Method for calibrating structural error parameters of two-dimensional orthogonal rotating mirror system

Abstract

The invention provides a method for calibrating structural error parameters of a two-dimensional orthogonal rotating mirror system, which can be applied to the technical field of large-size measurement. The calibration method comprises the following steps: acquiring measurement coordinate values and reference coordinate values of n spatial points; wherein the measurement coordinate value is a spherical coordinate system, the measurement coordinate value is measured by using a two-dimensional orthogonal rotating mirror system, and the reference coordinate value is measured by using a laser tracker; constructing an error model based on the q structural error parameters and the distance item, the azimuth angle and the pitch angle of the spherical coordinate system associated with each structural error parameter; wherein 1 < = q < = 3n-6; on the basis of the error model and the measurement coordinate values of the n space points, constructing correction coordinate quantities of the n space points; and on the basis of the correction coordinate quantities of the n space points and the reference coordinate values of the n space points, solving values of the q structural error parameters are obtained, and calibration of the structural error parameters is completed.

Description

Technical Field

[0001] At least one embodiment of the present invention relates to the field of large-size measurement, and more specifically to a calibration method for structural error parameters of a two-dimensional orthogonal mirror rotation system. Background Art

[0002] The large-size space precise pose measurement technology is the core technology for high-end equipment in the fields of aerospace, shipbuilding, etc. to achieve automated and high-precision assembly. The two-dimensional orthogonal mirror rotation system drives a mirror to guide a light beam based on two-dimensional orthogonal rotation axes, obtains distance information by using laser ranging technology, and combines a high-precision circular grating to obtain angle information to achieve spherical coordinate measurement, with the characteristics of high precision, wide range, high efficiency and automation. In the actual application process, the two-dimensional orthogonal mirror rotation system may be affected by multiple factors such as mechanical assembly errors, human operation errors, and external environmental changes, resulting in a decline in its measurement performance and further generating measurement errors.

[0003] Therefore, it is urgent to analyze the errors of the two-dimensional orthogonal mirror rotation system to improve the measurement accuracy. Summary of the Invention

[0004] In view of the above problems, the present invention provides a calibration method for structural error parameters of a two-dimensional orthogonal mirror rotation system to improve measurement accuracy. The above calibration method includes: obtaining the measured coordinate values and reference coordinate values of n spatial points; wherein, the above measured coordinate values are in the spherical coordinate system, the above measured coordinate values are measured by using a two-dimensional orthogonal mirror rotation system, and the above reference coordinate values are measured by using a laser tracker; constructing an error model based on q structural error parameters and the distance term, azimuth angle, and elevation angle of the above spherical coordinate system associated with each structural error parameter; wherein, 1≤q≤3n-6; constructing the corrected coordinate quantities of the above n spatial points based on the above error model and the measured coordinate values of the above n spatial points; obtaining the calculated values of the q structural error parameters based on the corrected coordinate quantities of the above n spatial points and the reference coordinate values of the above n spatial points, and completing the calibration of the structural error parameters.

[0005] According to an embodiment of the present invention, the structural errors of the above two-dimensional orthogonal mirror rotation system include an initial distance error term, an alignment offset error term, an alignment tilt error term, and a circular grating installation error term; the above method further includes: setting the above q structural error parameters based on the above initial distance error term, the above alignment offset error term, the above alignment tilt error term, and the above circular grating installation error term.

[0006] According to an embodiment of the present invention, constructing an error model based on the above-mentioned q structural error parameters and the distance term, azimuth angle, and elevation angle of the above-mentioned spherical coordinate system associated with each structural error parameter includes: constructing a first error sub-model based on the q structural error parameters and the distance term of the above-mentioned spherical coordinate system associated with each structural error parameter; constructing a second error sub-model based on the q structural error parameters and the azimuth angle of the above-mentioned spherical coordinate system associated with each structural error parameter; constructing a third error sub-model based on the q structural error parameters and the elevation angle of the above-mentioned spherical coordinate system associated with each structural error parameter; and constructing the above-mentioned error model based on the above-mentioned first error sub-model, the above-mentioned second error sub-model, and the above-mentioned third error sub-model.

[0007] According to an embodiment of the present invention, constructing the corrected coordinate quantities of the above-mentioned n spatial points based on the above-mentioned error model and the measured coordinate values of the above-mentioned n spatial points includes: constructing the distance term of the corrected coordinate quantities of the above-mentioned n spatial points based on the above-mentioned first error sub-model and the distance term of the measured coordinate values of the above-mentioned n spatial points; constructing the azimuth angle term of the corrected coordinate quantities of the above-mentioned n spatial points based on the above-mentioned second error sub-model and the azimuth angle term of the measured coordinate values of the above-mentioned n spatial points; and constructing the elevation angle term of the corrected coordinate quantities of the above-mentioned n spatial points based on the above-mentioned third error sub-model and the elevation angle term of the measured coordinate values of the above-mentioned n spatial points.

[0008] According to an embodiment of the present invention, obtaining the calculated values of the above-mentioned q structural error parameters based on the corrected coordinate quantities of the above-mentioned n spatial points and the reference coordinate values of the above-mentioned n spatial points includes: constructing a rotation matrix and a translation matrix between the coordinate systems of the above-mentioned two-dimensional orthogonal mirror system and the above-mentioned laser tracker; mapping the reference coordinate values of the above-mentioned n spatial points to the coordinate system of the above-mentioned two-dimensional orthogonal mirror system based on the above-mentioned rotation matrix and the above-mentioned translation matrix to obtain the reference coordinate quantities of the above-mentioned n spatial points; and obtaining the calculated values of the above-mentioned q structural error parameters based on the corrected coordinate quantities of the above-mentioned n spatial points and the reference coordinate quantities of the above-mentioned n spatial points.

[0009] According to an embodiment of the present invention, obtaining the calculated values of the above-mentioned q structural error parameters based on the corrected coordinate quantities of the above-mentioned n spatial points and the reference coordinate quantities of the above-mentioned n spatial points includes: constructing an objective function based on the corrected coordinate quantities of the above-mentioned n spatial points and the reference coordinate quantities of the above-mentioned n spatial points; using the Levenberg-Marquardt method to perform iterative optimization with minimizing the sum of squares of the above-mentioned objective function as the optimization objective to obtain the calculated values of the above-mentioned q structural error parameters.

[0010] According to an embodiment of the present invention, constructing an objective function based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points includes: converting the corrected coordinate quantities of the n spatial points into a Cartesian coordinate system to obtain the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points; constructing the objective function based on the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points.

[0011] According to an embodiment of the present invention, constructing an objective function based on the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points includes: taking the coincidence between the spatial point positions represented by the Cartesian coordinate quantities of the corrected coordinate quantities of each spatial point and the spatial point positions represented by the reference coordinate quantities of the corresponding each spatial point as a constraint term to construct a point position constraint equation; constructing the objective function based on the point position constraint equation.

[0012] According to an embodiment of the present invention, taking the coincidence between the spatial point positions represented by the Cartesian coordinate quantities of the corrected coordinate quantities of each spatial point and the spatial point positions represented by the reference coordinate quantities of the corresponding each spatial point as a constraint term to construct a point position constraint equation includes: taking the difference between the first item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the first item of the reference coordinate quantity of the corresponding each spatial point being zero as a constraint term to construct a first sub-constraint equation of the point position; taking the difference between the second item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the second item of the reference coordinate quantity of the corresponding each spatial point being zero as a constraint term to construct a second sub-constraint equation of the point position; taking the difference between the third item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the third item of the reference coordinate quantity of the corresponding each spatial point being zero as a constraint term to construct a third sub-constraint equation of the point position; constructing the point position constraint equation based on the first sub-constraint equation of the point position, the second sub-constraint equation of the point position, and the third sub-constraint equation of the point position of each spatial point.

[0013] According to an embodiment of the present invention, using the Levenberg-Marquardt method to perform iterative optimization with minimizing the sum of squares of the objective function as the optimization target to obtain the solution values of the q structural error parameters includes: determining the constraint conditions of the Levenberg-Marquardt method based on the rotation matrix; using the Levenberg-Marquardt method, based on the constraint conditions, to perform iterative optimization with minimizing the sum of squares of the objective function as the optimization target to obtain the solution values of the q structural error parameters.

[0014] According to an embodiment of the present invention, by constructing an error model for multiple structural error parameters of a two-dimensional orthogonal rotating mirror system and the distance terms, azimuth angles, and elevation angles of the spherical coordinate system associated with each structural error parameter, it is possible to analyze the structural errors of the two-dimensional orthogonal rotating mirror system more deeply and in more detail, and to quantify the structural errors in order to perform error compensation more precisely, improve the measurement accuracy of the two-dimensional orthogonal rotating mirror system, and also perform system calibration regularly to improve the reliability of the two-dimensional orthogonal rotating mirror system. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above content and other objects, features, and advantages of the present invention will become clearer through the following description of the embodiments of the present invention with reference to the accompanying drawings.

[0016] Figure 1 FIG. shows an operation flowchart of a calibration method for structural error parameters of a two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0017] Figure 2 FIG. shows a schematic diagram of the alignment offset error term of a two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0018] Figure 3 FIG. shows a schematic diagram of the alignment tilt error term of a two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0019] Figure 4 FIG. shows a schematic diagram of the circular grating installation error term of a two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0020] Figure 5 FIG. shows a schematic diagram of a control field network according to an experimental embodiment of the present invention.

[0021] Figure 6 FIG. shows a schematic diagram of the point position deviation between the corrected coordinate value and the reference coordinate value according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are merely exemplary and are not intended to limit the scope of the present invention. In the following detailed description, for the sake of explanation, many specific details are set forth to provide a comprehensive understanding of the embodiments of the present invention. However, obviously, one or more embodiments can also be implemented without these specific details. In addition, in the following description, descriptions of well-known structures and technologies are omitted to avoid unnecessarily confusing the concepts of the present invention.

[0023] The terms used herein are merely for describing specific embodiments and are not intended to limit the present invention. The terms "comprising", "including" and the like used herein indicate the presence of the described features, steps, operations and / or components, but do not preclude the presence or addition of one or more other features, steps, operations or components.

[0024] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0025] In the case of using expressions such as "at least one of A, B, and C, etc.", generally, it should be interpreted according to the meaning commonly understood by those skilled in the art (for example, "a system having at least one of A, B, and C" should include, but not be limited to, a system having only A, only B, only C, having A and B, having A and C, having B and C, and / or having A, B, and C, etc.).

[0026] The two-dimensional orthogonal mirror rotation system is a spherical coordinate measurement system composed of a two-dimensional turntable, a laser rangefinder, and a tracking mirror. The incident beam of the laser rangefinder is incident on the tracking mirror, and the tracking mirror reflects the incident beam to the spatial point to be measured. The azimuth angle, elevation angle, and distance term of the spherical coordinate measurement system can be obtained from the two-dimensional orthogonal rotation axes of the two-dimensional turntable and the ranging laser beam of the laser rangefinder, respectively. Mechanical errors such as the position error of the two-dimensional orthogonal rotation axes of the two-dimensional turntable and the installation error of the tracking mirror, and optical geometric errors such as the alignment error of the incident beam of the laser rangefinder directly affect the measurement performance and accuracy of the two-dimensional orthogonal mirror rotation system.

[0027] Figure 1 The operation flowchart of the calibration method for the structural error parameters of the two-dimensional orthogonal mirror rotation system according to an embodiment of the present invention is shown.

[0028] As Figure 1 shown, the calibration method for the structural error parameters of the two-dimensional orthogonal mirror rotation system includes operations S110 to S140.

[0029] In operation S110, the measured coordinate values and reference coordinate values of n spatial points are obtained; among them, the measured coordinate values are in the spherical coordinate system, the measured coordinate values are measured by the two-dimensional orthogonal mirror rotation system, and the reference coordinate values are measured by a laser tracker.

[0030] In operation S120, an error model is constructed based on q structural error parameters and the distance term, azimuth angle, and elevation angle of the spherical coordinate system associated with each structural error parameter; where 1 ≤ q ≤ 3n - 6, n ≥ 3, n is an integer, and q is an integer.

[0031] In operation S130, based on the error model and the measured coordinate values of n spatial points, correction coordinate quantities of the n spatial points are constructed.

[0032] In operation S140, based on the correction coordinate quantities of the n spatial points and the reference coordinate values of the n spatial points, solution values of q structural error parameters are obtained, and the calibration of the structural error parameters is completed.

[0033] According to an embodiment of the present invention, by constructing an error model for multiple structural error parameters of a two-dimensional orthogonal mirror rotating system and the distance term, azimuth angle, and pitch angle of the spherical coordinate system associated with each structural error parameter, it is possible to perform a more in-depth and detailed analysis of the structural errors of the two-dimensional orthogonal mirror rotating system, and to quantify the structural errors to perform error compensation more precisely, improve the measurement accuracy of the two-dimensional orthogonal mirror rotating system, and also regularly calibrate the structural error parameters of the system to improve the reliability of the two-dimensional orthogonal mirror rotating system.

[0034] In one embodiment, the two-dimensional orthogonal mirror rotating system includes a horizontal rotating table, a vertical rotating table, a tracking mirror, and a laser rangefinder. In an ideal situation, there are no structural errors in the two-dimensional orthogonal mirror rotating system, the rotation central axis of the horizontal rotating table and the rotation central axis of the vertical rotating table are orthogonal; the center of the tracking mirror is located at the orthogonal center of the rotation central axis of the horizontal rotating table and the rotation central axis of the vertical rotating table. In the Cartesian coordinate system of the two-dimensional orthogonal mirror rotating system, the rotation central axis of the horizontal rotating table is set as the Z axis, the rotation central axis of the vertical rotating table is set as the Y axis, and the X axis is set according to the right-hand rule.

[0035] In one embodiment, the measured coordinate values before correction of the two-dimensional orthogonal mirror rotating system can be expressed as ( ), where represents the distance term of the measured coordinate value, represents the azimuth angle of the measured coordinate value, represents the pitch angle of the measured coordinate value. The correction coordinate quantities after correction based on the correction relationship can be expressed as ( ), where represents the distance term of the correction coordinate quantity, represents the azimuth angle of the correction coordinate quantity, represents the pitch angle of the correction coordinate quantity.

[0036] According to an embodiment of the present invention, the structural errors of the two-dimensional orthogonal mirror rotating system may include an initial distance error term, an alignment offset error term, an alignment tilt error term, and a circular grating installation error term.

[0037] According to an embodiment of the present invention, q structural error parameters are set based on the initial distance error term, the alignment offset error term, the alignment tilt error term, and the circular grating installation error term.

[0038] In one embodiment, the initial distance error term can be expressed as the distance error between the laser emission point of the laser rangefinder and the center of the tracking rotating mirror. Based on the initial distance error , the distance term of the measured coordinate value is corrected, and the correction relationship can be expressed as:

[0039] (1).

[0040] Figure 2 FIG. shows a schematic diagram of the alignment offset error term of the two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0041] As Figure 2 shown in (a) of, in one embodiment, the alignment offset error term may include a horizontal axis offset error . The rotation center axis of the horizontal rotating table and the rotation center axis of the vertical rotating table are non-orthogonal, and the horizontal axis offset error characterizes the distance between the rotation center axis of the horizontal rotating table and the rotation center axis of the vertical rotating table . Based on the horizontal axis offset error , the distance term of the measured coordinate value and the pitch angle of the measured coordinate value are corrected, and the correction relationship can be expressed as:

[0042] (2);

[0043] (3).

[0044] As Figure 2 shown in (b) of, in one embodiment, the alignment offset error term may include a mirror surface offset error . The center of the tracking rotating mirror is not at the orthogonal center of the rotation center axis of the horizontal rotating table and the rotation center axis of the vertical rotating table , and the mirror surface offset error characterizes the distance between the center of the tracking rotating mirror and the orthogonal center. Based on the mirror surface offset error , the distance term of the measured coordinate value and the pitch angle of the measured coordinate value are corrected, and the correction relationship can be expressed as:

[0045] (4);

[0046] (5).

[0047] As Figure 2As shown in (c), in one embodiment, the alignment offset error term may include an incident beam offset error. The incident beam of the laser rangefinder does not enter the center of the tracking rotating mirror, and the first incident beam offset error characterizes the offset distance of the incident beam of the laser rangefinder in the first direction, and the second incident beam offset error characterizes the offset distance of the incident beam of the laser rangefinder in the second direction; wherein, the first direction represents the X-axis of the Cartesian coordinate system of the two-dimensional orthogonal rotating mirror system, and the second direction represents the Y-axis of the Cartesian coordinate system of the two-dimensional orthogonal rotating mirror system. Based on the first incident beam offset error and the second incident beam offset error , the azimuth angle of the measured coordinate value and the elevation angle of the measured coordinate value are corrected, and the correction relationship can be expressed as:

[0048] (6);

[0049] (7).

[0050] Figure 3 shows a schematic diagram of the alignment tilt error term of the two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0051] As Figure 3 shown in (a), in one embodiment, the alignment tilt error term may include a mirror tilt angle error . The plane where the tracking rotating mirror is located is not parallel to the rotation center axis of the vertical rotating table , and the mirror tilt angle error characterizes the angle between the plane where the tracking rotating mirror is located and the rotation center axis of the vertical rotating table . Based on the mirror tilt angle error , the azimuth angle of the measured coordinate value is corrected, and the correction relationship can be expressed as:

[0052] (8).

[0053] As Figure 3 shown in (b), in one embodiment, the alignment tilt error term may include a horizontal axis tilt angle error . The rotation center axis of the horizontal rotating table and the rotation center axis of the vertical rotating table are non-orthogonal, and the horizontal axis tilt angle error characterizes the angle between the rotation center axis of the horizontal rotating table and the rotation center axis of the vertical rotating table . Based on the horizontal axis tilt angle error , the azimuth angle of the measured coordinate value is corrected, and the correction relationship can be expressed as:

[0054] (9).

[0055] As Figure 3 shown in (c) thereof, in one embodiment, the alignment tilt error term may include an incident beam tilt error. The incident beam of the laser rangefinder is not parallel to the rotation center axis of the horizontal rotating table , and there is a tilt angle between the incident beam of the laser rangefinder and the rotation center axis of the horizontal rotating table . The first incident beam offset error characterizes the component of the tilt angle in the first direction, and the second incident beam offset error characterizes the component of the tilt angle in the second direction. Based on the first incident beam offset error and the second incident beam offset error , the azimuth angle of the measured coordinate value and the pitch angle of the measured coordinate value are corrected, and the correction relationship can be expressed as:

[0056] (10);

[0057] (11).

[0058] Figure 4 shows a schematic diagram of the circular grating installation error term of the two-dimensional orthogonal rotating mirror system according to an embodiment of the present invention.

[0059] As Figure 4 shown, in one embodiment, the circular grating installation error term may include a circular grating eccentricity error. As Figure 4 shown in (a) thereof, there is a deviation between the center of the circular grating of the horizontal rotating table and the rotation center of the horizontal rotating table (the position of the rotation center axis of the horizontal rotating table on the plane where the circular grating of the horizontal rotating table is located). As Figure 4 shown in (a) thereof, 0, 90, and 180 respectively represent the angle scales of the circular grating of the horizontal rotating table. As Figure 4 shown in (b) thereof, there is a deviation between the center of the circular grating of the vertical rotating table and the rotation center of the vertical rotating table (the position of the rotation center axis of the vertical rotating table on the plane where the circular grating of the vertical rotating table is located). As Figure 4 shown in (b) thereof, 90 and -90 respectively represent the angle scales of the circular grating of the vertical rotating table.

[0060] The first circular grating eccentricity error characterizes the offset distance between the center of the circular grating of the horizontal rotating table and the rotation center of the horizontal rotating table in the first direction; the second circular grating eccentricity error Characterize the offset distance between the center of the circular grating of the horizontal rotary table and the rotation center of the horizontal rotary table in the second direction. Based on the first circular grating eccentricity error and the second circular grating eccentricity error , correct the azimuth angle of the measured coordinate value, and the correction relationship can be expressed as:

[0061] (12).

[0062] The third circular grating eccentricity error Characterize the offset distance between the center of the circular grating of the vertical rotary table and the rotation center of the vertical rotary table in the first direction; the fourth circular grating eccentricity error Characterize the offset distance between the center of the circular grating of the vertical rotary table and the rotation center of the vertical rotary table in the second direction. Based on the third circular grating eccentricity error and the fourth circular grating eccentricity error , correct the pitch angle of the measured coordinate value, and the correction relationship can be expressed as:

[0063] (13).

[0064] In one embodiment, for example, q can be 13. Based on the initial distance error term, the initial distance error can be set as a structural error parameter; based on the alignment offset error term, the horizontal axis offset error , mirror offset error , first incident beam offset error , second incident beam offset error can be set as structural error parameters; based on the alignment tilt error term, the mirror tilt angle error , horizontal axis tilt angle error , first incident beam offset error , second incident beam offset error can be set as structural error parameters; based on the circular grating installation error term, the first circular grating eccentricity error , second circular grating eccentricity error , third circular grating eccentricity error , fourth circular grating eccentricity error can be set as structural error parameters, that is, a total of 13 structural error parameters are set.

[0065] According to an embodiment of the present invention, a first error sub-model is constructed based on q structural error parameters and the distance terms of the spherical coordinate system associated with each structural error parameter; a second error sub-model is constructed based on q structural error parameters and the azimuth angles of the spherical coordinate system associated with each structural error parameter; a third error sub-model is constructed based on q structural error parameters and the elevation angles of the spherical coordinate system associated with each structural error parameter; and an error model is constructed based on the first error sub-model, the second error sub-model, and the third error sub-model.

[0066] In one embodiment, based on the above 13 structural error parameters and the distance terms of the spherical coordinate system associated with each structural error parameter, and based on the above formulas (1), (2), and (4), a first error sub-model is constructed . The first error sub-model represents the correction relationship of the 13 structural error parameters to the distance term.

[0067] In one embodiment, based on the 13 structural error parameters and the azimuth angles of the spherical coordinate system associated with each structural error parameter, and based on the above formulas (6), (8), (9), (10), and (12), a second error sub-model is constructed . The second error sub-model represents the correction relationship of the 13 structural error parameters to the azimuth angle term.

[0068] In one embodiment, based on the 13 structural error parameters and the elevation angles of the spherical coordinate system associated with each structural error parameter, and based on the above formulas (3), (5), (7), (11), and (13), a third error sub-model is constructed . The third error sub-model represents the correction relationship of the 13 structural error parameters to the elevation angle term.

[0069] Based on the first error sub-model , the second error sub-model , and the third error sub-model , an error model is constructed , where represents the distance term of the error model, represents the azimuth angle term of the error model, represents the elevation angle term of the error model.

[0070] According to an embodiment of the present invention, based on the distance term of the first error sub-model and the measured coordinate values of n spatial points, the distance term of the corrected coordinate quantity of the n spatial points is constructed; based on the azimuth term of the second error sub-model and the measured coordinate values of the n spatial points, the azimuth term of the corrected coordinate quantity of the n spatial points is constructed; based on the elevation angle term of the third error sub-model and the measured coordinate values of the n spatial points, the elevation angle term of the corrected coordinate quantity of the n spatial points is constructed.

[0071] In one embodiment, the measured coordinate values of the n spatial points can be expressed as , where represents the distance term of the measured coordinate value of the -th spatial point, represents the azimuth angle of the measured coordinate value of the -th spatial point, represents the elevation angle of the measured coordinate value of the -th spatial point, where .

[0072] In one embodiment, the corrected coordinate quantity of the n spatial points can be expressed as:

[0073] (14);

[0074] where represents the distance term of the corrected coordinate quantity of the -th spatial point, represents the azimuth term of the corrected coordinate quantity of the -th spatial point, represents the elevation angle term of the corrected coordinate quantity of the -th spatial point.

[0075] In one embodiment, there are various ways to calibrate the parameters of the error model: point position constraint calibration method, plane constraint calibration method, straight line constraint calibration method, spherical surface constraint calibration method. For the plane constraint calibration method, it is difficult to obtain a high-precision constraint plane, and the error transfer coefficient of the plane constraint method itself is relatively high, resulting in low accuracy of the results. The straight line constraint also has a relatively high error transfer coefficient and low sensitivity of the error parameters. Although the spherical surface constraint is sensitive to all error parameters, it is difficult to obtain a high-precision standard sphere with a relatively large radius in practical applications. The point position constraint calibration method not only has a simple implementation method but also can provide stable constraints within a limited measurement range.

[0076] According to an embodiment of the present invention, a calibration method based on a control field network is adopted to fix the position of the calibration points in space, form point position constraints with the unchanged position of the calibration points, and establish a calibration field.

[0077] According to an embodiment of the present invention, a rotation matrix and a translation matrix between the coordinate systems of the two-dimensional orthogonal rotating mirror system and the laser tracker are constructed; based on the rotation matrix and the translation matrix, the reference coordinate values of n spatial points are mapped to the coordinate system of the two-dimensional orthogonal rotating mirror system to obtain the reference coordinate quantities of the n spatial points; based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points, the calculated values of q structural error parameters are obtained.

[0078] In one embodiment, the reference coordinate values of the n spatial points can be expressed as .

[0079] In one embodiment, a rotation matrix and a translation matrix are constructed as follows:

[0080] (15);

[0081] (16).

[0082] In one embodiment, the reference coordinate quantities of the n spatial points can be expressed as:

[0083] (17).

[0084] According to an embodiment of the present invention, based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points, an objective function is constructed; using the Levenberg-Marquardt method, the sum of the squares of the objective function is minimized as the optimization objective for iterative optimization to obtain the calculated values of q structural error parameters.

[0085] According to an embodiment of the present invention, the corrected coordinate quantities of the n spatial points are converted into the Cartesian coordinate system to obtain the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points; based on the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points, an objective function is constructed.

[0086] In one embodiment, the corrected coordinate quantities of the n spatial points are converted into the Cartesian coordinate system to obtain the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points .

[0087] According to an embodiment of the present invention, taking the coincidence between the spatial point positions represented by the Cartesian coordinate quantities of the corrected coordinate quantities of each spatial point and the spatial point positions represented by the corresponding reference coordinate quantities of each spatial point as a constraint term, a point position constraint equation is constructed; based on the point position constraint equation, an objective function is constructed.

[0088] In one embodiment, the point position constraint equation of the th spatial point It can be expressed as:

[0089] (18);

[0090] in, Indicates the parameter to be solved.

[0091] According to an embodiment of the present invention, the difference between the first item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the first item of the corresponding reference coordinate quantity of each spatial point is zero as a constraint item, and the first sub-constraint equation of the point position is constructed; the difference between the second item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the second item of the corresponding reference coordinate quantity of each spatial point is zero as a constraint item, and the second sub-constraint equation of the point position is constructed; the difference between the third item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the third item of the corresponding reference coordinate quantity of each spatial point is zero as a constraint item, and the third sub-constraint equation of the point position is constructed; based on the first sub-constraint equation of the point position, the second sub-constraint equation of the point position and the third sub-constraint equation of the point position of each spatial point, the point position constraint equation is constructed.

[0092] In one embodiment, The first sub-constraint equation of the position of a spatial point It can be expressed as:

[0093] (19);

[0094] No. The second sub-constraint equation of the position of a spatial point It can be expressed as:

[0095] (20);

[0096] No. The third sub-constraint equation of the position of a spatial point It can be expressed as:

[0097] (twenty one).

[0098] In one embodiment, there are A standardized equation is constructed to construct the objective function :

[0099] (twenty three).

[0100] According to an embodiment of the present invention, the constraints of the Levenberg-Marquardt method are determined based on the rotation matrix; the Levenberg-Marquardt method is used to perform iterative optimization based on the constraints with minimizing the sum of squares of the objective function as the optimization goal to obtain the solution values ​​of q structural error parameters.

[0101] In one embodiment, the rotation matrix is a 3×3 matrix obtained by rotating the three axes of the coordinate system, and thus satisfies the following six constraint conditions:

[0102] (24).

[0103] In one embodiment, using the least squares method to solve this system of equations is an efficient solution idea. Transform the non-linear multi-variable system of equations into a non-linear least squares problem, and solve the objective function in the least squares method through an iterative optimization method.

[0104] In one embodiment, transform formula (23) into a non-linear least squares problem for solution. At this time, the optimization objective function is:

[0105] (25);

[0106] wherein, the parameters to be solved include q structural error parameters, the construction parameters of the rotation matrix and the translation matrix , a total of q + 12. The total number of constraint equations is 3n + 6. When the total number of constraint equations satisfies 3n + 6 q + 12, the Levenberg-Marquardt algorithm can be used for solution to obtain the solution values of q structural error parameters, and the solution values of the construction parameters of 12 rotation matrices and the translation matrix .

[0107] The following further explains the calibration method for the structural error parameters of the two-dimensional orthogonal mirror rotation system of the present invention through an experimental example.

[0108] Figure 5 shows a schematic diagram of a control field network according to an experimental example of the present invention.

[0109] As Figure 5 shown, n spatial points are set in the control field network. For example, point 1, point 2,..., point j,..., point n. Use a laser tracker to measure the reference coordinate values of the n spatial points. The Cartesian coordinate system of the laser tracker is represented as . Use the two-dimensional orthogonal mirror rotation system to simultaneously measure the measured coordinate values in the spherical coordinate system of the same n spatial points. The Cartesian coordinate system of the two-dimensional orthogonal mirror rotation system is represented as .

[0110] In one embodiment, the reference coordinate values of 24 spatial points are measured by using a laser tracker with higher precision within a control field network, as shown in Table 1 below. The measured coordinate values in the spherical coordinate system of the same 24 spatial points are measured simultaneously by using a two-dimensional orthogonal mirror system, as shown in Table 2 below.

[0111] Table 1

[0112]

[0113] Table 2

[0114]

[0115] Based on the above 13 structural error parameters, an error model is constructed; based on the control field network, an objective function is constructed, and the Levenberg-Marquardt algorithm is used for solution to obtain the calculated values of the 13 structural error parameters, as shown in Table 3 below. At the same time, the calculated values of the construction parameters of 12 rotation matrices and translation matrices are obtained.

[0116] Table 3

[0117]

[0118] According to the calculated values of the above 13 structural error parameters, the measured coordinate values of the 24 spatial points are corrected to obtain the corrected coordinate values of the 24 spatial points. According to the calculated values of the construction parameters of 12 rotation matrices and translation matrices the reference coordinate values of the 24 spatial points are mapped to the coordinate system of the two-dimensional orthogonal mirror system to obtain the reference coordinate values of the 24 spatial points.

[0119] Figure 6 The figure shows a schematic diagram of the point position deviation between the corrected coordinate values and the reference coordinate values according to an embodiment of the present invention.

[0120] As Figure 6 shown, the abscissa represents the calibrated point positions of the 24 spatial points, and the ordinate represents the point position deviation, with the unit of mm. As Figure 6 shown, by using the calibration method for the structural error parameters of the two-dimensional orthogonal mirror system of the present invention, the maximum point position deviation value after correcting the measured coordinate values is 1.270 mm, and the average point position deviation value is 0.584 mm. By using the calibration method for the structural error parameters of the two-dimensional orthogonal mirror system of the present invention, the measurement accuracy after correcting the two-dimensional orthogonal mirror system can meet the accuracy requirements for large-size measurement.

[0121] The calibration method for the structural error parameters of the two-dimensional orthogonal mirror rotation system of the present invention constructs a geometric error model based on the system kinematic analysis to quantify the influence brought by each structural error term during measurement; constructs an objective function based on the control field network, and uses the Levenberg-Marquardt algorithm to solve the least squares problem to complete the calibration of the error parameters of the structural errors of the two-dimensional orthogonal mirror rotation system. The error model and the calibration method for the structural error parameters are verified by experiments to meet the coordinate measurement requirements in a large size range.

[0122] Those skilled in the art can understand that the features described in the various embodiments of the present invention can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in the present invention. In particular, without departing from the spirit and teachings of the present invention, the features described in the various embodiments of the present invention can be combined and / or combined in various ways. All such combinations and / or combinations fall within the scope of the present invention.

[0123] The embodiments of the present invention have been described above. However, these embodiments are for illustrative purposes only and not for limiting the scope of the present invention. Although the embodiments have been described separately above, this does not mean that the measures in each embodiment cannot be used advantageously in combination. Without departing from the scope of the present invention, those skilled in the art can make various substitutions and modifications, and all such substitutions and modifications should fall within the scope of the present invention.

Claims

1. A calibration method for structural error parameters of a two-dimensional orthogonal rotating mirror system, characterized in that The calibration method includes: Obtaining the measured coordinate values and reference coordinate values of n spatial points; wherein, the measured coordinate values are in a spherical coordinate system, the measured coordinate values are measured by a two-dimensional orthogonal mirror system, and the reference coordinate values are measured by a laser tracker; Based on q structural error parameters and the distance term, azimuth angle, and elevation angle of the spherical coordinate system associated with each structural error parameter, constructing an error model; where 1 ≤ q ≤ 3n - 6; Based on the error model and the measured coordinate values of the n spatial points, constructing the corrected coordinate quantities of the n spatial points; Based on the corrected coordinate quantities of the n spatial points and the reference coordinate values of the n spatial points, obtaining the calculated values of the q structural error parameters, and completing the calibration of the structural error parameters.

2. The method according to claim 1, wherein The structural errors of the two-dimensional orthogonal mirror system include an initial distance error term, an alignment offset error term, an alignment tilt error term, and a circular grating installation error term; The method further includes: Based on the initial distance error term, the alignment offset error term, the alignment tilt error term, and the circular grating installation error term, setting the q structural error parameters.

3. The method according to claim 2, wherein The constructing the error model based on q structural error parameters and the distance term, azimuth angle, and elevation angle of the spherical coordinate system associated with each structural error parameter includes: Based on q structural error parameters and the distance term of the spherical coordinate system associated with each structural error parameter, constructing a first error sub-model; Based on q structural error parameters and the azimuth angle of the spherical coordinate system associated with each structural error parameter, constructing a second error sub-model; Based on q structural error parameters and the elevation angle of the spherical coordinate system associated with each structural error parameter, constructing a third error sub-model; Based on the first error sub-model, the second error sub-model, and the third error sub-model, constructing the error model.

4. The method according to claim 3, characterized in that, The constructing the corrected coordinate quantities of the n spatial points based on the error model and the measured coordinate values of the n spatial points includes: Based on the first error sub-model and the distance term of the measured coordinate values of the n spatial points, constructing the distance term of the corrected coordinate quantities of the n spatial points; Based on the second error sub-model and the azimuth angle term of the measured coordinate values of the n spatial points, constructing the azimuth angle term of the corrected coordinate quantities of the n spatial points; Based on the third error sub-model and the elevation angle term of the measured coordinate values of the n spatial points, constructing the elevation angle term of the corrected coordinate quantities of the n spatial points.

5. The method according to claim 1, characterized in that, The obtaining the calculated values of the q structural error parameters based on the corrected coordinate quantities of the n spatial points and the reference coordinate values of the n spatial points includes: Constructing a rotation matrix and a translation matrix between the coordinate systems of the two-dimensional orthogonal mirror system and the laser tracker; Based on the rotation matrix and the translation matrix, mapping the reference coordinate values of the n spatial points to the coordinate system of the two-dimensional orthogonal mirror system to obtain the reference coordinate quantities of the n spatial points; Based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points, obtaining the calculated values of the q structural error parameters.

6. The method according to claim 5, wherein Obtaining the calculated values of the q structural error parameters based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points includes: Constructing an objective function based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points; Using the Levenberg-Marquardt method, taking the minimization of the sum of squares of the objective function as the optimization objective for iterative optimization to obtain the calculated values of the q structural error parameters.

7. The method according to claim 6, wherein The constructing an objective function based on the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points includes: Converting the corrected coordinate quantities of the n spatial points into a Cartesian coordinate system to obtain the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points; Constructing an objective function based on the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points.

8. The method according to claim 7, wherein The constructing an objective function based on the Cartesian coordinate quantities of the corrected coordinate quantities of the n spatial points and the reference coordinate quantities of the n spatial points includes: Taking the coincidence between the spatial point positions represented by the Cartesian coordinate quantities of the corrected coordinate quantities of each spatial point and the spatial point positions represented by the reference coordinate quantities of each corresponding spatial point as a constraint term to construct a point position constraint equation; Constructing the objective function based on the point position constraint equation.

9. The method according to claim 8, characterized in that The taking the coincidence between the spatial point positions represented by the Cartesian coordinate quantities of the corrected coordinate quantities of each spatial point and the spatial point positions represented by the reference coordinate quantities of each corresponding spatial point as a constraint term to construct a point position constraint equation includes: Taking the difference between the first item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the first item of the reference coordinate quantity of each corresponding spatial point being zero as a constraint term to construct a first sub-constraint equation of the point position; Taking the difference between the second item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the second item of the reference coordinate quantity of each corresponding spatial point being zero as a constraint term to construct a second sub-constraint equation of the point position; Taking the difference between the third item of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the third item of the reference coordinate quantity of each corresponding spatial point being zero as a constraint term to construct a third sub-constraint equation of the point position; Constructing the point position constraint equation based on the first sub-constraint equation of the point position, the second sub-constraint equation of the point position, and the third sub-constraint equation of the point position of each spatial point.

10. The method according to claim 9, wherein The using the Levenberg-Marquardt method, taking the minimization of the sum of squares of the objective function as the optimization objective for iterative optimization to obtain the calculated values of the q structural error parameters includes: Determining the constraint conditions of the Levenberg-Marquardt method based on the rotation matrix; Using the Levenberg-Marquardt method, based on the constraint conditions, taking the minimization of the sum of squares of the objective function as the optimization objective for iterative optimization to obtain the calculated values of the q structural error parameters.

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