Visual robot hand-eye calibration method based on circular hole calibration plate

Abstract

The invention relates to the field of intelligent industry, and discloses a visual robot hand-eye calibration method based on a circular hole calibration plate, which takes the circle center of a calibration plate circular hole as a fixed point as a constraint, establishes a hand-eye calibration model combined with robot kinematics parameters, and performs a contrast experiment with a traditional standard ball method under the same experiment platform. After a calibration result is obtained, a certain high-precision plane is scanned with reference to a flatness error evaluation method, a point cloud of the plane is obtained, the distance root-mean-square error between the point cloud and the least square fitting plane is calculated, and the distance root-mean-square error serves as an evaluation parameter of the hand-eye relation calibration precision. According to the method, the position coordinates of the fixed points in the space are collected more accurately under the on-line laser coordinate system, and kinematics parameters of the robot are incorporated into the hand-eye calibration model, so that the root-mean-square error of plane measurement can be reduced, and the superiority of the method is verified.

Description

Technical Field

[0001] The present invention relates to the field of intelligent industry, and specifically to a vision robot hand-eye calibration method based on a circular hole calibration plate. Background Art

[0002] As an important part of intelligent robots, the robot vision system can assist robots in completing various production and processing tasks in factories. In the field of engineering measurement, line laser sensors with the advantages of strong anti-interference ability and high precision have been widely used. Limited by the measurement range, the line laser sensor can only measure the local surface data of an object. However, after installing the line laser sensor on a flexible robot and driving the line laser sensor to move by the robot, the object can be completely measured, thereby improving the flexibility of the robot system.

[0003] After installing the line laser sensor on the robot, it is necessary to determine the pose transformation relationship between the robot flange coordinate system and the line laser sensor coordinate system. The process of solving this transformation relationship is called hand-eye calibration. Currently, the most common hand-eye calibration method is to use a specific calibration object. The calibration object is placed at a fixed position in space, and the relative movement between the vision sensor and the calibration object is caused by controlling the robotic arm. The vision sensor obtains the external shape measurement data of the calibration object, and then combines the movement data of the robotic arm to establish a calibration model. After solving, the transformation relationship matrix between the vision sensor coordinate system and the base coordinate system of the robotic arm can be obtained. This transformation matrix is the hand-eye calibration matrix. The traditional robot hand-eye calibration method uses a standard ball, and the method of using a standard ball for calibration requires circular fitting of the point coordinates on the cross-section of the ball generated by each scan to solve the coordinates of the center of the scan cross-section, which will increase the error of solving the coordinates of the center of the ball. Therefore, we propose a vision robot hand-eye calibration method based on a circular hole calibration plate. Summary of the Invention

[0004] (1) Technical Problems to be Solved

[0005] In view of the deficiencies of the prior art, the present invention provides a vision robot hand-eye calibration method based on a circular hole calibration plate, which solves the above problems.

[0006] (2) Technical Solutions

[0007] To achieve the above object, the present invention provides the following technical solutions: A vision robot hand-eye calibration method based on a circular hole calibration plate, comprising the following steps:

[0008] S1: Taking the center of the circular hole of the calibration plate as a fixed point as a constraint, establish a hand-eye calibration model combined with the kinematic parameters of the robot;

[0009] S2: Scan the center point of the round hole calibration plate according to the hand-eye calibration model combined with the robot kinematic parameters, preprocess the acquired data, and mark the center coordinate X B ;

[0010] S3: Obtain the hand-eye relationship matrix of the hand-eye calibration model in S1, calculate the initial value of the hand-eye relationship matrix, and initialize the robot MDH parameters;

[0011] S4: Establish a robot error model, identify and compensate for the robot kinematic parameter errors, and combine the kinematic errors to identify the robot MDH parameters and initial values;

[0012] S5: Determine whether the quantity to be compensated is less than the set threshold. If so, obtain the calibration result; if not, continuously iterate and update the MDH parameter error model and the hand-eye relationship matrix using the least squares method until the ideal value is reached.

[0013] Preferably, the hand-eye calibration model combined with the robot kinematic parameters in S1 consists of an industrial robot, a line laser sensor, and a round hole calibration plate.

[0014] Preferably, in S2, when scanning the center point of the round hole calibration plate, mark the center coordinate X B Specifically, it further includes: Install the line laser sensor on the end flange of the robot arm, and by changing the robot arm posture multiple times, the line laser sensor scans the center point of the round hole calibration plate, and the position X of the center point in the line laser sensor coordinate system O S -X S Y S Z S can be obtained, and the position X of the center point in the robot base coordinate system O S -X B -X B Y B Z B ; B ;

[0015] The conversion formula between the above two is:

[0016]

[0017] In the formula, is the abbreviation of the conversion matrix between the robot end coordinate system and the base coordinate system, is the abbreviation of the conversion matrix between the line laser sensor coordinate system and the robot end coordinate system, that is, the required hand-eye relationship matrix.

[0018] Preferably, the preprocessing of the data obtained in S2 specifically includes: for each scan of the center point of the round hole calibration plate, the robotic arm is controlled to align the blue light beam of the line laser scanner with the center marking point of the round hole. After obtaining the data, the point cloud data is preprocessed, and the cross-sectional two-dimensional point cloud data is processed to find the left and right edge points (x 1 , z 1 ) and (x 2 , z 2 ) of the round hole;

[0019] The point cloud data of the calibration object platform scanned is linearly fitted, and the linear formula obtained is:

[0020] z = kx + b (3)

[0021] Since the center point is on the fitted line, according to the following formula (4), the center point coordinates in the line laser sensor coordinate system can be obtained as (x d , 0, z d ).

[0022]

[0023] Preferably, the specific process of obtaining the hand-eye relationship matrix of the hand-eye calibration model in S3 is as follows: through the center coordinates of the standard sphere in space and the center coordinates of the round hole calibration object obtained in step S2, after multiple scans, the coordinate point set {P = X S -X S Y S Z S | i = 1, 2, 3,..., n} in the coordinate system O i can be obtained. Since the round hole calibration plate is fixed in space, the coordinates of the center point in the base coordinate system O B -X B Y B Z B are unchanged, and the following relationship can be obtained:

[0024]

[0025] Among them: can be obtained from the MDH parameters of each joint axis of the robot. After multiple scans with different postures, multiple transformation relationship matrices can be read. is the transformation relationship between the line laser sensor coordinate system and the robot end flange, that is, the required hand-eye relationship matrix. During the calibration process, the position between the hand and the eye is fixed, so the obtained by multiple scans is unchanged. X B is the coordinate of the center point in the base coordinate system, X 1 , X 2 , …, X nare the coordinates of the fixed points after multiple scans under the online laser sensor, and these coordinate values have been obtained through the previous acquisition method;

[0026] After obtaining the system of equations in Equation (5), the following relationships can be deduced:

[0027]

[0028] Equation (6) can be rewritten as:

[0029]

[0030] In Equation (7), R i is the rotation matrix, which is a 3×3 matrix, and T i is the translation matrix, t is the translation vector of, r is the hand-eye matrix the rotation components of the x-axis, y-axis, and z-axis in, subtracting the right side from the left side and simplifying gives:

[0031]

[0032] A system of equations of the form Ax = b is obtained, and the solution formula using the least squares method is:

[0033] x = (A T A) -1 A T b (9)

[0034] After solving for r 1 and r 3 and t, according to the right-hand rule of the coordinate system, it can be obtained that:

[0035] r 2 = r 1 × r 3 (10)

[0036] The matrix of the hand-eye relationship can be obtained through Equations (6)-(9).

[0037] Preferably, the hand-eye relationship matrix obtained in S3 and the initial values of the calculated hand-eye relationship matrix and the initialization of the robot MDH parameters do not take into account the kinematic errors of the robot, resulting in a large calibration result error. Therefore, the hand-eye calibration result is used as the initial value and then the kinematic parameter errors of the robot are added to optimize the hand-eye calibration result.

[0038] Preferably, the optimization of the hand-eye calibration result using the kinematic parameter errors in S4 specifically includes: establishing a kinematic error identification algorithm using the homogeneous transformation general formula of adjacent joints and the system error model, where the homogeneous transformation general formula of adjacent joints is:

[0039]

[0040]

[0041] The system error model is shown in Equation (13):

[0042]

[0043] Wherein is the deviation of the transformation matrix between the coordinate system of the robot end flange and the base coordinate system, is the deviation between the hand-eye relationship matrix and the true value, T is the transformation matrix between the coordinate system of the line laser sensor and the base coordinate system, and ΔT is its deviation. After eliminating the high-order terms, we can get:

[0044]

[0045] According to the principle of robot differential kinematics

[0046] ΔT = TδT (15)

[0047]

[0048] We can obtain:

[0049]

[0050] Combining the above equations (11)-(17), the error identification formula is written in the form of Equation (18):

[0051] Ax = b (18)

[0052] In the formula, A is a 3×36 error coefficient matrix, including 30 robot kinematic parameters and 6 hand-eye relationship matrix parameters, b is the difference between the actual position and the theoretical position of the end, and the unknown x is the parameter error Δq. The Δq parameter mainly includes three types: independent parameters, correlation parameters, and ineffective parameters.

[0053] Preferably, in the process of parameter optimization and solution in S4, the correlation parameters and ineffective parameters in Δq will affect the solution process, resulting in a reduction in the solution accuracy of Δq. Removing these parameters will not affect the error result. Therefore, before identification, QR decomposition is used to remove these redundant parameters to obtain the parameter error Δq to be identified, and then the error upper limit is set to continuously iterate the robot MDH parameters after adding compensation until convergence to the expected calibration result.

[0054] (III) Beneficial effects

[0055] Compared with the prior art, the present invention provides a vision robot hand-eye calibration method based on a circular hole calibration plate, which has the following beneficial effects:

[0056] 1. In the vision robot hand-eye calibration method based on a circular hole calibration plate, the center of the circular hole calibration plate is used as a fixed point in space to establish a hand-eye calibration model including the identification of the MDH parameter error of the robot, and the least squares method is used to continuously iterate and update the MDH parameter error model and the hand-eye relationship matrix until the ideal value is reached; and the traditional standard ball method and the circular hole calibration plate method are compared through simulation and experiments. In the simulation experiment, after a given MDH parameter error, this algorithm can identify it. After adding the same upper limit of random error to the scanned point cloud data, the calibration result of this method is more accurate and stable than that of the traditional standard ball method.

[0057] 2. In the vision robot hand-eye calibration method based on a circular hole calibration plate, the coordinates of the center point can be directly obtained through a line laser sensor. Since the coordinates of the center point are directly scanned by a line laser profile scanner, one of the three-dimensional coordinates of the center point in space can be set to zero for each measurement. Compared with the traditional standard ball measurement method, this method not only reduces the steps of fitting a circle, but also reduces the steps of solving the center coordinates, avoiding the errors generated in this step, thereby improving the calibration accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 is a schematic flow chart of the vision robot hand-eye calibration method based on a circular hole calibration plate of the present invention;

[0059] Figure 2 is a schematic diagram of the hand-eye calibration model of the present invention;

[0060] Figure 3 is a schematic diagram of scanning the center point of the circular hole calibration plate of the present invention;

[0061] Figure 4 is a schematic flow chart of the algorithm for optimizing the hand-eye calibration result by using the kinematic parameter error of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0062] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0063] Please refer to Figures 1-4 , the vision robot hand-eye calibration method based on a circular hole calibration plate includes the following steps:

[0064] S1: Taking the center of the circular hole on the calibration board as the fixed point as the constraint, establish a hand-eye calibration model combined with the kinematic parameters of the robot;

[0065] S2: Scan the center point of the circular hole calibration board according to the hand-eye calibration model combined with the kinematic parameters of the robot, preprocess the obtained data, and mark the center coordinate X B ;

[0066] S3: Calculate the hand-eye relationship matrix of the hand-eye calibration model in S1, calculate the initial value of the hand-eye relationship matrix, and initialize the robot MDH parameters;

[0067] S4: Establish a robot error model, identify the kinematic parameter errors of the robot and perform compensation optimization, and identify the robot MDH parameters and initial values in combination with the kinematic errors;

[0068] S5: Judge whether the quantity to be compensated is less than the set threshold. If so, obtain the calibration result. If not, continuously iterate and update the MDH parameter error model and the hand-eye relationship matrix using the least squares method until the ideal value is reached.

[0069] The hand-eye calibration model combined with the kinematic parameters of the robot in S1 consists of an industrial robot, a line laser sensor, and a circular hole calibration board, as Figure 2 shown.

[0070] In S2, scanning the center point of the circular hole calibration board to mark the center coordinate X B Specifically, it further includes: loading the line laser sensor on the end flange of the robot arm, and changing the posture of the robot arm multiple times to make the line laser sensor scan the center point of the circular hole calibration board, so as to obtain the position X of the center point in the line laser sensor coordinate system O S -X S Y S Z S and the position X in the robot base coordinate system O S ; B -X B Y B Z B ; B ;

[0071] The conversion formula between the above two is:

[0072]

[0073] In the formula, is the abbreviation of the conversion matrix between the robot end coordinate system and the base coordinate system, is the abbreviation of the conversion matrix between the line laser sensor coordinate system and the robot end coordinate system, that is, the required hand-eye relationship matrix;

[0074] Traditional robot hand-eye calibration methods use a standard ball. The method using a standard ball requires circular fitting of the point coordinates on the cross-section of the ball generated by each scan to solve the coordinates of the center of the scan cross-section, which will increase the error in solving the coordinates of the center of the ball. The circular hole calibration plate used in this method can directly obtain the coordinates of the center point through a line laser sensor. Since the coordinates of the center point are directly scanned by the line laser profile scanner, one of the three-dimensional coordinates of the center point in space can be set to zero for each measurement. Compared with the traditional standard ball measurement method, this method not only reduces the steps of fitting a circle but also reduces the steps of solving the coordinates of the center of the circle, avoiding the error generated in this step, thereby improving the calibration accuracy.

[0075] S2 Obtaining and preprocessing data specifically includes: As Figure 3 shown, for each scan of the center point of the circular hole calibration plate, the robotic arm is controlled to align the blue light of the line laser scanner with the center marking point of the circular hole. After obtaining the data, the point cloud data is preprocessed, and the two-dimensional cross-section point cloud data is processed to find the left and right edge points of the circular hole (x 1 , z 1 ), (x 2 , z 2 );

[0076] Perform linear fitting on the scanned point cloud data of the calibration object platform, and the fitted linear formula is:

[0077] z = kx + b (3)

[0078] Since the center point is on the fitted line, the coordinates of the center point in the line laser sensor coordinate system can be obtained as (x d, 0, z d ) according to the following formula (4).

[0079]

[0080] In S3, finding the hand-eye relationship matrix of the hand-eye calibration model in S1 specifically includes: Through the center coordinates of the standard ball in space and the center coordinates of the circular hole calibration object obtained in step S2, after multiple scans, a set of coordinate points {P = X S -X S Y S Z S |i = 1, 2, 3,..., n} in the coordinate system O i can be obtained. Since the circular hole calibration plate is fixed in space, the coordinates of the center point in the base coordinate system O B -X B Y B Z B are invariant, and the following relationship can be obtained:

[0081]

[0082] Among them: It can be obtained from the MDH parameters of each joint axis of the robot. After multiple pose scans, multiple transformation relationship matrices can be read. It is the transformation relationship between the coordinate system of the line laser sensor and the end flange of the robot, that is, the required hand-eye relationship matrix. During the calibration process, the position between the hand and the eye is fixed, so the is unchanged. X B is the coordinate of the center point in the base coordinate system. X 1 , X 2 , …, X n are the coordinates of the fixed points after multiple scans in the line laser sensor coordinate system. These coordinate values have been obtained through the previous acquisition method;

[0083] After obtaining the system of equations in formula (5), the following relationships can be deduced:

[0084]

[0085] Formula (6) can be rewritten as:

[0086]

[0087] In formula (7), R i is the rotation matrix, which is a 3×3 matrix. T i is the translation matrix. t is the translation vector of, and r is the hand-eye matrix the rotation components of the x-axis, y-axis, and z-axis in. Subtracting the right side from the left side and simplifying, we can get:

[0088]

[0089] A system of equations in the form of Ax = b is obtained, and the solution formula using the least squares method is:

[0090] x = (A T A) -1 A T b (9)

[0091] After solving for r 1 and r 3 and t, according to the right-hand rule of the coordinate system, it can be obtained that:

[0092] r 2 = r 1 × r 3 (10)

[0093] The matrix of the hand-eye relationship can be obtained through equations (6)-(9).

[0094] The hand-eye relationship matrix obtained in S3, as well as the initial values for calculating the hand-eye relationship matrix and the initialization of the robot's MDH parameters, do not take into account the kinematic errors of the robot, resulting in a relatively large calibration error. Therefore, the hand-eye calibration result is used as the initial value, and then the kinematic parameter errors of the robot are added to optimize the hand-eye calibration result. The robot error refers to the deviation between the actual pose and the theoretical pose of the robot's end flange. Due to temperature changes caused by heat generation during robot operation and machine wear, etc., there will be a deviation between the trajectory of the robot's end and the ideal trajectory. Therefore, in this method, a robot error model will be established to identify and compensate for the kinematic parameter errors of the robot and optimize them.

[0095] The optimization of the hand-eye calibration result using kinematic parameter errors in S4 specifically includes: establishing a kinematic error identification algorithm using the homogeneous transformation general formula of adjacent joints and the system error model, where the homogeneous transformation general formula of adjacent joints is:[[]]

[0096]

[0097]

[0098] The system error model is shown in equation (13):

[0099]

[0100] In the formula is the deviation of the transformation matrix between the coordinate system of the robot's end flange and the base coordinate system, is the deviation between the hand-eye relationship matrix and the true value, T is the transformation matrix between the coordinate system of the line laser sensor and the base coordinate system, and ΔT is its deviation. After eliminating the high-order terms, we can get:

[0101]

[0102] According to the principle of robot differential kinematics

[0103] ΔT = TδT (15)

[0104]

[0105] We can obtain:

[0106]

[0107] Combining the above equations (11)-(17), the error identification formula is written in the form of equation (18):

[0108] Ax = b (18)

[0109] In the formula, A is a 3×36 error coefficient matrix, including 30 robot kinematic parameters and 6 hand-eye relationship matrix parameters, b is the difference between the actual position and the theoretical position of the end effector, and the unknown x is the parameter error Δq. The Δq parameter mainly includes three types: independent parameters, correlation parameters, and ineffective parameters.

[0110] In the process of parameter optimization and solution in S4, the correlation parameters and ineffective parameters in Δq will affect the solution process, resulting in a decrease in the solution accuracy of Δq. Removing these parameters will not affect the error result. Therefore, before identification, QR decomposition is used to remove these redundant parameters to obtain the parameter error Δq to be identified. Then, an error upper limit is set, and the robot MDH parameters after adding compensation are continuously iterated until convergence to the expected calibration result. The overall flowchart of the algorithm is as Figure 4 shown.

[0111] This vision robot hand-eye calibration method based on a circular hole calibration plate aims at the hand-eye calibration problem of an intelligent robot system equipped with a line laser sensor, and proposes the application of a hand-eye calibration method based on a circular hole calibration plate. The center of the circular hole calibration plate is used as a fixed point in space, a hand-eye calibration model including the identification of robot MDH parameter errors is established, and the least squares method is used to continuously iterate and update the MDH parameter error model and the hand-eye relationship matrix until the ideal value is reached.

[0112] In addition, this method compares the traditional standard sphere method with the circular hole calibration plate method through simulation and experiments. In the simulation experiment, after given MDH parameter errors, the algorithm of this method can identify them. After adding random errors with the same upper limit to the scanned point cloud data, the calibration result of this method in this paper is more accurate and stable than that of the traditional standard sphere method. At the same time, this method adopts the evaluation method of flatness error. By scanning the point cloud data obtained from a precision-machined plane with a flatness error of 0.01 mm and inversely solving it back to the base coordinate system, compared with the standard sphere method, the root mean square error of this method after MDH parameter compensation drops from 0.212 mm to 0.065 mm, which is consistent with the simulation expected result, verifying the feasibility and practicality of this method.

[0113] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. Vision robot hand-eye calibration method based on a round-hole calibration plate, Characterized in that, It includes the following steps: S1: Taking the center of the round hole of the calibration plate as a fixed point as a constraint, establish a hand-eye calibration model combining the kinematic parameters of the robot; S2: Scan the center point of the circular hole calibration plate according to the hand-eye calibration model combined with the robot kinematic parameters, preprocess the acquired data, and identify the center coordinate X B ; S3: Obtain the hand-eye relationship matrix of the hand-eye calibration model in S1, calculate the initial value of the hand-eye relationship matrix, and initialize the robot MDH parameters; S4: Establish a robot error model, identify the kinematic parameter errors of the robot and perform compensation optimization, and identify the robot MDH parameters and initial values in combination with the kinematic errors; S5: Judge whether the quantity to be compensated is less than the set threshold. If so, obtain the calibration result. If not, continuously iterate and update the MDH parameter error model and the hand-eye relationship matrix using the least squares method until the ideal value is reached.

2. The vision robot hand-eye calibration method based on a round-hole calibration plate according to claim 1, Characterized in that, The hand-eye calibration model combining the kinematic parameters of the robot in S1 consists of an industrial robot, a line laser sensor, and a round-hole calibration plate.

3. The vision robot hand-eye calibration method based on a round-hole calibration plate according to claim 1, Characterized in that, In step S2, the center point of the round hole calibration plate is scanned to identify the center coordinate X B Specifically, it further includes: loading the line laser sensor on the end flange of the robotic arm, and by changing the posture of the robotic arm multiple times to make the line laser sensor scan the center point of the round hole calibration plate, the position X of the center point in the line laser sensor coordinate system O S -X S Y S Z S can be obtained, and the position X of the center point in the robot base coordinate system O S -X B Y B Y B Z B can also be obtained; B ; The conversion formula between the two is: wherein, is the abbreviation of the transformation matrix between the end - effector coordinate system of the robot and the base coordinate system, is the abbreviation of the transformation matrix between the line - laser sensor coordinate system and the end - effector coordinate system of the robot, that is, the required hand - eye relationship matrix.

4. The vision robot hand-eye calibration method based on a round-hole calibration plate according to claim 1, Characterized in that, The specific preprocessing of the data obtained in S2 includes: for each scan of the center point of the round hole calibration plate, the robotic arm is controlled to align the blue light of the line laser scanner with the center marking point of the round hole. After obtaining the data, the point cloud data is preprocessed, and the cross-sectional two-dimensional point cloud data is processed to find the left and right edge points of the round hole (x 1 , z 1 ), (x 2 , z 2 ); Perform linear fitting on the point cloud data of the calibration object platform scanned, and the fitted linear formula is: z = kx + b (3) Since the center point lies on the fitted line, the coordinates of the center point in the online laser sensor coordinate system can be obtained as (x d , 0, z d ) according to the following formula (4).

5. The vision robot hand-eye calibration method based on a round-hole calibration plate according to claim 1, Characterized in that, The specific process of obtaining the hand-eye relationship matrix of the hand-eye calibration model in S1 in S3 is as follows: By using the center coordinates of the standard sphere in space and the center coordinates of the circular hole calibration object obtained in step S2, after multiple scans, the coordinate point set {P = X S -X S Y S Z S in the online laser sensor coordinate system O can be obtained. Since the circular hole calibration plate is fixed in space, the center point coordinates in the base coordinate system O i |i = 1, 2, 3, …, n}. Because the circular hole calibration plate is fixed in space, the coordinates of the center point in the base coordinate system O B -X B Y B Z B are invariant, and the following relationships can be obtained: Wherein: It can be obtained from the MDH parameters of each joint axis of the robot. After multiple posture scans, multiple transformation relationship matrices can be read. It is the transformation relationship between the coordinate system of the line laser sensor and the end flange of the robot, that is, the required hand-eye relationship matrix. During the calibration process, the position between the hand and the eye is fixed. Therefore, the is invariant, X B is the coordinate of the center point in the base coordinate system, X 1 , X 2 , …, X n are the coordinates of the fixed point after multiple scans in the line laser sensor. Through the above-collected coordinate values; After obtaining the system of equations in formula (5), the following relationships can be deduced: Formula (6) can be rewritten as: In Equation (7), R i is rotation matrix, which is a 3×3 matrix, T i is translation matrix, t is translation vector, r is the rotation components of the x-axis, y-axis, and z-axis in the hand-eye matrix . Subtracting the right side from the left side and simplifying, we get: Obtained a system of equations of the form Ax = b, and the solution formula using the least squares method is: x = (A T A) -1 A T b(9) Solve for r 1 and r 3 and t, according to the right-hand rule of the coordinate system, it can be obtained that: r 2 ＝r 1 ×r 3 (10) The matrix of the hand-eye relationship can be obtained through formulas (6)-(9).

6. The vision robot hand-eye calibration method based on a round-hole calibration plate according to claim 1, Characterized in that, After obtaining the hand-eye relationship matrix in S3, calculating the initial value of the hand-eye relationship matrix, and initializing the robot MDH parameters, use the hand-eye calibration result as the initial value and add the robot kinematic parameter error to optimize the hand-eye calibration result.

7. The vision robot hand-eye calibration method based on a round-hole calibration plate according to claim 1, Characterized in that, The optimization of the hand-eye calibration result using the kinematic parameter error in S4 specifically includes: establishing a kinematic error identification algorithm using the homogeneous transformation general formula of adjacent joints and the system error model, where the homogeneous transformation general formula of adjacent joints is: The system error model is shown in formula (13): where is the deviation of the transformation matrix between the coordinate system of the robot's end flange and the base coordinate system, is the deviation between the hand-eye relationship matrix and the true value, T is the transformation matrix between the coordinate system of the line laser sensor and the base coordinate system, and ΔT is its deviation. After eliminating the high-order terms, we can obtain: According to the principle of robot differential kinematics ΔT = TδT (15) It can be obtained: Combining the above formulas (11)-(17), write the error identification formula in the form of formula (18): Ax = b (18) In the formula, A is a 3×36 error coefficient matrix, including 30 robot kinematic parameters and 6 hand-eye relationship matrix parameters, b is the difference between the actual position and the theoretical position of the end, and the unknown quantity x is the parameter error Δq. The Δq parameter mainly includes three types: independent parameters, correlation parameters, and ineffective parameters.

8. The vision robot hand-eye calibration method based on a round hole calibration plate according to claim 7, characterized in that, in the process of parameter optimization and solution in S4, the correlation parameters and ineffective parameters in Δq are removed. Before identification, these redundant parameters need to be removed using QR decomposition to obtain the parameter error Δq to be identified. Then, an error upper limit is set, and the robot MDH parameters after adding compensation are continuously iterated until they converge to the expected calibration result.

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