CN110426991B - Composite position error compensation method and device - Google Patents
Composite position error compensation method and device Download PDFInfo
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- G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
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Abstract
The invention discloses a composite position error compensation method and a device, which comprises the steps of correcting acquired discrete measured position data of original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, wherein error data generated by correction is stored in the corrected position data; carrying out curve reconstruction on each group of correction position data which are one-dimensional and non-uniformly distributed to form corresponding correction position data which are one-dimensional and uniformly distributed; performing curve reconstruction based on all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface; and generating a corresponding compensation table based on the reconstructed curved surface for realizing composite position error compensation. According to the invention, the original multi-dimensional non-uniformly distributed discrete measured position data is corrected, error reconstruction is carried out on the basis of the corrected data, and then the compensation table is generated, so that the high-precision and high-complexity composite position error compensation is realized.
Description
Technical Field
The invention belongs to the technical field of ultra-precision motion control application, relates to a composite position error compensation method, and more particularly relates to a composite position error compensation method and device based on non-uniform discrete composite position errors.
Background
At present, in high-precision and ultra-precision motion control systems, compensation of compound errors including various mechanical and electrical non-ideal states is an important means for obtaining higher precision. Generally, simple error compensation measures such as 1-dimensional and 2-dimensional are common in most motion control systems, however, limited by data storage space and real-time calculation speed of the compensation tables, usually, only one motion axis can have a very limited compensation table, and for the case of multi-dimensional cross compensation, the number of the compensation tables and the compensation method are greatly limited in complex high-precision or ultra-precision motion control systems. For high-precision and ultra-precision motion control systems, the composite position errors generally include various errors such as mechanical parallelism, straightness, perpendicularity, thermal deformation, force deformation, assembly errors, various mechanical and electrical offsets, and the like, and generally the errors also have quite complex cross-coupling, so that theoretical modeling is almost impossible. For most occasions, the composite position error is usually obtained by using a higher-precision measuring device such as a laser interferometer or a high-resolution camera, so how to realize real-time dynamic compensation of the composite position error measured in the system in the multi-axis motion control process becomes a technical bottleneck restricting the overall dynamic and static precision of the high-precision and ultra-precision motion control system.
Generally, we can assume that a multi-dimensional spatial error curved surface exists in the composite position error of the system, and if the composite position error curved surface of the whole system space can be reconstructed by the composite position error of discrete measurement points, a global composite position error compensation table with any precision can be realized, so that dynamic real-time composite position error compensation is realized in the motion controller. Due to the fact that various nonlinear deformations or random noises often exist in an actual electromechanical system, the position distribution of actual measurement points presents the characteristic of discrete non-uniform distribution, and the reconstruction work of an error curved surface becomes extremely complex. Taking a high-precision wafer probe station as an example, due to the nonlinear deformation of the wafer caused by the vacuum adsorption device and other composite errors and random noise of the system, the actually measured composite error points have multi-dimensional non-uniform distribution errors, and the subsequent reconstruction of the composite position error curved surface becomes extremely complex.
As shown in fig. 1, due to the nonlinear deformation of the wafer caused by the vacuum adsorption device and the compounding of nonlinear errors and random noise of other mechanisms, the situation that the originally collinear measuring points are subjected to 2-dimensional non-uniform distribution after the pixel alignment correction of the high-resolution camera is caused, and the reconstruction work of the spatial compound position error curved surface at the later stage becomes abnormally complex.
Disclosure of Invention
Aiming at the problems, the invention provides a composite position error compensation method and a composite position error compensation device, which can effectively solve the reconstruction problem of the Hermite spline surface of the non-uniform discrete composite position error, not only can ensure the reconstruction precision of the error surface, but also can be popularized to the reconstruction of the composite position error surface of a 3-dimensional or multi-dimensional space and the real-time dynamic compensation of a control system.
In order to achieve the technical purpose and achieve the technical effects, the invention is realized by the following technical scheme:
in a first aspect, the present invention provides a method for compensating a composite position error, including:
correcting the acquired discrete measured position data of the original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, wherein error data generated by correction are stored in the corrected position data;
carrying out curve reconstruction on each group of correction position data which are one-dimensional and non-uniformly distributed to form corresponding correction position data which are one-dimensional and uniformly distributed;
performing curve reconstruction based on all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface;
and generating a corresponding compensation table based on the reconstructed curved surface for realizing composite position error compensation.
Optionally, the measured position data structure is [ X ]ij,Yij,ΔXij+εxij,ΔYij+εyij]Wherein X isijX-coordinate, Y, representing actual measuring pointijY-coordinate, Δ X, representing actual measuring pointijX coordinate compound error, epsilon, representing actual measured pointsxijThe X coordinate of the real measuring point is corrected by the pixel position of the camera and then has a nonlinear random error, delta Y, with the theoretical X coordinateijComplex error of Y coordinate, epsilon, representing measured positionyijY coordinate warp camera for representing real measuring pointNonlinear random errors exist between the corrected pixel positions and theoretical Y coordinates;
the corrected position data structure is [ X ]ij,Yci,ΔXij+εxij,ΔYij-(Yci-Yij)]Or [ X ]cj,Yij,ΔXij-(Xcj-Xij),ΔYij+εyij]Wherein Y isciIs the Y-axis coordinate, X-axis coordinate, of the uniform grid line with the nearest distance from the average line of the Y-axis coordinate of the real measuring point of the ith rowcjAnd the Y-axis coordinate of the uniform grid line closest to the X-axis coordinate mean line of the j-th row of actual measurement points is shown.
Optionally, the one-dimensional unevenly distributed corrected position data is one-dimensional row unevenly distributed corrected position data or one-dimensional column unevenly distributed corrected position data;
the method for performing curve reconstruction on each group of correction position data with one-dimensional non-uniform distribution to form corresponding correction position data with one-dimensional uniform distribution specifically comprises the following steps:
performing hermitian spline curve reconstruction on the corrected position data of the one-dimensional row in non-uniform distribution line by line to form corrected position data of the corresponding one-dimensional row in uniform distribution;
and performing Hermite spline curve reconstruction on the corrected position data of the one-dimensional row non-uniform distribution column by column to form the corrected position data of the corresponding one-dimensional row uniform distribution.
Optionally, the curve reconstruction is performed on the corrected position data based on all one-dimensional uniform distributions to obtain uniform grid point subdivision position data, so as to obtain a reconstructed surface, and the method specifically includes the following steps:
respectively reconstructing a hermitian spline curve based on data in the same column in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional column;
respectively reconstructing a hermitian spline curve based on data in the same row in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional row;
repeating the two steps until uniform grid point subdivision position data are obtained;
and (5) connecting all the uniform grid points to subdivide the position data to obtain a reconstructed surface.
Optionally, the generating a corresponding compensation table based on the reconstructed surface specifically includes:
reading data in each grid point in the reconstructed curved surface, and obtaining error data;
a compensation table is generated based on each error data.
Optionally, the method further comprises:
and performing online compensation of the measured position data based on the compensation table.
In a second aspect, the present invention provides a composite position error compensation apparatus, comprising:
the correction module is used for correcting the acquired discrete measured position data of the original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, and error data generated by correction is stored in the corrected position data;
the first reconstruction module is used for performing curve reconstruction on each group of correction position data which are one-dimensionally and non-uniformly distributed to form corresponding correction position data which are one-dimensionally and uniformly distributed;
the second reconstruction module is used for carrying out curve reconstruction on the basis of all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface;
and the generating module is used for generating a corresponding compensation table based on the reconstructed curved surface and realizing the composite position error compensation.
Optionally, the measured position data structure is [ X ]ij,Yij,ΔXij+εxij,ΔYij+εyij]Wherein X isijX-coordinate, Y, representing actual measuring pointijY-coordinate, Δ X, representing actual measuring pointijX coordinate compound error, epsilon, representing actual measured pointsxijThe X coordinate of the real measuring point is corrected by the pixel position of the camera and then has a nonlinear random error, delta Y, with the theoretical X coordinateijIndicating actual measurementComposite error of Y coordinate of position, epsilonyijThe Y coordinate of the real measuring point represents a nonlinear random error between the Y coordinate and a theoretical Y coordinate after being corrected by the pixel position of the camera;
the corrected position data structure is [ X ]ij,Yci,ΔXij+εxij,ΔYij-(Yci-Yij)]Or [ X ]cj,Yij,ΔXij-(Xcj-Xij),ΔYij+εyij]Wherein Y isciIs the Y-axis coordinate, X-axis coordinate, of the uniform grid line with the nearest distance from the average line of the Y-axis coordinate of the real measuring point of the ith rowcjAnd the Y-axis coordinate of the uniform grid line closest to the X-axis coordinate mean line of the j-th row of actual measurement points is shown.
Optionally, the one-dimensional unevenly distributed corrected position data is one-dimensional row unevenly distributed corrected position data or one-dimensional column unevenly distributed corrected position data;
the method for performing curve reconstruction on each group of correction position data with one-dimensional non-uniform distribution to form corresponding correction position data with one-dimensional uniform distribution specifically comprises the following steps:
performing hermitian spline curve reconstruction on the corrected position data of the one-dimensional row in non-uniform distribution line by line to form corrected position data of the corresponding one-dimensional row in uniform distribution;
performing Hermite spline curve reconstruction on the corrected position data of the one-dimensional row non-uniform distribution column by column to form corrected position data of the corresponding one-dimensional row uniform distribution;
the method comprises the following steps of performing curve reconstruction on the corrected position data based on all one-dimensional uniform distribution to obtain uniform grid point subdivision position data and further obtain a reconstructed surface, and specifically comprises the following steps:
respectively reconstructing a hermitian spline curve based on data in the same column in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional column;
respectively reconstructing a hermitian spline curve based on data in the same row in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional row;
repeating the two steps until uniform grid point subdivision position data are obtained;
and (5) connecting all the uniform grid points to subdivide the position data to obtain a reconstructed surface.
Optionally, the composite position error compensation apparatus further includes:
and the compensation module is used for performing online compensation on the actually measured position data based on the compensation table.
Compared with the prior art, the invention has the beneficial effects that:
according to the composite position error compensation method and device provided by the invention, the original multi-dimensional unevenly distributed discrete measured position data is corrected, error reconstruction is carried out on the basis of the corrected data, and a compensation table is further generated.
Drawings
In order that the present disclosure may be more readily and clearly understood, reference is now made to the following detailed description of the present disclosure taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a diagram of a distribution of real measurement points of compound errors of an XY platform of a wafer probe station in an embodiment of the present invention;
FIG. 2 is a distribution diagram of an average line pre-processed distribution of measured non-uniform discrete composite error measurement points;
FIG. 3 is a distribution diagram of the pre-processed uniform grid lines of the measured non-uniform discrete composite error measurement points;
FIG. 4 is a non-uniform discrete composite error progressive hermite spline curve reconstruction and target uniform composite error grid point subdivision;
FIG. 5 is a block-by-block Hermite spline curve reconstruction of non-uniform discrete composite errors and realization of target uniform composite error grid point subdivision;
FIG. 6 is a grid point row traversal of a target uniform composite position error and a subdivision of a Humidt spline curve target uniform composite position error grid points;
FIG. 7 is a traversal of a grid point row of target uniform composite position errors and a subdivision of grid points of target uniform composite position errors of a Hermite spline curve;
FIG. 8 is a target uniform composite error hermitian spline surface reconstruction and a corresponding compensation table.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the scope of the invention.
The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.
Example 1
The embodiment of the invention provides a composite position error compensation method, which comprises the following steps:
(1) correcting the acquired discrete measured position data of the original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, wherein error data generated by correction are stored in the corrected position data;
(2) carrying out curve reconstruction on each group of correction position data which are one-dimensional and non-uniformly distributed to form corresponding correction position data which are one-dimensional and uniformly distributed;
(3) performing curve reconstruction based on all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface;
(4) and generating a corresponding compensation table based on the reconstructed curved surface for realizing composite position error compensation.
In a specific implementation manner of the embodiment of the present invention, the measured position data (i.e. the measured composite error data) has a structure that:
[Xij,Yij,ΔXij+εxij,ΔYij+εyij]
wherein, XijX-coordinate, Y, representing actual measuring pointijY-coordinate, Δ X, representing actual measuring pointijX coordinate compound error, epsilon, representing actual measured pointsxijThe X coordinate of the real measuring point is corrected by the pixel position of the camera and then has a nonlinear random error, delta Y, with the theoretical X coordinateijComplex error of Y coordinate, epsilon, representing measured positionyijThe Y coordinate of the real measuring point represents a nonlinear random error between the Y coordinate and a theoretical Y coordinate after being corrected by the pixel position of the camera;
the corrected position data structure is [ X ]ij,Yci,ΔXij+εxij,ΔYij-(Yci-Yij)]Or [ X ]cj,Yij,ΔXij-(Xcj-Xij),ΔYij+εyij]Wherein Y isciIs the Y-axis coordinate, X-axis coordinate, of the uniform grid line with the nearest distance from the average line of the Y-axis coordinate of the real measuring point of the ith rowcjAnd the Y-axis coordinate of the uniform grid line closest to the X-axis coordinate mean line of the j-th row of actual measurement points is shown.
The step (1) is used for correcting non-collinear row and column data points in original measured data to a nearest target uniform compensation row and column grid line, and correspondingly superposing X-axis and Y-axis position errors caused in the correction process to an original X-coordinate composite error and a Y-coordinate composite error respectively, so that multi-dimensional uneven distribution is corrected to be 1-dimensional uneven distribution, the measurement precision is guaranteed not to be lost, and data preparation and data simplification are made for subsequent row-column-based one-dimensional hermite spline curve subdivision, and the method specifically comprises the following steps:
for an n-degree-of-freedom motion control mechanism, assuming that the generalized coordinate vector of the system is θ and the composite error vector of the generalized coordinate of the system is Δ θ, a new composite error data set Ω ═ θ, Δ θ can be established. In the embodiment of the present invention, any point in space has a unique composite error data set Ω corresponding to it. Taking a high-precision wafer probe station as an example, the principle of the wafer probe station is to perform various voltage and current tests on semiconductor chips on a wafer by a probe to determine whether each chip on the wafer works normally. In order to ensure that the probe can be rigidly contacted with the chip pins and the position of the wafer is not changed in the process of probe plate-punching, a vacuum adsorption device is usually adopted to fix the wafer on an operation table, however, due to the insufficient rigidity of the wafer, the wafer can be subjected to nonlinear deformation in the vacuum adsorption process, so that the positions of the originally uniform measurement points are subjected to nonlinear random offset after the wafer is subjected to nonlinear deformation by the chip pins which are uniformly distributed at the positions on the row, and thus, a composite position error data set omega of each point is subjected to nonlinear random change, the changes not only cause the originally uniform generalized coordinate position to be subjected to random nonlinear change, but also cause the composite error delta theta of the generalized coordinate corresponding to each point to be subjected to random nonlinear change, so that the originally theoretically uniformly distributed measurement points become non-uniform, and the multi-dimensional non-uniform distribution can be presented along with the difference of the number of the degrees of freedom of the system, so that the reconstruction of the composite position error curved surface of the system is changed from the simple one-dimensional uniform distribution problem into the complex multi-dimensional non-uniform distribution problem, and the reconstruction difficulty of the composite position error space curved surface is greatly increased.
Taking the wafer probe station application as an example, in order to reconstruct a composite error curved surface of the whole measurement area, composite error detection is usually performed on m rows and n columns of m × n measurement points in the whole measurement area, for easy understanding, it is assumed that m is 5 rows and n is 5 columns, i.e. the original measurement data is 25 points in 5 rows and 5 columns, and since the axes to be compensated by the wafer probe station only have two axes of X and Y, it is assumed that X isij，Yij，ΔXij,ΔYijRespectively, the X coordinate and the Y coordinate of the ith row and the jth column measuring point in the original measured data of the system, the X coordinate composite error of the measured position, and the Y coordinate composite error of the measured position, so that the system composite error data set is shown as the following formula:
[Xij,Yij,ΔXij,ΔYij],i＝1..5,j＝1..5 (1)
for a wafer probe station, due to nonlinear random deformation of a wafer caused by a vacuum adsorption device, nonlinear random errors respectively appear in X and Y coordinates which can be uniformly measured originally, so that the X coordinate of an actual measurement point and a theoretical X coordinate have nonlinear random errors after being corrected by a high-resolution camera pixel positionRandom error epsilonxWhile the Y coordinate of the actual measuring point has a nonlinear random error epsilonyThereby causing the position of the system measuring point to generate two-dimensional non-uniform distribution, and changing the actual composite error data set of the measuring point into [ X + epsilon ]x,Y+εy,ΔX,ΔY]。
[Xij+εxij,Yij+εyij,ΔXij,ΔYij],i＝1..5,j＝1..5 (2)
Due to Δ X, Δ Y and εxAnd εyThe non-uniform measurement points are restored to the theoretical uniform measurement points, and the reconstruction precision of the composite error curved surface of the system is not influenced, so that the practical composite error data set can be equivalently transformed into [ X, Y, delta X + epsilon ]x,ΔY+εy]Therefore, the conversion from the multi-dimensional non-uniform measuring points to the one-dimensional uniform measuring points can be realized, the difficulty of the system composite error curved surface reconstruction can be reduced, the precision of any curved surface reconstruction is not sacrificed, and the effect of killing two birds with one stone is achieved.
[Xij,Yij,ΔXij+εxij,ΔYij+εyij],i＝1..5,j＝1..5 (3)
However, due to the existence of random errors, even after the data preprocessing, a certain random error exists in the X and Y values of each point, so that in order to change the two-dimensional non-uniform distribution into one-dimensional non-uniform distribution, for different measurement points in the same row, because the variation of the Y value is not large, the actually measured Y values of each point in the same row can be averaged to eliminate the influence caused by random noise, and for different measurement points in the same column, because the variation of the X value is not large, the X values of each point in the same column can be averaged to eliminate the influence caused by random errors. Therefore, the average value of the Y values of the measurement points in a certain row is assumed to be YcAnd the average value of the X values of the measuring points in the same column is XcThen the composite error data value for each point in the same line can be corrected to [ X [ ]i,Yc,ΔXi+εxi,ΔYi-(Yc-Yi)]I representsThe serial number i of the same line of measuring points is 1.. n, and the composite error data value of each point in the same column can be corrected to be [ Xc,Yi,ΔXi-(Xc-Xi),ΔXi+εyi,]I represents the serial number i of the same line of measuring points as 1.. n,
therefore, by the above method for preprocessing the composite error measurement data, original data (as shown in fig. 1) that 5 rows and 5 columns have nonlinear random unequal interval errors in both the X direction and the Y direction, that is, no actual measurement data is on the 5 rows and 5 columns of intersection points, can be converted into data that all 25 correction points are on the 5 rows and 5 columns of intersection points (as shown in fig. 2), and therefore, for any row or any column, the corrected composite error test points become one-dimensional non-uniform data.
In order to realize the final dynamic composite error compensation by the motion control system, a composite position error compensation table with uniform spacing needs to be established, and assuming that a composite position error compensation table with uniform spacing of 50 rows and 50 columns needs to be realized, the whole test range needs to be uniformly divided into 50 rows and columns with equal spacing on the rows and the columns, namely 50 rows and 50 columns and 2500 error compensation points need to be generated from the previous 5 rows and 5 columns of 25 measurement points. In order to further simplify the reconstruction of the compound error surface and then achieve 2500 uniform compensation point data, the data after the previous preprocessing needs to be further processed, specifically, the Y coordinate (previous average line) of each row of data correction points is corrected to a certain row in 50 rows nearest to the row, the X coordinate (previous average line) of each column of data correction points is corrected to a certain column in 50 columns nearest to the column, the processing method is as formulas (4) - (5), except that Yci and Xcj at this time are not the average value of the row and the row, but become the Y axis and the X axis coordinates corresponding to the nearest row and the column, and the effect of fig. 2 is achieved through the processing that all the finally corrected measurement points are at the intersection points of the 5 row and 5 column uniform grids, so that for any row, the Y axis coordinates of 5 data points are unchanged, only the X-axis coordinate exhibits a 1-dimensional non-uniform distribution variation, while for any column, the X-axis coordinate of the 5 data points is unchanged and only the Y-axis coordinate exhibits a 1-dimensional non-uniform distribution variation. This fully completes the first feature of the claims, namely the preprocessing of the non-uniform discrete composite error data.
In a specific implementation manner of the embodiment of the present invention, the correction position data that is one-dimensional non-uniformly distributed is correction position data that is one-dimensional row non-uniformly distributed or correction position data that is one-dimensional column non-uniformly distributed;
the method for performing curve reconstruction on each group of correction position data with one-dimensional non-uniform distribution to form corresponding correction position data with one-dimensional uniform distribution specifically comprises the following steps:
performing hermitian spline curve reconstruction on the corrected position data of the one-dimensional row in non-uniform distribution line by line to form corrected position data of the corresponding one-dimensional row in uniform distribution;
and performing Hermite spline curve reconstruction on the corrected position data of the one-dimensional row non-uniform distribution column by column to form the corrected position data of the corresponding one-dimensional row uniform distribution.
Specifically, the method comprises the following steps: for 50 rows and 50 columns of uniform grids and 5 rows and 5 columns of non-uniform grids obtained after the actual measurement composite error data is preprocessed, if the row number of the 5 rows of correction data corresponding to the 50 rows of fine data is k, and the column number of the 5 columns of correction data corresponding to the 50 columns of fine data is l, on any row of the 5 rows of non-uniform grids, the X-axis direction Hermite spline fitting needs to be performed on the composite error data set of the 5 corrected non-uniform test points, as shown in the following formula,
Fxkis that the kth subdivision line respectively passes through (X)kl,ΔXkl) Segmented hermite spline functionNumber, and FykIs that the kth subdivision line respectively passes through (X)kl,ΔYkl) Segmented hermitian spline function of (1). Has a k line DeltaXklAnd Δ YklAfter the X-axis Humidt spline function, the Δ X for the other 45 unelculated equidistant points on the row can be calculatedklAnd Δ YklThe numerical values of the k-th row are subdivided on the corresponding uniform grid points according to the functional relationship of respective hermitian spline curves, so as to obtain composite error compensation values corresponding to all 50 points on the k-th row, which is specifically shown in fig. 3;
for 50 rows and 50 columns of uniform grids and 5 rows and 5 columns of non-uniform grids obtained after the actual measurement composite error data is preprocessed, if the row number of the 5 rows of correction data corresponding to the 50 rows of fine data is k, and the column number of the 5 columns of correction data corresponding to the 50 columns of fine data is l, on any one column of the 5 columns of non-uniform grids, the Y-axis direction Hermite spline fitting needs to be performed on the composite error data set of the 5 corrected non-uniform test points, as shown in the following formula,
Fxlis that the first sub-division passes through (Y)kl,ΔXkl) Segmented hermite spline function of, whereas FylIs that the first sub-division passes through (Y)kl,ΔYkl) Segmented hermitian spline function of (1). Has the l column DeltaXklAnd Δ YklAfter the Y-axis hermite spline function, we can then compute Δ X for the other 45 unelculated equidistant points on this columnklAnd Delta YklThe values of (a) are subdivided on the corresponding uniform grid points according to the functional relationship of the respective hermitian spline curves, so as to obtain the composite error compensation values corresponding to all 50 points in the l column, see in particular fig. 4.
In a specific implementation manner of the embodiment of the present invention, the performing curve reconstruction on the corrected position data based on all one-dimensional uniform distributions to obtain uniform grid point subdivision position data, and further obtain a reconstructed surface specifically includes the following steps:
respectively reconstructing a hermitian spline curve based on data in the same column in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional column;
respectively reconstructing a hermitian spline curve based on data in the same row in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional row;
repeating the two steps until uniform grid point subdivision position data are obtained;
and (5) connecting all the uniform grid points to subdivide the position data to obtain a reconstructed surface.
Specifically, the method comprises the following steps:
after completing the uniform grid point hermite spline subdivision of 5 lines in 50 lines of the target, we calculate 50 subdivided composite error points per line on 5 lines from the first 25 non-uniform composite error test points, for a total of 250 subdivided composite error points, and the remaining 45 lines of composite error data of 50 subdivided error points per line need to be calculated at this step. Since in step 3 we have completed the composite error calculation for 5 columns and 50 subdivided error points per column, for the remaining 45 rows of non-calculated subdivided composite error points, there have been 5 non-uniform composite error point data for each row since each row already had composite error data calculated on 5 columns for which row in step 3, the composite error calculation to achieve a uniform subdivided point for that row is exactly the same as the method of step two. By analogy, we can calculate the composite error data of 50 subdivided error points in each row of the remaining 45 rows, so as to finally realize the subdivided composite error data based on the row information of all 2500 points, specifically referring to fig. 5;
after completing the subdivision of 5 columns of uniform grid point hermite splines in 50 columns of the target, we calculated 50 subdivided composite error points per column of 5 columns from the first 25 non-uniform composite error test points, for a total of 250 subdivided composite error points, and the remaining 45 columns of composite error data for 50 subdivided error points per column we needed to calculate at this step. Since in step 2 we have completed the composite error calculation for 5 rows of 50 subdivided error points per row, for the remaining 45 columns of non-calculated subdivided composite error points, there have been 5 non-uniform composite error point data for each column since each column already had composite error data calculated on 5 columns for which column in step 2, the composite error calculation to achieve this column uniform subdivided point is exactly the same as the method of step three. By analogy, we can realize the composite error data calculation of the remaining 45 columns and 50 subdivided error points in each column, so as to finally realize the subdivided composite error data based on the column information of all 2500 points, and see fig. 6 specifically.
Optionally, the generating a corresponding compensation table based on the reconstructed surface specifically includes:
reading data in each grid point in the reconstructed curved surface, and obtaining error data;
a compensation table is generated based on each error data.
Specifically, the method comprises the following steps:
in the foregoing step 4 and step 5, we respectively obtain the composite error data of all 2500 equidistant error points, and the difference between the two steps is that the composite error data of the 2500 equidistant error points obtained in the step 4 is generated based on line information, and the composite error data of the 2500 equidistant error points obtained in the step 5 is generated based on column information, so that to obtain the most accurate composite error data, we need to average the composite error data of the step 4 and the step 5 point by point, and thus, the uniform composite error compensation table after reconstructing the composite error curved surface based on the hermite spline required by the present invention is finally and successfully realized, and a foundation is laid for generating real-time dynamic coincidence position error compensation of the motion controller used in the next step, see fig. 7.
Example 2
The embodiment of the present invention is different from embodiment 1 in that: the method further comprises the following steps:
and performing online compensation of the measured position data based on the compensation table.
Example 3
Based on the same inventive concept as embodiment 1, an embodiment of the present invention provides a composite position error compensation device, including:
the correction module is used for correcting the acquired discrete measured position data of the original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, and error data generated by correction is stored in the corrected position data;
the first reconstruction module is used for performing curve reconstruction on each group of correction position data which are one-dimensionally and non-uniformly distributed to form corresponding correction position data which are one-dimensionally and uniformly distributed;
the second reconstruction module is used for carrying out curve reconstruction on the basis of all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface;
and the generating module is used for generating a corresponding compensation table based on the reconstructed curved surface and realizing the composite position error compensation.
Optionally, the measured position data structure is [ X ]ij,Yij,ΔXij+εxij,ΔYij+εyij]Wherein X isijX-coordinate, Y, representing actual measuring pointijY-coordinate, Δ X, representing actual measuring pointijX coordinate compound error, epsilon, representing actual measured pointsxijThe X coordinate of the real measuring point is corrected by the pixel position of the camera and then has a nonlinear random error, delta Y, with the theoretical X coordinateijComplex error of Y coordinate, epsilon, representing measured positionyijThe Y coordinate of the real measuring point represents a nonlinear random error between the Y coordinate and a theoretical Y coordinate after being corrected by the pixel position of the camera;
the corrected position data structure is [ X ]ij,Yci,ΔXij+εxij,ΔYij-(Yci-Yij)]Or [ X ]cj,Yij,ΔXij-(Xcj-Xij),ΔYij+εyij]Wherein Y isciIs the Y-axis coordinate, X-axis coordinate, of the uniform grid line with the nearest distance from the average line of the Y-axis coordinate of the real measuring point of the ith rowcjIs the X-axis coordinate plane of the j-th row of actual measurement pointsThe Y-axis coordinate of the uniform grid line whose mean line is closest to it.
Optionally, the one-dimensional unevenly distributed corrected position data is one-dimensional row unevenly distributed corrected position data or one-dimensional column unevenly distributed corrected position data;
the method for performing curve reconstruction on each group of correction position data with one-dimensional non-uniform distribution to form corresponding correction position data with one-dimensional uniform distribution specifically comprises the following steps:
performing hermitian spline curve reconstruction on the corrected position data of the one-dimensional row in non-uniform distribution line by line to form corrected position data of the corresponding one-dimensional row in uniform distribution;
performing Hermite spline curve reconstruction on the corrected position data of the one-dimensional row non-uniform distribution column by column to form corrected position data of the corresponding one-dimensional row uniform distribution;
the method comprises the following steps of performing curve reconstruction on the corrected position data based on all one-dimensional uniform distribution to obtain uniform grid point subdivision position data and further obtain a reconstructed surface, and specifically comprises the following steps:
respectively reconstructing a hermitian spline curve based on data in the same column in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional column;
respectively reconstructing a hermitian spline curve based on data in the same row in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional row;
repeating the two steps until uniform grid point subdivision position data are obtained;
and (5) connecting all the uniform grid points to subdivide the position data to obtain a reconstructed surface.
The rest of the process was the same as in example 1.
Example 4
The embodiment of the present invention is different from embodiment 3 in that:
the composite position error compensation device further includes: and the compensation module is used for performing online compensation on the actually measured position data based on the compensation table.
The rest of the process was the same as in example 3.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.
Claims (8)
1. A method of compensating for compound position error, comprising:
correcting the acquired discrete measured position data of the original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, wherein error data generated by correction are stored in the corrected position data;
carrying out curve reconstruction on each group of correction position data which are one-dimensional and non-uniformly distributed to form corresponding correction position data which are one-dimensional and uniformly distributed;
performing curve reconstruction based on all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface;
generating a corresponding compensation table based on the reconstructed curved surface for realizing composite position error compensation;
the measured position data structure is [ X ]ij,Yij,ΔXij+εxij,ΔYij+εyij]Wherein X isijX-coordinate, Y, representing actual measuring pointijY-coordinate, Δ X, representing actual measuring pointijX coordinate compound error, epsilon, representing actual measured pointsxijThe X coordinate of the real measuring point is corrected by the pixel position of the camera and then has a nonlinear random error, delta Y, with the theoretical X coordinateijComplex error of Y coordinate, epsilon, representing measured positionyijThe Y coordinate of the real measuring point is corrected by the pixel position of the camera and then forms a non-line with the theoretical Y coordinateA random error of nature;
the corrected position data structure is [ X ]ij,Yci,ΔXij+εxij,ΔYij-(Yci-Yij)]Or [ X ]cj,Yij,ΔXij-(Xcj-Xij),ΔYij+εyij]Wherein Y isciIs the Y-axis coordinate, X-axis coordinate, of the uniform grid line with the nearest distance from the average line of the Y-axis coordinate of the real measuring point of the ith rowcjAnd the Y-axis coordinate of the uniform grid line closest to the X-axis coordinate mean line of the j-th row of actual measurement points is shown.
2. A composite position error compensation method according to claim 1, characterized by: the correction position data of the one-dimensional non-uniform distribution is correction position data of one-dimensional row non-uniform distribution or correction position data of one-dimensional column non-uniform distribution;
the method for performing curve reconstruction on each group of correction position data with one-dimensional non-uniform distribution to form corresponding correction position data with one-dimensional uniform distribution specifically comprises the following steps:
performing hermitian spline curve reconstruction on the corrected position data of the one-dimensional row in non-uniform distribution line by line to form corrected position data of the corresponding one-dimensional row in uniform distribution;
and performing Hermite spline curve reconstruction on the corrected position data of the one-dimensional row non-uniform distribution column by column to form the corrected position data of the corresponding one-dimensional row uniform distribution.
3. A composite position error compensation method according to claim 2, characterized by: the method comprises the following steps of performing curve reconstruction on the corrected position data based on all one-dimensional uniform distribution to obtain uniform grid point subdivision position data and further obtain a reconstructed surface, and specifically comprises the following steps:
respectively reconstructing a hermitian spline curve based on data in the same column in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional column;
respectively reconstructing a hermitian spline curve based on data in the same row in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional row;
repeating the two steps until uniform grid point subdivision position data are obtained;
and (5) connecting all the uniform grid points to subdivide the position data to obtain a reconstructed surface.
4. A composite position error compensation method according to claim 1, characterized by: the generating of the corresponding compensation table based on the reconstructed curved surface specifically includes:
reading data in each grid point in the reconstructed curved surface, and obtaining error data;
a compensation table is generated based on each error data.
5. The method of claim 1, further comprising: and performing online compensation of the measured position data based on the compensation table.
6. A composite position error compensation apparatus, comprising:
the correction module is used for correcting the acquired discrete measured position data of the original multi-dimensional non-uniform distribution into a plurality of groups of corrected position data of one-dimensional non-uniform distribution, and error data generated by correction is stored in the corrected position data;
the first reconstruction module is used for performing curve reconstruction on each group of correction position data which are one-dimensionally and non-uniformly distributed to form corresponding correction position data which are one-dimensionally and uniformly distributed;
the second reconstruction module is used for carrying out curve reconstruction on the basis of all the corrected position data which are uniformly distributed in one dimension to obtain uniform grid point subdivision position data and further obtain a reconstructed surface;
the generating module is used for generating a corresponding compensation table based on the reconstructed curved surface and realizing composite position error compensation;
the measured position data nodeIs formed as [ X ]ij,Yij,ΔXij+εxij,ΔYij+εyij]Wherein X isijX-coordinate, Y, representing actual measuring pointijY-coordinate, Δ X, representing actual measuring pointijX coordinate compound error, epsilon, representing actual measured pointsxijThe X coordinate of the real measuring point is corrected by the pixel position of the camera and then has a nonlinear random error, delta Y, with the theoretical X coordinateijComplex error of Y coordinate, epsilon, representing measured positionyijThe Y coordinate of the real measuring point represents a nonlinear random error between the Y coordinate and a theoretical Y coordinate after being corrected by the pixel position of the camera;
the corrected position data structure is [ X ]ij,Yci,ΔXij+εxij,ΔYij-(Yci-Yij)]Or [ X ]cj,Yij,ΔXij-(Xcj-Xij),ΔYij+εyij]Wherein Y isciIs the Y-axis coordinate, X-axis coordinate, of the uniform grid line with the nearest distance from the average line of the Y-axis coordinate of the real measuring point of the ith rowcjAnd the Y-axis coordinate of the uniform grid line closest to the X-axis coordinate mean line of the j-th row of actual measurement points is shown.
7. A composite position error compensation apparatus according to claim 6, wherein: the correction position data of the one-dimensional non-uniform distribution is correction position data of one-dimensional row non-uniform distribution or correction position data of one-dimensional column non-uniform distribution;
the method for performing curve reconstruction on each group of correction position data with one-dimensional non-uniform distribution to form corresponding correction position data with one-dimensional uniform distribution specifically comprises the following steps:
performing hermitian spline curve reconstruction on the corrected position data of the one-dimensional row in non-uniform distribution line by line to form corrected position data of the corresponding one-dimensional row in uniform distribution;
performing Hermite spline curve reconstruction on the corrected position data of the one-dimensional row non-uniform distribution column by column to form corrected position data of the corresponding one-dimensional row uniform distribution;
the method comprises the following steps of performing curve reconstruction on the corrected position data based on all one-dimensional uniform distribution to obtain uniform grid point subdivision position data and further obtain a reconstructed surface, and specifically comprises the following steps:
respectively reconstructing a hermitian spline curve based on data in the same column in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional column;
respectively reconstructing a hermitian spline curve based on data in the same row in the corrected position data uniformly distributed in each one-dimensional row to obtain corrected position data uniformly distributed in the corresponding one-dimensional row;
repeating the two steps until uniform grid point subdivision position data are obtained;
and (5) connecting all the uniform grid points to subdivide the position data to obtain a reconstructed surface.
8. A composite position error compensation apparatus according to claim 6, wherein: the composite position error compensation device further includes:
and the compensation module is used for performing online compensation on the actually measured position data based on the compensation table.
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