Error modeling and path planning method for linear laser in-situ measurement system

Abstract

This invention discloses an error modeling and path planning method for a line laser in-situ measurement system. The specific steps are as follows: First, the in-machine measurement system is calibrated by hand and eye. Then, by comprehensively analyzing the sources of errors in line laser in-situ measurement, a model of robot end-effector positioning error and optical plane triangulation error is established. Finally, the sensor attitude constraints are solved according to the measurement parameter requirements, thereby generating a measurement path that adapts to the characteristics of curved surfaces, which can effectively improve the stability and reliability of the system.

Description

Technical Field

[0001] This invention belongs to the field of laser measurement and processing integration technology in intelligent manufacturing, and involves the accuracy analysis and measurement path planning of in-situ line laser measurement of robots, especially a method for error modeling and path planning of in-situ line laser measurement system. Background Technology

[0002] In laser measurement and processing integration technology, laser sensors are used to detect workpiece contour information in real time and generate a model for processing. Therefore, the accuracy and stability of laser measurement are particularly important. Current related technologies mainly include robot error analysis, point laser sensor triangulation modeling, and path generation, but these are significantly limited in efficiency. Therefore, there is an urgent need for a method or device that ensures both the reliability of measurement accuracy and the stability of the measurement path.

[0003] Existing technologies only target point-source laser sensors, resulting in low measurement efficiency. Furthermore, the original error formula is not applicable to line laser sensors and does not adequately consider the coupling analysis of errors during on-machine measurement, thus failing to solve the problems of accuracy and efficiency in on-machine measurement of line lasers.

[0004] Therefore, the low measurement efficiency of point laser sensors limits their application when inspecting large and complex workpieces, leading to the adoption of line laser sensors as a means of information sensing. However, in-situ line laser measurement systems for robots suffer from technical problems such as insufficient accuracy and suboptimal path design. Based on this, this invention proposes an error modeling and path planning method for in-situ line laser measurement systems.

[0005] A search revealed that Chinese invention patent CN113566735A discloses an in-situ measurement method for the cooling channel of a rocket engine nozzle using a line laser, belonging to the field of in-situ measurement technology. First, a line laser sensor is integrated into the end effector of an industrial robot using a fixture, and the positional relationship between the line laser sensor and the industrial robot is determined using a hand-eye calibration method based on a standard sphere. Then, the scanning path of the line laser sensor is planned based on the nozzle's theoretical profile and the sensor's range, and the industrial robot drives the line laser sensor to acquire the outer contour data of the rocket engine nozzle. Finally, based on the nozzle outer contour data acquired by the line laser sensor, an algorithm based on sigmoid function fitting is used to accurately obtain edge feature points, and the dimensions of the nozzle cooling channel rib width, groove depth, and nozzle wall thickness are calculated based on the edge information. This achieves efficient in-situ measurement of the rocket engine nozzle cooling channel, improving measurement efficiency, and offering advantages such as low cost, high flexibility, and simple operation.

[0006] The technical comparison between this application and the aforementioned patent is as follows:

[0007] 1. The essential difference between core technical solutions and principles

[0008] The core technology of the patent "A Line Laser In-Situ Measurement Method for Cooling Channels of Rocket Engine Nozzles" focuses on the measurement of specific dimensions of cooling channels in rocket engine nozzles. Its technical approach involves: determining the positional relationship between the sensor and the robot through standard ball-and-eye calibration; planning the scanning path based on the nozzle's theoretical profile and sensor range; and finally, using a sigmoid function to extract edge features to calculate parameters such as rib width and groove depth. Its technical focus is on "edge feature extraction" and "path planning based on theoretical models," without addressing error modeling and compensation for the line laser measurement system, particularly neglecting triangulation errors caused by the tilt of the measured surface or error differences at different positions on the laser line.

[0009] The core technologies of this invention lie in "error modeling" and "adaptive path planning": First, based on the Lambert diffuse reflection model, the position of the light energy centroid angle is derived, and a laser triangulation error model is established (considering the influence of the object surface tilt angle and the laser line position on the error) to achieve error compensation; second, the surface region is divided through patch neighborhood search, and the sensor attitude is determined according to the surface normal vector to generate a scanning path adapted to the curvature characteristics. Its technical principles cover error source analysis, mathematical modeling, and dynamic path optimization, which are fundamentally different from the patent "A Method for In-situ Measurement of Linear Laser in the Cooling Channel of a Rocket Engine Nozzle" and the "Path Planning + Edge Extraction Based on Theoretical Profile" scheme.

[0010] 2. The essential difference between application scenarios and measurement targets

[0011] The patent "A Linear Laser In-Situ Measurement Method for Cooling Channel of Rocket Engine Nozzle" is designed for the specific structure of the cooling channel of rocket engine nozzle. The measurement targets are discrete dimensional parameters such as rib width and groove depth. Its path planning depends on the theoretical profile of the nozzle and is suitable for efficient detection of regular channel-type components.

[0012] This invention targets large, complex curved surface workpieces (such as aerospace components). The measurement objective is to obtain a complete and high-precision three-dimensional contour point cloud. It addresses issues such as surface tilt and differences in error at different laser line positions. Error compensation and adaptive path planning ensure the accuracy and completeness of the point cloud. It is suitable for measuring free-form surfaces without a fixed theoretical profile. There is a fundamental difference between this invention and others in terms of the complexity of the application objects and the comprehensiveness of the measurement objectives.

[0013] A search revealed Chinese invention patent CN116117818A, which discloses a method and system for robot sensor hand-eye calibration, relating to the field of sensor calibration technology. The key technical points of this invention include: acquiring point cloud data of the calibration object and determining the robot scanning path; calculating the line laser sensor measurement data for each robot pose; optimizing the rotation component in hand-eye calibration using the particle swarm optimization-Gaussian process algorithm based on the line laser sensor measurement data; and solving the translation component in hand-eye calibration using a least squares method based on the calculation results of the rotation component of the hand-eye matrix, thereby completing the overall calibration of the hand-eye matrix. This invention concludes from the perspective of 3D reconstruction that the error index of traditional methods is relatively unreasonable; and the calibration results of this invention can meet most measurement requirements. Compared with traditional methods, the method proposed in this invention is more convenient and accurate, and the evaluation index is more intuitive.

[0014] The technical comparison between this application and the aforementioned patent is as follows:

[0015] 1. The essential difference between technological focus and solutions

[0016] The core technology of the patent "A Method and System for Hand-Eye Calibration of Robot Sensors" is "Optimization of Hand-Eye Calibration Method": the rotation component of the hand-eye matrix is ​​optimized by using the particle swarm optimization-Gaussian process algorithm, and the translation component is solved by the least squares method. This solves the problem of unreasonable error indicators in traditional calibration methods. Its technical scope is limited to the calibration process and does not involve subsequent measurement error modeling or path planning.

[0017] In this invention, hand-eye calibration is only a basic step (used to calculate the three-dimensional coordinates of the measurement point cloud). Its core technology lies in error modeling and path planning after calibration: by analyzing the robot's end-effector positioning error and optical plane triangulation error, a compensation model based on the Lambert model is established; a scanning path is generated through region division and posture constraints. The two technologies have completely different focuses. The patent "A Method and System for Hand-Eye Calibration of Robot Sensors" does not involve error compensation and path planning, and is fundamentally different from the complete technology chain of this invention (calibration → error modeling → path planning).

[0018] 2. The essential difference between the technical problem solved and the technology chain

[0019] The patent "A Method and System for Hand-Eye Calibration of Robot Sensors" addresses the problem of "accuracy of hand-eye calibration," aiming to optimize the accuracy of the calibration matrix solution. It is a preliminary step in the construction of a measurement system.

[0020] This invention addresses the problems of insufficient accuracy and suboptimal path in in-situ line laser measurement. Its technology chain covers "system calibration → error modeling → data processing → path planning → accuracy verification," forming a complete measurement closed loop, aiming to improve the accuracy, efficiency, and stability of complex curved surface measurements. The problem domains and technology coverage of the two inventions are fundamentally different. Summary of the Invention

[0021] To address the aforementioned technical problems, this invention proposes an error modeling and path planning method for a line laser in-situ measurement system. First, the in-machine measurement system undergoes hand-eye calibration. Then, by comprehensively analyzing the sources of errors in the line laser in-situ measurement, a model for robot end-effector positioning error and optical plane triangulation error is established. Finally, the attitude constraints of the line laser sensor are solved according to the measurement parameter requirements, thereby generating a measurement path adapted to the curved surface characteristics, which can effectively improve the stability and reliability of the system.

[0022] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0023] A method for error modeling and path planning in a line laser in-situ measurement system, characterized by comprising the following steps:

[0024] S1. Analysis of the measurement principle of the line laser in-situ system;

[0025] S2. Derive the position of the centroid angle of light energy based on the Lambert diffuse reflection model;

[0026] S3. Analysis and modeling of line laser measurement errors caused by laser triangulation;

[0027] S4. In-situ system measurement scan constraint strategy;

[0028] S5. Measurement data processing;

[0029] S6. Measurement path generation and planning;

[0030] Simulation of S7, spherical and freeform surface path planning algorithms;

[0031] S8, Measurement accuracy and path control case verification.

[0032] As a preferred technical solution of the present invention: In step S1, the measurement principle analysis is as follows:

[0033] When the robot is equipped with a line laser sensor for measurement, the X-plane and coordinate system of the line laser sensor are clearly defined. The three-dimensional coordinates of the measurement point cloud are calculated by combining the robot's hand-eye coordinate positioning posture to obtain the contour information of the workpiece.

[0034] As a preferred technical solution of the present invention: In step S2, the position of the centroid angle of light energy is derived based on the Lambert diffuse reflection model as follows:

[0035] S21. Treating the workpiece as a diffuse reflector, assuming the measured surface of the workpiece is an ideal diffuse reflector, the spatial distribution of scattered light is described according to Lambert's law:

[0036] I(θ)=k d I L cosθ (1);

[0037] The parameters of the S22 line laser sensor are defined as follows:

[0038] Let point A be the measurement reference origin, z represent the displacement of the workpiece, where upward movement is negative and downward movement is positive, x represent the distance of the point on the laser line relative to the origin A, α represent the tilt angle of the measured surface of the workpiece, and β represent the angle between the center L2 of the imaging lens (4) and the center of the optical axis. R represents the normal of the surface being measured on the workpiece, R represents the radius of the imaging lens (4), a represents the distance from the center L2 of the imaging lens (4) to the origin A, and b represents the distance from the receiving surface to the imaging lens (4). When the surface being measured on the workpiece moves upward by z, the light spot moves upward by -z' accordingly. When the point on the laser line moves along the front-back direction by x, the light spot will also move by -x' accordingly.

[0039] S23. Consider a strip-shaped element dS perpendicular to the receiving plane on the receiving lens. The light energy at its center is the same as at other locations. Based on this, the light energy received by the strip-shaped element dS per unit time can be expressed as:

[0040] dE=I0cos(θ0-θ)dΩ (2);

[0041] Let r be the distance from the object point B to the center of the receiving lens, and dΩ represent the solid angle formed by the strip element dS relative to the object point. Then:

[0042] dΩ=dS / (r / cosθ) 2 =(1 / r 2 cos 2 θdS (3);

[0043] Where dS=2(R 2 -r 2 tan 2 θ) 1 / 2 Substituting (r / cosθ)dθ into equation (3), we get:

[0044] dΩ=2(R 2 -r 2 tan 2 θ) 1 / 2 (cosθ / r)dθ (4);

[0045] dE=2I0cos(θ0-θ)(R 2 -r 2 tan 2 θ) 1 / 2 (cosθ / r)dθ (5);

[0046] When performing displacement measurement, since the distance r from the object light point B to the receiving lens is much larger than the lens radius R, it can be approximated that sinθ = tanθ. Expanding cos(θ0-θ), we can derive the relationship (6):

[0047]

[0048] by For reference, the angle θ formed by counterclockwise rotation is taken as positive, and the angle formed by clockwise rotation is taken as negative. Let the position of the centroid angle of the light energy of the light cone inside the receiving lens be θ1. Then, at θ = θ1, the receiving lens is divided into two parts. Both parts are perpendicular to the receiving surface and receive equal light energy. The corresponding light energy integral equation is shown in equation (7):

[0049]

[0050] In the formula:

[0051]

[0052] make cos 2 θ≈|cosθ|, and within the integration limit from -Δθ to Δθ, we have cosθ≈|cosθ|, so equations (8) and (9) become:

[0053]

[0054] Substituting equations (10) and (11) into equation (7), and integrating, we get:

[0055] (r / R)cosθ0sinθ1[1-(r / R) 2 sin 2 θ1] 1 / 2 +cosθ0sin -1 [(r / R)sinθ1]

[0056] =(R / 3r)sinθ0{(1-(r / R)} 2 sin 2 θ1) 3 / 2 -(1-(r / R) 2 sin 2 Δθ) 3 / 2} (12);

[0057] Make (r / R) 2 sin2 θ1 << 1, so we take approximations sinθ1 ≈ θ1 and 1 - (r / R) 2 sin 2 θ1≈1, after simplification we get:

[0058] θ1=(R 2 / 3r 2 )tanθ0 (13);

[0059] Therefore, in the ΔOAC formed at the location of the convergent light spot when the object surface is tilted,

[0060]

[0061] In ΔOGC formed at the location where the light spot converges at an inclined surface,

[0062] ∠OGC=arccos((GC 2 +GO 2 -OC 2 ) / 2·GC·GO) (15);

[0063] In the ΔOBG formed at the convergence point of the light spot on the tilted object surface, due to (z / a) 2 <<1, taking the first-order approximation, we get:

[0064]

[0065] In the ΔCDE formed at the location where the light spot converges when the object surface is tilted.

[0066]

[0067] By combining equations (17), (18), and (19), we can obtain:

[0068]

[0069] ∠OBF is the value of θ0. Substituting equations (16) and (20) into equation (13), we get:

[0070]

[0071] in,

[0072] In the formula, θ1 represents the angular position of the light energy centroid line in the light cone received by the receiving lens. The projection point of this light energy centroid line on the photosensitive surface is the position of the light energy centroid of the converged spot on the photosensitive surface of the linear CCD.

[0073] As a preferred technical solution of the present invention: in step S3...

[0074] S31. The specific analysis of the line laser measurement error caused by laser triangulation is as follows:

[0075] For the same laser point on the laser line of a line laser sensor, when the tilt angle α of the workpiece surface is fixed, the measurement error of the line laser sensor will increase accordingly as the depth of field increases.

[0076] If a fixed point on the laser line is selected, the measurement error will increase as the workpiece surface tilt angle α increases, provided that the workpiece displacement z remains constant.

[0077] If the workpiece surface tilt angle α and displacement z are fixed, on the same laser line, the smaller the distance x from the laser point at different positions to the center, the smaller the measurement error, and vice versa. That is, the closer the position is to the center of the laser line, the smaller the error of the line laser sensor.

[0078] When the workpiece surface tilt angle α > 0, the positive and negative directions of the measurement error of the line laser sensor are consistent with the workpiece displacement direction, while when the workpiece surface tilt angle α < 0, the positive and negative directions of the error are opposite to the workpiece displacement direction.

[0079] S32. The specific modeling of the line laser measurement error caused by laser triangulation is as follows:

[0080] Let the center of mass of light energy be... Light energy centroid line through The light energy center of mass, after refraction, is projected onto the linear CCD to form a converging light spot. dot, make ,set up The image point is Its object distance Image distance satisfy Then it's like a point. Distance to the optical axis of the receiving lens It can be represented as:

[0081] O2P1'=P1P2·(b' / a')=P1P2·f / (a'-f) (22);

[0082] Since the distance O'B from the projection point B of ray P1O1 on the linear CCD to the optical axis of the receiving lens satisfies O'B=(P1P2·b) / a', and the angle of the object plane converges to form ΔCBP1'~ΔAO1P1', we can obtain:

[0083] BC=AO1·BP1' / O1P1' (23)

[0084] From the geometric relation AO1=rθ1, we can obtain O1P1'=rf / (a'-f).

[0085] BP1'=DP1' / sinγ=(O2P1'-O2D) / sinγ=(O2P1'-O'B) / sinγ (24);

[0086] Since sinγ=P1P2 / r, substituting equation (22) into equation (23), we get:

[0087]

[0088] Substituting equation (24) into equation (23), we can derive:

[0089] BC=θ1·b·P1G·cos∠P1GP2 / a (26);

[0090] Since O'C = O'B - BC, therefore:

[0091]

[0092] When the incident beam of the line laser sensor is perpendicular and the object surface is not tilted, we have θ'=θ1| α＝0 If the incident beam is incident at an angle α, i.e., the object surface is tilted, then θ'=θ1| α≠0 Therefore, the tilt angle error can be expressed as:

[0093]

[0094] in,

[0095] As a preferred technical solution of the present invention: in step S4...

[0096] S41, Constraint Strategy

[0097] Line laser sensors use the triangulation principle to determine the position of the laser line and the distance between the line laser sensor and the workpiece surface in the sensor coordinate system. By moving the workpiece or the line laser sensor, a set of 3D measurement points can be obtained. During the scanning process, the characteristics of the line laser sensor and the relative distance between the line laser sensor and the workpiece determine the quality of the measurement data. Therefore, the following constraints are applied:

[0098] Direction angle θ T Direction angle θ T The angle between the linear laser sensor orientation l and the workpiece surface normal vector n is the angle between the two. The magnitude of this angle directly affects the measurement results. When the scanning direction is parallel to the workpiece surface normal vector n, the maximum surface point cloud density can be achieved.

[0099] cos(θ T )<-l·n (29);

[0100] Depth of field: A line laser sensor can only measure surface data within the depth of field in a single scan. Assume a point in the sensor coordinate system is (x... s ,0,z s If so, then the following needs to be satisfied:

[0101] Hh / 2≤z s ≤H+h / 2 (30);

[0102] Optimal distance H: The optimal distance H is the distance from the laser source to the scanning reference plane located in half the depth of field, which allows the laser beam to be focused on the reference plane;

[0103] Scan width w: The scan width w is the width of the laser beam located at half the field of view depth, and is also the length of the scan line;

[0104] Field of view (FOV): The area is defined by the scanning angle δ and the scanning width, within which the line laser sensor can scan points;

[0105] Field of view angle δ: the angle of the laser beam plane;

[0106] Collision-free constraints: During the scanning process, ensure that the line laser sensor does not collide with the robot or workpiece;

[0107] S42, Neighborhood Search Algorithm

[0108] The workpiece being measured is a triangular mesh model described in STL file format. STL files are the standard format for triangular mesh models, consisting of vertex and face normals. A half-edge structure is used for topological reconstruction of the triangular mesh. After reconstructing the faces, a facet neighborhood search algorithm is used to search the nth-order neighborhood of the facets. f0 is a facet in the mesh model, IF0 is the index of facet f0, and IF... fi It is the corresponding facet f i A set of adjacent facets,

[0109] The algorithm for obtaining the nth-order neighborhood of facet f0 is as follows:

[0110] S421. To find the first-order neighborhood NH1 of facet f0, first, find the three half-edges contained in f0. Then, find the corresponding neighborhood half-edges and calculate the neighborhood face set of neighborhood f0, which is called the first-order neighborhood face set.

[0111]

[0112] S422. Find the second-order neighborhood NH2 of the facet f0. NH2 is obtained by searching the facet in the first-order neighborhood.

[0113]

[0114] S423. Find the n-th order neighborhood NH of the facet f0. n NH n Obtained by searching for facets in the N-1 order neighborhood:

[0115]

[0116] As a preferred technical solution of the present invention: In step S5, the measurement data processing specifically includes:

[0117] S51. A radius filtering algorithm is used to filter and reduce noise in the point cloud data, as detailed below:

[0118] S511. First, set the discrete threshold K and the filter radius r;

[0119] S512, then import the point cloud data;

[0120] S513. Next, filter the point cloud data according to the set parameters;

[0121] S514. Points with fewer than the discrete threshold K within a radius r are identified as noise and removed.

[0122] S515. Finally, save the filtered point cloud data.

[0123] S52. A downsampling algorithm is used to reduce the number of points in the point cloud data while retaining the key features of the point cloud, as detailed below:

[0124] First, a 3D voxel mesh is constructed, and the centroid of all points within each voxel is used as the representative point to approximate all points within that voxel. By traversing all voxels, a downsampled point cloud composed of the centroids of each voxel is finally obtained.

[0125] Suppose the input point cloud dataset P is divided into N voxels of uniform size, and the length, width, and height of each voxel are all set to 1 mm. For the i-th voxel, its center point can be represented as:

[0126]

[0127] Among them, c i Let n represent the center coordinates of the i-th voxel. i It is the number of points contained within that voxel; V i p represents the set of point clouds contained in the i-th voxel; j ∈V i Void i The coordinates of the j-th point in the array.

[0128] As a preferred technical solution of the present invention: In step S6, the generation and planning of the measurement path are specifically as follows:

[0129] S61, Surface Region Division

[0130] S611. Traverse all unmarked faces and find the two faces with the largest normal vectors. The angle between the two faces with the largest normal vectors is θ. If the angle between the two normal vector angles θ satisfies: θ < 2θ T This indicates that all faces can be scanned from a single viewpoint. If the angle does not meet this condition, proceed to the next step.

[0131] S612. Consider the two faces with the largest included angle between their normal vectors as seed triangle faces f. i and f j Where i≠0 and j≠0, the scanning region Φ is formed by patches using a neighborhood search algorithm. i The patches within the region and the seed patch f i The included angles between them are all less than 2θ T Similarly, the scanning area Φ is obtained. j Mark the planned facets;

[0132] S613. Calculate the average normal vector of the initial scanning area, then detect the orientation angle of each face in the area, remove the marking of the face that does not meet the viewpoint constraint, and determine the scanning area. If all face is marked, the division ends; otherwise, return to step S611.

[0133] S62. Determining the sensor orientation

[0134] Sensor direction S z Determined according to the following formula:

[0135]

[0136] In the formula, m is the number of triangular patches in the scanned area, and n i It is the normal vector of each facet;

[0137] S63, Generation of Scanning Viewpoint

[0138] Project all vertices of the faces within the region onto S. z The coordinates of the projection points are calculated using equation (36), and then the maximum distance between the projection points is determined.

[0139] p i =-(v i ·S z )S z (36);

[0140] In the formula, v i Let be the coordinates of the vertices of the face.

[0141] Let ΔH represent S zThe maximum distance between all projected points in the direction is calculated according to equation (37), P H and P L It is -S z The highest and lowest projection points in the direction,

[0142] ΔH=|p H -p L | (37);

[0143] If ΔH ≤ h, then all patches belong to the same depth range and can be scanned within the same optimal distance plane; if ΔH > h, the same S z The directional patches need to be classified according to the depth range, and the classification data is determined by equation (38), where Indicates rounding down.

[0144]

[0145] S64. Generation of Scan Path

[0146] Containing points But perpendicular to The face is marked as ,point Calculated by equation (39), firstly, the patches in the scanned region that satisfy the depth constraint are projected onto the plane. The coordinates of the projection point are calculated using equation (40). (39);

[0147] p ij =v i +(v i O j ·S z )S z (40);

[0148] Where, p ij The coordinates of the projection point, v i Represents the vertex coordinates of the face.

[0149] After projection, plane Π j The small planes in the middle form a polygon.

[0150] The convex hull of the projection plane is calculated using Graham's algorithm, and then the minimum outer rectangle of the convex hull is obtained through rotation, which is the region to be scanned.

[0151] Taking the length of the outer rectangle as the direction of sensor movement, i.e., the Y-axis direction of the sensor coordinate system, and the width direction of the rectangle as the X-axis, assuming that the four points constituting the minimum outer rectangle are A, B, C, and D in the workpiece coordinate system, if |AB|>|CD|, then the sensor's attitude in this region can be obtained from equation (41):

[0152]

[0153] If |AD|≤w, the region can be scanned according to a scan line segment; otherwise, the width of the minimum outer rectangle is divided, and the number of scan lines N in the region is obtained by equation (42), where This indicates rounding up. Finally, different scan lines are connected to form the scan path for the region.

[0154]

[0155] As a preferred technical solution of the present invention: in step S7...

[0156] S71, Simulation of Freeform Surface Path Planning Algorithm

[0157] The freeform surface model consists of 1594 faces and 862 points. The maximum angle θ between the surface normals of the triangular mesh of the freeform surface model is determined by traversing the surface. max = 95.67°, because θ max >2θ T The pose needs to be changed for measurement, and the two faces with the largest angle between their normal vectors, i.e., f, should be selected. i =126 and f j =893, perform a neighborhood search to form the scan area Φ i and Φ j Calculate the sensor pose S z According to equation (37), the depth is calculated to obtain ΔH = 4.92. Since the depth of field h is 8, ΔH < h, each region block satisfies the depth constraint. Finally, the final scanning path is generated for each region.

[0158] S72, Simulation of Hemispherical Path Planning Algorithm

[0159] The hemispherical model has 3484 faces and 1804 points. Find the maximum angle θ between the normal vectors of the triangular blocks in the hemispherical model. max It is 179.84°, due to θ max >2θ T To achieve a complete scan of the workpiece surface, the sensor's orientation needs to be changed. First, all unmarked surfaces of the workpiece are traversed, and the two surfaces with the largest angles, i.e., f, are selected. i =115 and f j =3284, used as the seed triangle facet, and the neighborhood of the seed facet is searched, scanning region Φ. i From facet f i and the angle with the facet is less than 2θ T Composed of all facets, the scanning area Φ j Similarly, in region Φ i and Φj In the detection viewpoint, remove facet marks that do not meet the viewpoint constraints, and then calculate the sensor pose S. z Since ΔH = 15.905 is greater than the depth of field h, k = 1 is calculated according to equation (38). The regions are further classified, and four different scanning regions are generated. The final scanning path is generated for each region.

[0160] As a preferred technical solution of the present invention: in step S8...

[0161] S81. Verify the hemispherical workpiece.

[0162] After the workpiece pose is known and hand-eye calibration is completed, the scanning path of the robot end can be obtained using equation (43). The line laser sensor collects point clouds of different sections of the workpiece surface at different scanning times. When the scanning is completed, the data needs to be converted to the same coordinate system to achieve point cloud registration. According to equation (44), the scanning data can be unified into the robot's base coordinate system:

[0163] T BE =T BO T OS T ES -1 (43);

[0164] P B =T BE T ES P S (44);

[0165] In the formula, P S It is the position of the scanning point in the sensor coordinate system, P B It is the position of the scan point in the base coordinate system;

[0166] The collected data is preprocessed to remove noise and outliers. After obtaining the point cloud data of the hemispherical surface, the scanned model is first aligned with the corresponding CAD model. Then, the difference threshold method is used to determine whether there are defects in the workpiece. Geomagic Qualify software is used as an auxiliary inspection tool. The specific operation process is as follows:

[0167] First, the scanned point cloud model was imported into the software as the test object, and then the CAD model was imported as the reference model. Next, by utilizing the software's best fit and alignment functions, the matching between the test model and the reference model was gradually adjusted and optimized until the minimum deviation was achieved. Subsequently, the software's comparative analysis function was used to generate a 3D deviation map, comprehensively reflecting the differences between the two models. Finally, the deviation results were obtained from the experiment.

[0168] The maximum deviation, average deviation, and standard deviation between the point cloud model obtained by scanning and the CAD reference model are obtained, and the robot positioning error is compensated. The tilt error of the sensor part and the laser line error are compensated using the error model. The compensated point cloud model is compared with the CAD model, and the comparison results meet the requirements of in-machine measurement accuracy.

[0169] S82. Verification of complex curved surface workpieces.

[0170] The machined complex curved surface workpiece is scanned and measured. The workpiece before and after compensation is compared with the standard model. The comparison results meet the requirements of in-machine measurement accuracy.

[0171] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0172] This invention constructs an in-situ line laser measurement system by employing a six-degree-of-freedom robot equipped with a line laser sensor. To improve measurement accuracy, it analyzes the error principle of laser triangulation based on the Lambert diffuse reflection model and proposes an error compensation strategy to solve the measurement inaccuracies caused by tilt angles when measuring complex curved surfaces. To improve measurement efficiency and stability, it divides the measurement posture according to scanning constraints and generates measurement paths to meet both accuracy requirements and improve measurement efficiency. This enhances the adaptability to the measurement needs of large and complex components in aerospace applications. Attached Figure Description

[0173] Figure 1 This is a schematic diagram of the laser scanning platform structure in an embodiment of the present invention;

[0174] Figure 2 This is a schematic diagram of coordinate transformation in an embodiment of the present invention;

[0175] Figure 3 This is a schematic diagram illustrating the relevant parameter definitions of the line laser sensor in an embodiment of the present invention;

[0176] Figure 4 This is a schematic diagram of the receiving element in an embodiment of the present invention;

[0177] Figure 5 This is a derivation diagram of the convergence spot position when the object surface is tilted in an embodiment of the present invention;

[0178] Figure 6 This is a schematic diagram of the position of the optical energy centroid line and the convergent light spot in an embodiment of the present invention;

[0179] Figure 7 This describes the laser scanning principle and constraints in the embodiments of the present invention;

[0180] Figure 8 This is a triangular neighborhood search graph in an embodiment of the present invention;

[0181] Figure 9 This is a schematic diagram of the radius filtering algorithm in an embodiment of the present invention;

[0182] Figure 10 This refers to the selection of the seed triangular facet in this embodiment of the invention;

[0183] Figure 11 This is the average normal vector diagram in the embodiment of the present invention;

[0184] Figure 12 This is a pattern of projection from a vertex on the surface to a line laser sensor in an embodiment of the present invention;

[0185] Figure 13 S is an embodiment of the present invention. z Distance between the projection points of the direction;

[0186] Figure 14 This is a schematic diagram of a region patch projected onto a plane in an embodiment of the present invention;

[0187] Figure 15 This is the smallest outer rectangle diagram in the embodiments of the present invention;

[0188] Figure 16 This is a scan path diagram in a scan area in an embodiment of the present invention;

[0189] Figure 17 This is a schematic diagram of a freeform surface model in an embodiment of the present invention;

[0190] Figure 18 This is a schematic diagram of the freeform surface scanning path in an embodiment of the present invention;

[0191] Figure 19 This is a schematic diagram of a hemispherical model in an embodiment of the present invention;

[0192] Figure 20 This is a schematic diagram of the hemispherical scanning path in an embodiment of the present invention;

[0193] Figure 21 This is a comparison diagram between the hemispherical measurement results and the theoretical model in an embodiment of the present invention;

[0194] Figure 22 This is a comparison diagram of the point cloud after complex surface compensation and the theoretical model in an embodiment of the present invention.

[0195] List of reference numerals in the attached diagram:

[0196] 1. Robot; 2. Line laser sensor; 3. Workpiece; 4. Imaging lens. Detailed Implementation

[0197] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0198] The present invention proposes an error modeling and path planning method for a line laser in-situ measurement system, the specific steps of which are as follows:

[0199] S1. Measurement Principle Analysis of Linear Laser In-Situ System:

[0200] like Figure 1-2 As shown, when robot 1 is equipped with line laser sensor 2 for measurement, the X-plane and coordinate system of line laser sensor 2 are defined, and the three-dimensional coordinates of the measurement point cloud are calculated by combining the hand-eye coordinate positioning posture of robot 1, thereby obtaining the contour information of workpiece 3.

[0201] S2. Deriving the position of the centroid angle of light energy based on the Lambert diffuse reflection model:

[0202] When the surface being measured is tilted, the spatial distribution of scattered light relative to the receiving lens changes, causing the center of mass of the focused light spot on the photosensitive surface of the linear CCD to shift compared to the case of perpendicular incidence. If the displacement calculation model established for perpendicular incidence is still used for data processing, errors will inevitably occur. Therefore, the measurement deviation caused by the tilt of the object surface is fundamentally due to the discrepancy between the actual optical path change and the ideal model.

[0203] The specific derivation process is as follows:

[0204] Since the actual objects being measured are mostly opaque and have relatively rough surfaces, they are usually treated as diffuse reflectors. Assuming the measured surface is an ideal diffuse reflective surface, the spatial distribution of scattered light is described according to Lambert's law.

[0205] I(θ)=k d I L cosθ (1);

[0206] The relevant parameter definitions for line laser sensor 2 are as follows: Figure 3 As shown, point A is the measurement reference origin, z represents the displacement of the object being measured (negative for upward movement and positive for downward movement), x represents the distance of the point on the laser line relative to the origin A, α is the tilt angle of the object surface, and β represents the angle between the center L2 of the imaging lens 4 and the center of the optical axis. R represents the normal to the surface being measured, R represents the radius of the imaging lens 4, a represents the distance from the center L2 of the imaging lens 4 to the origin, and b represents the distance from the receiving surface to the imaging lens 4. When the object surface moves upward by z, the light spot moves upward by -z' accordingly; when a point on the laser line moves forward and backward by x, the light spot will also shift by -x' accordingly.

[0207] Consider a strip-shaped element dS perpendicular to the receiving plane on the receiving lens. Since the lens is relatively small, the scattered light field distribution on this element can be approximated as uniform, with the light energy at its center being the same as at other locations. Based on this, the light energy received by the strip-shaped element dS per unit time can be expressed as:

[0208] dE=I0cos(θ0-θ)dΩ (2);

[0209] like Figure 4 As shown, a schematic diagram of the receiving surface element is presented, where r is the distance from the object light point B to the center of the lens, and dΩ represents the solid angle formed by the strip surface element dS relative to the object light point.

[0210] dΩ=dS / (r / cosθ) 2 =(1 / r 2 cos 2 θdS (3);

[0211] Where dS = 2(R) 2 -r 2 tan 2 θ) 1 / 2 Substituting (r / cosθ)dθ into equation (3), we get:

[0212] dΩ=2(R 2 -r 2 tan 2 θ) 1 / 2 (cosθ / r)dθ (4)

[0213] dE=2I0cos(θ0-θ)(R 2 -r 2 tan 2 θ) 1 / 2 (cosθ / r)dθ (5)

[0214] When performing displacement measurement, since the distance r from the object light point B to the lens is much greater than the lens radius R, it can be approximated that sinθ = tanθ. Expanding cos(θ0-θ), we can derive the relationship (6):

[0215]

[0216] by For reference, the angle θ formed by counterclockwise rotation is taken as positive, and the angle formed by clockwise rotation is taken as negative. Let the position of the centroid angle of the light cone inside the receiving lens be θ1. Then, at θ = θ1, the receiving lens is divided into two parts. Both parts are perpendicular to the receiving surface and receive equal light energy. The corresponding light energy integral equation is shown in equation (7):

[0217]

[0218] In the formula:

[0219]

[0220] Since the angle θ is very small, it can be approximated, cos 2 θ≈|cosθ|, and within the integration limit from -Δθ to Δθ, we have cosθ≈|cosθ|, so equations (8) and (9) become:

[0221]

[0222] Substituting equations (10) and (11) into equation (7), and integrating, we get:

[0223] (r / R)cosθ0sinθ1[1-(r / R) 2 sin 2 θ1] 1 / 2 +cosθ0sin -1 [(r / R)sinθ1]

[0224] =(R / 3r)sinθ0{(1-(r / R)} 2 sin 2 θ1) 3 / 2 -(1-(r / R) 2 sin 2 Δθ) 3 / 2} (12);

[0225] Since θ1 is very small, in general (r / R) 2 sin 2 Since θ1 << 1, we can approximate it as sinθ1 ≈ θ1 and 1 - (r / R). 2 sin 2 θ1≈1, after simplification we get:

[0226] θ1=(R 2 / 3r 2 )tanθ0 (13);

[0227] like Figure 5 As shown, in ΔOAC,

[0228]

[0229] In ΔOGC,

[0230] ∠OGC=arccos((GC 2 +GO 2 -OC 2 ) / 2·GC·GO) (15);

[0231] In ΔOBG, due to (z / a) 2 <<1, taking the first-order approximation, we get:

[0232]

[0233] In ΔCDE,

[0234]

[0235] By combining equations (17), (18), and (19), we can obtain:

[0236]

[0237] ∠OBF is the value of θ0. Substituting equations (16) and (20) into equation (13), we get:

[0238]

[0239] in,

[0240] In the formula, θ1 represents the angular position of the light energy centroid line in the light cone received by the receiving lens. The projection point of this light energy centroid line onto the photosensitive surface is the position of the light energy centroid of the converging spot on the photosensitive surface of the linear CCD.

[0241] S3. Analysis and Modeling of Line Laser Measurement Errors Caused by Laser Triangulation:

[0242] S31. The error analysis of line laser measurement caused by laser triangulation is as follows:

[0243] (1) For the same laser point on the laser line of the line laser sensor 2, when the tilt angle α of the object surface is fixed, the measurement error of the line laser sensor 2 will increase accordingly as the depth of field increases.

[0244] (2) If a fixed point on the laser line is selected, the measurement error will increase with the increase of the object's surface tilt angle, provided that the object's displacement z remains constant.

[0245] (3) If the tilt angle α and displacement z of the object surface are fixed, the smaller the distance x from the laser point at different positions to the center on the same laser line, the smaller the measurement error, and vice versa. That is, the closer the position is to the center of the laser line, the smaller the error of the line laser sensor 2.

[0246] (4) When the tilt angle α > 0, the positive and negative directions of the measurement error of the line laser sensor 2 are consistent with the direction of the object displacement; while when the tilt angle α < 0, the positive and negative directions of the error are opposite to the direction of the object displacement.

[0247] S32. The specific modeling of the line laser measurement error caused by laser triangulation is as follows:

[0248] like Figure 6 As shown, the light energy centroid P1A is refracted by L2 and projected onto the linear CCD array, forming a converging light spot at point C. Let P1P2⊥O1G. Let the image point of P1 be P1', and its object distance a' and image distance b' satisfy b'=a'f / (a'-f). Then the distance O2P1' from the image point P1' to the optical axis of the receiving lens can be expressed as:

[0249] O2P1'=P1P2·(b' / a')=P1P2·f / (a'-f) (22);

[0250] Since the distance O'B from the projection point B of ray P1O1 on the linear CCD to the optical axis of the receiving lens satisfies O'B=(P1P2·b) / a', and ΔCBP1'~ΔAO1P1', we can obtain:

[0251] BC = AO1·BP1' / O1P1' (23);

[0252] From the geometric relation AO1=rθ1, we can obtain O1P1'=rf / (a'-f).

[0253] BP1'=DP1' / sinγ=(O2P1'-O2D) / sinγ=(O2P1'-O'B) / sinγ (24);

[0254] Since sinγ=P1P2 / r, substituting equation (22) into equation (23), we get:

[0255]

[0256] Substituting equation (24) into equation (23), we can derive:

[0257] BC=θ1·b·P1G·cos∠P1GP2 / a (26);

[0258] Since O'C = O'B - BC, therefore:

[0259]

[0260] When the incident beam from the line laser sensor 2 is perpendicular and the object surface is not tilted, then θ' = θ1| α＝0 If the incident beam is incident at an angle α, i.e., the object surface is tilted, then θ'=θ1| α≠0 Therefore, the tilt angle error can be expressed as:

[0261]

[0262] in,

[0263] S4. In-situ system measurement scan constraint strategy:

[0264] S41, Constraint Strategy

[0265] like Figure 7 As shown, the line laser sensor 2 uses the triangulation measurement principle, which can easily obtain the position of the laser line (called the X-axis) and the distance between the line laser sensor 2 and the surface of the workpiece 3 (called the Z-axis) in the sensor coordinate system. By moving the workpiece 3 or the position of the line laser sensor 2, a set of 3D measurement points can be obtained. During the scanning process, the characteristics of the line laser sensor 2 and the relative distance between the line laser sensor 2 and the workpiece 3 determine the quality of the measurement data, therefore, it is necessary to consider... Figure 7 The constraints shown.

[0266] (1) Direction angle: θ T The angle between the orientation l of the linear laser sensor 2 and the surface normal vector n of the workpiece 3 is directly affected by the measurement results. When the scanning direction is parallel to the surface normal vector of the workpiece 3, the maximum surface point cloud density can be achieved, thereby improving the scanning quality.

[0267] cos(θ T )<-l·n (29);

[0268] (2) Depth of field: The line laser sensor 2 can only measure surface data within the depth of field during a single scan. Assume the point in the sensor coordinate system is (x... s ,0,z s If ), then equation (29) needs to be satisfied.

[0269] Hh / 2≤z s ≤H+h / 2 (30);

[0270] (3) Optimal distance (H): The distance H is from the laser source to the scanning reference plane located in half the depth of field. It can focus the laser beam on the reference plane.

[0271] (4) Scan width (w): The scan width is the width of the laser beam at half the field of view depth, which is also the length of the scan line.

[0272] (5) Field of view (FOV): The area is defined by the scanning angle δ and the scanning width, and the line laser sensor 2 can scan points within this range.

[0273] (6) Field of view (δ): The angle of the laser beam plane.

[0274] (7) No collision constraint: During the scanning process, ensure that the line laser sensor 2 will not collide with the robot 1 or the workpiece 3.

[0275] S42, Neighborhood Search Algorithm

[0276] The measured workpiece 3 is typically a triangular mesh model described in stereolithography (STL) file format. STL files are the standard format for triangular mesh models, consisting of vertex and face normals. Half-edge structures are used for topological reconstruction of the triangular mesh. After reconstructing the facets, a facet neighborhood search algorithm is used, which can search the nth-order neighborhood of the facets.

[0277] like Figure 8 As shown, f0 is a facet in the mesh model, and IF0 is the index of facet f0. IF fi It is the corresponding facet f i A set of adjacent facets.

[0278] The algorithm for obtaining the nth-order neighborhood of facet f0 is as follows:

[0279] S421: Find the first-order neighborhood NH1 of facet f0: First, find the three half-edges contained in f0; then, find the corresponding neighborhood half-edges; find the neighborhood face set of neighborhood f0, which is called the first-order neighborhood face set;

[0280]

[0281] S422: Find the second-order neighborhood NH2 of the facet f0: NH2 is obtained by searching the facet in the first-order neighborhood;

[0282]

[0283] S423: Find the n-th order neighborhood NH of the facet f0. n NH n Obtained by searching for facets in the N-1 order neighborhood;

[0284]

[0285] S5. Measurement Data Processing:

[0286] S51, Radius Filtering Algorithm

[0287] Ideally, point cloud data should exhibit continuous and uniform distribution characteristics. However, in actual scanning, the acquisition of key feature areas by the line laser sensor 2 may be affected by factors such as insufficient light, equipment heating and mechanical vibration, and a certain number of noise points are often mixed into the point cloud. These noise points destroy the continuity and integrity of the point cloud. If there are too many noise points, it will not only hinder the extraction of real and effective information, but also reduce the accuracy and reliability of subsequent point cloud processing algorithms. Therefore, when the noise in the point cloud data is significant, filtering and noise reduction techniques must be used for preprocessing to improve the data quality and the effect of subsequent analysis

[69] .

[0288] Radius filtering is a commonly used method for removing discrete points from point clouds. Its basic principle is to utilize the sparse and spatially disordered distribution of discrete points, combined with a set filtering radius *r* and a discrete threshold *K*, to perform local density analysis on the point cloud data. Specifically, for each point in the point cloud, the number of its neighboring points within the radius *r* is calculated iteratively. If the number of neighboring points is less than the set discrete threshold *K*, the point is considered discrete and removed. This method is fast and can effectively preserve densely structured and rationally distributed regions in the point cloud while removing isolated and scattered noise points, thereby improving the overall quality of the point cloud data and the accuracy of subsequent processing.

[0289] In radius filtering algorithms, the selection of the discrete threshold K and the filtering radius r plays a crucial role in the filtering effect of point cloud data. For example... Figure 9 As shown, a neighborhood region with radius r is established centered on a target point, and the number of neighboring points within this region is counted. If the discrete threshold K is set to 5, only target point 3 satisfies the condition that the number of points in its neighborhood is no less than 5, and is therefore retained; while points 1 and 2, due to insufficient points in their neighborhoods, will be marked as discrete points and removed. The specific operation steps of radius filtering are as follows: First, set the discrete threshold K and the filtering radius r; import point cloud data; then import point cloud data; next, perform filtering processing on the point cloud data according to the set parameters; for points within the radius r with fewer neighboring points than the discrete threshold K, they are judged as noise and removed; finally, save the filtered point cloud data.

[0290] S52, Downsampling Algorithm

[0291] Point cloud data acquired by a single line laser sensor 2 typically contains millions of points. Directly processing such a massive dataset consumes significant computing resources, especially in both spatial and temporal dimensions, potentially leading to computational delays of tens of minutes and impacting the real-time performance of the machine measurement system. To effectively address this issue, point cloud downsampling techniques are commonly employed. This method significantly reduces the number of point clouds while preserving key features, thereby improving subsequent processing efficiency. In its implementation, the algorithm first constructs a three-dimensional voxel mesh and uses the centroid of all points within each voxel as a representative point to approximate all points within that voxel. By traversing all voxels, a downsampled point cloud composed of the centroids of each voxel is finally obtained. Compared to directly using the geometric centers of voxels for approximation, using the centroids of points within voxels, although computationally more complex, more accurately preserves the local structural features of the point cloud.

[0292] Suppose the input point cloud dataset P is divided into N voxels of uniform size, each voxel having a length, width, and height of 1 mm. For the i-th voxel, its center point can be represented as:

[0293]

[0294] Among them, c i Let n represent the center coordinates of the i-th voxel. i It is the number of points contained within that voxel; V i p represents the set of point clouds contained in the i-th voxel; j ∈V i Void i The coordinates of the j-th point in the array.

[0295] S6. Measurement Path Generation and Planning:

[0296] During the scanning of workpiece 3 by robot 1 and line laser sensor 2, certain constraints must be followed. To ensure the completeness of the collected surface information of workpiece 3, the pose of line laser sensor 2 needs to be planned in advance. In addition, since each scan can only cover one scan line on the surface of workpiece 3, a suitable measurement path also needs to be planned to ensure that the entire surface of workpiece 3 is fully inspected.

[0297] S61, Surface Region Division

[0298] like Figure 10 As shown, when the orientation (S) of the line laser sensor 2 is... z The point cloud acquisition effect is best when the direction of the line laser sensor 2 is parallel to the surface normal vector of workpiece 3. To reduce the additional operation time caused by frequent changes in the direction of the line laser sensor 2, the surface of workpiece 3 needs to be segmented to ensure that the direction of the line laser sensor 2 is constant in each segment, i.e., the direction of the line laser sensor 2 (S...) z The angle between the direction angle and the normal vector of all small planes in the cross section is within the threshold of the direction angle.

[0299] The steps for dividing the region are as follows:

[0300] S611. Traverse all unmarked faces and find the two faces with the largest normal vectors, such as... Figure 10 As shown, the normal angle θ of the red and green facets is the largest. If the included angle between two angles satisfies: θ < 2θ T This indicates that all faces can be scanned within a single viewpoint. If the angle does not meet this condition, proceed to the next step.

[0301] S612. Consider the two faces with the largest included angle between their normal vectors as seed triangle faces f. i and f j Where i≠0 and j≠0. Using a neighborhood search algorithm, the scanning region Φ is formed by patches. i The patches within the region and the seed patch f i The included angles between them are all less than 2θ TSimilarly, the scanning area Φ is obtained. j Mark the planned facets;

[0302] S613. Calculate the average normal vector of the initial scan area, then detect the orientation angle of each face within the area, and remove the markings from faces that do not meet the viewpoint constraints to determine the scan area. If all faces are marked, the segmentation ends; otherwise, return to step S611.

[0303] S62. Determining the sensor orientation

[0304] The direction of line laser sensor 2 is the Z-axis of the sensor coordinate system. Within a region satisfying the orientation angle constraint, the direction of line laser sensor 2 is defined as the opposite direction to the average normal vector of all surfaces in that region, such as... Figure 11 As shown.

[0305] Line laser sensor 2-direction S z Determined according to formula (35).

[0306]

[0307] In the formula, m is the number of triangular patches in the scanned area, and n i It is the normal vector of each facet.

[0308] S63, Generation of Scanning Viewpoint

[0309] Project all vertices of the faces within the region onto S. z Above, such as Figure 12 As shown.

[0310] The coordinates of the projection points are calculated using equation (36), and then the maximum distance between the projection points is determined.

[0311] p i =-(v i ·S z )S z (36);

[0312] In the formula, v i These are the vertex coordinates of the face.

[0313] S z The calculation of the maximum distance between directional projection points is as follows: Figure 13 As shown.

[0314] In the diagram, red dots represent the projection points of all vertices of the facets in that region, and black circles represent the highest and lowest points in that direction. ΔH represents S. z The maximum distance between all projected points in the direction. Calculated according to equation (37), P H and P L It is -S zThe highest and lowest projection points in the direction.

[0315] ΔH=|p H -p L | (37)

[0316] exist Figure 13 In the process, if ΔH ≤ h, all patches belong to the same depth range and can be scanned within the same optimal distance plane; if ΔH > h, the same S... z The directional patches need to be classified according to the depth range, and the classification data is determined by equation (38), where Indicates rounding down:

[0317]

[0318] S644, Generation of Scan Path

[0319] Containing point O j But perpendicular to S z The face is marked as Π j Point O j Calculated from equation (39),

[0320] First, project the facets in the scanned region that satisfy the depth constraints onto the plane Π. j The coordinates of the projection point are calculated using equation (40), and the projection effect is as follows: Figure 14 As shown.

[0321]

[0322] p ij =v i +(v i O j ·S z )S z (40);

[0323] Where, p ij The coordinates of the projection point, v i Represents the vertex coordinates of the face.

[0324] After projection, from plane Π j The polygon formed by the small planes in the middle, such as Figure 14 As shown by the middle red line.

[0325] To obtain the scan path, the convex hull of the projection plane is calculated using Graham's algorithm, and then the minimum outer rectangle of the convex hull is obtained using a rotation method, such as... Figure 15 As shown. The green dashed line represents the minimum convex hull of the projected polygon, and the blue dashed line represents the minimum outer rectangle, which is the area to be scanned.

[0326] To reduce the number of turns in the scanning path, the longitudinal direction of the outer rectangle is taken as the direction of movement of the line laser sensor 2, i.e., the Y-axis direction of the sensor coordinate system, and the width direction of the rectangle is taken as the X-axis. Assuming that the four points constituting the minimum outer rectangle are A, B, C, and D in the coordinate system of the workpiece 3, if |AB|>|CD|, then the orientation of the line laser sensor 2 in this region can be obtained by equation (41).

[0327]

[0328] If |AD|≤w, the region can be scanned using a single scan line segment. Otherwise, the width of the minimum outer rectangle is divided, and the number of scan lines N for the region is obtained from equation (42), where... This indicates rounding up. The scan path for this region is as follows: Figure 16 As shown in the diagram, the blue lines with arrows represent scan segments. Each scan segment is divided according to the scan step size, resulting in a scan viewpoint within the projection plane. The blue lines consist of global scan viewpoints, and the arrows indicate the direction of movement of the line laser sensor 2. The attitude of the line laser sensor 2 remains constant throughout the scanning process. Finally, different scan lines are connected to form the scan path for the region.

[0329]

[0330] Simulation of S7, spherical and freeform surface path planning algorithms:

[0331] The path planning algorithm is based on an STL faceted file, requiring the side length of the facet to be less than the width of the scanning line of the line laser sensor 2. Path planning is performed by refining the triangular mesh model of the workpiece 3. The freeform surface model is as follows: Figure 17 As shown. The model consists of 1594 faces and 862 points. The maximum angle θ between the surface normals of the triangular mesh of the traversed surface model is calculated. max = 95.67°, because θ max >2θ T It is necessary to change the pose for measurement, and select the two faces with the largest angle between their normal vectors (f). i =126 and f j =893) Perform a neighborhood search to form the scanned region Φ i and Φ j Calculate the 2-position pose of the line laser sensor. z According to equation (37), the depth is calculated to be ΔH = 4.92. Since the depth of field h is 8, ΔH < h, and each region block satisfies the depth constraint. Finally, the final scanning path is generated for each region according to the method described above, such as... Figure 18 As shown in the figure, the freeform surface is divided into two regions, red and blue. The red and blue lines are the average normal vectors of the two regions, which are also the opposite directions of the line laser sensor 2. The green line is the final generated scanning path.

[0332] hemispherical model such as Figure 19 As shown. The model has 3484 faces and 1804 points. Find the maximum angle θ between the normal vectors of the triangular blocks in the model. max It is 179.84°, due to θ max >2θ T To achieve a complete scan of the surface of workpiece 3, the orientation of the line laser sensor 2 needs to be changed. First, all unmarked surfaces of workpiece 3 are traversed, and the two surfaces with the largest angle (f) are selected. i =115 and f j =3284) is used as the seed triangle facet, and the neighborhood of the seed facet is searched, scanning region Φ i From facet f i and the angle with the facet is less than 2θ T Composed of all facets, the scanning area Φ j Similarly, in region Φ i and Φ j In the detection viewpoint, facet marks that do not meet the viewpoint constraints are removed. Then, the 2-position pose S of the line laser sensor is calculated. z Since ΔH = 15.905 is greater than the depth of field h, k = 1 is calculated according to equation (38), and the regions are further classified. Finally, four different scanning regions are generated, and a final scanning path is generated for each region, such as... Figure 20 As shown.

[0333] S8. Case study verification of measurement accuracy and path control:

[0334] The measurement platform consists of an ABB robot and a line laser sensor 2. When the line laser sensor 2 receives a trigger signal from the robot control system, it projects a linear laser beam onto the surface of the workpiece 3, forming its local contour line. On this laser stripe, the line laser sensor 2 acquires the coordinates of a series of approximately uniformly distributed sampling points and outputs the X-axis and Z-axis positions of these points in the sensor coordinate system. Simultaneously, the robot controller 1 records the spatial pose information of the robot's end effector each time a scan is triggered. To meet the measurement accuracy requirements, the step size of the movement of two adjacent laser stripes in the Y-axis direction of the measurement coordinate system must be strictly controlled according to the set parameters throughout the scanning process.

[0335] The scanning path planning based on the hemispherical model includes six steps: triangular mesh model processing, scanning path planning, workpiece 3 positioning, workpiece 3 surface point cloud acquisition, and point cloud registration. The main experimental parameters are as follows: the length of the linear laser beam is 10 mm, the installation height is 56.5 mm, the depth of field is 8 mm, and the measurement frequency is 300 Hz. During the scanning process, robot 1 acts as the executor of mechanical motion. The linear laser sensor 2 mounted on the end of robot 1 drives the scanning, and the repeatability of robot 1 is 0.01 mm.

[0336] After the pose of workpiece 3 is known and hand-eye calibration is completed, the scanning path of robot 1 can be obtained using equation (43). Line laser sensor 2 collects point clouds of different cross sections of the surface of workpiece 3 at different scanning times. When the scanning is completed, the data needs to be converted to the same coordinate system to achieve point cloud registration. According to equation (44), the scanning data can be unified into the base coordinate system of robot 1.

[0337] T BE =T BO T OS T ES -1 (43);

[0338] P B =T BE T ES P S (44);

[0339] In the formula, P S It is the position of the scanning point in the sensor coordinate system, P B It is the position of the scan point in the base coordinate system.

[0340] Due to the influence of the scanning environment, object surface characteristics, and lighting conditions, the point cloud data acquired by the line laser sensor 2 is usually accompanied by noise and outliers. Therefore, it is necessary to preprocess the acquired data using the point cloud processing algorithm described above to remove noise and outliers. After obtaining the point cloud data of the hemispherical surface, the scanned model is first aligned with the corresponding CAD model, and then the difference threshold method is used to determine whether there are defects in the workpiece 3. This invention uses GeomagicQualify software as an auxiliary detection tool, which is known for its ease of operation and powerful detection functions. The specific operation process is as follows: First, the scanned point cloud model is imported into the software as the test object, and then the CAD model is imported as the reference model. Then, by using the software's best fit and alignment functions, the matching between the test model and the reference model is gradually adjusted and optimized until the minimum deviation is reached. Subsequently, the software's comparative analysis function is used to generate a three-dimensional deviation map, which comprehensively reflects the differences between the two models. Finally, Figure 21 The results show the bias obtained from the experiment.

[0341] from Figure 21 The results show that the maximum deviation between the scanned point cloud model and the CAD reference model is 0.4251 mm, the average deviation is 0.0876 mm, and the standard deviation is 0.1206 mm. Using the algorithm described in this invention to compensate for the positioning error of robot 1, and using the error model to compensate for the tilt angle error of the sensor and the laser line error, the compensated point cloud model is compared with the CAD model. The results are as follows: the maximum deviation is 0.1645 mm, the average deviation is 0.0437 mm, and the standard deviation is 0.0544 mm. The maximum deviation of the point cloud decreased from 0.4251 mm to 0.1645 mm, a decrease of 61.29%, and the average deviation decreased from 0.0876 mm to 0.0437 mm, a decrease of 50.11%. After compensation, the percentage of points with an error of 0-0.01mm was 12.98%, those with an error of 0.01mm-0.02mm were 14.12%, those with an error of 0.02mm-0.03mm were 11.61%, those with an error of 0.03-0.04mm were 10.74%, those with an error of 0.04mm-0.05mm were 9.86%, and those with an error greater than 0.05mm were 40.69%.

[0342] Next, the machined complex curved surface workpiece is scanned and measured. A comparison of workpiece 3 before and after compensation with the standard model is shown below. Figure 22 As shown.

[0343] As shown in the figure, the maximum deviation before compensation was 0.4812 mm, the average deviation was 0.1004 mm, and the standard deviation was 0.1964 mm. After compensation using the algorithm and model of this invention, the maximum deviation was 0.2365 mm, a decrease of 50.85%, the average deviation was 0.0497 mm, a decrease of 50.47%, and the standard deviation was 0.0967 mm. After compensation, the percentage of points with errors between 0 and 0.01 mm was 9.49%, those between 0.01 mm and 0.02 mm were 11.85%, those between 0.02 mm and 0.03 mm were 7.23%, those between 0.03 mm and 0.04 mm were 10.67%, those between 0.04 mm and 0.05 mm were 14.48%, and those greater than 0.05 mm accounted for 46.28%. Experimental results show that the error compensation algorithm and model proposed in this invention are effective in optimizing the accuracy of in-machine measurement and meet the requirements for high accuracy in in-machine measurement.

[0344] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for error modeling and path planning in a line laser in-situ measurement system, characterized in that, Includes the following steps: S1. Analysis of the measurement principle of the line laser in-situ system; In step S1, the measurement principle analysis is as follows: When the robot (1) is equipped with a line laser sensor (2) for measurement, the X plane and coordinate system of the line laser sensor (2) are determined, and the three-dimensional coordinates of the measurement point cloud are calculated by combining the hand and eye positioning posture of the robot (1) to obtain the contour information of the workpiece (3). S2. Derive the position of the centroid angle of light energy based on the Lambert diffuse reflection model; In step S2, the position of the centroid angle of light energy is derived based on the Lambert diffuse reflection model as follows: S21. Treat the workpiece (3) as a diffuse reflector. Assume that the surface of the workpiece (3) being measured is an ideal diffuse reflector surface, and the spatial distribution of scattered light is described according to Lambert's law: （1）； The parameters of S22 and the line laser sensor (2) are defined as follows: Setting points To measure the reference origin, This represents the displacement of workpiece (3), where upward movement is taken as a negative value and downward movement as a positive value. This indicates that the point on the laser line is relative to the origin. distance, The inclination angle of the measured surface of workpiece (3), Indicates the center of the imaging lens (4) The angle with the center of the optical axis, This represents the normal to the measured surface of the workpiece (3). Indicates the radius of the imaging lens (4), Indicates the center of the imaging lens (4) To the origin distance, This indicates the distance from the receiving surface to the imaging lens (4), when the measured surface of the workpiece (3) moves upward. At that time, the light spot moves upward accordingly. When the point on the laser line moves in the forward and backward direction At that time, the light spot will also shift accordingly. ; S23. Take a strip-shaped element perpendicular to the receiving plane on the receiving lens. The light energy at its center is the same as that at other locations; based on this, the strip element... The light energy received per unit time can be expressed as: （2）； set up object light spot Distance to the center of the receiving lens Represents a bar element Relative to the solid angle formed by the object light point, then: （3）； in, Substituting it into equation (3), we get: （4）； （5）； During displacement measurement, due to the object light point Distance to the receiving lens Much larger than the lens radius Therefore, it can be approximated as ,right By expanding, we can derive relation (6): （6）； by For reference, the counterclockwise rotation forms Angles are taken as positive values, and clockwise rotation results in negative values. Let the position of the centroid angle of the light cone inside the receiving lens be . Then in The receiving lens is divided into two parts, both of which are perpendicular to the receiving surface and receive equal amounts of light energy. The corresponding light energy integral equation is shown in equation (7): （7） In the formula: （8）； （9）； make Within the points limit arrive Within the range, there are Equations (8) and (9) become: （10）； （11）； Substituting equations (10) and (11) into equation (7), and integrating, we get: （12）； make Take approximation and After simplification, we get: （13）； Therefore, the spot formed at the location where the object surface is tilted and converges. middle, （14）； The point where the light spot converges is formed when the object surface is tilted. middle, （15）； The point where the light spot converges is formed when the object surface is tilted. In China, due to Taking a first-order approximation, we get: （16）； The point where the light spot converges is formed when the object surface is tilted. middle, （17）； （18）； （19）； By combining equations (17), (18), and (19), we can obtain: （20） That is Substituting the values ​​of equations (16) and (20) into equation (13), we get: （21）； in, , In the formula, This indicates the angular position of the light energy centroid line in the light cone received by the receiving lens. The projection point of this light energy centroid line onto the photosensitive surface is the position of the light energy centroid of the converged spot on the photosensitive surface of the linear CCD. S3. Analysis and modeling of line laser measurement errors caused by laser triangulation; In step S3, S31. The specific analysis of the line laser measurement error caused by laser triangulation is as follows: For the same laser point on the laser line of the line laser sensor (2), when the surface tilt angle of the workpiece (3) is... When fixed, the measurement error of the line laser sensor (2) will increase accordingly as the depth of field increases; If a fixed point is selected on the laser line, the workpiece (3) will be displaced. Assuming the surface remains constant, the measurement error will vary with the tilt angle of the workpiece (3) surface. It increases with the increase; If the surface tilt angle of workpiece (3) and displacement Fixed, on the same laser line, the distance from different laser points to the center. The smaller the value, the smaller the measurement error; conversely, the larger the value, the larger the error. That is, the closer the position is to the center of the laser line, the smaller the error of the line laser sensor (2). When the surface tilt angle of the workpiece (3) When the linear laser sensor (2) measures an error, the positive and negative directions of the error are consistent with the displacement direction of the workpiece (3). However, when the surface of the workpiece (3) is tilted at an angle... At that time, the positive and negative directions of the error are opposite to the displacement direction of the workpiece (3); S32. The specific modeling of the line laser measurement error caused by laser triangulation is as follows: Let the center of mass of light energy be... Light energy centroid line through The light energy center of mass, after refraction, is projected onto the linear CCD to form a converging light spot. dot, make ,set up The image point is Its object distance Image distance satisfy Then it's like a point. Distance to the optical axis of the receiving lens It can be represented as: （22）； Due to light Projection points on a linear CCD Distance to the optical axis of the receiving lens satisfy Furthermore, the tilt of the object surface will cause the light spot to converge at a certain position. Therefore, we can conclude that: （23） Based on geometric relationships , can be obtained , （24）； because Substituting equation (22) into equation (23), we get: （25）； Substituting equation (24) into equation (23), we can derive: （26）； because Therefore: （27）； When the incident beam of the line laser sensor (2) is incident perpendicularly and the object surface is not tilted, there is If the incident beam is at an angle When the incident surface is tilted, then Therefore, the tilt angle error can be expressed as: （28）； in, ; S4. In-situ system measurement scan constraint strategy; In step S4, S41, Constraint Strategy The line laser sensor (2) uses the triangulation method to obtain the position of the laser line and the distance between the line laser sensor (2) and the surface of the workpiece (3) in the sensor coordinate system. By moving the workpiece (3) or the position of the line laser sensor (2), a set of 3D measurement points can be obtained. During the scanning process, the characteristics of the line laser sensor (2) and the relative distance between the line laser sensor (2) and the workpiece (3) determine the quality of the measurement data. Therefore, the following constraints are applied: Direction angle Direction angle The orientation of the linear laser sensor (2) With the surface normal vector of workpiece (3) The angle between the two, the size of which directly affects the measurement effect, when the scanning direction is perpendicular to the surface normal vector of the workpiece (3) Maintaining parallelism allows for the achievement of maximum surface point cloud density: （29）； Depth of field: The line laser sensor (2) can only measure surface data in the depth of field during a single scan. Assuming the point in the sensor coordinate system is Then it needs to satisfy: （30）； Optimal distance Optimal distance It is a scanning reference plane located in half the depth of field from the laser source, which can focus the laser beam onto the reference plane; Scan width Scan width It is the width of the laser beam located at half the field of view depth, and also the length of the scan line; Field of View (FOV): The area is determined by the scanning angle. And the scanning width is defined, the line laser sensor (2) can scan points within this range; Field of view : The angle of the laser beam plane; Collision-free constraint: During the scanning process, ensure that the line laser sensor (2) does not collide with the robot (1) or the workpiece (3); S42, Neighborhood Search Algorithm The measured workpiece (3) is a triangular mesh model described in STL file format. STL file is the standard format for triangular mesh models, consisting of vertex and face normals. Half-side structure is used for topological reconstruction of the triangular mesh. After reconstructing the face patches, the face patch neighborhood search algorithm is used to search for the face patches. Rank neighborhood, It is a facet in the mesh model. It is a facet index, The corresponding facet A set of adjacent facets, Obtain facets of The algorithm for the order neighborhood is as follows: S421. Find the facets. First-order neighborhood First, find It contains three half-edges, then finds the corresponding neighborhood half-edges, and calculates the neighborhood. The set of neighborhood surfaces is called the first-order neighborhood surface set: （31）； S422, Find the facets second-order neighborhood , Obtained by searching the facets in the first-order neighborhood: （32）； S423, Find the facets of Rank Neighborhood , Through The facets are obtained by searching the neighborhood of the order: （33）； S5. Measurement data processing; S6. Measurement path generation and planning; Simulation of S7, spherical and freeform surface path planning algorithms; S8, Measurement accuracy and path control case verification.

2. The method for error modeling and path planning of a line laser in-situ measurement system according to claim 1, characterized in that, In step S5, the measurement data processing specifically includes: S51. A radius filtering algorithm is used to filter and reduce noise in the point cloud data, as detailed below: S511, First, set the discrete threshold. and filter radius ; S512, then import the point cloud data; S513. Next, filter the point cloud data according to the set parameters; S514, For the radius The number of neighboring points within the range is less than the discrete threshold. Points that are not identified as noise are removed. S515. Finally, save the filtered point cloud data. S52. A downsampling algorithm is used to reduce the number of points in the point cloud data while retaining the key features of the point cloud, as detailed below: First, a 3D voxel mesh is constructed, and the centroid of all points within each voxel is used as the representative point to approximate all points within that voxel. By traversing all voxels, a downsampled point cloud composed of the centroids of each voxel is finally obtained. Suppose the input point cloud dataset Classified as A set of voxels of uniform size, each with a length, width, and height of 1 mm. For the first voxel... Individual elements, whose central points can be represented as: （34）； in, Indicates the first The central coordinates of the individual element It is the number of points contained within that voxel; Indicates the first The set of point clouds contained in an individual element; Voxel representation The first in The coordinates of the points.

3. The method for error modeling and path planning of a line laser in-situ measurement system according to claim 1, characterized in that, In step S6, the generation and planning of the measurement path are as follows: S61, Surface Region Division S611. Traverse all unmarked faces and find the two faces with the largest normal vectors. The maximum normal angle between the two faces is... If the angle between two normal vectors The included angle between them satisfies: This indicates that all faces can be scanned from a single viewpoint. If the angle does not meet this condition, proceed to the next step. S612. Consider the two faces with the largest included angle between their normal vectors as seed triangle faces. and ,in and Using a neighborhood search algorithm, the scanning region is composed of patches. The area contains both the surface patches and the seed surface patches. The included angles between them are all less than Similarly, the scanning area is obtained. Mark the planned facets; S613. Calculate the average normal vector of the initial scanning area, then detect the orientation angle of each face in the area, remove the marking of the face that does not meet the viewpoint constraint, and determine the scanning area. If all face is marked, the division ends; otherwise, return to step S611. S62. Determining the sensor orientation Sensor direction Determined according to the following formula: （35） In the formula, It represents the number of triangular faces within the scanned area. It is the normal vector of each facet; S63, Generation of Scanning Viewpoint Project all vertices of the faces within the region onto... The coordinates of the projection points are calculated using equation (36), and then the maximum distance between the projection points is determined. （36）； In the formula, Let be the coordinates of the vertices of the face. set up express The maximum distance between all projected points in the direction is calculated according to equation (37). and yes The highest and lowest projection points in the direction, （37）； if If all patches belong to the same depth range, they can be scanned within the same optimal distance plane; if ,same The directional patches need to be classified according to the depth range, and the classification data is determined by equation (38), where Indicates rounding down. （38）； S64. Generation of Scan Path Containing points But perpendicular to The face is marked as ,point Calculated by equation (39), firstly, the patches in the scanned region that satisfy the depth constraint are projected onto the plane. The coordinates of the projection point are calculated using equation (40). (39); （40）； in, These are the coordinates of the projection point. Represents the vertex coordinates of the face. After projection, the plane The small planes in the middle form a polygon. The convex hull of the projection plane is calculated using Graham's algorithm, and then the minimum outer rectangle of the convex hull is obtained through rotation, which is the region to be scanned. The longitudinal direction of the outer rectangle is taken as the direction of movement of the line laser sensor (2), i.e., the Y-axis direction of the sensor coordinate system, and the width direction of the rectangle is taken as the X-axis. It is assumed that the four points constituting the smallest outer rectangle are in the workpiece (3) coordinate system. , , and ,if Then the attitude of the line laser sensor (2) in this region can be obtained from equation (41): （41）； if The region can be scanned based on a single scan line segment; otherwise, the width of the minimum outer rectangle is divided, and the number of scan lines in the region is determined. From equation (42), we get, where This indicates rounding up. Finally, different scan lines are connected to form the scan path for the region. （42）。 4. The method for error modeling and path planning of a line laser in-situ measurement system according to claim 1, characterized in that, In step S7, S71, Simulation of Freeform Surface Path Planning Algorithm The freeform surface model consists of 1594 faces and 862 points. The maximum angle between the surface normals of the triangular mesh of the freeform surface model is determined by traversing this surface. ,because The pose needs to be changed for measurement; the two faces with the largest angle between their normal vectors should be selected. and Perform a neighborhood search to form a scan area. and Calculate sensor pose The depth is calculated according to equation (37). Because of depth of field The value is 8. Each region block satisfies the depth constraint, and finally, the final scan path is generated for each region; S72, Simulation of Hemispherical Path Planning Algorithm The hemispherical model has 3484 faces and 1804 points. Find the maximum included angle between the normal vectors of the triangular blocks in the hemispherical model. It is 179.84°, because To achieve a complete scan of the workpiece (3) surface, the orientation of the line laser sensor (2) needs to be changed. First, all unmarked surfaces of the workpiece (3) are traversed, and the two surfaces with the largest angles are selected. and This serves as the seed triangle facet, and the neighborhood of each seed facet is searched, scanning the region. From facets and the angle with the facet is less than All facets constitute the scan area Similarly, in the region and In the detection viewpoint, remove facet markers that do not meet the viewpoint constraints, and then calculate the sensor pose. ,because greater than depth of field Calculate according to formula (38) The regions are further classified, and four different scanning regions are generated, with a final scanning path generated for each region.

5. The method for error modeling and path planning of a line laser in-situ measurement system according to claim 1 or 4, characterized in that, In step S8, S81. Verify the hemispherical workpiece. After the pose of the workpiece (3) is known and the hand-eye calibration is completed, the scanning path of the robot (1) can be obtained using equation (43). The line laser sensor (2) collects point clouds of different sections of the workpiece (3) surface at different scanning times. When the scanning is completed, the data needs to be converted to the same coordinate system to achieve point cloud registration. According to equation (44), the scanning data can be unified into the base coordinate system of the robot (1): （43）； （44）； In the formula, It is the position of the scanning point in the sensor coordinate system. It is the position of the scan point in the base coordinate system; The collected data is preprocessed to remove noise and abnormal data. After obtaining the point cloud data of the hemispherical surface, the scanning model is first aligned with the corresponding CAD model. Then, the difference threshold method is used to determine whether there are defects in the workpiece (3). Geomagic Qualify software is used as an auxiliary detection tool. The specific operation process is as follows: First, the scanned point cloud model is imported into an auxiliary inspection tool as the test object, and then the CAD model is imported as the reference model. Next, by utilizing the best-fit and alignment functions of the auxiliary inspection tool, the matching between the test model and the reference model is gradually adjusted and optimized until the minimum deviation is achieved. Subsequently, the comparative analysis function of the auxiliary inspection tool is used to generate a 3D deviation map, comprehensively reflecting the differences between the two models. Finally, the deviation results are obtained from the experiment. The maximum deviation, average deviation and standard deviation between the point cloud model obtained by scanning and the CAD reference model are obtained, and the robot (1) positioning error is compensated. The error model is used to compensate the tilt error of the sensor part and the laser line error. The compensated point cloud model is compared with the CAD model. The comparison results meet the requirements of in-machine measurement accuracy. S82. Verification of complex curved surface workpieces. The machined complex curved surface workpiece is scanned and measured. The workpiece before and after compensation is compared with the standard model. The comparison results meet the requirements of in-machine measurement accuracy.

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