A hand-eye calibration method based on the characteristics of a standard cylindrical axis

Abstract

This invention relates to the field of line laser and robot hand-eye calibration technology, and discloses a hand-eye calibration method based on the characteristics of a standard cylindrical axis. The method involves fixing a line laser to the end effector of a robot and fixing the cylinder at an arbitrary position in the robot's space. While keeping the robot's posture constant, the line laser acquires the cylinder's contour edge data by changing the robot's position. An objective function is constructed to obtain the rotation matrix in the hand-eye transformation matrix. Principal component analysis is used to obtain the unit direction vector of the cylinder's axis in the robot's base coordinate space, thus obtaining the translation vector in the hand-eye transformation matrix. The accuracy of the hand-eye transformation matrix is ​​determined by multiplying the unit space vector by the unit direction vector of the cylinder's axis. The advantages of this method are that it does not require a cumbersome sampling procedure and is less susceptible to human error.

Description

Technical Field

[0001] This invention relates to the field of line laser and robot hand-eye calibration technology, specifically to a hand-eye calibration method based on the characteristics of a standard cylindrical axis. Background Technology

[0002] When robots perform tasks such as welding, cutting, and assembly, precise control of the relative position between tools and workpieces is required. Line laser hand-eye calibration provides robots with accurate positional information about tools (such as welding guns and cutting tools) and target objects, enabling robots to perform precise path planning and motion control based on this information. For example, in automobile manufacturing, line laser hand-eye calibration allows robots to accurately position the welding gun to the area to be welded, ensuring welding quality and precision, improving production efficiency and product quality, and reducing errors and labor intensity from manual operation.

[0003] The standard sphere method is a commonly used hand-eye calibration method for line laser sensors, but it has obvious drawbacks. In terms of operation, it is necessary to collect standard sphere point cloud data multiple times at different positions and postures, which is cumbersome, time-consuming and labor-intensive. The standard sphere requires extremely high processing precision. Once there are shape errors such as ellipticity or surface roughness, the point cloud data will be deviated, affecting the calibration accuracy. In addition, when fitting the cross-sectional circle to find the sphere center coordinates, the error is large due to data interference and algorithm limitations, making it difficult to guarantee the calibration accuracy.

[0004] Patent CN111735390A discloses a calibration block and hand-eye calibration method for a line laser sensor. This method has a complex scanning positioning device structure, requires high precision from the linear motor, and is prone to deviations in the position of the measured scanning light on the checkerboard. Patent CN113237434A discloses an eye-in-hand calibration method for a laser contour sensor based on a stepped calibration object. This method uses the maximum distance method to calculate the corner points of the contour data as feature points, relying on a user-set threshold. Setting the threshold too high leads to incomplete feature point extraction; setting it too low results in the inclusion of incorrect feature points, thus affecting the accuracy of subsequent line fitting and hand-eye matrix equation construction. Patent CN113681559A discloses a hand-eye calibration method for a line laser scanning robot based on a standard cylinder. This method requires known axis direction; manufacturing errors or installation deviations directly affect ellipse fitting and axis distance calculation, and introduces a complex high-dimensional optimization problem. Patent CN118636157A discloses a hand-eye calibration method for a line laser camera and a robot flange. This method uses only the intersection of the top edge of a triangular calibration block and the marking line as the target point during calibration. If this point is unusable due to damage or contamination of the calibration block, or if an anomaly occurs during measurement and there are no alternative target points, the calibration process will be interrupted. Furthermore, a single target point cannot fully reflect the overall characteristics of the calibration block, affecting calibration accuracy. Patent CN118776462A discloses a registration method, system, and device for a freeform surface wear model. This method, based on freeform surface calibration, is mainly for registering freeform surface wear models. When the wear condition of the measured part is very complex, such as large-area wear or discontinuous wear regions, relying solely on the normal differential factor for wear region segmentation and model registration may not accurately reflect the actual wear condition of the part, leading to a decrease in registration accuracy. Summary of the Invention

[0005] Therefore, the present invention provides a hand-eye calibration method based on the characteristics of a standard cylindrical axis.

[0006] This invention provides the following technical solution: a hand-eye calibration method based on the characteristics of a standard cylindrical axis, the method comprising the following steps:

[0007] S1: Fix the line laser to the end of the robot and fix the cylinder at any position in the application space of the robot;

[0008] S2: Keeping the robot's posture unchanged, the position of the robot is changed so that the line laser can acquire the contour edge data of the cylinder;

[0009] S3: By fitting the contour edge data of the cylinder through an optimization algorithm, the position of the elliptical center of the cross-section of the cylinder in the coordinate system of the line laser is obtained; and an objective function is constructed based on the rotation invariance of the spatial vector of the same cylinder axis, and the rotation matrix of the hand-eye transformation matrix is ​​obtained by calculating the objective function.

[0010] S4: Combining the rotation matrix of the hand-eye transformation matrix, the unit direction vector of the cylinder's axis in the robot's base coordinate space can be obtained. Based on the principle that the orthogonal Euclidean distance between vectors of the same axis is 0, the translation vector of the hand-eye transformation matrix can be obtained.

[0011] S5: Combining the rotation matrix and translation vector of the hand-eye transformation matrix, use the line laser to scan the bottom surface of the cylinder to obtain a unit space vector; determine whether the value of the hand-eye transformation matrix meets the engineering construction range threshold by multiplying the unit space vector by the unit direction vector. If the required construction scope threshold is not met, The requirements then need to be recalibrated.

[0012] As a preferred embodiment of the present invention, the transformation function relationship between the line laser and the robot's coordinate system is as follows: ,in, ;

[0013] Data in the line laser coordinate system. Let be the homogeneous transformation matrix from the line laser to the robot's end effector. Let be the homogeneous transformation matrix from the robot's end effector to the robot's base coordinates. The data in the robot's base coordinate system is obtained by transforming the data in the line laser coordinate system. Here is the x-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. This represents the z-coordinate of the center point of the cylindrical cross-section in the laser coordinate system.

[0014] As a preferred embodiment of the present invention, the optimization algorithm is the least squares method. By fitting the contour edge data of the cylinder using the least squares method, the general quadratic equation of the ellipse is obtained as follows: Where A is the first parameter of the ellipse, B is the second parameter of the ellipse, C is the third parameter of the ellipse, D is the fourth parameter of the ellipse, E is the fifth parameter of the ellipse, and F is the sixth parameter of the ellipse;

[0015] The coordinates of the center point of the cross-section of the cylinder can be calculated from the general quadratic equation of the ellipse: ,in, This represents the x-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. Here is the y-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. This represents the z-coordinate of the center point of the cylindrical cross-section in the laser coordinate system.

[0016] As a preferred embodiment of the present invention, the cylinder axis vector is calculated as follows: = ( - )+ = Where i is the number of position changes of the robot in the first unchanged posture, n is the number of position changes of the robot in the second unchanged posture, and i < n; R is the robot rotation matrix. Let be the rotation matrix obtained in hand-eye calibration. This is the translation matrix obtained in hand-eye calibration. This is the robot's translation matrix during the first data collection. Let be the translation matrix of the robot during the i-th data collection. This refers to the data of the center point of the cylindrical cross-section obtained in the i-th acquisition under the online laser. Let be the i-th vector, where and For numerical values, ; .

[0017] As a preferred embodiment of the present invention, the step of calculating the rotation matrix of the hand-eye transformation matrix includes: multiplying two different spatial vectors to obtain:

[0018] ,

[0019] Where i < n, j < n, and i ≠ j, j is the number of times the robot changes position in the third unchanged posture; Let j be the j-th vector; and For numerical values, = ; = The rotation matrix of the hand-eye transformation matrix is ​​obtained according to the least squares method: ,in, The rotation matrix obtained in hand-eye calibration The vector form, where H is a numerical value. , , Represented as the Kronecker product of two matrices, ; ; .

[0020] As a preferred embodiment of the present invention, the translation matrix obtained in hand-eye calibration... for: ,in, For numerical values, ; For numerical values, , Let be the unit direction vector of the cylinder axis. and Different robot rotation matrices represent different robot poses. and This represents the data of the center point of the cylindrical cross-section obtained under the online laser, acquired in the corresponding robot pose. In order to be in The corresponding translation matrix below; In order to be in The corresponding translation matrix.

[0021] As a preferred embodiment of the present invention, the step of combining the rotation matrix and the translation vector of the hand-eye transformation matrix, using the line laser to scan the bottom surface of the cylinder to obtain a unit space vector; and determining whether the accuracy obtained by the hand-eye transformation matrix meets the engineering requirements by dot product of the unit space vector and the unit direction vector, and recalibrating if it does not meet the engineering requirements, includes:

[0022] By maintaining the robot's posture and changing its position so that the laser scans the top surface of the cylinder, a unit space vector can be obtained: In the formula, L is the unit spatial vector in the upper base of the cylinder; and These are different translation matrices for the same robot posture; and They are respectively in and Data points acquired by the offline laser;

[0023] By dot product of the unit space vector and the unit direction vector of the cylinder axis: Where e is the calibration performance index; under ideal conditions, the unit direction vector of the cylinder's axis and the base vector are perpendicular, so their dot product is 0; determine whether the calibration performance index is related to the engineering construction range threshold. If the value is greater than the threshold of the engineering construction scope, Then recalibrate.

[0024] As a preferred embodiment of the present invention, under the same posture, the number of times the robot changes position n≥3 under a constant posture.

[0025] As a preferred technical solution of the present invention, the engineering construction range threshold The value range is 0.1 to 0.2.

[0026] Compared with existing technologies, this invention provides a hand-eye calibration method based on the characteristics of a standard cylindrical axis, which has the following advantages: The hand-eye calibration method provided by this invention is based on the geometric concept of collecting samples from the surface of the cylinder under different robot poses, and using implicit linear relationships to form a system of equations to obtain the rotation and translation of the line laser; this method does not require a cumbersome sampling procedure and is not easily affected by human error. The operator only needs to ensure that the laser line passes through the edge, unlike other methods that require the operator to visually ensure that the laser accurately passes through the center of the body or is aligned with the crosshair target, and the calibration block can be placed arbitrarily in the robot space. Attached Figure Description

[0027] Figure 1 This is a flowchart of a hand-eye calibration method based on the characteristics of a standard cylindrical axis, according to an embodiment of the present invention.

[0028] Figure 2 This is a schematic diagram of a line laser fixed to the end effector of a robot and performing data sampling, according to an embodiment of the present invention.

[0029] Figure 3 This is a schematic diagram of the unit direction vector of the axis in an embodiment of the present invention. Detailed Implementation

[0030] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] A hand-eye calibration method based on the characteristics of a standard cylindrical axis, the method comprising the following steps:

[0032] S1: Fix the line laser to the end of the robot and fix the cylinder at any position in the robot's application space;

[0033] S2: Keep the robot's posture unchanged, and change the robot's position so that the line laser can acquire the contour edge data of the cylinder;

[0034] S3: By fitting the contour edge data of the cylinder through an optimization algorithm, the position of the elliptical center of the cylinder's cross-section in the coordinate system of the online laser is obtained; and an objective function is constructed based on the rotation invariance of the spatial vector of the same cylinder axis, and the rotation matrix of the hand-eye transformation matrix is ​​obtained by calculating the objective function.

[0035] S4: Combining the rotation matrix of the hand-eye transformation matrix, the unit direction vector of the cylinder's axis in the robot's base coordinate space can be obtained. Based on the principle that the orthogonal Euclidean distance between vectors on the same axis is 0, the translation vector of the hand-eye transformation matrix can be obtained.

[0036] S5: Combining the rotation matrix and translation vector of the hand-eye transformation matrix, use a line laser to scan the bottom surface of the cylinder to obtain the unit space vector; determine whether the accuracy obtained by the hand-eye transformation matrix meets the engineering requirements by multiplying the unit space vector and the unit direction vector; if it does not meet the engineering requirements, recalibrate.

[0037] The transformation function relationship between the line laser and the robot's coordinate system is as follows: ,in, , Data in the line laser coordinate system. Let be the homogeneous transformation matrix from the line laser to the robot's end effector. Let be the homogeneous transformation matrix from the robot's end effector to the robot's base coordinates. The data in the robot's base coordinate system is obtained by transforming the data in the line laser coordinate system. Here is the x-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. This represents the z-coordinate of the center point of the cylindrical cross-section in the laser coordinate system.

[0038] These technical features work together to solve the transformation relationship between the line laser and the robot coordinate system through transformation function relationships. They can accurately convert data in the line laser coordinate system to the robot base coordinate system, thereby achieving precise transformation between the line laser and the robot coordinate system and ensuring that the robot can accurately control the relative position between the tool and the workpiece when performing tasks.

[0039] A line laser captures an elliptical cross-section of a cylinder. Using a fitting optimization algorithm, the general quadratic equation of the ellipse is obtained through least-squares fitting. The general quadratic equation of the ellipse is:

[0040] The general quadratic equation of the ellipse is obtained by fitting using the least squares method. The general quadratic equation of the ellipse is: Where A is the first parameter of the ellipse, which is the value of the semi-major axis of the ellipse; B is the second parameter of the ellipse, which is the value of the semi-minor axis of the ellipse; C is the third parameter of the ellipse, which is the circumference of the ellipse; D is the fourth parameter of the ellipse, which is the eccentricity of the ellipse; E is the fifth parameter of the ellipse, which is the focal length of the ellipse; and F is the sixth parameter of the ellipse, which is the focal radius of the ellipse.

[0041] The coordinates of the center point of the cross-section of the cylinder can be calculated from the general quadratic equation of the ellipse: ,in, This represents the x-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. Here is the y-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. This represents the z-coordinate of the center point of the cylindrical cross-section in the laser coordinate system.

[0042] By fitting the general quadratic equation of an ellipse using the least squares method, the profile shape of the cylindrical cross-section can be more accurately fitted. Furthermore, by calculating the coordinates of the center point of the cylindrical cross-section using the ellipse parameters, the accuracy and reliability of the calibration can be improved. Compared with traditional calibration methods, the method of this application is simpler and more efficient, reduces the dependence on equipment accuracy, and lowers the complexity and error of operation.

[0043] Keeping the robot's posture unchanged, changing its position and taking two of the positions yields the cylinder's axis vector: = ( - )+ = ,

[0044] Where i represents the number of position changes of the robot in the first unchanged posture, n represents the number of position changes of the robot in the second unchanged posture, and i < n; R is the robot rotation matrix. Let be the rotation matrix obtained in hand-eye calibration. This is the translation matrix obtained in hand-eye calibration. This is the robot's translation matrix during the first data collection. Let be the translation matrix of the robot during the i-th data collection. This refers to the data of the center point of the cylindrical cross-section obtained in the i-th acquisition under the online laser. For the i-th vector, and For numerical values, ; .

[0045] By fixing the robot's posture, the complexity and errors caused by posture adjustment are reduced, and the stability and consistency of data acquisition are improved. Through multiple data acquisitions and optimized algorithm processing, the accuracy and integrity of the data are ensured, thereby improving the accuracy of the cylinder axis vector calculation. The use of high-precision equipment and multiple data processing technologies further improves the quality of data acquisition and processing, ensuring the accuracy and reliability of hand-eye calibration.

[0046] Based on the rotation invariance of spatial vectors along the same cylindrical axis, the steps for constructing the objective function and calculating the rotation matrix of the hand-eye transformation matrix include: multiplying two different spatial vectors together to obtain: ,

[0047] Where i < n, j < n, and i ≠ j, j is the number of times the robot changes position in the third unchanged posture, where n ≥ 3; after simplification, we get:

[0048] ,

[0049] in, Represented as the Kronecker product of two matrices, It can be represented as the transpose of a skew-symmetric matrix of vectors. The rotation matrix obtained in hand-eye calibration The vector form, where R is the robot rotation matrix. , ; , ;

[0050] After sorting, we can conclude that:

[0051] ,

[0052] in, ; ; ;

[0053] The rotation matrix is ​​obtained using the least squares method: ,

[0054] in, .

[0055] The rotation matrix in hand-eye calibration can be obtained by solving the expression. The rotation matrix in hand-eye calibration is the rotation matrix of the hand-eye transformation matrix. Substituting the obtained result into the expression... = ( - )+ = Vectors can be obtained from To extract the most representative features from the above vectors, principal component analysis was used to process the obtained vectors and normalize the results, thus obtaining the unit direction vector of the cylinder axis. .

[0056] Furthermore, by simultaneously changing the robot's pose and position, the following equation is obtained: ,

[0057] Where i < k, j < k, k is the number of different robot poses, and k ranges from 5 to 10. For numerical values, ; For numerical values, , Let be the unit direction vector of the cylinder axis. and Different robot rotation matrices represent different robot poses. This is the translation matrix obtained in hand-eye calibration. and This represents the data of the center point of the cylindrical cross-section obtained under the online laser, acquired in the corresponding robot pose. In order to be in The corresponding translation matrix is ​​below. In order to be in The corresponding translation matrix below;

[0058] After sorting, we can conclude that: In the formula, ; ; The axis vector of the cylinder; This is the translation matrix obtained in hand-eye calibration.

[0059] Furthermore, by maintaining the robot's posture and changing its position so that the laser scans the bottom surface of the cylinder, a unit spatial vector can be obtained. In the formula, L is the unit spatial vector in the upper base of the cylinder. and For different translation matrices under the same robot posture, and They are respectively in and Data points acquired by the offline laser;

[0060] By dot product of the unit space vector and the unit direction vector of the cylinder axis: Where e is the calibration performance index, which measures the performance of hand-eye calibration results; L is the unit spatial vector on the top surface of the cylinder; ideally, the unit direction vector of the cylinder's axis and the vector on the bottom surface are perpendicular, so their dot product is 0; the calibration performance index is compared with the engineering construction range threshold. The size, if the value is greater than the threshold of the engineering construction scope Then recalibrate.

[0061] Example 1:

[0062] S1, such as Figure 1 As shown, the line laser is fixed to the tooling fixture at the end of the multi-degree-of-freedom robotic arm;

[0063] The transformation relationship between data in the line laser coordinate system and robot base coordinates is as follows: (1), where, (2).

[0064] S2. Keeping the robot's posture unchanged, the line laser acquires the edge data of the cylindrical profile by changing the robot's position; the profile data is fitted by an optimization algorithm to obtain the position of the center of the cylindrical section in the line laser coordinate system; based on the rotation invariance of spatial vectors, an objective function is constructed to obtain the rotation matrix in the hand-eye transformation matrix.

[0065] The specific implementation steps of step S2 are as follows:

[0066] Specifically, such as Figure 1 As shown, This involves using a laser to acquire edge data of a cylindrical profile, controlling a robot to acquire the profile of a standard cylindrical cross-section in different poses, and solving for the feature positions by fitting an ellipse of the cutting surface. The calculation formula is as follows: (3), (4);

[0067] By maintaining the robot's posture and changing its position, and taking two of the positions, the cylinder's axis vector can be obtained as follows: = ( - )+ = (5);

[0068] Based on the rotation invariance of the cross product (the rotation invariance of spatial vectors along the same cylinder axis), we get:

[0069] (6);

[0070] Arrangement (6), etc.:

[0071] (7);

[0072] in:

[0073] (8);

[0074] (9);

[0075] Based on matrix vectorization, rearranging equation (7) yields:

[0076] (10);

[0077] in,

[0078] (11);

[0079] The rotation matrix is ​​obtained using the least squares method:

[0080] (12);

[0081] in, , The rotation matrix to be determined The vectorized form of .

[0082] like Figure 2 As shown, based on the desired Use the PCA algorithm to obtain the unit direction vector of the cylinder axis. .

[0083] S3. Combining the rotation matrix obtained from S2, principal component analysis is used to obtain the unit direction vector of the cylindrical profile in the robot's base coordinate space. The translation vector in the hand-eye transformation matrix is ​​obtained based on the principle that vectors on the same axis have an orthogonal Euclidean distance of 0. The specific implementation steps are as follows:

[0084] The equation is obtained by changing the robot's pose:

[0085] (13);

[0086] Arrangement of equation (13) yields:

[0087] (14);

[0088] in:

[0089] (15);

[0090] S4. Combining the hand-eye transformation matrix obtained in steps S2 and S3, use a laser to scan the bottom surface of the cylinder to obtain the unit space vector; determine whether the accuracy of the hand-eye transformation matrix meets the engineering requirements by multiplying the unit space vector by the unit direction vector of the cylinder axis.

[0091] Furthermore, the specific implementation steps of step S4 are as follows:

[0092] Step S401, as follows Figure 1 As shown, a unit space vector is obtained by scanning the top surface of the cylinder with a laser:

[0093] (16);

[0094] Step S402: Multiply the unit space vector by the unit direction vector of the cylinder axis:

[0095] (17);

[0096] In an ideal state, the unit direction vector of the cylinder's axis and the vector of its base are perpendicular, so their dot product is 0.

[0097] Step S403: Determine whether e calculated in S02 is less than the threshold value for the engineering construction range. If it exceeds the threshold of the construction area Then recalibrate.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A hand-eye calibration method based on the characteristics of a standard cylindrical axis, characterized in that, The steps of the method include: S1: Fix the line laser to the end of the robot and fix the cylinder at any position in the application space of the robot; S2: Keeping the robot's posture unchanged, the position of the robot is changed so that the line laser can acquire the contour edge data of the cylinder; S3: Fit the contour edge data of the cylinder using the least squares method to obtain the position of the elliptical center of the cylinder's cross-section in the coordinate system of the line laser; and construct an objective function based on the rotation invariance of the spatial vector of the same cylinder axis, and calculate the rotation matrix of the hand-eye transformation matrix using the objective function; S4: Combining the rotation matrix of the hand-eye transformation matrix, the unit direction vector of the cylinder's axis in the robot's base coordinate space can be obtained. Based on the principle that the orthogonal Euclidean distance between vectors of the same axis is 0, the translation vector of the hand-eye transformation matrix is ​​obtained. The steps for calculating the rotation matrix of the hand-eye transformation matrix include: Multiplying two distinct space vectors yields: , where i < n, j < n, and i ≠ j, j is the number of times the robot changes position in the third unchanged posture; Let j be the j-th vector; and For numerical values, = ; = ; The rotation matrix of the hand-eye transformation matrix is ​​obtained using the least squares method: ,in, The rotation matrix obtained in hand-eye calibration The vector form, where H is a numerical value. , , Represented as the Kronecker product of two matrices, ; ; ; Translation matrix obtained in hand-eye calibration for: ,in, For numerical values, ; For numerical values, , Let be the unit direction vector of the cylinder axis. and Different robot rotation matrices represent different robot poses. and This represents the data of the center point of the cylindrical cross-section obtained under the online laser, acquired in the corresponding robot pose. In order to be in The corresponding translation matrix below; In order to be in The corresponding translation matrix below; S5: Combining the rotation matrix and translation vector of the hand-eye transformation matrix, use the line laser to scan the bottom surface of the cylinder to obtain a unit space vector; determine whether the value of the hand-eye transformation matrix meets the engineering construction range threshold by multiplying the unit space vector by the unit direction vector. If the required construction scope threshold is not met, The requirements are then redefined, among which, By maintaining the robot's posture and changing its position so that the laser scans the top surface of the cylinder, a unit space vector can be obtained: In the formula, L is the unit spatial vector in the upper base of the cylinder; and These are different translation matrices for the same robot posture; and They are respectively in and Data points acquired by the offline laser; By dot product of the unit space vector and the unit direction vector of the cylinder axis: Where e is the calibration performance index; under ideal conditions, the unit direction vector of the cylinder's axis and the base vector are perpendicular, so their dot product is 0; determine whether the calibration performance index is related to the engineering construction range threshold. If the value is greater than the threshold of the engineering construction scope, Then recalibrate.

2. The hand-eye calibration method based on the characteristics of a standard cylindrical axis according to claim 1, characterized in that: The transformation function relationship between the line laser and the robot's coordinate system is as follows: ,in, ; Data in the line laser coordinate system. Let be the homogeneous transformation matrix from the line laser to the robot's end effector. Let be the homogeneous transformation matrix from the robot's end effector to the robot's base coordinates. The data in the robot's base coordinate system is obtained by transforming the data in the line laser coordinate system. Here is the x-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. This represents the z-coordinate of the center point of the cylindrical cross-section in the laser coordinate system.

3. The hand-eye calibration method based on the characteristics of a standard cylindrical axis according to claim 1, characterized in that: By fitting the contour edge data of the cylinder using the least squares method, the general quadratic equation of the ellipse is obtained as follows: Where A is the first parameter of the ellipse, B is the second parameter of the ellipse, C is the third parameter of the ellipse, D is the fourth parameter of the ellipse, E is the fifth parameter of the ellipse, and F is the sixth parameter of the ellipse; The coordinates of the center point of the cross-section of the cylinder can be calculated from the general quadratic equation of the ellipse: ,in, This represents the x-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. Here is the y-coordinate of the center point of the cylindrical cross-section in the laser coordinate system. This represents the z-coordinate of the center point of the cylindrical cross-section in the laser coordinate system.

4. The hand-eye calibration method based on the characteristics of a standard cylindrical axis according to claim 3, characterized in that, The axis vector of the cylinder is calculated as follows: = ( - )+ = Where i is the number of position changes of the robot in the first unchanged posture, n is the number of position changes of the robot in the second unchanged posture, and i < n; R is the robot rotation matrix. Let be the rotation matrix obtained in hand-eye calibration. This is the translation matrix obtained in hand-eye calibration. This is the robot's translation matrix during the first data collection. Let be the translation matrix of the robot during the i-th data collection. This refers to the data of the center point of the cylindrical cross-section obtained in the i-th acquisition under the online laser. Let be the i-th vector, where and For numerical values, ; .

5. The hand-eye calibration method based on the characteristics of a standard cylindrical axis according to claim 4, characterized in that: Under the same posture, the number of times the robot changes position n≥3 in the second unchanged posture.

6. The hand-eye calibration method based on the characteristics of a standard cylindrical axis according to claim 1, characterized in that: The threshold of the construction scope of the project The value range is 0.1 to 0.2.

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