car shells, multi-view registration can ensure that their three-dimensional shape can be completely reconstructed even in the case of severe occlusion, providing high-quality data support for a series of subsequent operations such as surface reconstruction and shape analysis. In summary, the entire process from the initial scanning of the structured light 3D scanner to the final generation of the 3D point cloud data set is an interlocking and progressive process. Each link is closely centered on improving data accuracy and integrity, aiming to provide the most detailed and realistic digital expression for the target curved surface workpiece after laser multi-axis linkage processing. This not only helps to improve product quality, but also provides strong support for the development of complex curved surface processing technology in modern manufacturing.

[0085] In a specific embodiment, the target curved surface workpiece is reconstructed based on the three-dimensional point cloud data set to obtain a digital curved surface model, including:

[0086] The three-dimensional point cloud data set is hierarchically partitioned by an octree space segmentation algorithm to obtain a set of spatial sub-regions, and a density clustering analysis is performed on the set of spatial sub-regions to obtain a regional feature distribution map; wherein the regional feature distribution map includes a point cloud density gradient, a local curvature change rate, and a boundary jump point position;

[0087] Performing feature extraction on the regional feature distribution map to obtain a local geometric feature group, and performing least squares projection on the local geometric feature group to obtain a feature projection matrix;

[0088] Performing surface fitting on the set of spatial sub-regions based on the feature projection matrix to obtain a surface fitting grid framework, and performing boundary constraint optimization on the surface fitting grid framework to obtain a boundary constraint curve family;

[0089] Performing topological optimization on the surface fitting grid framework based on the boundary constraint curve family to obtain an optimized grid model;

[0090] The optimized grid model is parameterized by discrete Riemann mapping to obtain a parameter domain mapping relationship, and the parameter domain mapping relationship is isometrically transformed to obtain a standardized parameter grid;

[0091] The standardized parameter grid is subjected to NURBS surface construction based on Gregory patches to obtain a rational spline surface equation, and the target surface workpiece is subjected to geometric continuity surface reconstruction based on the rational spline surface equation to obtain a digital surface model.

[0092] Specifically, in the process of realizing "reconstructing the surface of the target curved workpiece based on the three-dimensional point cloud data set to obtain a digital surface model", it is first necessary to use an efficient and accurate method to process the original point cloud data. To achieve this goal, engineers usually use the octree space segmentation algorithm to hierarchically partition the point cloud data set to obtain a series of spatial sub-region sets. This method can not only effectively manage large-scale data sets, but also provide a clear and orderly infrastructure for subsequent analysis. For example, in the field of aviation manufacturing, when dealing with complex shapes such as aircraft engine parts, these parts often have rich geometric features and complex internal structures. Through the octree space segmentation algorithm, the entire workpiece can be decomposed into multiple small parts that are easy to handle, each of which contains a certain amount of point cloud data. Next, a density clustering analysis is performed on the obtained spatial sub-region set to reveal the feature distribution in each region. At this stage, engineers will calculate information such as point cloud density gradient, local curvature change rate, and boundary jump point location to form a detailed regional feature distribution map. This image can not only intuitively show the density and curvature change trend of point cloud data in different regions, but also identify important geometric feature points, such as the location of sharp edges or mutation areas. For parts such as automobile shells that have extremely high requirements for appearance, it is crucial to accurately identify these feature points, because they are often the key factors affecting the aesthetics and performance of the product. By accurately locating these feature points, reliable guidance can be provided for subsequent surface reconstruction. Subsequently, feature extraction is performed based on the information in the regional feature distribution map to obtain a set of data describing the local geometric features of each region, namely the local geometric feature group. In order to make these features more suitable for surface fitting operations, it is also necessary to perform least squares projection on the local geometric feature group to obtain the feature projection matrix. Least squares projection is a commonly used mathematical method that can find the best linear approximation solution by reducing the sum of squared errors. In this example, the application of this method can ensure that the feature projection matrix can retain the main features of the original data to the greatest extent while eliminating unnecessary noise interference. For example, when dealing with aircraft engine blades with subtle morphological changes, least squares projection helps to highlight the important geometric characteristics of the blade surface, such as curvature and smoothness, providing high-quality data support for subsequent surface fitting. With the feature projection matrix, we can perform surface fitting on the set of spatial sub-regions based on it to generate a preliminary surface fitting grid framework. However, this step alone is not enough to ensure the quality of the final model, so it is necessary to further perform boundary constraint optimization on the surface fitting grid framework to obtain a family of boundary constraint curves. The purpose of boundary constraint optimization is to ensure the continuity and smoothness of the surface at the boundary and avoid unnatural mutations or discontinuities.This step is very important for maintaining the overall shape of the workpiece, especially when dealing with components such as car shells that have strict appearance requirements. By introducing a family of boundary constraint curves, the shape at the boundary can be accurately adjusted without affecting other areas, making the entire surface smoother and more harmonious. Next, the surface fitting mesh framework is topologically optimized based on the family of boundary constraint curves to obtain an optimized mesh model. Topological optimization refers to improving the quality of the model by adjusting the connection relationship between mesh nodes while maintaining the basic shape of the model. This optimization can not only simplify the model structure, but also enhance its stability and accuracy. For example, in the field of aviation manufacturing, for parts that need to withstand high pressure or high temperature environments, such as the combustion chamber wall of a jet engine, the optimized mesh model can better reflect the stress distribution under actual working conditions, thereby providing more reliable data support for design and manufacturing. Finally, in order to convert the optimized mesh model into a standardized parameter representation, it is necessary to perform discrete Riemann mapping processing on it, obtain the parameter domain mapping relationship, and perform isometric transformation on this relationship to obtain a standardized parameter mesh. Discrete Riemann mapping is a technique for mapping complex surfaces to simple planes. It can effectively keep the distance and angle on the surface unchanged, thereby ensuring that the parameterized result is as faithful to the original surface as possible. The standardized parameter grid provides a unified operating platform for subsequent surface construction. Based on the Gregory patch, the standardized parameter grid is constructed with NURBS (non-uniform rational B-spline) surface to obtain the rational spline surface equation, which is a powerful mathematical tool that can flexibly express various types of surfaces and ensure geometric continuity. In this way, the target surface workpiece can be reconstructed with high precision and geometric continuity, and finally a digital surface model that fully meets the design requirements can be obtained. In summary, from the initial space segmentation to the final NURBS surface construction, the whole process is an interlocking and progressive process, and each link is closely centered on improving the accuracy and quality of surface reconstruction. This method is not only suitable for processing complex parts in the field of aviation manufacturing, such as aircraft engine parts, but also can well meet the needs of streamlined design in the automotive manufacturing industry, such as car shells. Through the above steps, engineers can provide the most detailed and realistic digital expression for the target surface workpiece after laser multi-axis linkage processing, which not only helps to improve product quality, but also provides strong support for the development of complex surface processing technology in modern manufacturing.

[0093] In a specific embodiment, the shape analysis of the digitized surface model based on differential geometry theory to obtain the surface feature descriptor includes:

[0094] The curvature tensor of the digital surface model is calculated by the Weingarten mapping algorithm to obtain a shape operator matrix, and the shape operator matrix is ​​subjected to eigenvalue decomposition to obtain a surface principal direction field; wherein the surface principal direction field includes a maximum principal curvature direction, a minimum principal curvature direction and a normal curvature distribution;

[0095] Based on the Frenet frame theory, coordinate transformation is performed on the principal direction field of the surface to obtain a parametric expression of the local surface, and geodesic curvature is calculated on the parametric expression of the local surface to obtain an intrinsic geometric feature set;

[0096] The covariant derivative of the intrinsic geometric feature set is calculated by Christoffel symbol to obtain the surface shape change rate, and the surface shape change rate is decomposed into a tensor field to obtain a set of geometric invariants; wherein the set of geometric invariants includes Gaussian curvature, mean curvature and shape factor;

[0097] Based on the Ricci flow theory, a curvature flow evolution analysis is performed on the geometric invariant set to obtain a geometric flow field distribution, and topological features are extracted from the geometric flow field distribution to obtain a singular point distribution map, wherein the singular point distribution map includes a ridge network, a valley network and critical point positions;

[0098] An exterior differential operation is performed on the singular point distribution diagram in a discrete differential form to obtain a surface feature form, and a surface feature descriptor is obtained based on the surface feature form.

[0099] Specifically, in the process of realizing "shape analysis of the digital surface model based on differential geometry theory to obtain surface feature descriptors", it is first necessary to deeply understand the basic principles of differential geometry theory and its application in surface analysis. This process starts with the calculation of the curvature tensor of the digital surface model through the Weingarten mapping algorithm, that is, using the local properties of the surface in differential geometry to quantify its morphological changes. Weingarten mapping is a method used to describe the law of change of the normal vector at each point on the surface with position, which can generate a shape operator matrix. This matrix not only contains the curvature information of each point, but also reveals the degree and direction of curvature of the surface near the point. For example, in the field of aviation manufacturing, for parts with streamlined designs such as aircraft engine components or car shells with complex shapes, engineers can accurately capture every subtle morphological change through Weingarten mapping. Then, by performing eigenvalue decomposition on the shape operator matrix, the main direction field of the surface can be obtained, including the maximum main curvature direction, the minimum main curvature direction and the normal curvature distribution. This information provides an important basis for subsequent geometric analysis. In order to further understand and describe the local characteristics of the surface, it is necessary to perform coordinate transformation on the principal direction field of the surface based on the Frenet frame theory to obtain a parametric expression of the local surface. The Frenet frame is a set of orthogonal bases defined along the curve, which can be used to describe the instantaneous direction and rotation of the space curve. Here, by introducing appropriate coordinate transformation, the principal direction field of the surface can be more intuitively expressed as a set of easy-to-operate parameters. This step not only simplifies the mathematical expression, but also paves the way for the subsequent calculation of geodesic curvature. Geodesic curvature refers to the curvature measured along any given path on the surface, which reflects the degree of curvature of the path itself and the change of the path relative to the overall shape of the surface. By calculating the intrinsic geometric feature set, detailed information about the internal structure of the surface can be obtained, which is particularly important for processing aircraft engine components with complex internal structures. For example, when analyzing key areas such as the root or tip of an engine blade, the intrinsic geometric feature set can help identify which parts have potential problems, such as excessive curvature or insufficient smoothness. With the above intrinsic geometric feature set, it is necessary to conduct a deeper analysis to extract information that can fully describe the changes in the surface morphology. This step involves using Christoffel symbols to calculate the covariant derivatives of the intrinsic geometric features to obtain the rate of change of the surface shape. Covariant derivatives are a way to measure the rate at which a vector field or other tensor field changes along a specific direction, taking into account the existence of the surface itself rather than just a simple derivative in Euclidean space. Through this calculation method, we can accurately capture the speed and manner of shape changes at each point on the surface, and ultimately form a set of geometric invariants, including Gaussian curvature, mean curvature and shape factor.These geometric invariants are one of the most basic and important concepts in differential geometry. They can describe the essential properties of surfaces independently of the choice of coordinates. For example, in the automotive manufacturing industry, for components such as car shells that have extremely high requirements for appearance, geometric invariants such as Gaussian curvature and mean curvature can help designers evaluate the aesthetics and aerodynamic performance of products and ensure that every detail meets the expected design standards. In order to further explore the changes in surface morphology over time or processing conditions, it is also necessary to perform curvature flow evolution analysis on the set of geometric invariants based on Ricci flow theory to obtain the geometric flow field distribution. Ricci flow is a mathematical tool used to study the evolution of curvature on Riemann manifolds. It can simulate how a surface gradually changes its shape under different conditions. By extracting topological features from the geometric flow field distribution, the distribution map of singular points can be identified, including ridge networks, valley networks, and critical point locations. These feature points often mark the places where the morphology changes most significantly on the surface, and are also the key to affecting the performance and quality of the workpiece. For example, when dealing with the complex combustion chamber wall inside an aircraft engine, engineers can find out which areas may have the risk of stress concentration or thermal deformation through Ricci flow analysis and topological feature extraction, and propose improvement measures accordingly to improve the reliability and safety of the product. Finally, in order to combine all the above analysis results to form a complete surface feature descriptor, it is also necessary to perform external differential operations on the singular point distribution map through discrete differential forms to obtain the surface feature form. The discrete differential form provides a method for performing differential operations on discrete data sets, which can effectively maintain the main features of the original data while eliminating unnecessary noise interference. Based on the surface feature form, the final surface feature descriptor can not only fully reflect the geometric characteristics of the target surface workpiece, but also serve as an important basis for subsequent processing path planning, error correction and other optimization operations. For example, when fine-machining the car shell, an accurate surface feature descriptor can guide the laser multi-axis linkage processing equipment to move along the optimal path, ensuring that each cut can be accurately placed, which not only improves the processing efficiency but also ensures product quality. In summary, the entire process from Weingarten mapping to the final generation of surface feature descriptors is an interlocking and progressive process, and each link is closely centered around improving the accuracy and reliability of surface analysis. This method is not only suitable for processing complex parts in the field of aviation manufacturing, such as aircraft engine components, but can also well meet the needs of streamlined design in the automotive manufacturing industry, such as car shells. Through the above steps, engineers can provide the most detailed and realistic digital expression for the target surface workpiece after laser multi-axis linkage processing, which not only helps to improve product quality, but also provides strong support for the development of complex surface processing technology in modern manufacturing.

[0100] In a specific embodiment, the spectral decomposition of the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum includes:

[0101] Based on the Laplace-Beltrami operator and the surface feature descriptor, the digitized surface model is subjected to spectral decomposition to obtain a feature spectrum sequence;

[0102] Performing opening and closing operations on the feature map sequence through mathematical morphology to obtain a filtered feature map, and performing edge detection on the filtered feature map to obtain a contour line set; wherein the contour line set includes a main contour line, a secondary contour line and a feature point sequence;

[0103] Performing topological reconstruction based on the contour line set to obtain a characteristic network graph; wherein the characteristic network graph includes critical point connection relationships, curvature extreme points and singular point distribution;

[0104] Based on the graph theory optimization method, feature association analysis is performed based on the feature network graph to obtain a profile feature map.

[0105] Specifically, in the process of realizing "spectral decomposition of the digital surface model based on the surface feature descriptor to obtain the contour feature map", it is first necessary to introduce the Laplace-Beltrami operator to process the surface feature descriptor. The Laplace-Beltrami operator is a differential operator defined on the surface, which can capture the essential information of the internal structure of the surface and is used to calculate the frequency domain representation of the surface. Specifically, by applying the Laplace-Beltrami operator to the digital surface model, it can be converted into a series of feature map sequences with different frequency components. These feature map sequences not only retain the main morphological features of the original surface, but also reveal the subtle changes hidden under its surface. For example, in the field of aviation manufacturing, when analyzing complex shapes such as aircraft engine components or car shells with streamlined designs, engineers can use the spectral decomposition of the Laplace-Beltrami operator to deeply explore the geometric characteristics behind the surface, providing an important reference for subsequent optimization and processing. Next, in order to improve the quality of the feature map and extract more meaningful information, it is necessary to perform mathematical morphological processing on the feature map sequence. Mathematical morphology is a set of techniques for image processing and analysis, in which opening and closing operations can effectively remove noise and unnecessary details without changing the overall structure. By applying opening and closing operations to the feature map sequence, a clearer and smoother filtered feature map can be obtained. Subsequently, the filtered feature map is edge detected to obtain a contour set containing main contours, secondary contours and feature point sequences. This process is similar to finding the main road network from a complex map, that is, identifying the most significant geometric boundaries on the surface. For the automotive manufacturing industry, accurate edge detection can help designers quickly locate and analyze key parts, such as door edges or body lines, to ensure the aesthetics and functionality of the final product. For example, when dealing with aircraft engine parts with complex internal structures, edge detection helps highlight important locations such as blade tips or roots, which is of great significance for ensuring processing quality and safety. With a contour set, the next step is to perform topological reconstruction based on the set to generate a feature network diagram. This stage involves establishing a graphical structure that can describe the geometric relationship of the surface, which contains information such as critical point connection relationships, curvature extreme points and singular point distribution. The feature network diagram is like a skeleton of a surface. It not only shows the interconnections between the various parts, but also identifies those areas that are particularly sensitive to morphological changes. For large workpieces or parts with complex structures, such as aircraft engines or car shells, building such a detailed feature network diagram can help engineers understand the overall morphology of the workpiece more intuitively and provide a solid foundation for subsequent feature association analysis.For example, when analyzing a component such as a car shell that has extremely high requirements for appearance, the feature network diagram can help identify which areas may have problems that affect aerodynamic performance, thereby guiding designers to make necessary adjustments. Finally, in order to integrate all the above analysis results and form a complete contour feature map, it is also necessary to perform feature association analysis on the feature network diagram based on the graph theory optimization method. Graph theory optimization is a powerful tool that can find the optimal path or shortest distance in a graph through an algorithm, thereby revealing the relationship hidden behind the data. In this example, the application of graph theory optimization methods can systematically evaluate each element in the feature network diagram, determine the intrinsic connection between them, and construct a contour feature map based on this. The contour feature map can not only fully reflect the geometric characteristics of the target surface workpiece, but also serve as an important basis for subsequent processing path planning, error correction and other optimization operations. For example, when fine processing the car shell, an accurate contour feature map can guide the laser multi-axis linkage processing equipment to move along the optimal path, ensuring that each cut can be accurately placed, which not only improves processing efficiency but also ensures product quality. In summary, the whole process from the spectral decomposition of the Laplace-Beltrami operator to the final contour feature map generation is an interlocking and progressive process, and each link is closely centered on improving the accuracy and reliability of surface analysis. This method is not only suitable for processing complex parts in the field of aviation manufacturing, such as aircraft engine components, but also can well meet the needs of streamlined design in the automotive manufacturing industry, such as car shells. Through the above steps, engineers can provide the most detailed and realistic digital expression for the target surface workpiece after laser multi-axis linkage processing, which not only helps to improve product quality, but also provides strong support for the development of complex surface processing technology in modern manufacturing. In addition, it is worth noting that this series of operations not only improves the understanding of surface geometric characteristics, but also plays an important role in practical applications. For example, in the aerospace industry, accurate contour feature maps can help engineers optimize the design of aircraft, reduce air resistance, and improve fuel efficiency; while in the field of automotive manufacturing, it helps to improve the aerodynamic performance of vehicles and enhance driving stability and safety. Therefore, whether facing the complex demands of the aviation or automotive industries, by combining differential geometry theory with advanced mathematical tools, the quality of surface analysis can be effectively improved, thereby guiding more precise processing operations.

[0106] In a specific embodiment, the path planning is performed on the contour feature map based on the geodesic theory to obtain a processing trajectory sequence, including:

[0107] Using geodesic theory to calculate the distance field of the contour feature map to obtain a geodesic distance field, and performing gradient vector calculation on the geodesic distance field to obtain a geodesic gradient vector field;

[0108] Performing a geodesic path search on the geodesic gradient vector field by a preset fast marching method to obtain an initial geodesic path, and performing path smoothing processing on the initial geodesic path to obtain a smoothed geodesic path;

[0109] The curvature analysis method is used to calculate the curvature of the smooth geodesic path to obtain the curvature distribution of the curve, and the curvature constraint judgment is performed on the curvature distribution of the curve to obtain the curve segment that meets the curvature constraint;

[0110] The speed of the curve segment is distributed by a speed planning algorithm to obtain a speed curve, and the acceleration constraint is judged on the speed curve to obtain a processing trajectory segment that satisfies the acceleration constraint;

[0111] Based on a trajectory splicing algorithm, trajectory segment splicing and path planning are performed on the processing trajectory segments to obtain a processing trajectory sequence.

[0112] Specifically, in the process of realizing "path planning for the contour feature map based on geodesic theory to obtain a processing trajectory sequence", it is first necessary to use geodesic theory to calculate the distance field of the contour feature map. Geodesic theory provides a method to define the shortest path between two points on a surface, namely the so-called geodesic. By applying this theory, a complex surface can be converted into an easy-to-understand and process distance field, which reflects the shortest path length from the starting point to any point on the surface. For example, in the field of aviation manufacturing, when dealing with complex shapes such as aircraft engine components or car shells with streamlined designs, engineers can use geodesic theory to accurately calculate the distance of each position relative to a reference point, thereby constructing a geodesic distance field. Then, by calculating the gradient vector of this geodesic distance field, a geodesic gradient vector field can be obtained. The gradient vector field indicates the direction and speed of movement along the shortest path at each position, which provides a direction guide for subsequent path search. Once the geodesic gradient vector field is obtained, it is necessary to use the preset fast marching method to perform geodesic path search. The fast marching method is a numerical algorithm for solving front propagation problems efficiently. It can significantly reduce the calculation time while ensuring accuracy. In this example, the fast marching method can find the initial geodesic path from the starting point to the target point. However, the initial path directly obtained may contain non-smooth parts, so it is necessary to smooth the path to eliminate unnecessary twists and jitters, and finally obtain a smooth geodesic path. For components with extremely high requirements on appearance, such as car shells, the smoothed path not only improves processing efficiency but also ensures the consistency of surface quality. For example, when processing car shells, a smooth path can help laser multi-axis linkage processing equipment work more stably and avoid processing errors caused by sudden changes in the path. Next, in order to ensure that the tool or laser head in the processing process can move in the expected way, curvature analysis is needed to calculate the curvature of the smoothed geodesic path to obtain the curvature distribution of the curve. Curvature is an important parameter that describes the degree of curvature of each point on the curve. By calculating the curvature of each point on the path, the characteristics of its morphological changes can be understood. Then, the curvature distribution of the curve is judged according to the set curvature constraints, and the curve segments that meet these constraints are screened out. Curvature constraints are designed to ensure that machining tools do not cause unstable operation or exceed their physical limits due to excessive curvature. For example, in the machining of complex structures inside aircraft engines, reasonable curvature constraints can prevent tool breakage or wear while maintaining machining accuracy. For components such as car shells that require high finish and good aerodynamic performance, curvature constraints are equally important because they directly affect the product's appearance quality and driving performance. After determining the curve segment that meets the curvature constraint, it is also necessary to use a speed planning algorithm to distribute the speed to obtain a speed curve.Speed ​​planning refers to the reasonable arrangement of processing speed according to the geometric characteristics of the path to achieve the best processing effect. Specifically, speed planning should not only consider the straight and curved parts of the path, but also combine the capabilities of the processing equipment, such as maximum speed and acceleration limit. After completing the speed distribution, it is also necessary to judge the acceleration constraint of the speed curve to ensure that the maximum allowed acceleration value is not exceeded during the entire processing process. This is because sudden acceleration or deceleration may cause processing errors or mechanical failures, affecting product quality. For example, when processing aircraft engine parts, strict acceleration constraints can help maintain the stability of the processing process, reduce the negative impact of vibration, and improve the quality of the workpiece. Finally, in order to generate a complete processing trajectory sequence, it is necessary to perform trajectory segment splicing and path planning on the above-mentioned processing trajectory segments that meet the acceleration constraints based on the trajectory splicing algorithm. Trajectory splicing is a process of connecting multiple independent processing trajectory segments into a continuous and smooth overall path. This step is not just a simple connection of each segment, but also needs to consider whether the transition between segments is smooth and natural, and whether there are potential risk points. Through a carefully designed trajectory splicing algorithm, it can be ensured that all processing trajectory segments are seamlessly connected to form a processing trajectory sequence that meets both geometric requirements and is suitable for actual operations. For example, when fine-machining a large automobile shell, good trajectory splicing can not only improve the machining efficiency, but also ensure that each cut can be accurately placed, which not only improves the machining quality but also reduces material waste. In summary, the entire process from the calculation of the geodesic distance field to the generation of the final machining trajectory sequence is an interlocking and progressive process, and each link is closely centered on improving the accuracy and reliability of path planning. This method is not only suitable for processing complex parts in the field of aviation manufacturing, such as aircraft engine components, but also can well meet the needs of streamlined design in the automotive manufacturing industry, such as automobile shells. Through the above steps, engineers can provide the most detailed and realistic digital expression for the target surface workpiece after laser multi-axis linkage machining, which not only helps to improve product quality, but also provides strong support for the development of complex surface machining technology in modern manufacturing. In addition, it is worth noting that this series of operations not only improves the understanding of the geometric characteristics of the surface, but also plays an important role in practical applications. For example, in the aerospace industry, accurate path planning can help optimize the design of aircraft, reduce air resistance, and improve fuel efficiency; while in the field of automotive manufacturing, it helps to improve the aerodynamic performance of the vehicle and enhance driving stability and safety. Therefore, whether facing the complex demands of the aviation or automotive industries, by combining geodesic theory with advanced mathematical tools, the quality of path planning can be effectively improved, thereby guiding more precise processing operations.

[0113] In a specific embodiment, the kinematic solution of the machining trajectory sequence is performed through dynamic constraint analysis to obtain the linkage control parameters of each axis, including:

[0114] The machining trajectory sequence is subjected to variational analysis through the Hamilton-Jacobi equation to obtain the trajectory energy functional, and the trajectory energy functional is subjected to optimal control solution to obtain a group of motion state equations;

[0115] Based on the Lagrange multiplier method, the motion state equation group is constrained and optimized to obtain a multi-axis coupled dynamic equation, and the multi-axis coupled dynamic equation is numerically integrated to obtain a joint motion parameter set, wherein the joint motion parameter set includes an angular displacement sequence, an angular velocity curve, and an angular acceleration distribution;

[0116] Performing dynamic inversion on the joint motion parameter set through dynamic constraint analysis to obtain a driving torque sequence, and performing harmonic analysis on the driving torque sequence to obtain a frequency domain characteristic spectrum, wherein the frequency domain characteristic spectrum includes amplitude response, phase delay and resonance frequency;

[0117] Reconstructing the frequency domain characteristic spectrum in the time domain based on a Runge-Kutta integrator to obtain an axial motion trajectory, and interpolating and smoothing the axial motion trajectory to obtain a continuous motion curve;

[0118] The continuous motion curve is optimally time-planned by the Pontryagin minimum principle to obtain a synchronous control sequence, and error compensation is performed on the synchronous control sequence to obtain linkage control parameters of each axis.

[0119] Specifically, in the process of realizing "solving the kinematics of the processing trajectory sequence through dynamic constraint analysis to obtain the linkage control parameters of each axis", it is first necessary to use the Hamilton-Jacobi equation to perform variational analysis on the processing trajectory sequence. The Hamilton-Jacobi equation is a differential equation used to describe the dynamic behavior of the system. It can simplify a complex multi-body system into a single energy function, namely the trajectory energy functional. By solving the optimal control of this energy functional, a set of motion state equations can be obtained, which accurately describes the motion state of the system at each moment. For example, in the field of aviation manufacturing, when dealing with streamlined parts with complex shapes such as aircraft engine components or car shells, engineers can obtain the optimal motion path through variational analysis to ensure that every action in the processing process is the most efficient and has the smallest error. This energy functional-based method not only takes into account the geometric characteristics of the path itself, but also combines physical laws to guide motion planning. Once the motion state equations are obtained, they are constrained and optimized based on the Lagrange multiplier method to construct multi-axis coupled dynamic equations. The Lagrange multiplier method is a technique used to solve optimization problems with constraints. It can introduce additional variables (called Lagrange multipliers) to balance the relationship between the objective function and the constraints. In this example, by applying the Lagrange multiplier method, the complexity brought by the interaction between multiple axes can be effectively handled, thereby obtaining a multi-axis coupled dynamic model. This model not only reflects the mechanical connection between the axes, but also takes into account various constraints that may exist in the actual processing environment, such as the working range, maximum speed and acceleration of the robot arm. In order to further solve these dynamic equations, numerical integration methods such as the Runge-Kutta method are also needed to obtain a joint motion parameter set, which includes an angular displacement sequence, an angular velocity curve and an angular acceleration distribution. For components with extremely high appearance requirements, such as car shells, an accurate joint motion parameter set can help ensure that each cut is accurate, which not only improves processing efficiency but also ensures product quality. After obtaining the joint motion parameter set, it is necessary to perform dynamic inversion on it to obtain the driving torque sequence. Dynamic inversion refers to the process of inversely deriving the external force or torque required to produce the motion based on the known motion parameters. This is crucial to understanding the actual loads borne by each axis during the machining process, because reasonable drive torque distribution can directly affect the machining effect and equipment life. For example, when processing workpieces such as aircraft engine parts that require high precision and stability, dynamic inversion can obtain a more scientific and reasonable drive torque configuration to avoid mechanical failure or machining errors caused by excessive torque. In addition, it is also necessary to perform harmonic analysis on the drive torque sequence to obtain the frequency domain characteristic spectrum, including amplitude response, phase delay and resonant frequency.Harmonic analysis can reveal the periodic and non-periodic components in the driving torque, help identify potential problem points, such as resonance, and then take corresponding measures to optimize. In order to convert the above frequency domain characteristic spectrum back to the time domain representation for practical operation, it is necessary to reconstruct it in the time domain based on the Runge-Kutta integrator to obtain the axial motion trajectory. The Runge-Kutta integrator is an efficient numerical integration method that can accurately simulate the motion process that changes with time. In this way, not only can the original motion trajectory be restored, but also its continuity and smoothness can be maintained. However, the trajectory returned directly from the frequency domain may have uneven places, so it is also necessary to interpolate and smooth the axial motion trajectory to obtain a continuous motion curve. This process is similar to adding a transition segment to a broken line, making the entire trajectory look more natural and smooth. For example, when fine-machining large automobile shells, a smooth continuous motion curve can help laser multi-axis linkage processing equipment work more stably and avoid machining errors caused by sudden changes in the path. Finally, in order to ensure that all axes can operate in a coordinated manner, it is also necessary to perform optimal timing planning on the continuous motion curve through the Pontryagin minimum principle to obtain a synchronous control sequence. The Pontryagin minimum principle is a mathematical tool for finding the optimal control strategy. It can find the control input that minimizes the objective function under certain constraints. In this example, the principle can be applied to assign the most suitable time schedule to each axis to ensure that they can reach the right position at the right time. At the same time, considering the various uncertainties that may occur in the actual processing process, it is also necessary to perform error compensation on the synchronous control sequence to finally obtain the linkage control parameters of each axis. Error compensation refers to adjusting the predetermined control parameters according to the actual situation to eliminate or reduce the deviation and ensure the consistency of processing quality. For example, when processing aircraft engine parts with complex internal structures, accurate error compensation can help maintain the stability of the processing process, reduce the negative impact of vibration, and improve the quality of the workpiece. In summary, the entire process from variational analysis to the final generation of linkage control parameters for each axis is an interlocking and progressive process, and each link is closely centered on improving the accuracy and reliability of kinematic solutions. This method is not only suitable for processing complex parts in the field of aviation manufacturing, such as aircraft engine parts, but also can well meet the needs of streamlined design in the automotive manufacturing industry, such as car shells. Through the above steps, engineers can provide the most detailed and realistic digital expression for the target surface workpiece after laser multi-axis linkage processing, which not only helps to improve product quality, but also provides strong support for the development of complex surface processing technology in modern manufacturing. In addition, it is worth noting that this series of operations not only improves the understanding of the geometric and dynamic characteristics of the surface, but also plays an important role in practical applications.For example, in the aerospace industry, accurate dynamic constraint analysis can help optimize the design of aircraft, reduce air resistance, and improve fuel efficiency; while in the field of automobile manufacturing, it helps improve the aerodynamic performance of vehicles and enhance driving stability and safety. Therefore, whether facing the complex demands of the aviation or automotive industries, by combining advanced mathematical tools with dynamics theory, the quality of kinematic solutions can be effectively improved, thereby guiding more precise processing operations.

[0120] The above describes the surface profile analysis method of laser multi-axis linkage processing in the embodiment of the present invention. The following describes the surface profile analysis device of laser multi-axis linkage processing in the embodiment of the present invention. Figure 2 In one embodiment of the present invention, a surface profile analysis device for laser multi-axis linkage processing includes:

[0121] The scanning module 21 is used to scan the target curved surface workpiece after the laser multi-axis linkage processing by means of a structured light three-dimensional scanner to obtain a three-dimensional point cloud data set;

[0122] A reconstruction module 22, configured to reconstruct the target curved surface workpiece based on the three-dimensional point cloud data set to obtain a digital curved surface model;

[0123] An analysis module 23 is used to perform shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor. If the surface feature descriptor does not meet the expected geometric characteristic standard, the digitized surface model is subjected to spectral decomposition based on the surface feature descriptor to obtain a contour feature spectrum.

[0124] A planning module 24 is used to perform path planning on the contour feature map based on geodesic theory to obtain a processing trajectory sequence;

[0125] The solution module 25 is used to perform kinematic solution on the machining trajectory sequence through dynamic constraint analysis to obtain the linkage control parameters of each axis, and adjust the linkage control parameters of each axis based on the expected geometric characteristic standard.

[0126] In this embodiment, for the specific implementation of each unit in the above device embodiment, please refer to the above method embodiment, which will not be repeated here.

[0127] Reference Figure 3 The present invention also provides a computer device in an embodiment, wherein the internal structure of the computer device can be as follows: Figure 3As shown. The computer device includes a processor, a memory, a display screen, an input device, a network interface and a database connected through a system bus. Among them, the processor designed by the computer is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store the corresponding data in this embodiment. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the above method is implemented.

[0128] Those skilled in the art will understand that Figure 3 The structure shown in the figure is merely a block diagram of a portion of the structure related to the solution of the present invention, and does not constitute a limitation on the computer device to which the solution of the present invention is applied.

[0129] An embodiment of the present invention further provides a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the above method is implemented. It can be understood that the computer-readable storage medium in this embodiment can be a volatile readable storage medium or a non-volatile readable storage medium.

[0130] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media provided by the present invention and used in the embodiments may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in a variety of forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double-speed data rate SDRAM (SSRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM.

[0131] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, device, article or method. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the presence of other identical elements in the process, device, article or method including the element.

[0132] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A surface profile analysis method for laser multi-axis machining, characterized in that: The following steps are involved: The target curved workpiece after laser multi-axis linkage processing is scanned by a structured light 3D scanner to obtain a 3D point cloud data set; Reconstructing the target curved surface workpiece based on the three-dimensional point cloud data set to obtain a digital curved surface model; Performing shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor; if the surface feature descriptor does not meet the expected geometric characteristic standard, performing spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum; Performing path planning on the contour feature map based on geodesic theory to obtain a processing trajectory sequence; Performing kinematics solution on the machining trajectory sequence through dynamic constraint analysis to obtain linkage control parameters of each axis, and adjusting the linkage control parameters of each axis based on the expected geometric characteristic standard; The step of performing shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor includes: The curvature tensor of the digital surface model is calculated by the Weingarten mapping algorithm to obtain a shape operator matrix, and the shape operator matrix is ​​subjected to eigenvalue decomposition to obtain a surface principal direction field; wherein the surface principal direction field includes a maximum principal curvature direction, a minimum principal curvature direction and a normal curvature distribution; Based on the Frenet frame theory, coordinate transformation is performed on the principal direction field of the surface to obtain a parametric expression of the local surface, and geodesic curvature is calculated on the parametric expression of the local surface to obtain an intrinsic geometric feature set; The covariant derivative of the intrinsic geometric feature set is calculated by Christoffel symbol to obtain the surface shape change rate, and the surface shape change rate is decomposed into a tensor field to obtain a set of geometric invariants; wherein the set of geometric invariants includes Gaussian curvature, mean curvature and shape factor; Based on the Ricci flow theory, a curvature flow evolution analysis is performed on the geometric invariant set to obtain a geometric flow field distribution, and topological features are extracted from the geometric flow field distribution to obtain a singular point distribution map, wherein the singular point distribution map includes a ridge network, a valley network and critical point positions; Performing an exterior differential operation on the singular point distribution diagram in a discrete differential form to obtain a surface feature form, and obtaining a surface feature descriptor based on the surface feature form; The step of performing spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum comprises: Based on the Laplace-Beltrami operator and the surface feature descriptor, the digitized surface model is subjected to spectral decomposition to obtain a feature spectrum sequence; Performing opening and closing operations on the feature map sequence through mathematical morphology to obtain a filtered feature map, and performing edge detection on the filtered feature map to obtain a contour line set; wherein the contour line set includes a main contour line, a secondary contour line and a feature point sequence; Performing topological reconstruction based on the contour line set to obtain a characteristic network graph; wherein the characteristic network graph includes critical point connection relationships, curvature extreme points and singular point distribution; Based on the graph theory optimization method, feature association analysis is performed based on the feature network graph to obtain a profile feature map.

2. The surface profile analysis method of laser multi-axis machining according to claim 1, characterized in that: The structured light 3D scanner is used to scan the target curved workpiece after the laser multi-axis linkage processing to obtain a 3D point cloud data set, including: The target curved surface workpiece after laser multi-axis linkage processing is scanned by a structured light 3D scanner to obtain a surface projection stripe pattern of the target curved surface workpiece; Phase unwrapping is performed on the surface projected fringe pattern by a phase shift method to obtain phase distribution data; wherein the phase distribution data includes an absolute phase value and a relative phase difference; By using the triangulation principle, the surface depth of the target curved workpiece is calculated based on the phase distribution data to obtain an original depth map; wherein the original depth map includes a surface height value and a depth gradient; Performing texture enhancement on the original depth map by using bidirectional Gabor filtering to obtain an enhanced surface feature map; Performing edge detection on the enhanced surface feature map through an adaptive threshold segmentation algorithm to obtain a contour boundary set; wherein the contour boundary set includes boundary point coordinates and boundary curvature; Applying tensor voting technology to extract feature points from the contour boundary set to obtain a key feature point set; wherein the key feature point set includes corner point positions and curvature extreme value points; Through the multi-view registration algorithm, the key feature point sets from different viewpoints are fused to obtain a three-dimensional point cloud data set.

3. The surface profile analysis method of laser multi-axis machining according to claim 1, characterized in that: The target curved surface workpiece is reconstructed based on the three-dimensional point cloud data set to obtain a digital curved surface model, including: The three-dimensional point cloud data set is hierarchically partitioned by an octree space segmentation algorithm to obtain a set of spatial sub-regions, and a density clustering analysis is performed on the set of spatial sub-regions to obtain a regional feature distribution map; wherein the regional feature distribution map includes a point cloud density gradient, a local curvature change rate, and a boundary jump point position; Performing feature extraction on the regional feature distribution map to obtain a local geometric feature group, and performing least squares projection on the local geometric feature group to obtain a feature projection matrix; Performing surface fitting on the set of spatial sub-regions based on the feature projection matrix to obtain a surface fitting grid framework, and performing boundary constraint optimization on the surface fitting grid framework to obtain a boundary constraint curve family; Performing topological optimization on the surface fitting grid framework based on the boundary constraint curve family to obtain an optimized grid model; The optimized grid model is parameterized by discrete Riemann mapping to obtain a parameter domain mapping relationship, and the parameter domain mapping relationship is isometrically transformed to obtain a standardized parameter grid; The standardized parameter grid is subjected to NURBS surface construction based on Gregory patches to obtain a rational spline surface equation, and the target surface workpiece is subjected to geometric continuity surface reconstruction based on the rational spline surface equation to obtain a digital surface model.

4. The surface profile analysis method for laser multi-axis machining according to claim 1, characterized in that: The path planning of the contour feature map based on the geodesic theory to obtain a processing trajectory sequence includes: Using geodesic theory to calculate the distance field of the contour feature map to obtain a geodesic distance field, and performing gradient vector calculation on the geodesic distance field to obtain a geodesic gradient vector field; Performing a geodesic path search on the geodesic gradient vector field by a preset fast marching method to obtain an initial geodesic path, and performing path smoothing processing on the initial geodesic path to obtain a smoothed geodesic path; The curvature analysis method is used to calculate the curvature of the smooth geodesic path to obtain the curvature distribution of the curve, and the curvature constraint judgment is performed on the curvature distribution of the curve to obtain the curve segment that meets the curvature constraint; The speed of the curve segment is distributed by a speed planning algorithm to obtain a speed curve, and the acceleration constraint is judged on the speed curve to obtain a processing trajectory segment that satisfies the acceleration constraint; Based on a trajectory splicing algorithm, trajectory segment splicing and path planning are performed on the processing trajectory segments to obtain a processing trajectory sequence.

5. The surface profile analysis method of laser multi-axis machining according to claim 1, characterized in that: The kinematic solution of the machining trajectory sequence is performed through the dynamic constraint analysis to obtain the linkage control parameters of each axis, including: The machining trajectory sequence is subjected to variational analysis through the Hamilton-Jacobi equation to obtain the trajectory energy functional, and the trajectory energy functional is subjected to optimal control solution to obtain a group of motion state equations; Based on the Lagrange multiplier method, the motion state equation group is constrained and optimized to obtain a multi-axis coupled dynamic equation, and the multi-axis coupled dynamic equation is numerically integrated to obtain a joint motion parameter set, wherein the joint motion parameter set includes an angular displacement sequence, an angular velocity curve, and an angular acceleration distribution; Performing dynamic inversion on the joint motion parameter set through dynamic constraint analysis to obtain a driving torque sequence, and performing harmonic analysis on the driving torque sequence to obtain a frequency domain characteristic spectrum, wherein the frequency domain characteristic spectrum includes amplitude response, phase delay and resonance frequency; Reconstructing the frequency domain characteristic spectrum in the time domain based on a Runge-Kutta integrator to obtain an axial motion trajectory, and interpolating and smoothing the axial motion trajectory to obtain a continuous motion curve; The continuous motion curve is optimally time-planned by the Pontryagin minimum principle to obtain a synchronous control sequence, and error compensation is performed on the synchronous control sequence to obtain linkage control parameters of each axis.

6. A surface profile analysis device for laser multi-axis linkage processing, characterized in that: include: A scanning module is used to scan the target curved surface workpiece after laser multi-axis linkage processing through a structured light 3D scanner to obtain a 3D point cloud data set; A reconstruction module, used for reconstructing the surface of the target curved workpiece based on the three-dimensional point cloud data set to obtain a digital curved surface model; An analysis module, configured to perform shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor; if the surface feature descriptor does not meet the expected geometric characteristic standard, perform spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum; A planning module, used for performing path planning on the contour feature map based on geodesic theory to obtain a processing trajectory sequence; A solution module, used for performing kinematic solution on the machining trajectory sequence through dynamic constraint analysis to obtain linkage control parameters of each axis, and adjusting the linkage control parameters of each axis based on the expected geometric characteristic standard; The step of performing shape analysis on the digitized surface model based on differential geometry theory to obtain a surface feature descriptor includes: The curvature tensor of the digital surface model is calculated by the Weingarten mapping algorithm to obtain a shape operator matrix, and the shape operator matrix is ​​subjected to eigenvalue decomposition to obtain a surface principal direction field; wherein the surface principal direction field includes a maximum principal curvature direction, a minimum principal curvature direction and a normal curvature distribution; Based on the Frenet frame theory, coordinate transformation is performed on the principal direction field of the surface to obtain a parametric expression of the local surface, and geodesic curvature is calculated on the parametric expression of the local surface to obtain an intrinsic geometric feature set; The covariant derivative of the intrinsic geometric feature set is calculated by Christoffel symbol to obtain the surface shape change rate, and the surface shape change rate is decomposed into a tensor field to obtain a set of geometric invariants; wherein the set of geometric invariants includes Gaussian curvature, mean curvature and shape factor; Based on the Ricci flow theory, a curvature flow evolution analysis is performed on the geometric invariant set to obtain a geometric flow field distribution, and topological features are extracted from the geometric flow field distribution to obtain a singular point distribution map, wherein the singular point distribution map includes a ridge network, a valley network and critical point positions; Performing an exterior differential operation on the singular point distribution diagram in a discrete differential form to obtain a surface feature form, and obtaining a surface feature descriptor based on the surface feature form; The step of performing spectral decomposition on the digitized surface model based on the surface feature descriptor to obtain a contour feature spectrum comprises: Based on the Laplace-Beltrami operator and the surface feature descriptor, the digitized surface model is subjected to spectral decomposition to obtain a feature spectrum sequence; Performing opening and closing operations on the feature map sequence through mathematical morphology to obtain a filtered feature map, and performing edge detection on the filtered feature map to obtain a contour line set; wherein the contour line set includes a main contour line, a secondary contour line and a feature point sequence; Performing topological reconstruction based on the contour line set to obtain a characteristic network graph; wherein the characteristic network graph includes critical point connection relationships, curvature extreme points and singular point distribution; Based on the graph theory optimization method, feature association analysis is performed based on the feature network graph to obtain a profile feature map.

7. A computer device comprising a memory and a processor, wherein a computer program is stored in the memory, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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