A motion platform compensation method considering overall deviation

Abstract

The present application discloses a motion platform compensation method that takes into account overall deviation, which relates to the field of industrial technology. The method places a standard calibration plate containing several calibration points with known theoretical positions on the motion platform of the device to be calibrated, uses the device to be calibrated to detect and determine the actual position of each calibration point on the standard calibration plate, and then calculates the lateral tilt angle and longitudinal tilt angle based on the actual position of each calibration point. The actual position of each calibration point is then rotated and sheared to obtain the actual position after compensation. The method performs overall error modeling on the motion platform of the device to be calibrated, considering the error characteristics of the motion platform as a whole, thereby improving the accuracy and reliability of calibration. The method achieves a higher calibration effect with a relatively simple calculation method and a lower cost. Based on the established model, the error trend under specific conditions can be predicted, so that measures can be taken in advance to prevent the occurrence or expansion of errors.

Description

Technical Field

[0001] The present application relates to the field of industrial technology, and in particular to a motion platform compensation method considering overall deviation. Background Art

[0002] Motion platforms are essential components for achieving precise position control and motion trajectory in many industrial applications. However, due to factors such as manufacturing errors, wear, and load variations, motion platforms can exhibit deviations during operation, affecting their accuracy and stability. To address this, compensation is often required.

[0003] Existing compensation methods for motion platforms primarily rely on table lookup compensation. The resulting compensation data is loaded into the motion platform in the form of a compensation table. The motion position of each point is compensated based on the difference between the device's position data and the target data. Compensation methods vary, including global compensation and block compensation. However, both methods use a linear approximation of the error process rather than analyzing the overall error of the motion platform's deviation model. This method is highly susceptible to environmental influences, exhibits poor stability, and places extremely high demands on the repeatability of the device's hardware. Consequently, the error between fixed points can differ significantly from actual results. Summary of the Invention

[0004] In response to the above-mentioned problems and technical requirements, this application proposes a motion platform compensation method that takes into account the overall deviation. The technical solution of this application is as follows:

[0005] A motion platform compensation method considering overall deviation, the motion platform compensation method comprising:

[0006] Place the standard calibration plate on the motion platform of the device to be calibrated, and use the device to be calibrated to detect and determine the actual position of each calibration point on the standard calibration plate;

[0007] Calculate the lateral tilt angle α and longitudinal tilt angle β according to the actual position of each calibration point.

[0008] The actual position of each calibration point is subjected to rotation transformation and shear transformation according to the lateral tilt angle α and the longitudinal tilt angle β to obtain the compensated actual position.

[0009] A further technical solution is to perform rotation transformation and shear transformation on the actual position of each calibration point, including:

[0010] Determine the platform rotation angle γ according to the lateral tilt angle α and the longitudinal tilt angle β;

[0011] The actual position q of any nth calibration point according to the platform rotation angle γ n =(xn ,y n ) to perform rotation transformation and obtain the actual position of the nth calibration point after rotation correction

[0012] The actual position after rotation correction of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β Perform shear transformation to obtain the actual position q′ of the nth calibration point after compensation n =(x′ n , y′ n ).

[0013] A further technical solution is that the actual position of the nth calibration point after the rotation correction is performed according to the lateral tilt angle α and the longitudinal tilt angle β, including:

[0014] The actual position after rotation correction of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β Perform shear transformation to obtain the actual position of the nth calibration point after shear correction

[0015] The compensation value is calculated based on the actual position of each calibration point and the corresponding actual position after misalignment correction;

[0016] The actual position after the offset correction of the nth calibration point according to the compensation value Compensate and obtain the actual position q′ of the nth calibration point after compensation n .

[0017] A further technical solution is to calculate the compensation value according to the actual position of each calibration point and the corresponding actual position after the misalignment correction, including:

[0018] Determine the compensation value in the x direction Determine the compensation value in the y direction The standard calibration plate includes N calibration points in total.

[0019] A further technical solution is to compensate for the actual position of any nth calibration point after compensation.

[0020] A further technical solution is to calculate the actual position of the nth calibration point after rotation correction. Perform shear transformation to obtain the actual position after shear correction in

[0021] A further technical solution is that the actual position of any nth calibration point after rotation correction in

[0022] A further technical solution is to determine the platform rotation angle according to the lateral tilt angle α and the longitudinal tilt angle β

[0023] A further technical solution is that the standard calibration plate includes calibration points arranged in an array form with M1 rows and M2 columns;

[0024] Calculating the lateral tilt angle α and the longitudinal tilt angle β according to the actual position of each calibration point includes:

[0025] The tilt angle of the current row is calculated based on the actual positions of the M2 calibration points in each row, and the lateral tilt angle α is calculated based on the tilt angles of all M1 rows;

[0026] The tilt angle of the current column is calculated based on the actual positions of the M1 calibration points in each column, and the longitudinal tilt angle β is calculated based on the tilt angles of all M2 columns.

[0027] A further technical solution is that the calculation of the lateral tilt angle α and the longitudinal tilt angle β further includes:

[0028] Solve the linear equation of the actual positions of the M2 calibration points in each row using the least squares method, obtain the inclination angle corresponding to the linear equation as the inclination angle of the current row, and calculate the average of the inclination angles of all M1 rows as the lateral inclination angle α;

[0029] The linear equation of the actual position of the M1 calibration points in each column is solved by the least squares method, the inclination angle corresponding to the linear equation is obtained as the inclination angle of the current column, and the average value of the inclination angles of all M2 columns is calculated as the longitudinal inclination angle β.

[0030] The beneficial technical effects of this application are:

[0031] This application discloses a motion platform compensation method that takes into account overall deviation. This method utilizes a standard calibration plate to perform overall error modeling of the motion platform of the device to be calibrated using calibration points on the standard calibration plate with known theoretical positions. Error calibration of the motion platform is achieved through shearing and rotation transformations. This method considers the error characteristics of the motion platform as a whole, thereby improving the accuracy and reliability of calibration. The correction accuracy is improved by more than 50% compared to traditional methods. This method achieves a high calibration effect with a relatively simple calculation method and low cost. Based on the established model, the error trend under specific conditions can be predicted, so that measures can be taken in advance to prevent the occurrence or expansion of errors. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1This is a flow chart of a motion platform compensation method according to an embodiment of the present application.

[0033] Figure 2 This is a structural diagram of a standard calibration plate used in one embodiment of the present application.

[0034] Figure 3 It is a flowchart of a motion platform compensation method according to an embodiment of the present application.

[0035] Figure 4 It is a diagram showing the theoretical positions of the calibration points on the standard calibration plate in an example.

[0036] Figure 5 yes Figure 4 In the example, the actual position of each calibration point on the standard calibration plate is determined by detecting the device to be calibrated before compensation to generate a map.

[0037] Figure 6 According to the method of this application Figure 5 The actual position of each calibration point in the image is rotated and transformed to obtain the actual position generated by rotation correction.

[0038] Figure 7 According to the method of this application Figure 6 The actual position after rotation correction is subjected to shear transformation to generate the compensated actual position diagram.

[0039] Figure 8 yes Figure 4 In the example, a schematic diagram of the actual positions of various calibration points obtained after compensating the motion platform of the calibration device according to the traditional table lookup compensation method. DETAILED DESCRIPTION

[0040] The specific implementation of this application will be further described below with reference to the accompanying drawings.

[0041] This application discloses a motion platform compensation method considering overall deviation, please refer to Figure 1 As shown in the flowchart, the motion platform compensation method includes:

[0042] Step 1: Place the standard calibration plate on the motion platform of the device to be calibrated, and use the device to be calibrated to detect and determine the actual position of each calibration point on the standard calibration plate.

[0043] The standard calibration plate includes N calibration points with known theoretical positions. In one embodiment, the standard calibration plate is in the form of a mask plate, and the standard calibration plate includes calibration points arranged in an array form with M1 rows and M2 columns. Then N = M1 × M2, where M1 and M2 are integer parameters and are both greater than or equal to 2. Please refer to Figure 2 The schematic diagram takes M1=M2=7 as an example.

[0044] The device to be calibrated detects and determines the actual position q of any nth calibration point n =(x n ,y n ), the various positions appearing in this application are all coordinates in the same pre-set plane coordinate system, and the plane coordinate system is on the plane where the motion platform of the device to be calibrated is located. This application does not limit the specific form of constructing the plane coordinate system. Integer parameter 1≤n≤N. Based on Figure 2 The standard calibration plate of this structure is The order of represents the first calibration point to the Nth calibration point, O ij Represents the calibration point at row i and column j, with integer parameters 1≤i≤M1 and 1≤j≤M2. Based on the actual position q of each calibration point n =(x n ,y n ) can construct the corresponding homogeneous coordinates From this, we can get the actual position matrix of the homogeneous coordinates of the actual positions of N calibration points

[0045] Step 2: Calculate the horizontal tilt angle α and the vertical tilt angle β according to the actual position of each calibration point.

[0046] In one embodiment, the method for calculating the lateral tilt angle α and the longitudinal tilt angle β includes the following steps, please refer to Figure 3 The flowchart shown:

[0047] (1) Calculate the tilt angle of the current row based on the actual positions of the M2 calibration points in each row, and calculate the lateral tilt angle α based on the tilt angles of all M1 rows. This includes: solving the linear equation of the actual positions of the M2 calibration points in each row using the least squares method, obtaining the tilt angle corresponding to the linear equation as the tilt angle of the current row, and calculating the average of the tilt angles of all M1 rows as the lateral tilt angle α.

[0048] (2) Calculate the tilt angle of the current column based on the actual positions of the M1 calibration points in each column, and calculate the longitudinal tilt angle β based on the tilt angles of all M2 columns. This includes: solving the linear equation of the actual positions of the M1 calibration points in each column using the least squares method, obtaining the tilt angle corresponding to the linear equation as the tilt angle of the current column, and calculating the average of the tilt angles of all M2 columns as the longitudinal tilt angle β.

[0049] Step 3: Perform rotation and shear transformation on the actual position of each calibration point according to the lateral tilt angle α and the longitudinal tilt angle β to obtain the actual position after compensation. This includes the following steps:

[0050] (1) Determine the platform rotation angle γ based on the lateral tilt angle α and the longitudinal tilt angle β: Platform rotation angle

[0051] (2) The actual position q of any nth calibration point according to the platform rotation angle γ n =(x n ,y n ) to perform rotation transformation and obtain the actual position of the nth calibration point after rotation correction

[0052] The actual position of any nth calibration point after rotation correction in Then, corresponding to the actual position matrix Q obtained above, after rotation correction, the actual position matrix composed of the actual positions of all calibration points after rotation correction can be obtained: for:

[0053]

[0054] Then, the actual position of the nth calibration point after rotation correction is calculated based on the lateral tilt angle α and the longitudinal tilt angle β. Perform shear transformation to obtain the actual position q′ of the nth calibration point after compensation n =(x′ n , y′ n ), further comprising the following steps (4) to (6):

[0055] (4) The actual position after rotation correction of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β Perform shear transformation to obtain the actual position of the nth calibration point after shear correction

[0056] The actual position of the nth calibration point after misalignment correction in Expressed in the form of a matrix, this step can obtain the actual position matrix composed of the actual positions of all calibration points after misalignment correction for:

[0057]

[0058] (5) Compensation values ​​are calculated based on the actual positions of the calibration points and the corresponding actual positions after misalignment correction, including the compensation value Δx in the x-direction and the compensation value Δy in the y-direction:

[0059]

[0060]

[0061] (6) The actual position after the offset correction of the nth calibration point according to the compensation value Compensate and obtain the actual position q′ of the nth calibration point after compensation n The actual position after compensation of any nth calibration point It is expressed in the form of a matrix, and the actual position matrix composed of the actual positions of all calibration points after compensation can be obtained.

[0062] In one example, the theoretical position of each calibration point on the standard calibration plate is generated as shown in the figure below: Figure 4 The actual position of each calibration point is determined by detecting the device to be calibrated and the generated image is shown in Figure 5 As shown, after the actual position of each calibration point is rotated and transformed according to the compensation method of this application, the actual position of each calibration point after rotation correction is generated as shown in FIG. Figure 6 As shown, the actual position of each calibration point after compensation is generated by further performing the shear transformation according to the method of the present application as shown in FIG. Figure 7 As shown. Compare Figure 5 and Figure 7 and Figure 4 It can be seen that before compensation, the actual position of the calibration point detected by the device to be calibrated ( Figure 5 ) and theoretical position ( Figure 4 ) has a large error, and after compensation according to the method of this application, the actual position after compensation ( Figure 7 ) and theoretical position ( Figure 4 ) is significantly reduced.

[0063] In addition, after compensating the motion platform of the calibration equipment according to the existing traditional table lookup compensation, the positions of each calibration point are obtained. Figure 8 As shown. Compare Figure 7 and Figure 8 and Figure 4 It can be seen that the compensation method of this application effectively reduces the error between the theoretical position and the actual position. Figure 7 Compared to Figure 8 , and the error with the theoretical position is smaller, which fully demonstrates the effectiveness of the compensation method of this application.

[0064] The above description is only a preferred embodiment of the present application, and the present application is not limited to the above embodiments. It is understood that other improvements and variations directly derived or imagined by those skilled in the art without departing from the spirit and concept of the present application should be considered to be included in the scope of protection of the present application.

Claims

1. A motion platform compensation method considering overall deviation, characterized in that: The motion platform compensation method includes: Placing the standard calibration plate on the motion platform of the device to be calibrated, and using the device to be calibrated to detect and determine the actual position of each calibration point on the standard calibration plate; Calculate the lateral tilt angle α and longitudinal tilt angle β of the motion platform according to the actual position of each calibration point. According to the lateral tilt angle α and the longitudinal tilt angle β, the actual position of each calibration point is rotated and sheared to obtain the actual position after compensation; The rotation transformation and shear transformation of the actual position of each calibration point include: Determine the platform rotation angle γ according to the lateral tilt angle α and the longitudinal tilt angle β; The actual position q of any nth calibration point according to the platform rotation angle γ n =(x n ,y n ) to perform rotation transformation and obtain the actual position of the nth calibration point after rotation correction The actual position after rotation correction of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β Perform shear transformation to obtain the actual position q′ of the nth calibration point after compensation n =(x′ n ,y′ n ).

2. The motion platform compensation method according to claim 1, characterized in that: Performing a shear transformation on the rotation-corrected actual position of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β includes: The actual position after rotation correction of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β Perform shear transformation to obtain the actual position of the nth calibration point after shear correction The compensation value is calculated based on the actual position of each calibration point and the corresponding actual position after misalignment correction; The actual position after the misalignment correction of the nth calibration point according to the compensation value Compensate and obtain the actual position q′ of the nth calibration point after compensation n .

3. The motion platform compensation method according to claim 2, characterized in that: The compensation values ​​calculated based on the actual position of each calibration point and the corresponding actual position after misalignment correction include: Determine the compensation value in the x direction Determine the compensation value in the y direction Wherein, the standard calibration plate includes N calibration points in total.

4. The motion platform compensation method according to claim 3, characterized in that: Compensation is used to obtain the actual position of any nth calibration point after compensation 5. The motion platform compensation method according to claim 2, characterized in that: The actual position after rotation correction of the nth calibration point Perform shear transformation to obtain the actual position after shear correction in 6. The motion platform compensation method according to claim 1, characterized in that: The actual position of any nth calibration point after rotation correction in 7. The motion platform compensation method according to claim 1, characterized in that: Determine the platform rotation angle based on the lateral tilt angle α and the longitudinal tilt angle β 8. The motion platform compensation method according to any one of claims 1 to 7, characterized in that: The standard calibration plate includes calibration points arranged in an array of M1 rows and M2 columns; Calculating the lateral tilt angle α and the longitudinal tilt angle β according to the actual position of each calibration point includes: The tilt angle of the current row is calculated based on the actual positions of the M2 calibration points in each row, and the lateral tilt angle α is calculated based on the tilt angles of all M1 rows; The tilt angle of the current column is calculated based on the actual positions of the M1 calibration points in each column, and the longitudinal tilt angle β is calculated based on the tilt angles of all M2 columns.

9. The motion platform compensation method according to claim 8, characterized in that: Calculation of the transverse tilt angle α and the longitudinal tilt angle β also includes: Solve the linear equation of the actual positions of the M2 calibration points in each row using the least squares method, obtain the inclination angle corresponding to the linear equation as the inclination angle of the current row, and calculate the average of the inclination angles of all M1 rows as the lateral inclination angle α; The linear equation of the actual position of the M1 calibration points in each column is solved by the least squares method, the inclination angle corresponding to the linear equation is obtained as the inclination angle of the current column, and the average value of the inclination angles of all M2 columns is calculated as the longitudinal inclination angle β.

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