Calibration method of structural error parameters of two-dimensional orthogonal rotating mirror system

Abstract

The present invention provides a calibration method for the structural error parameters of a two-dimensional orthogonal rotating mirror system, which can be applied to the field of large-scale measurement technology. The calibration method includes: obtaining measured coordinate values ​​and reference coordinate values ​​of n spatial points; wherein the measured coordinate values ​​are in a spherical coordinate system and are measured using the two-dimensional orthogonal rotating mirror system, and the reference coordinate values ​​are measured using a laser tracker; constructing an error model based on q structural error parameters and a distance term, azimuth angle, and pitch angle of the spherical coordinate system associated with each structural error parameter; wherein 1≤q≤3n-6; constructing corrected coordinate values ​​of the n spatial points based on the error model and the measured coordinate values ​​of the n spatial points; and obtaining solution values ​​of the q structural error parameters based on the corrected coordinate values ​​of the n spatial points and the reference coordinate values ​​of the n spatial points, thereby completing the calibration of the structural error parameters.

Description

Technical Field

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

[0002] Large-scale spatial precision pose measurement technology is a core technology for automated, high-precision assembly of high-end equipment in fields such as aerospace and shipbuilding. A two-dimensional orthogonal rotating mirror system uses two-dimensional orthogonal axes to drive a rotating mirror to guide a light beam, utilizes laser ranging technology to obtain distance information, and combines it with a high-precision circular grating to obtain angle information for spherical coordinate measurement. It features high accuracy, a wide range, and efficient automation. However, in actual applications, a two-dimensional orthogonal rotating mirror system can be affected by multiple factors, including mechanical assembly errors, human error, and changes in the external environment, which can lead to reduced measurement performance and, in turn, measurement errors.

[0003] Therefore, it is urgent to conduct error analysis on the two-dimensional orthogonal rotating mirror 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 the structural error parameters of a two-dimensional orthogonal rotating mirror system to improve measurement accuracy. 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 using a two-dimensional orthogonal rotating mirror system, and the reference coordinate values ​​are measured using a laser tracker; constructing an error model based on q structural error parameters and the distance term, azimuth angle, and pitch angle of the spherical coordinate system associated with each structural error parameter; wherein 1≤q≤3n-6; constructing the corrected coordinate values ​​of the n spatial points based on the error model and the measured coordinate values ​​of the n spatial points; obtaining the solution values ​​of the q structural error parameters based on the corrected coordinate values ​​of the n spatial points and the reference coordinate values ​​of the n spatial points, thereby completing the calibration of the structural error parameters.

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

[0006] According to an embodiment of the present invention, the error model is constructed based on q structural error parameters and the distance terms, azimuth angles and pitch angles of the spherical coordinate system associated with each structural error parameter, including: constructing a first error sub-model based on the q structural error parameters and the distance terms of the 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 angles of the spherical coordinate system associated with each structural error parameter; constructing a third error sub-model based on the q structural error parameters and the pitch angles of the spherical coordinate system associated with each structural error parameter; and constructing the error model based on the first error sub-model, the second error sub-model and the third error sub-model.

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

[0008] According to an embodiment of the present invention, the above-mentioned correction coordinates of the n spatial points and the reference coordinates of the n spatial points are used to obtain the solution values ​​of q structural error parameters, including: constructing a rotation matrix and a translation matrix between the two-dimensional orthogonal mirror system and the coordinate system of 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 coordinates of the n spatial points; based on the correction coordinates of the n spatial points and the reference coordinates of the n spatial points, obtaining the solution values ​​of the q structural error parameters.

[0009] According to an embodiment of the present invention, the above-mentioned solution values ​​of the q structural error parameters are obtained based on the corrected coordinate values ​​of the n spatial points and the reference coordinate values ​​of the n spatial points, including: constructing an objective function based on the corrected coordinate values ​​of the n spatial points and the reference coordinate values ​​of the 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 goal, to obtain the solution values ​​of the above-mentioned q structural error parameters.

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

[0011] According to an embodiment of the present invention, the objective function is constructed based on the Cartesian coordinates of the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points, including: constructing a point constraint equation with the overlap between the spatial point position represented by the Cartesian coordinates of the corrected coordinates of each spatial point and the corresponding spatial point position represented by the reference coordinates of each spatial point as a constraint item; and constructing the objective function based on the point constraint equation.

[0012] According to an embodiment of the present invention, the point constraint equation is constructed with the overlap between the spatial point position represented by the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the spatial point position represented by the corresponding reference coordinate quantity of each spatial point as a constraint item, including: constructing a point first sub-constraint equation with 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 item; constructing a point second sub-constraint equation with 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 item; constructing a point third sub-constraint equation with 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 item; constructing the above-mentioned point constraint equation based on the above-mentioned point first sub-constraint equation, the above-mentioned point second sub-constraint equation and the above-mentioned point third sub-constraint equation of each spatial point.

[0013] According to an embodiment of the present invention, the above-mentioned Levenberg-Marquardt method is used to perform iterative optimization with minimizing the sum of squares of the above-mentioned objective function as the optimization goal to obtain the solution values ​​of the above-mentioned q structural error parameters, including: determining the constraints of the above-mentioned Levenberg-Marquardt method based on the above-mentioned rotation matrix; using the Levenberg-Marquardt method, based on the above-mentioned constraints, to perform iterative optimization with minimizing the sum of squares of the above-mentioned objective function as the optimization goal to obtain the solution values ​​of the above-mentioned q structural error parameters.

[0014] According to an embodiment of the present invention, by constructing an error model for multiple structural error parameters of the two-dimensional orthogonal rotating mirror system and the distance terms, azimuth angles and pitch angles of the spherical coordinate system associated with each structural error parameter, the structural error of the two-dimensional orthogonal rotating mirror system can be analyzed more deeply and detailed, and the structural error can be quantified to more accurately perform error compensation and improve the measurement accuracy of the two-dimensional orthogonal rotating mirror system. The system can also be calibrated regularly to improve the reliability of the two-dimensional orthogonal rotating mirror system. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

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

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

[0021] Figure 6 A schematic diagram illustrating a point position deviation between a corrected coordinate value and a reference coordinate value according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[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 exemplary only and are not intended to limit the scope of the present invention. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of embodiments of the present invention. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concept of the present invention.

[0023] The terms used herein are only for describing specific embodiments and are not intended to limit the present invention. The terms "comprise", "include", etc. used herein indicate the presence of the features, steps, operations and / or components, but do not exclude 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] When expressions such as "at least one of A, B, and C, etc." are used, they should generally be interpreted in accordance with 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 is not limited to a system having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, C, etc.).

[0026] A 2D orthogonal mirror system is a spherical coordinate measurement system consisting of a 2D turntable, a laser rangefinder, and a tracking mirror. The incident beam from the laser rangefinder is incident on the tracking mirror, which reflects the incident beam to the spatial point to be measured. The 2D orthogonal rotation axes of the 2D turntable and the ranging laser beam of the laser rangefinder respectively determine the azimuth, pitch, and distance terms of the spherical coordinate measurement system. Mechanical errors such as positional errors of the 2D turntable's orthogonal rotation axes, installation errors of the tracking mirror, and optical geometric errors such as alignment errors of the laser rangefinder's incident beam directly impact the measurement performance and accuracy of the 2D orthogonal mirror system.

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

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

[0029] In operation S110, measurement coordinate values ​​and reference coordinate values ​​of n spatial points are obtained; wherein the measurement coordinate values ​​are in a spherical coordinate system, the measurement coordinate values ​​are measured using a two-dimensional orthogonal rotating mirror system, and the reference coordinate values ​​are measured using a laser tracker.

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

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

[0032] In operation S140 , based on the corrected coordinate values ​​of the n spatial points and the reference coordinate values ​​of the n spatial points, solution values ​​of q structural error parameters are obtained, thereby completing the calibration of the structural error parameters.

[0033] According to an embodiment of the present invention, by constructing an error model for multiple structural error parameters of the two-dimensional orthogonal rotating mirror system and the distance terms, azimuth angles and pitch angles of the spherical coordinate system associated with each structural error parameter, the structural error of the two-dimensional orthogonal rotating mirror system can be analyzed more deeply and detailed, and the structural error can be quantified to more accurately perform error compensation and improve the measurement accuracy of the two-dimensional orthogonal rotating mirror system. The structural error parameters of the system can also be calibrated regularly to improve the reliability of the two-dimensional orthogonal rotating mirror system.

[0034] In one embodiment, a two-dimensional orthogonal mirror system includes a horizontal rotation stage, a vertical rotation stage, a tracking mirror, and a laser rangefinder. Ideally, the two-dimensional orthogonal mirror system has no structural errors, with the horizontal and vertical rotation stage's central axes of rotation being orthogonal. The tracking mirror's center is located at the orthogonal center of the horizontal and vertical rotation stages' central axes of rotation. In a Cartesian coordinate system for the two-dimensional orthogonal mirror system, the horizontal rotation stage's central axis is designated as the Z axis, the vertical rotation stage's central axis is designated as the Y axis, and the X axis is determined according to the right-hand rule.

[0035] In one embodiment, the measured coordinate value of the two-dimensional orthogonal rotating mirror system before correction can be expressed as ( ),in, The distance term representing the measured coordinate value, Indicates the azimuth of the measured coordinate value, Indicates the pitch angle of the measured coordinate value. The corrected coordinate value based on the correction relationship can be expressed as ( ),in, The distance term representing the corrected coordinate quantity, Indicates the azimuth of the corrected coordinates. Indicates the pitch angle of the corrected coordinates.

[0036] According to an embodiment of the present invention, the structural error of the two-dimensional orthogonal rotating mirror 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 mirror. , the distance term of the measured coordinate value is corrected, and the correction relationship can be expressed as:

[0039] (1).

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

[0041] like Figure 2 As shown in (a), in one embodiment, the alignment offset error term may include a horizontal axis offset error The center axis of rotation of the horizontal rotary table and the rotation center axis of the vertical rotation stage Non-orthogonality, horizontal axis offset error Characterizes the central axis of rotation of the horizontal rotation stage and the rotation center axis of the vertical rotation stage Based on the horizontal axis offset error , the distance item of the measured coordinate value and the pitch angle of the measured coordinate value are corrected. The correction relationship can be expressed as:

[0042] (2);

[0043] (3).

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

[0045] (4);

[0046] (5).

[0047] like 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 is not incident on the center of the tracking mirror, and the first incident beam offset error Characterizes the offset distance of the incident beam of the laser rangefinder in the first direction, the offset error of the second incident beam Characterizes the offset distance of the incident light 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 light beam offset error and the second incident beam deviation error , the azimuth and elevation angles of the measured coordinate values ​​are corrected. The correction relationship can be expressed as:

[0048] (6);

[0049] (7).

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

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

[0052] (8).

[0053] like Figure 3 As shown in (b), in one embodiment, the alignment tilt error term may include a horizontal axis tilt angle error The center axis of rotation of the horizontal rotary table and the rotation center axis of the vertical rotation stage Non-orthogonality, horizontal axis tilt angle error Characterizes the central axis of rotation of the horizontal rotation stage With the rotation center axis of the vertical rotation stage Based on the horizontal axis tilt angle error , the azimuth of the measured coordinate value is corrected, and the correction relationship can be expressed as:

[0054] (9).

[0055] like Figure 3 As shown in (c), 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 rotation stage. , the incident beam of the laser rangefinder and the rotation center axis of the horizontal rotating stage There is a tilt angle between the first incident beam and the deviation error Characterizing the component of the tilt angle in the first direction, the second incident beam deviation error Characterizes the component of the tilt angle in the second direction. Based on the deviation error of the first incident beam and the second incident beam deviation error , the azimuth and elevation angles of the measured coordinate values ​​are corrected. The correction relationship can be expressed as:

[0056] (10);

[0057] (11).

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

[0059] like Figure 4 As shown, in one embodiment, the circular grating installation error term may include the circular grating eccentricity error. Figure 4 As shown in (a), the center of the circular grating on the horizontal rotating stage is aligned with the rotation center of the horizontal rotating stage (the rotation center axis of the horizontal rotating stage). There is a deviation in the position of the circular grating on the horizontal rotating stage, such as Figure 4 As shown in (a), 0, 90, and 180 respectively represent the angle scales of the circular grating on the horizontal rotating stage. Figure 4 As shown in (b), the center of the circular grating of the vertical rotating stage is aligned with the rotation center of the vertical rotating stage (the rotation center axis of the vertical rotating stage). There is a deviation in the position of the circular grating on the vertical rotating stage, such as Figure 4 As shown in (b), 90 and -90 represent the angular scales of the circular grating on the vertical rotation stage.

[0060] The eccentricity error of the first circular grating Characterizes the offset distance between the center of the circular grating of the horizontal rotating stage and the rotation center of the horizontal rotating stage in the first direction; the eccentricity error of the second circular grating Characterizes the offset distance between the center of the circular grating of the horizontal rotating stage and the rotation center of the horizontal rotating stage in the second direction. Based on the eccentricity error of the first circular grating and the eccentricity error of the second circular grating , the azimuth of the measured coordinate value is corrected, and the correction relationship can be expressed as:

[0061] (12).

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

[0063] (13).

[0064] In one embodiment, for example, q may be 13. Based on the initial distance error term, the initial distance error may be set is the structural error parameter; based on the alignment offset error term, the horizontal axis offset error can be set separately , mirror offset error , the first incident beam deviation error , the second incident beam deviation error is the structural error parameter; based on the alignment tilt error term, the mirror tilt angle error can be set separately , horizontal axis tilt angle error , the first incident beam deviation error , the second incident beam deviation error is the structural error parameter; based on the circular grating installation error term, the first circular grating eccentricity error can be set separately , the eccentricity error of the second circular grating , the eccentricity error of the third circular grating , the fourth circular grating eccentricity error is the structural error parameter, 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 term 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 angle 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 pitch angle 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 term of the spherical coordinate system associated with each structural error parameter, the first error sub-model is constructed based on the above formulas (1), (2), and (4): The first error sub-model It represents the correction relationship between 13 structural error parameters and distance terms.

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

[0068] In one embodiment, based on the 13 structural error parameters and the pitch angle of the spherical coordinate system associated with each structural error parameter, the third error sub-model is constructed based on the above formulas (3), (5), (7), (11), and (13): The third error sub-model It shows the correction relationship between 13 structural error parameters and pitch angle terms.

[0069] Based on the first error submodel , the second error sub-model and the third error submodel , build the error model ,in, represents the distance term of the error model, represents the azimuth term of the error model, represents the pitch angle term of the error model.

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

[0071] In one embodiment, the measured coordinate values ​​of n spatial points can be expressed as ,in, Indicates the The distance term of the measured coordinate values ​​of the spatial points, Indicates the The azimuth of the measured coordinate value of a spatial point, Indicates the The pitch angle of the measured coordinates of a space point, where .

[0072] In one embodiment, the corrected coordinates of n spatial points are It can be expressed as:

[0073] (14);

[0074] in, Indicates the The distance term of the corrected coordinates of the space points, Indicates the The azimuth term of the corrected coordinates of a spatial point, Indicates the The pitch angle term of the corrected coordinates of a spatial point.

[0075] In one embodiment, there are multiple ways to calibrate the parameters of the error model: point constraint calibration method, plane constraint calibration method, straight line constraint calibration method, and spherical constraint calibration method. The plane constraint calibration method is difficult to obtain a high-precision constraint plane, and the error transfer coefficient of the plane constraint method itself is high, so the result accuracy is not high. The straight line constraint also has a high error transfer coefficient, and the error parameter sensitivity is not high. Although the spherical 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 constraint calibration method is not only simple to implement, 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 positions of calibration points in space, to form point position constraints with the positions of the calibration points remaining unchanged, and to establish a calibration field.

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

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

[0079] In one embodiment, the rotation matrix is ​​constructed and translation matrices :

[0080] (15);

[0081] (16).

[0082] In one embodiment, the reference coordinates of n spatial points are It can be expressed as:

[0083] (17).

[0084] According to an embodiment of the present invention, an objective function is constructed based on the corrected coordinates of n spatial points and the reference coordinates of n spatial points; using the Levenberg-Marquardt method, iterative optimization is performed with minimizing the sum of squares of the objective function as the optimization goal to obtain the solution values ​​of q structural error parameters.

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

[0086] In one embodiment, the corrected coordinates of n spatial points are Convert to Cartesian coordinate system and get the Cartesian coordinates of the corrected coordinates of n spatial points .

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

[0088] In one embodiment, The position constraint equation of a 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 first sub-constraint equation of the point position is constructed by taking the difference between the first term of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the first term of the corresponding reference coordinate quantity of each spatial point as zero as a constraint term; the second sub-constraint equation of the point position is constructed by taking the difference between the second term of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the second term of the corresponding reference coordinate quantity of each spatial point as zero as a constraint term; the third sub-constraint equation of the point position is constructed by taking the difference between the third term of the Cartesian coordinate quantity of the corrected coordinate quantity of each spatial point and the third term of the corresponding reference coordinate quantity of each spatial point as zero as a constraint term; the point position constraint equation 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.

[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 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, which satisfies the following six constraints:

[0102] (twenty four).

[0103] In one embodiment, using the least squares method to solve the system of equations is an efficient solution. The nonlinear multivariate equations are transformed into a nonlinear least squares problem, and the objective function in the least squares method is solved through iterative optimization.

[0104] In one embodiment, formula (23) is transformed into a nonlinear least squares problem and the optimization objective function is:

[0105] (25);

[0106] Among them, the parameters to be solved Including q structural error parameters, rotation matrix and translation matrices The number of construction parameters is 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 to solve and obtain the solution values ​​of q structural error parameters and 12 rotation matrices and translation matrices The calculated values ​​of the construction parameters of .

[0107] The following is an experimental example to further illustrate the calibration method of the structural error parameters of the two-dimensional orthogonal rotating mirror system of the present invention.

[0108] Figure 5 A schematic diagram of a control field network according to an experimental embodiment of the present invention is shown.

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

[0110] In one embodiment, a higher-precision laser tracker is used within the control field network to measure the reference coordinate values ​​of 24 spatial points, as shown in Table 1. A two-dimensional orthogonal rotating mirror system is used to simultaneously measure the spherical coordinate system coordinate values ​​of the same 24 spatial points, as shown in Table 2.

[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 solved using the Levenberg-Marquardt algorithm to obtain the solution values ​​of the 13 structural error parameters, as shown in Table 3 below. At the same time, 12 rotation matrices are obtained. and translation matrices The calculated values ​​of the construction parameters of .

[0116] Table 3

[0117]

[0118] According to the calculated values ​​of the 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. and translation matrices The solution values ​​of the construction parameters are used to map the reference coordinate values ​​of the 24 space points to the coordinate system of the two-dimensional orthogonal rotating mirror system to obtain the reference coordinate values ​​of the 24 space points.

[0119] Figure 6 A schematic diagram illustrating a point position deviation between a corrected coordinate value and a reference coordinate value according to an embodiment of the present invention is shown.

[0120] like Figure 6 As shown in the figure, the horizontal axis represents the calibration points of 24 spatial points, and the vertical axis represents the point deviation, in mm. Figure 6 As shown, using the structural error parameter calibration method for a two-dimensional orthogonal rotating mirror system of the present invention, the maximum point deviation after correction of the measured coordinate values ​​is 1.270mm, and the average point deviation is 0.584mm. Using the structural error parameter calibration method for a two-dimensional orthogonal rotating mirror system of the present invention, the measurement accuracy of the corrected two-dimensional orthogonal rotating mirror system can meet the accuracy requirements of large-scale measurements.

[0121] The present invention's method for calibrating the structural error parameters of a two-dimensional orthogonal rotating mirror system constructs a geometric error model based on system kinematic analysis to quantify the impact of various structural error terms during measurement. An objective function is constructed based on a control field network, and the Levenberg-Marquardt algorithm is used to solve the least squares problem. This method calibrates the structural error parameters of the two-dimensional orthogonal rotating mirror system. Experimental verification demonstrates that the error model and structural error parameter calibration method meet the requirements of large-scale coordinate measurement.

[0122] It will be understood by those skilled in the art that the features described in the various embodiments of the present invention may be combined and / or coupled in various ways, even if such combinations or couplings are not explicitly described in the present invention. In particular, the features described in the various embodiments of the present invention may be combined and / or coupled in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or couplings fall within the scope of the present invention.

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

Claims

1. A method for calibrating the structural error parameters of a two-dimensional orthogonal rotating mirror system, characterized in that: The calibration method comprises: Obtaining measurement coordinate values ​​and reference coordinate values ​​of n spatial points; wherein the measurement coordinate values ​​are in a spherical coordinate system, the measurement coordinate values ​​are measured using a two-dimensional orthogonal rotating mirror system, and the reference coordinate values ​​are measured using a laser tracker; An error model is constructed based on q structural error parameters and a distance term, an azimuth angle, and an elevation angle of the spherical coordinate system associated with each structural error parameter; wherein 1≤q≤3n-6; The constructing of the error model based on the 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: constructing a first error sub-model based on q structural error parameters and a distance term of the spherical coordinate system associated with each structural error parameter; constructing a second error sub-model based on q structural error parameters and an azimuth of the spherical coordinate system associated with each structural error parameter; constructing a third error sub-model based on q structural error parameters and the pitch angle of the spherical coordinate system associated with each structural error parameter; and constructing the error model based on the first error sub-model, the second error sub-model and the third error sub-model; Constructing corrected coordinates of the n spatial points based on the error model and the measured coordinate values ​​of the n spatial points; Based on the corrected coordinate values ​​of the n spatial points and the reference coordinate values ​​of the n spatial points, the solution values ​​of q structural error parameters are obtained, and the calibration of the structural error parameters is completed.

2. The method according to claim 1, characterized in that The structural error of the two-dimensional orthogonal rotating mirror system includes 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 comprises: The 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.

3. The method according to claim 2, characterized in that The constructing the corrected coordinates of the n spatial points based on the error model and the measured coordinate values ​​of the n spatial points includes: constructing distance terms of the corrected coordinates of the n spatial points based on the first error sub-model and the distance terms of the measured coordinate values ​​of the n spatial points; constructing azimuth terms of the corrected coordinates of the n spatial points based on the second error sub-model and the azimuth terms of the measured coordinate values ​​of the n spatial points; Based on the third error sub-model and the pitch angle terms of the measured coordinate values ​​of the n spatial points, the pitch angle terms of the corrected coordinate values ​​of the n spatial points are constructed.

4. The method according to claim 1, wherein The method of obtaining the solution values ​​of q structural error parameters based on the corrected coordinate values ​​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 two-dimensional orthogonal mirror system and the coordinate system of the laser tracker; Based on the rotation matrix and the translation matrix, the reference coordinate values ​​of the n spatial points are mapped to the coordinate system of the two-dimensional orthogonal mirror system to obtain the reference coordinate values ​​of the n spatial points; Based on the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points, the calculated values ​​of the q structural error parameters are obtained.

5. The method according to claim 4, characterized in that The step of obtaining the solution values ​​of the q structural error parameters based on the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points includes: constructing an objective function based on the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points; The Levenberg-Marquardt method is used to perform iterative optimization with minimizing the sum of squares of the objective function as the optimization goal, thereby obtaining the solution values ​​of the q structural error parameters.

6. The method according to claim 5, characterized in that The constructing of the objective function based on the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points includes: Converting the corrected coordinates of the n spatial points into a Cartesian coordinate system to obtain Cartesian coordinates of the corrected coordinates of the n spatial points; An objective function is constructed based on the Cartesian coordinates of the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points.

7. The method according to claim 6, characterized in that The constructing of the objective function based on the Cartesian coordinates of the corrected coordinates of the n spatial points and the reference coordinates of the n spatial points includes: The point position constraint equation is constructed by taking the coincidence between the spatial point position represented by the Cartesian coordinate value of the corrected coordinate value of each spatial point and the spatial point position represented by the corresponding reference coordinate value of each spatial point as a constraint term; Based on the point constraint equation, the objective function is constructed.

8. The method according to claim 7, characterized in that The point position constraint equation is constructed by taking the overlap between the spatial point position represented by the Cartesian coordinate value of the corrected coordinate value of each spatial point and the spatial point position represented by the corresponding reference coordinate value of each spatial point as a constraint term, including: The first sub-constraint equation of the point position is constructed by taking the difference between the first term of the Cartesian coordinate of the corrected coordinate of each spatial point and the first term of the corresponding reference coordinate of each spatial point as zero as the constraint term; The second sub-constraint equation of the point position is constructed by taking the difference between the second term of the Cartesian coordinate of the corrected coordinate of each spatial point and the second term of the corresponding reference coordinate of each spatial point as zero as a constraint term; The third sub-constraint equation of the point position is constructed by taking the difference between the third term of the Cartesian coordinate of each spatial point's corrected coordinate and the third term of the corresponding reference coordinate of each spatial point as zero as the constraint term; The point constraint equation is constructed based on the point first sub-constraint equation, the point second sub-constraint equation and the point third sub-constraint equation of each spatial point.

9. The method according to claim 8, characterized in that The Levenberg-Marquardt method is used to perform iterative optimization with minimizing the sum of squares of the objective function as the optimization goal to obtain the solution values ​​of the q structural error parameters, including: Determining constraints of the Levenberg-Marquardt method based on the rotation matrix; The Levenberg-Marquardt method is used to perform iterative optimization based on the constraints and with minimizing the sum of squares of the objective function as the optimization goal, to obtain the solution values ​​of the q structural error parameters.

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