CN117519312A - Motion platform compensation method considering integral deviation - Google Patents
Motion platform compensation method considering integral deviation Download PDFInfo
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- CN117519312A CN117519312A CN202311679225.XA CN202311679225A CN117519312A CN 117519312 A CN117519312 A CN 117519312A CN 202311679225 A CN202311679225 A CN 202311679225A CN 117519312 A CN117519312 A CN 117519312A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D3/00—Control of position or direction
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- G05D3/20—Control of position or direction using feedback using a digital comparing device
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Abstract
The method comprises the steps of placing a standard calibration plate comprising a plurality of calibration points with known theoretical positions on a motion platform of equipment to be calibrated, detecting and determining actual positions of all the calibration points on the standard calibration plate by using the equipment to be calibrated, calculating transverse inclination angles and longitudinal inclination angles according to the actual positions of all the calibration points, and carrying out rotary transformation and miscut transformation on the actual positions of all the calibration points to obtain compensated actual positions. The method realizes higher calibration effect by a simpler calculation method and lower cost, and based on the established model, the error trend under specific conditions can be predicted, so that measures are taken in advance to prevent error generation or expansion.
Description
Technical Field
The application relates to the technical field of industry, in particular to a motion platform compensation method considering integral deviation.
Background
In many industrial applications, motion platforms are an important component for achieving accurate position control and motion trajectories. However, due to factors such as manufacturing errors, wear, load variation, etc., the motion platform may deviate during actual operation, thereby affecting the accuracy and stability thereof. To address this problem, compensation for the motion platform is often required.
The existing compensation method for the motion platform mainly relies on table lookup compensation, obtained compensation data are loaded into the motion platform in a compensation table mode, and the motion positions of all points are compensated according to the difference between the position data moved by the equipment and target data. According to different compensation modes, the method is divided into global compensation and block compensation, but no matter which compensation mode is linear approximation of an error process, but error analysis is not carried out on the whole deviation model of a motion platform, the method is very easy to be influenced by environment, has poor stability and extremely high requirement on hardware repeatability of equipment, so that the error between fixed points and actual access are larger.
Disclosure of Invention
Aiming at the problems and the technical requirements, the application provides a motion platform compensation method considering integral deviation, and the technical scheme of the application is as follows:
a motion platform compensation method taking into account global bias, the motion platform compensation method comprising:
the method comprises the steps of placing a standard calibration plate on a motion platform of equipment to be calibrated, and detecting and determining actual positions of all calibration points on the standard calibration plate by using the equipment to be calibrated;
the lateral-tilt angle alpha and the longitudinal-tilt angle beta are calculated based on the actual positions of the respective calibration points,
the actual positions of the respective calibration points are subjected to rotation transformation and miscut transformation according to the transverse inclination angle alpha and the longitudinal inclination angle beta, and the compensated actual positions are obtained.
The further technical scheme is that the rotary transformation and the shear transformation of the actual positions of the calibration points comprise:
determining a platform rotation angle gamma from the transverse tilt angle alpha and the longitudinal tilt angle beta;
the actual position q of any nth calibration point according to the rotation angle gamma of the platform n ＝(x n ，y n ) Performing rotation transformationObtaining the actual position of the nth calibration point after rotation correction
Rotation corrected actual position of the nth calibration point according to the transverse inclination angle alpha and the longitudinal inclination angle betaPerforming error shear conversion to obtain the compensated actual position q 'of the nth calibration point' n ＝(x′ n ，y′ n )。
A further aspect of the present invention is that performing a shear shift 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:
rotation corrected actual position of the nth calibration point according to the transverse inclination angle alpha and the longitudinal inclination angle betaPerforming shear conversion to obtain the actual position of the nth calibration point after shear correction
Calculating to obtain a compensation value according to the actual positions of the calibration points and the corresponding actual positions after miscut correction;
miscut corrected actual position of nth calibration point according to compensation valueCompensating to obtain the compensated actual position q 'of the nth calibration point' n 。
According to the further technical scheme, the compensation value obtained by calculating according to the actual positions of the calibration points and the corresponding actual positions after miscut correction comprises the following steps:
determining compensation values in the x-directionDetermining compensation values in the y-directionWherein, the standard calibration plate comprises N calibration points in total.
The further technical proposal is that the compensated actual position of any nth calibration point is obtained by compensation
The further technical proposal is that the rotation corrected actual position of the nth calibration point is rotated and correctedPerforming error shear conversion to obtain the actual position +.>In (a) and (b)
The further technical proposal is that the actual position of any nth calibration point after rotation correctionIs->
It is a further technical proposal that the rotation angle of the platform is determined according to the transverse inclination angle alpha and the longitudinal inclination angle beta
The further technical proposal is that the standard calibration plate comprises M 1 Row M 2 The columns are arranged according to the calibration points in the form of an array;
calculating the lateral-tilt angle α and the longitudinal-tilt angle β from the actual positions of the respective calibration points includes:
according to M in each row 2 Calculating the inclination angle of the current line according to the actual positions of the marked points and all M 1 Calculating the inclination angle of the row to obtain a transverse inclination angle alpha;
according to M in each column 1 Calculating the tilt angle of the current column according to the actual positions of the marked points, and calculating the tilt angles of the current column according to all M 2 The inclination angle of the column is calculated to obtain the longitudinal inclination angle beta.
Further, the method for calculating the transverse tilt angle α and the longitudinal tilt angle β further includes:
solving M in each row by least square method 2 Straight line equations of actual positions of the calibration points are obtained, inclination angles corresponding to the straight line equations are obtained to be used as inclination angles of the current row, and all M are calculated 1 The average value of the inclination angles of the rows is taken as the transverse inclination angle alpha;
solving M in each column by least square method 1 Straight line equation of actual position of each calibration point, calculating inclination angle corresponding to straight line equation as inclination angle of current column, and calculating all M 2 The average value of the inclination angles of the columns is taken as the longitudinal inclination angle beta.
The beneficial technical effects of this application are:
the method utilizes a standard calibration plate, carries out error integral modeling on a motion platform of equipment to be calibrated through all calibration points with known theoretical positions on the standard calibration plate, realizes error calibration on the motion platform in a mode of miscut transformation and rotation transformation, and integrally considers the error characteristics of the motion platform, thereby improving the calibration precision and reliability, and the correction precision is improved by more than 50 percent compared with that of the traditional method. The method realizes higher calibration effect with simpler calculation method and lower cost, and based on the established model, the error trend under specific conditions can be predicted, so that measures are taken in advance to prevent error generation or expansion.
Drawings
Fig. 1 is a method flow diagram of a motion platform compensation method according to one embodiment of the present application.
FIG. 2 is a block diagram of a standard calibration plate used in one embodiment of the present application.
Fig. 3 is a flow chart of a motion platform compensation method according to an embodiment of the present application.
FIG. 4 is a plot of theoretical position generation for various calibration points on a standard calibration plate in one example.
FIG. 5 is a plot of the actual position of various calibration points on a calibration plate detected and determined using the device to be calibrated prior to compensation in the example of FIG. 4.
Fig. 6 is a rotation corrected actual position generation map obtained by rotationally transforming the actual positions of the calibration points in fig. 5 according to the method of the present application.
Fig. 7 is a compensated actual position generation map obtained by performing a shear-shift on the rotation corrected actual position of fig. 6 according to the method of the present application.
FIG. 8 is a schematic diagram of actual positions of calibration points obtained after compensating a motion platform of a device to be calibrated according to a conventional table look-up compensation method in the example of FIG. 4.
Detailed Description
The following describes the embodiments of the present application further with reference to the accompanying drawings.
The application discloses a motion platform compensation method considering overall deviation, please refer to a flowchart shown in fig. 1, the motion platform compensation method includes:
and step 1, placing the standard calibration plate on a motion platform of equipment to be calibrated, and detecting and determining the actual positions of all calibration points on the standard calibration plate by using the equipment to be calibrated.
The standard calibration plate comprises N calibration points with known theoretical positions. In one embodiment, the standard calibration plate takes the form of a mask plate, and comprises M 1 Row M 2 The columns are arranged in an array of index points, then n=m 1 ×M 2 ，M 1 And M 2 Respectively, integer parameters which are all equal to or greater than 2, please refer to the schematic diagram of FIG. 2 with M 1 ＝M 2 =7 isExamples are shown.
The equipment to be calibrated detects and determines the actual position q of any nth calibration point n ＝(x n ，y n ) The various positions in the application are coordinates in the same preset plane coordinate system, the plane coordinate system is on a plane where a motion platform of the equipment to be calibrated is located, and the application does not limit the form of a specific construction plane coordinate system. The integer parameter is 1-N-N. Standard calibration plate based on the structure of figure 2 to Sequentially from the 1 st index point to the N th index point, O ij Indicating the index point of the ith row and the jth column, and the integer parameter is 1-i-M 1 And j is more than or equal to 1 and less than or equal to M 2 . Then based on the actual position q of each index point n ＝(x n ，y n ) Corresponding homogeneous coordinates +.>Thus, an actual position matrix of the N calibration points after homogeneous coordinates of the actual positions can be obtained>
Step 2, calculating the transverse tilt angle alpha and the longitudinal tilt angle beta according to the actual positions of the respective calibration points,
in one embodiment, the method of calculating the lateral-tilt angle α and the longitudinal-tilt angle β includes the steps of, referring to the flowchart shown in fig. 3:
(1) According to M in each row 2 Calculating the inclination angle of the current line according to the actual positions of the marked points and all M 1 The inclination angle of the row is calculated to obtain the lateral inclination angle alpha. Comprising the following steps: solving M in each row by least square method 2 Straight line equations of actual positions of the calibration points are obtained, inclination angles corresponding to the straight line equations are obtained to be used as inclination angles of the current row, and all M are calculated 1 The average value of the inclination angles of the rows is taken as the lateral inclination angle α.
(2) According to M in each column 1 Calculating the tilt angle of the current column according to the actual positions of the marked points, and calculating the tilt angles of the current column according to all M 2 The inclination angle of the column is calculated to obtain the longitudinal inclination angle beta. Comprising the following steps: solving M in each column by least square method 1 Straight line equation of actual position of each calibration point, calculating inclination angle corresponding to straight line equation as inclination angle of current column, and calculating all M 2 The average value of the inclination angles of the columns is taken as the longitudinal inclination angle beta.
And 3, performing rotation transformation and miscut transformation on the actual positions of the calibration points according to the transverse inclination angle alpha and the longitudinal inclination angle beta to obtain the compensated actual positions. The method comprises the following steps:
(1) Determining a platform rotation angle gamma from the transverse tilt angle alpha and the longitudinal tilt angle beta: rotation angle of platform
(2) The actual position q of any nth calibration point according to the rotation angle gamma of the platform n ＝(x n ，y n ) Performing rotation transformation to obtain the actual position of the nth calibration point after rotation correction
Actual position after rotation correction of any nth calibration pointIn (a) and (b)Corresponding to the obtained actual position matrix Q, the actual position matrix formed by the actual positions of all the calibration points after rotation correction can be obtained after rotation correction>The method comprises the following steps:
then the actual position after the rotation correction of the nth calibration point according to the transverse inclination angle alpha and the longitudinal inclination angle betaPerforming error shear conversion to obtain the compensated actual position q 'of the nth calibration point' n ＝(x′ n ，y′ n ) The method also comprises the following steps (4) to (6):
(4) Rotation corrected actual position of the nth calibration point according to the transverse inclination angle alpha and the longitudinal inclination angle betaPerforming shear conversion to obtain the actual position of the nth calibration point after shear correction
Actual position after miscut correction of nth calibration pointIn (a) and (b)The method adopts a matrix form to represent, and the step can obtain an actual position matrix consisting of the actual positions after the miscut correction of all the calibration points>The method comprises the following steps:
(5) Calculating to obtain compensation values according to the actual positions of the calibration points and the corresponding miscut corrected actual positions, wherein the compensation values comprise compensation values delta x in the x direction and compensation values delta y in the y direction are obtained:
(6) Miscut corrected actual position of nth calibration point according to compensation valueCompensating to obtain the compensated actual position q 'of the nth calibration point' n . Compensated actual position of any nth calibration pointThe actual position matrix formed by the compensated actual positions of all the calibration points can be obtained by matrix representation>
In one example, a plot of the theoretical position of each calibration point on a standard calibration plate is shown in FIG. 4. The actual position generation diagram of each calibration point obtained by detection and determination of equipment to be calibrated is shown in fig. 5, the actual position of each calibration point is subjected to rotation transformation according to the compensation method of the application, the obtained actual position generation diagram after rotation correction of each calibration point is shown in fig. 6, and the actual position generation diagram after compensation of each calibration point obtained after error shear transformation according to the method of the application is shown in fig. 7. As can be seen by comparing fig. 5 and fig. 7 with fig. 4, respectively, the error between the actual position (fig. 5) and the theoretical position (fig. 4) of the calibration point detected by the device to be calibrated is larger before compensation, and the error between the actual position (fig. 7) and the theoretical position (fig. 4) after compensation obtained by the method of the present application is obviously reduced.
In addition, after the motion platform of the equipment to be calibrated is compensated according to the conventional table look-up compensation, the obtained positions of the calibration points are shown in fig. 8. As can be seen by comparing fig. 7 and fig. 8 with fig. 4, the error between the compensation method and the theoretical position is effectively reduced after the compensation, and the error between the compensation method and the theoretical position is smaller in fig. 7 compared with fig. 8, which fully illustrates the effectiveness of the compensation method.
What has been described above is only a preferred embodiment of the present application, which is not limited to the above examples. It is to be understood that other modifications and variations which may be directly derived or contemplated by those skilled in the art without departing from the spirit and concepts of the present application are to be considered as being included within the scope of the present application.
Claims (10)
1. A motion platform compensation method taking into account global bias, the motion platform compensation method comprising:
the method comprises the steps of placing a standard calibration plate on a motion platform of equipment to be calibrated, and detecting and determining actual positions of all calibration points on the standard calibration plate by using the equipment to be calibrated;
the lateral-tilt angle alpha and the longitudinal-tilt angle beta are calculated based on the actual positions of the respective calibration points,
the actual positions of the respective calibration points are subjected to rotation transformation and miscut transformation according to the transverse inclination angle alpha and the longitudinal inclination angle beta, and the compensated actual positions are obtained.
2. The motion platform compensation method of claim 1, wherein performing a rotation transform and a shear-shift on the actual positions of the respective calibration points comprises:
determining a platform rotation angle gamma from the transverse tilt angle alpha and the longitudinal tilt angle beta;
according to the platformThe actual position q of the rotation angle gamma to any nth calibration point n ＝(x n ，y n ) Performing rotation transformation to obtain the actual position of the nth calibration point after rotation correction
Rotation corrected actual position of the nth calibration point according to the transverse inclination angle alpha and the longitudinal inclination angle betaPerforming error shear conversion to obtain the compensated actual position q 'of the nth calibration point' n ＝(x′ n ，y′ n )。
3. The motion platform compensation method according to claim 2, wherein performing the offset shear conversion of the rotation corrected actual position of the rotation corrected of the nth calibration point according to the lateral tilt angle α and the longitudinal tilt angle β includes:
rotation corrected actual position of the nth calibration point according to the transverse inclination angle alpha and the longitudinal inclination angle betaPerforming shear conversion to obtain the actual position of the nth calibration point after shear correction
Calculating to obtain a compensation value according to the actual positions of the calibration points and the corresponding actual positions after miscut correction;
miscut corrected actual position of the nth calibration point according to the compensation valueCompensating to obtain the compensated actual position q 'of the nth calibration point' n 。
4. A motion platform compensation method according to claim 3, wherein calculating the compensation value based on the actual positions of the calibration points and the corresponding miscut corrected actual positions comprises:
determining compensation values in the x-directionDetermining compensation values in the y-directionWherein, the standard calibration plate comprises N calibration points in total.
5. The method of claim 4, wherein the compensating obtains a compensated actual position of any nth calibration point
6. A motion platform compensation method according to claim 3, wherein the rotation corrected actual position of the nth calibration point is rotation correctedPerforming error shear conversion to obtain the actual position +.>Is->
7. The motion platform compensation method of claim 2, wherein the rotation corrected actual position of any nth calibration pointIs->
8. The motion platform compensation method according to claim 2, wherein the platform rotation angle is determined according to the lateral tilt angle α and the longitudinal tilt angle β
9. The method of any one of claims 1-8, wherein the standard calibration plate includes M thereon 1 Row M 2 The columns are arranged according to the calibration points in the form of an array;
calculating the lateral-tilt angle α and the longitudinal-tilt angle β from the actual positions of the respective calibration points includes:
according to M in each row 2 Calculating the inclination angle of the current line according to the actual positions of the marked points and all M 1 Calculating the inclination angle of the row to obtain a transverse inclination angle alpha;
according to M in each column 1 Calculating the tilt angle of the current column according to the actual positions of the marked points, and calculating the tilt angles of the current column according to all M 2 The inclination angle of the column is calculated to obtain the longitudinal inclination angle beta.
10. The motion platform compensation method of claim 9, wherein calculating the lateral tilt angle α and the longitudinal tilt angle β further comprises:
solving M in each row by least square method 2 Straight line equations of actual positions of the calibration points are obtained, the inclination angles corresponding to the straight line equations are obtained to be used as the inclination angles of the current row, and all M are calculated 1 Average value of inclination angles of rows as transverse directionAn inclination angle alpha;
solving M in each column by least square method 1 Straight line equations of actual positions of the calibration points are obtained, the inclination angles corresponding to the straight line equations are obtained to be used as the inclination angles of the current column, and all M are calculated 2 The average value of the inclination angles of the columns is taken as the longitudinal inclination angle beta.
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