Mechanical arm fan blade morphology measurement method based on ICP algorithm splicing

Abstract

The invention discloses a mechanical arm fan blade morphology measurement method based on ICP algorithm splicing. The method comprises the following steps that 1, a measurement system is calibrated; 2, blade measurement path planning is carried out based on model driving; and step 3, carrying out point cloud splicing based on an ICP algorithm. According to the method, the theoretical model of the blade flexible measurement system is established, the scanning path is automatically planned according to the CAD model of the blade, and the multi-view collection point cloud is subjected to fine matching through the ICP algorithm, so that the influence of the multi-view splicing error on the subsequent feature extraction precision is effectively reduced, and the three-dimensional reconstruction of the processed complete point cloud is visualized.

Description

Technical Field

[0001] The invention belongs to the technical field of surface profile measurement, and in particular relates to a method for measuring the profile of a mechanical arm fan blade based on ICP algorithm splicing. Background Art

[0002] As the heart of an aircraft, the aircraft engine directly determines the performance of the aircraft. It is closely related to the technological progress of the aircraft engine, and is therefore regarded as a core technology to ensure the country's strategic advantage. Although the development cycle and industrial chain of aircraft engines are long, once they are successfully developed, they will play a huge role in the progress of the economy and science and technology. In recent years, with the development of aircraft technology, higher requirements for engine performance are also constantly improving the thrust-to-weight ratio, compressor pressure ratio and combustion chamber temperature of aircraft engines, and putting forward stringent requirements on the performance of important components. According to authoritative flight accident investigation statistics, about 36% of aircraft mechanical failures occur in aircraft engines. According to statistics in my country, aircraft engine failures account for more than 60% of accidents in the past decade, so there is an urgent need to improve engine manufacturing related technologies.

[0003] The methods for obtaining blade measurement data are mainly divided into contact and non-contact methods according to whether there is direct contact with the workpiece. The contact measurement method usually has high measurement accuracy, but the measurement range is small, the degree of automation is low, and edge jumps are prone to occur in parts with poor rigidity such as the blade edge. The non-contact measurement method has high measurement accuracy, large measurement range, and high scanning efficiency. Combined with industrial robotic arms, flexible mass measurement can be achieved to meet the efficiency requirements of blade scanning in aero-engine production, and avoids the measurement error caused by blade edge jump caused by contact force. Due to the low accuracy of the robotic arm, the blade model obtained by directly splicing the robotic arm and hand-eye calibration data is prone to misalignment, so it needs to be further aligned through auxiliary algorithms. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing.

[0005] The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing of the present invention comprises the following steps:

[0006] Step 1: Calibrate the measurement system;

[0007] Step 2: Plan the blade measurement path based on model drive;

[0008] Step 3: Perform point cloud stitching based on the ICP algorithm.

[0009] Further, in step 1, the method for calibrating the measurement system is as follows: for the blade flexibility measurement system, the point cloud data of the matte ceramic standard ball obtained by binocular structured light measurement is in its own camera coordinate system O c The coordinate system is the same as the coordinate system O of the end effector of the robot arm. t The transformation relationship between them remains unchanged, and the transformation relationship is assumed to be the homogeneous coordinate transformation matrix The transformation matrix of the rotation part is The translation part transformation matrix is It represents the transformation relationship between the robot end coordinate system and the sensor coordinate system;

[0010] Robot arm base coordinate system O b When the base is installed in a fixed position, it is fixed to the world coordinate system O w Equivalently, let O t With O b The transformation relationship between them is The ultimate goal of the measurement system is to convert the measured c The point cloud data is transformed into the world coordinate system O w Under the unified measurement coordinate system, a complete scanning result is obtained; suppose that the binocular structured light coordinate system O c The next point is P c =[x c ,y c ,z c ,1] T , the coordinate transformation relationship can be used to obtain the coordinate unified formula as follows:

[0011]

[0012] Furthermore, in step 1, the center position of the standard sphere in the binocular structured light coordinate system is obtained by the least square method, and the spatial sphere function equation is assumed to be:

[0013] (xx o ) 2 +(yy o ) 2 +(zz o ) 2 =R 2

[0014] Let 2x0 = A, 2y0 = B, 2z0 = C, Suppose a certain measurement obtains a total of n points on the sphere, and the jth measurement point is set to Written in matrix form:

[0015]

[0016] According to the least squares criterion, we need to determine the values ​​of A, B, C, and D so that the following equation holds:

[0017]

[0018] For an equation of the form Ax=b, when x=(A T A) -1 A T b can meet the above requirements, and we can get:

[0019]

[0020] but That is, the center of the sphere measured for the i-th time is

[0021] Furthermore, in step 1, the rotation part transformation matrix is ​​calculated Here’s how:

[0022] Assume that the robot arm drives the binocular structured light to perform m translation scans on the standard ball, keeping the posture of each scan unchanged, and the center of the ball obtained in the i-th scan is The homogeneous coordinate form is Since the standard sphere is fixed in the robot base coordinate system, for each scan:

[0023]

[0024] Get the homogeneous matrix and expand it to get:

[0025]

[0026] The robot arm performs translational motion between each scan, and the posture does not change. There has been a change, The position of the standard ball in the robot base coordinate system remains unchanged. For m scans, for any two scans, and The formula can be obtained:

[0027]

[0028] For m scans, the following holds true:

[0029]

[0030] The above formula can be written as R x A = b, where This is the hand-eye matrix to be determined; Size: 3m; The size is 3m, and the solution is obtained by SVD decomposition. T Perform SVD decomposition to obtain the left and right singular matrices V and U, then:

[0031]

[0032] Furthermore, in step 1, solve the translation part transformation matrix Here’s how:

[0033] Solution When the robot arm is controlled to shoot k times from multiple angles and multiple positions to the standard ball fixed in the robot arm base coordinate system, the coordinates of the center of the standard ball shot in the i-th time are obtained by fitting. It can be known from the standard ball that Therefore, we can get:

[0034]

[0035] For k measurements we have:

[0036]

[0037] For the above formula, the least squares method can be used for calculation:

[0038]

[0039] Then the hand-eye matrix in homogeneous coordinate form can be obtained as:

[0040]

[0041] The method for measuring the shape of a fan blade by a robotic arm based on ICP algorithm splicing according to claim 1 is characterized in that, in step 2, the blade CAD model is sampled:

[0042] The blade CAD model is extracted by PCL point cloud and converted into a point cloud model. In order to ensure that there are overlapping areas between multiple scans in the height direction for ICP stitching, the height interval is 40% of the scanning height and the model is segmented.

[0043] Furthermore, in step 2, the cross-sectional scanning viewing angle is calculated as follows:

[0044] Perform cross-sectional projection on each segment of the point cloud, and select a certain height range above and below each interception height; segment the point cloud of the leaf basin and the leaf back, and straighten the leaf section by performing least squares fitting on the straight lines of the point cloud of each section and rotating them to the horizontal direction, and take the point x with the minimum x coordinate value. min With the maximum point x maxCalculate the standard parabolas P1 and P2 with the coordinate origin respectively; for each point with abscissa less than 0, determine whether it is above the parabola P1. If it is, it is the leaf basin, otherwise it is the leaf back. Similarly, for each point with abscissa greater than or equal to 0, determine whether it is above the parabola P2. The segmented leaf basin and leaf back are further divided into three parts according to the size of the abscissa to ensure that the overlapping area can meet the correct ICP stitching requirements; draw a perpendicular line to the straight line after least squares fitting each part, and according to the depth of field range of the structured light, take the point 700mm away from the intersection of the two along the perpendicular line as the origin of the shooting angle of view.

[0045] Furthermore, in step 3, when the pre-processed data is stitched into multi-view point clouds, the two point clouds are roughly registered by coarse registration to provide a relatively good initial value; c Point cloud data Coordinate system O of the end effector of the robot arm t With the robot base coordinate system O b The transformation relationship between and the hand-eye matrix Then the following formula holds:

[0046]

[0047] For a given point cloud, the coordinates of the reference point cloud are fixed. Another point cloud to be registered that has overlapping features The registration of point clouds is described as how to find the optimal transformation matrix R*,t* to minimize the following equation:

[0048]

[0049] By continuously searching for the nearest point between the initial two point clouds or the point clouds obtained after multiple transformations, the transformation matrices Rn and Tn that can make the nearest points coincide with each other more highly are obtained to transform the point clouds until the iteration conditions are met.

[0050] Furthermore, in step 8, the corresponding point matching method is as follows: for the point cloud C to be registered a And the reference point cloud C b , traverse C a Points in Calculate the point with the minimum Euclidean distance in the reference point cloud as the matching point Form a corresponding point set;

[0051] The optimal transformation method is as follows:

[0052] Corresponding point set C c The analytical solution to the optimal transformation is computed with the help of SVD decomposition:

[0053]

[0054] in and are the centroids of the point cloud to be registered and the reference point cloud respectively; SVD decomposition of H can obtain the left and right singular matrices U and V, and the optimal transformation matrix for this transformation is:

[0055] R k =VU T

[0056]

[0057] The homogeneous coordinate form is:

[0058]

[0059] Furthermore, in step 9, the iteration method is as follows:

[0060] Each iteration can get R k With T k Acting on the point cloud C to be registered a ,have The iteration stops when any of the following conditions is met, otherwise the corresponding point matching and solving the optimal transformation are repeated;

[0061] A: The maximum number of iterations has been reached; B: E(R * ,t * ) is less than the set value; C: R k , T k The change is less than the set value;

[0062] Visualization of the visual collection effect of point cloud data. After completing point cloud collection, preprocessing and splicing, visualization can be achieved by performing 3D reconstruction of the blade point cloud surface:

[0063] A NURBS curve is defined as a piecewise polynomial as

[0064]

[0065] where {P i} is the control point, {N i,p (u)} is the p-order basis function defined on the non-uniform knot vector;

[0066] The following equation defines a NURBUS surface of order p in the u direction and order q in the v direction, which is a two-dimensional vector-valued piecewise rational function of the following form:

[0067]

[0068] where {P i,j} is a binary control mesh point, {w i,j} is the weight, {N i,p (u)} and {N j,q (v)} is a basis function defined on a non-uniform knot vector; the leaf basin and leaf back are segmented by the parabola segmentation method, and the leaf basin and leaf back are fitted separately to obtain a visible graph of the leaf surface.

[0069] Beneficial Effects

[0070] The present invention establishes a theoretical model of the blade flexibility measurement system, automatically plans the scanning path according to the CAD model of the blade, and accurately matches the multi-view acquisition point cloud through the ICP algorithm, effectively reducing the impact of the multi-view stitching error on the subsequent feature extraction accuracy, and realizing the visualization of the three-dimensional reconstruction of the processed complete point cloud. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a schematic diagram of the sampling point cloud of the blade CAD model in the present invention.

[0072] Figure 2 It is a schematic diagram of each height cross section in the present invention.

[0073] Figure 3 It is a schematic diagram of the division of the blade basin and blade back of the fan blade cross section in the present invention.

[0074] Figure 4 This is a schematic diagram of cross-sectional viewing angle selection in the present invention.

[0075] Figure 5 This is a flow chart of the ICP matching algorithm in the present invention.

[0076] Figure 6 It is a schematic diagram of the reconstructed blade model in the present invention.

[0077] Figure 7 This is a diagram of the hand-eye calibration experimental setup in the present invention.

[0078] Figure 8 This is a schematic diagram of the point cloud sphere center fitting data in the present invention.

[0079] Fig. 9 This is a diagram of the blade flexibility measurement device in the present invention.

[0080] Fig.10 Schematic diagram of coordinate transformation of the turntable considered in the present invention.

[0081] Fig.11 It is a schematic diagram of the rough matching and splicing of blades in the present invention.

[0082] Fig.12 It is a schematic diagram of the precise matching and splicing of blades in the present invention. DETAILED DESCRIPTION

[0083] The following combination Figures 1 to 12 This embodiment will be described in detail.

[0084] The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing of the present invention comprises the following steps:

[0085] Step 1: Calibrate the measurement system

[0086] For the blade flexibility measurement system, the point cloud data obtained by binocular structured light measurement is in its own camera coordinate system O c The coordinate system is the same as the coordinate system O of the end effector of the robot arm. t The transformation relationship between them remains unchanged, and the transformation relationship is assumed to be the homogeneous coordinate transformation matrix (The rotation matrix is The translation matrix is ), which represents the transformation relationship between the robot end coordinate system and the sensor coordinate system, that is, the hand-eye matrix. Its specific value is related to the robot controller tool coordinate system setting, the binocular structured light measurement coordinate system, and the design size of the adapter. Robot base coordinate system O b When the base is installed in a fixed position, it is fixed to the world coordinate system O w Equivalently, let O t With O b The transformation relationship between them is (The rotation matrix is The translation matrix is ). The ultimate goal of the measurement system is to convert the measured c The point cloud data is transformed into the world coordinate system O w Under the unified measurement coordinate system, a complete scanning result is obtained. Assume that the binocular structured light coordinate system O c The next point is P c =[x c ,y x ,z c ,1] T , the coordinate transformation relationship can be used to obtain the coordinate unified formula as follows:

[0087]

[0088] Step 11: Obtain the center position of the sphere in the binocular structured light coordinate system by the least squares method, and assume that the spatial sphere function equation is:

[0089] (xx o ) 2 +(yy o ) 2 +(zz o )2 =R 2

[0090] Let 2x0 = A, 2y0 = B, 2z0 = C, Suppose a certain measurement obtains a total of n points on the sphere, and the jth measurement point is set to Written in matrix form:

[0091]

[0092] According to the least squares criterion, we need to determine the values ​​of A, B, C, and D so that the following equation holds:

[0093]

[0094] For an equation of the form Ax=b, when x=(A T A) -1 A T b can meet the above requirements, and we can get:

[0095]

[0096] but That is, the center of the sphere measured for the i-th time is

[0097] Step 12: Calculate the rotation part of the hand-eye matrix

[0098] Assume that the robot arm drives the binocular structured light to perform m translation scans on the standard ball, keeping the posture of each scan unchanged, and the center of the ball obtained in the i-th scan is The homogeneous coordinate form is Since the standard sphere is fixed in the robot base coordinate system, for each scan:

[0099]

[0100] Get the homogeneous matrix and expand it to get:

[0101]

[0102] Between each scan, the robot arm performs translational motion and its posture does not change. There has been a change, The position of the standard ball in the robot base coordinate system remains unchanged, so for these m scans, for any two scans, and The formula can be obtained:

[0103]

[0104] For m scans, the following holds true:

[0105]

[0106] The above formula can be written as R x A = b, where This is the hand-eye matrix to be determined; Size: 3m; The size is 3m. This form of equation can be solved by SVD decomposition. T Perform SVD decomposition to obtain the left and right singular matrices V and U, then:

[0107]

[0108] Step 13: Solve the translation transformation matrix

[0109] Solution When the robot arm is controlled to shoot k times from multiple angles and multiple positions to the standard ball fixed in the robot arm base coordinate system, the coordinates of the center of the standard ball shot in the i-th time are obtained by fitting. It can be known from the standard ball that Therefore, we can get:

[0110]

[0111] For k measurements we have:

[0112]

[0113] For the above formula, the least squares method can be used for calculation:

[0114]

[0115] Then the hand-eye matrix in homogeneous coordinate form can be obtained as:

[0116]

[0117] Step 2: Blade measurement path planning based on model drive

[0118] In order to improve the ICP stitching accuracy, it is necessary to determine the blade placement and automatically plan the robotic arm measurement path based on the performance of the measurement sensor and the size and shape characteristics of the blade CAD model, and finally achieve complete measurement of the blade. The details are as follows:

[0119] Step 21, blade CAD model sampling: extract the PCL point cloud of the blade CAD model and convert it into a point cloud model. In order to ensure that there are overlapping areas between multiple scans in the height direction for ICP stitching, the height interval is 40% of the scanning height for segmentation. The point cloud is as follows: Figure 2 shown.

[0120] Step 22, cross-sectional scanning angle calculation: perform cross-sectional projection on each segment of the point cloud, and take a certain height range above and below each interception height. Project the plane perpendicular to the blade height direction as Figure 2 In order to realize the planning of the front and back sides of the blade, it is necessary to segment the point cloud of the blade basin and the back of the blade. The blade section is straightened by performing the least squares fitting on the straight lines of the point cloud of each section and rotating it to the horizontal direction. The point with the minimum x coordinate value is taken. min With the maximum point x max Calculate the standard parabola P1 and P2 with the coordinate origin respectively as follows Figure 3 As shown, for each point with a horizontal coordinate less than 0, determine whether it is above the parabola P1. If it is, it is the leaf basin, otherwise it is the leaf back. Similarly, for each point with a horizontal coordinate greater than or equal to 0, determine whether it is above the parabola P2. The segmented leaf basin and leaf back are further divided into three parts according to the size of the horizontal coordinate to ensure that the overlapping area can meet the correct ICP stitching requirements. After the least squares fitting straight line is performed on each part, a perpendicular line is drawn to the straight line. According to the depth of field range of the structured light, the point 700mm away from the intersection of the two along the vertical line is used as the origin of the shooting angle of view, and the angle of view of the section is calculated as follows Figure 4 shown.

[0121] After the theoretical model of the blade flexibility measurement system is built, the point cloud data needs to be preprocessed to enable the subsequent calculation steps to process the point cloud data more conveniently, quickly and accurately without affecting the authenticity of the point cloud data. The two processing methods are the outlier removal method based on statistical analysis and the voxel grid downsampling method.

[0122] Step 3: Point cloud stitching based on ICP algorithm

[0123] When the preprocessed data is used for multi-view point cloud stitching, the two point clouds are roughly registered through coarse registration to provide a better initial value. From the above formula, it can be seen that after obtaining the nth scan in the camera coordinate system O c Point cloud data Coordinate system O of the end effector of the robot arm t With the robot base coordinate system O b The transformation relationship between and the hand-eye matrix Then the following formula holds:

[0124]

[0125] Affected by the positioning accuracy of the robot arm, the actual There will be a certain error, which will cause the point cloud to be misaligned after the transformation, and further point cloud fine alignment is required. The ICP algorithm and its variants are the most common and effective fine alignment methods.

[0126] For a given point cloud, the coordinates of the reference point cloud are fixed. Another point cloud to be registered that has overlapping features The registration of point clouds can be described as the problem of how to find the optimal transformation matrix R*,t* to minimize the following equation:

[0127]

[0128] It is based on the idea of ​​iterative optimization. By continuously searching for the closest point between the initial two point clouds or the point clouds obtained after multiple transformations, the transformation matrices Rn and Tn that can make the closest point coincide with a higher degree are obtained to transform the point clouds until the iterative conditions are met. The ICP matching algorithm flow chart is as follows: Figure 5 The basic steps are as follows:

[0129] Step 31: Corresponding point matching

[0130] For point clouds with good initial values, that is, after rough registration, the calculation process of the traditional ICP algorithm is as follows: a And the reference point cloud C b , traverse C a Points in Calculate the point with the minimum Euclidean distance in the reference point cloud as the matching point Form a corresponding point set.

[0131] Step 32: Find the optimal transformation

[0132] For the traditional registration problem between two point clouds, according to the corresponding point set C c The analytical solution to the optimal transformation can be calculated with the help of SVD decomposition:

[0133]

[0134] in and are the centroids of the point cloud to be registered and the reference point cloud respectively. By performing SVD decomposition on H, we can get the left and right singular matrices U and V, and then we can get the optimal transformation matrix of this transformation (set as the kth transformation):

[0135] R k =VU T

[0136]

[0137] The homogeneous coordinate form is:

[0138]

[0139] Step 33: Iteration

[0140] Each iteration can get R k With T k Acting on the point cloud C to be registered a ,have The iteration stops when any of the following conditions is met, otherwise repeat steps (1) and (2):

[0141] A: The maximum number of iterations has been reached.

[0142] B:E(R * ,t * ) is less than the set value.

[0143] C: R k , T k The change is less than the set value.

[0144] Step 34: In order to realize the visualization of the point cloud data collection effect, after completing the point cloud collection, preprocessing and splicing, visualization can be achieved by performing 3D reconstruction on the blade point cloud surface. NURBS surface fitting is usually used in computer graphics or design in CAD / CAM. NURBS fitting can effectively reduce the amount of point cloud data without affecting the reconstruction accuracy. The basic principles are as follows:

[0145] A NURBS curve is defined as a piecewise polynomial as

[0146]

[0147] where {P i} is the control point, {N i,p (u)} is the p-order basis function defined on the non-uniform knot vector.

[0148] The following equation defines a NURBUS surface of order p in the u direction and order q in the v direction, which is a two-dimensional vector-valued piecewise rational function of the following form.

[0149]

[0150] where {P i,j} is a binary control mesh point, {w i,j} is the weight, {N i,p (u)} and {N j,q(v)} are basis functions defined on the non-uniform knot vectors.

[0151] Since NURBS surface fitting requires selecting two main directions for fitting, and the blade is a closed surface in the direction perpendicular to the height, the blade basin and the back of the blade are segmented by the aforementioned parabola segmentation method. The blade basin and the back of the blade are fitted separately to obtain the visible graph of the blade surface, as shown in Figure 6 shown.

[0152] Example

[0153] The experimental device in this embodiment is as follows Figure 7 As shown in the figure, the moveit control node program in the ros system controls the robot arm to perform the specified movement and outputs the position and posture of each shooting point in the form of a txt homogeneous coordinate matrix file; at the same time, the relevant software is used to control the FARO binocular structured light to shoot the 3D printed standard ball to obtain the point cloud, and the spherical part of the point cloud in each shooting point cloud is selected to perform the least squares fitting of the spherical center as shown in the figure. Figure 8 shown.

[0154] The coordinates of the center of the sphere and the homogeneous coordinate matrix obtained from each shot are saved in the corresponding order. In Qtcreator, the C++ language is used to call the eigen matrix library to write the hand-eye calibration calculation program. The hand-eye matrix is ​​solved using the above data. The final hand-eye matrix is:

[0155]

[0156] Considering that the blade to be tested is a large-sized aircraft engine fan blade, a large-load air-floating turntable is used to build a blade flexibility measurement device. Fig. 9 For subsequent splicing, the turntable axis parameters need to be obtained. Figure 7 As shown in the figure, the axis is calibrated by a standard ball, the standard ball is fixed on the turntable, and the center position of the ball is obtained by multiple rotations. The center position of the ball is fitted with a space circle, and the axis parameters can be determined by fitting the center of the circle and the normal vector. Due to the limited range of scanning the standard ball, the center of the ball cannot form a complete circle, and the results of using ordinary least squares to fit the space circle are prone to deviation. Therefore, the space circle fitting of the least squares method with random sampling consistency is adopted.

[0157] Considering the range of movement of the robot arm, the path is planned in combination with a large load-bearing air-floating turntable, and the viewing angles at different heights are rotated around the axis to the same direction. Fig.10 As shown in the figure, the range of the path can be reduced, which can also reduce the error caused by the large movement of the robot arm and improve the measurement efficiency. Fig.11 shown.

[0158] It can be seen that due to the error in the robot arm posture data, there is a misalignment phenomenon between multiple scans (in order to observe the phenomenon clearly, the adjacent misaligned point clouds after enlargement are changed to white for comparison) and the binocular structured light sensor introduces noise and environmental point clouds. After deleting the environmental object point cloud and filtering out the stray points by statistical filtering, the ICP precise matching algorithm is used for splicing to reduce the posture error. The splicing result is shown in the figure. Fig.12 As shown (adjacent point clouds are distinguished by yellow and green).

[0159] The above contents of the present invention are only preferred embodiments of the present invention and are not intended to limit the implementation scheme of the present invention. A person skilled in the art can easily make corresponding changes or modifications based on the main concept and spirit of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope required by the claims.

Claims

1. A method for measuring the shape of a fan blade of a robotic arm based on ICP algorithm splicing, characterized in that: The steps include: Step 1: Calibrate the measurement system; Step 2: Plan the blade measurement path based on model drive; Step 3: Perform point cloud stitching based on the ICP algorithm.

2. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing according to claim 1 is characterized in that: In step 1, the method for calibrating the measurement system is as follows: For the blade flexibility measurement system, the point cloud data of the matte ceramic standard ball obtained by binocular structured light measurement is in its own camera coordinate system O c The coordinate system is the same as the coordinate system O of the end effector of the robot arm. t The transformation relationship between them remains unchanged, and the transformation relationship is assumed to be the homogeneous coordinate transformation matrix The transformation matrix of the rotation part is The translation part transformation matrix is It represents the transformation relationship between the robot end coordinate system and the sensor coordinate system; Robot arm base coordinate system O b When the base is installed in a fixed position, it is fixed to the world coordinate system O w Equivalently, let O t With O b The transformation relationship between them is The ultimate goal of the measurement system is to convert the measured c The point cloud data is transformed into the world coordinate system O w Under the unified measurement coordinate system, a complete scanning result is obtained; suppose that the binocular structured light coordinate system O c The next point is P c =[x c ,y c , z c , 1] T , the coordinate transformation relationship can be used to obtain the coordinate unified formula as follows:

3. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing as claimed in claim 2, characterized in that: In step 1, the center position of the standard sphere in the binocular structured light coordinate system is obtained by the least squares method, and the spatial sphere function equation is assumed to be: (x-x o ) 2 +(y-y o ) 2 +(z-z o ) 2 =R 2 Let 2x0 = A, 2y0 = B, 2z0 = C, Suppose a certain measurement obtains a total of n points on the sphere, and the jth measurement point is set to Written in matrix form: According to the least squares criterion, we need to determine the values ​​of A, B, C, and D so that the following equation holds: For an equation of the form Ax=b, when x=(A T A) -1 A T b can meet the above requirements, and we can get: but That is, the center of the sphere measured for the i-th time is 4. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing as claimed in claim 2, characterized in that: In step 1, calculate the rotation part transformation matrix Here’s how: Assume that the robot arm drives the binocular structured light to perform m translation scans on the standard ball, keeping the posture of each scan unchanged, and the center of the ball obtained in the i-th scan is The homogeneous coordinate form is Since the standard sphere is fixed in the robot base coordinate system, for each scan: Get the homogeneous matrix and expand it to get: The robot arm performs translational motion between each scan, and the posture does not change. There has been a change, The position of the standard ball in the robot base coordinate system remains unchanged. For m scans, for any two scans, and The formula can be obtained: For m scans, the following holds true: The above formula can be written as R x A = b, where This is the hand-eye matrix to be determined; Size: 3m; The size is 3m, and the solution is obtained by SVD decomposition. T Perform SVD decomposition to obtain the left and right singular matrices V and U, then:

5. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing as claimed in claim 2, characterized in that: In step 1, solve the translation part transformation matrix Here’s how: Solution When the robot arm is controlled to shoot k times from multiple angles and multiple positions to the standard ball fixed in the robot arm base coordinate system, the coordinates of the center of the standard ball shot in the i-th time are obtained by fitting. It can be known from the standard ball that Therefore, we can get: For k measurements we have: For the above formula, the least squares method can be used for calculation: Then the hand-eye matrix in homogeneous coordinate form can be obtained as:

6. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing according to claim 1, characterized in that: In step 2, the blade CAD model is sampled: The blade CAD model is extracted by PCL point cloud and converted into a point cloud model. In order to ensure that there are overlapping areas between multiple scans in the height direction for ICP stitching, the height interval is 40% of the scanning height and the model is segmented.

7. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing according to claim 1, characterized in that: In step 2, the cross-section scanning viewing angle is calculated as follows: Perform cross-sectional projection on each segment of the point cloud, and select a certain height range above and below each interception height; segment the point cloud of the leaf basin and the leaf back, and straighten the leaf section by performing least squares fitting on the straight lines of the point cloud of each section and rotating them to the horizontal direction, and take the point x with the minimum x coordinate value. min With the maximum point x max Calculate the standard parabolas P1 and P2 with the coordinate origin respectively; for each point with abscissa less than 0, determine whether it is above the parabola P1. If it is, it is the leaf basin, otherwise it is the leaf back. Similarly, for each point with abscissa greater than or equal to 0, determine whether it is above the parabola P2. The segmented leaf basin and leaf back are further divided into three parts according to the size of the abscissa to ensure that the overlapping area can meet the correct ICP stitching requirements; draw a perpendicular line to the straight line after least squares fitting each part, and according to the depth of field range of the structured light, take the point 700mm away from the intersection of the two along the perpendicular line as the origin of the shooting angle of view.

8. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing according to claim 1, characterized in that: In step 3, when the pre-processed data is stitched into multi-view point clouds, the two point clouds are roughly registered by coarse registration to provide a relatively good initial value; c Point cloud data Coordinate system O of the end effector of the robot arm t With the robot base coordinate system O b The transformation relationship between and the hand-eye matrix Then the following formula holds: For a given point cloud, the coordinates of the reference point cloud are fixed. Another point cloud to be registered that has overlapping features The registration of point clouds is described as how to find the optimal transformation matrix R*,t* to minimize the following equation: By continuously searching for the nearest point between the initial two point clouds or the point clouds obtained after multiple transformations, the transformation matrices Rn and Tn that can make the nearest points coincide with each other more highly are obtained to transform the point clouds until the iteration conditions are met.

9. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing according to claim 1, characterized in that: In step 8, the corresponding point matching method is as follows: for the point cloud C to be registered a And the reference point cloud C b , traverse C a Points in Calculate the point with the minimum Euclidean distance in the reference point cloud as the matching point Form a corresponding point set; The optimal transformation method is as follows: Corresponding point set C c The analytical solution to the optimal transformation is computed with the help of SVD decomposition: in and are the centroids of the point cloud to be registered and the reference point cloud respectively; SVD decomposition of H can obtain the left and right singular matrices U and V, and the optimal transformation matrix for this transformation is: R k =VU T The homogeneous coordinate form is:

10. The method for measuring the shape of a fan blade of a robot arm based on ICP algorithm splicing according to claim 8, characterized in that: In step 9, the iteration method is as follows: Each iteration can get R k With T k Acting on the point cloud C to be registered a ,have The iteration stops when any of the following conditions is met, otherwise the corresponding point matching and solving the optimal transformation are repeated; A: The maximum number of iterations has been reached; B: E(R * ,t * ) is less than the set value; C: R k , T k The change is less than the set value; Visualization of the visual collection effect of point cloud data. After completing point cloud collection, preprocessing and splicing, visualization can be achieved by performing 3D reconstruction of the blade point cloud surface: A NURBS curve is defined as a piecewise polynomial as where {P i } is the control point, {N i,p (u)} is the p-order basis function defined on the non-uniform knot vector; The following equation defines a NURBUS surface of order p in the u direction and order q in the v direction, which is a two-dimensional vector-valued piecewise rational function of the following form: j=0,…,m 0≤u,v≤1 where {P i,j } is a binary control mesh point, {w i,j } is the weight, {N i,p (u)} and {N j,q (v)} is a basis function defined on a non-uniform knot vector; the leaf basin and leaf back are segmented by the parabola segmentation method, and the leaf basin and leaf back are fitted separately to obtain a visible graph of the leaf surface.

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