A combined measurement method of a laser tracker and a binocular camera

Abstract

This invention discloses a combined measurement method consisting of a laser tracker and a binocular camera. The laser tracker measures the spatial coordinates of multiple target spheres, whose spatial distribution configurations have different lengths along all three axes. The coordinates of the measurement points are fitted into a spatial rectangular coordinate system to obtain the target sphere tool coordinate system. Coordinate axes with different directional accuracies are determined sequentially, with the X-axis representing the axis of highest accuracy. The homogeneous transformation matrix of the coordinate system is determined. A combined measurement system consisting of the laser tracker and the binocular camera is established, and error compensation is used within the combined measurement system to improve the overall system error and enhance the measurement system's accuracy. This improves the numerical stability of the coordinate system fitting, reducing uncertainty in the error aggregation stage from the source; it suppresses the leverage amplification effect of error in specific directions, controlling the growth trend of error during transmission. The two methods work together to achieve systematic suppression of error transmission throughout the entire process.

Description

Technical Field

[0001] This invention relates to a combined measurement method consisting of a laser tracker and a binocular camera, belonging to the field of optical three-dimensional measurement equipment applications. Background Technology

[0002] With the increasing demands for precision in 3D measurement of complex workpieces and large-scale measurements in advanced manufacturing, aerospace, and large equipment inspection, single measurement methods are no longer sufficient to meet the diverse measurement needs of high precision, high efficiency, and large range. Therefore, multi-sensor fusion-based combined optical 3D measurement systems are gradually becoming an important development direction, with the combination of laser trackers and binocular vision systems being particularly typical. Laser trackers possess extremely high absolute ranging accuracy and tracking capabilities, making them suitable for constructing global coordinate frames and control points; binocular vision systems, on the other hand, offer high efficiency and good visibility, making them suitable for the rapid acquisition of fine local features of complex structures. Combined measurement systems composed of laser trackers and binocular cameras offer comprehensive advantages in measurement performance, including large size, high precision, high efficiency, flexibility, and good visibility, and have a very broad range of engineering application prospects. However, these combined measurement systems are typically integrated in a chain-like manner, that is, by transforming the local coordinate system to the global coordinate system through multiple sets of common points. This can lead to the measurement errors of the preceding measurement devices being transmitted, accumulated, and even amplified step by step along the measurement chain during the coordinate system transformation process, ultimately affecting the overall measurement accuracy of the system.

[0003] Currently, research on accuracy optimization for such combined systems mainly focuses on two aspects: first, improving the accuracy of each individual sensor, such as by improving optomechanical design, optimizing calibration algorithms, or improving image processing accuracy; second, using traditional common point matching and least squares fitting methods for coordinate system alignment, and then performing simple error statistical analysis or compensation. However, the existing optimization methods have limited effectiveness and have reached a bottleneck, failing to significantly improve the accuracy of the measurement system. This is because, on the one hand, the sensing accuracy of a single measuring device has reached a bottleneck, and optimizing the device itself can no longer achieve significant accuracy improvements. On the other hand, after years of research, the algorithms for optimizing common point matching have become similar, resulting in very limited improvement in system accuracy. This invention focuses on improving and optimizing the errors generated by coordinate system transmission during the combination process of a combined measurement system, providing a new direction for improving the accuracy of combined measurement systems. Furthermore, in chain-like combined measurement systems, the measurement errors of the preceding measuring devices often exhibit a geometric amplification effect during transmission. Therefore, suppressing and optimizing transmission errors will play a significant role in improving the accuracy of the entire system. Summary of the Invention

[0004] The purpose of this invention is to provide a combined measurement method consisting of a laser tracker and a binocular camera, addressing the aforementioned problems.

[0005] The technical solution adopted in this invention is as follows: A combined measurement method consisting of a laser tracker and a binocular camera includes the following steps: S1, the laser tracker measures the spatial coordinates of multiple target spheres, with no fewer than 3 measurement points, and these points cannot be collinear. The spatial distribution configuration of the target spheres has different lengths along all three axes. The measured coordinates are marked as follows: where n is the number of measurement points; S2, fit the coordinates of the measuring point S1 into a spatial rectangular coordinate system to represent the spatial pose information of the target ball tool, and obtain the target ball tool coordinate system; S3, determine the homogeneous coordinate transformation matrix between the target ball tool coordinate system and the binocular camera; S4 obtains the complete coordinate transformation relationship from the laser tracker coordinate system to the binocular camera coordinate system, thereby establishing a combined measurement system composed of the laser tracker and the binocular camera.

[0006] Alternatively, the target sphere can be configured as an elongated ellipsoid.

[0007] Alternatively, in the target sphere spatial distribution configuration of the oblate spheroid, the dimensional ratio of the major and minor semi-axis and the thickness direction is 3.2:1:0.5.

[0008] A combined measurement method consisting of a laser tracker and a binocular camera includes the following steps: S1, the laser tracker measures the spatial coordinates of multiple target spheres, with at least 3 measurement points that are not collinear. The measured coordinates are then marked as follows: where n is the number of measurement points; S2, fit the coordinates of the measuring point S1 into a spatial rectangular coordinate system to represent the spatial pose information of the target ball tool, obtain the target ball tool coordinate system, and determine the coordinate axes of the target ball tool coordinate system with different directional accuracies in turn, with the X-axis being the coordinate axis direction with the highest accuracy; S3, determine the homogeneous coordinate transformation matrix between the target ball tool coordinate system and the binocular camera; S4 obtains the complete coordinate transformation relationship from the laser tracker coordinate system to the binocular camera coordinate system, thereby establishing a combined measurement system composed of the laser tracker and the binocular camera. In the combined measurement system, error compensation is used to improve the overall error of the system and improve the accuracy of the measurement system.

[0009] Alternatively, S2 can fit the coordinates of the S1 measurement point into a spatial rectangular coordinate system based on principal component analysis to obtain the pose relationship of the fitted coordinate system.

[0010] S21 is an alternative to the n measurement points in S1. Principal component analysis was used to fit the coordinate system and establish a rectangular coordinate system. Its origin is denoted as ; Origin of coordinates The coordinates are

[0011] Furthermore, the covariance matrix along the coordinate axes is calculated.

[0012]

[0013] In the above formula, It is a 3×3 symmetric positive semi-definite matrix. Eigenvalue decomposition of this matrix yields three eigenvalues. and eigenvectors , .

[0014]

[0015] Among them, eigenvalues The corresponding unit eigenvector , , They are orthogonal to each other in pairs.

[0016] S22, the rectangular coordinate system obtained from S21 by principal component analysis. Assign a coordinate system to the target ball tool .in, The origin of the coordinate system is eigenvectors As a coordinate system The X-axis, eigenvectors As a coordinate system Y-axis, eigenvector As a coordinate system The Z-axis. A coordinate system is established based on this. Not only do the coordinate axes have excellent directional accuracy, but the eigenvalue corresponding to the X-axis is the largest, making it the coordinate axis with the highest accuracy among the three coordinate axes.

[0017] Alternatively, in S4, Towards When performing coordinate system transformation, X-axis and Align the Z-axis with axial constraints.

[0018] Alternatively, in S4, let the initial state be denoted as the measurement coordinate system of the binocular camera. , Towards The rotation matrix in the homogeneous transformation matrix of the transformation is The corresponding translation vector is Based on the requirements of coupling compensation, X-axis and The Z-axis satisfies the collinearity requirement after homogeneous transformation; let ,represent The X-axis direction; let ,represent The Z-axis direction is then the final optimized rotation matrix. R satisfy

[0019] calculate The column vector of the first column

[0020]

[0021] Further calculations R The minimum required rotation angle, assuming the axis of rotation is... k The rotation angle is Then there is

[0022] The Rodriguez formula can be used to calculate

[0023]

[0024] In the above formula, K is the cross product matrix of k, and we have ;pass The original The first column is transformed as follows Then, further optimization is performed to achieve the minimum alignment residual. Let's assume that after... The transformed matrix is ,but

[0025] In the above formula accomplish Towards After coordinate system transformation X-axis and Alignment is achieved along the Z-axis, and then a rotation is obtained. rotation angle getting closer To minimize coordinate system transformation deviation, let's assume... The rotation matrix is

[0026]

[0027] The final rotation matrix is

[0028] To minimize alignment error, it is equivalent to... Maximize the trace

[0029] Maximize the above expression. ( (It is the arctangent function in the four quadrants), the following equation holds.

[0030] Therefore, the final rotation matrix R have

[0031] Determining the rotation matrix R Then, the translation vector t It can be obtained by minimizing the alignment error.

[0032] By combining all the formulas in S4, the original coordinate system transformation matrix is ​​optimized to achieve coordinate system transformation based on error coupling compensation, thereby improving the overall accuracy of the combined measurement system.

[0033] A combined measurement method consisting of a laser tracker and a binocular camera includes the two methods described above.

[0034] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: This invention provides a combined measurement method using a laser tracker and a binocular camera. Addressing the root causes of error generation and propagation, it employs a system-level optimization strategy that combines point set distribution configuration optimization with coordinate axis constraint alignment. This significantly improves the overall accuracy of the combined laser tracker and binocular camera measurement system. This invention not only provides a quantifiable, predictable, and optimizable accuracy improvement scheme for combined laser tracker and binocular camera systems, but also offers new theoretical basis and engineering practice paths for error control and accuracy design in a wider range of multi-level optical measurement systems. It possesses significant theoretical value and broad application prospects. Attached Figure Description

[0035] Figure 1 It is a combined measurement system of laser tracker and binocular camera.

[0036] Figure 2 It is a measurement working principle combining a laser tracker and a binocular camera.

[0037] Figure 3 This is a schematic diagram of the coordinate distribution of three target ball distribution configurations.

[0038] Figure 4 This is a schematic diagram of the physical experimental layout of the laser tracker and binocular camera measurement system. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings.

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0041] A combined measurement method consisting of a laser tracker and a binocular camera. S1, the laser tracker measures the spatial coordinates of multiple target spheres, with no fewer than 3 measurement points, and these points cannot be collinear. The spatial distribution configuration of the target spheres has different lengths along all three axes. The measured coordinates are marked as follows: where n is the number of measurement points; S2, fit the coordinates of the measuring point S1 into a spatial rectangular coordinate system to represent the spatial pose information of the target ball tool, and obtain the target ball tool coordinate system; S3, determine the homogeneous coordinate transformation matrix between the target ball tool coordinate system and the binocular camera; S4 obtains the complete coordinate transformation relationship from the laser tracker coordinate system to the binocular camera coordinate system, thereby establishing a combined measurement system composed of the laser tracker and the binocular camera.

[0042] like Figure 1 , 2As shown, the combined measurement system of laser tracker and binocular camera mainly consists of four parts. The laser tracker, as the first-stage measurement device, can perform high-precision spatial coordinate measurements on multiple target spheres. Generally, to reduce random errors in measurement, and considering the cost of target sphere arrangement and the ease of structural design of the target sphere tool, the number of target spheres at each measurement point needs to be no less than four and no more than six. The measurement target spheres are physically fixed to the target sphere tool, which is also bolted to the binocular camera. In other words, the measurement target spheres, the target sphere tool, and the binocular camera are physically connected to form a unified whole, and their relative pose relationships remain constant. The laser tracker fits the spatial coordinates of multiple target spheres to determine the coordinate system of the target sphere tool. The pose error of the coordinate system obtained by fitting the coordinates of the measurement points can be expressed as a six-degree-of-freedom uncertainty, specifically divided into the origin position error (the three-coordinate uncertainty of the origin position) and the direction errors of the three coordinate axes (manifested as a conical uncertainty domain formed by the uncertainty of the axis-end directions). Since the pose error of the fitted coordinate system directly intervenes in and is transmitted to the coordinate system of the subsequent binocular camera, affecting the measurement error of the entire measurement system, it is essential to optimize the pose accuracy of the fitted coordinate system. The method proposed in this invention optimizes the spatial distribution structure of the measurement target spheres involved in coordinate system fitting, thereby obtaining a more accurate fitted coordinate system. Under the premise that the number of target spheres remains constant and the spatial envelope volume composed of all target spheres remains constant, improving the spatial distribution configuration of the target spheres can significantly improve the accuracy of the fitted coordinate system. The underlying logic is that by changing the spatial distribution configuration of the target spheres, the directional error of each axis of the fitted coordinate system can be effectively changed. Simultaneously, under the premise that the overall number of target spheres and the envelope volume remain constant, the impact of changing the target sphere distribution configuration on the position error of the coordinate system origin is negligible. In summary, changing the target sphere distribution configuration can effectively affect the overall pose error of the fitted coordinate system.

[0043] As another specific implementation, the target sphere's spatial distribution configuration is an elongated ellipsoid. Without considering the single-point errors and differences in the number of points, the changes in eigenvalues ​​caused by the spatial configuration of the point set will alter the directional errors of the coordinate axes. Calculations show that when the eigenvalues ​​of the fitted coordinate system are large and the differences between eigenvalues ​​are significant, the resulting coordinate system directional error is smaller. Furthermore, in engineering applications, the distribution of the measurement point set in a chain measurement system usually depends on a specific physical structure. Therefore, considering that the physical structure of the target tool always has size limitations, and generally should be smaller for easier portability and cost control, a necessary premise can be proposed before analyzing the optimal configuration of the point set: the volume contained in the spatial configuration of the measurement point set is fixed. Therefore, adopting an elongated ellipsoid ensures that the eigenvalues ​​and differences of the fitted coordinate system are large, while the volume is relatively small compared to other configurations.

[0044] In another specific implementation, in a target sphere spatial distribution configuration shaped like an oblate spheroid, the dimensional ratio of the major and minor axes and the thickness direction is 3.2:1:0.5. Theoretical calculations and analysis show that when the point set distribution exhibits a major-to-minor axis ratio of approximately 3.2:1: ( When the shape is an oblate spheroid (with a very small non-zero positive number), the overall error in the coordinate system orientation is minimized. This is considering the derived approximately optimal proportion. At that time, especially small This is not feasible in engineering applications. Furthermore, to ensure consistency between simulation analysis and physical experiments, and considering the robot's motion errors and arm span, the thickness of the oblate spheroid should not be too small. After comprehensive consideration, the final selected dimensional ratios of the oblate spheroid's semi-major and minor axes and its thickness are as follows: By adopting the distribution configuration and proportional relationship proposed in this invention, the optimal fitting coordinate system pose accuracy can be obtained, thereby improving the overall accuracy of the combined measurement system.

[0045] A combined measurement method consisting of a laser tracker and a binocular camera includes the following steps: S1, the laser tracker measures the spatial coordinates of multiple target spheres, with at least 3 measurement points that are not collinear. The measured coordinates are then marked as follows: where n is the number of measurement points; S2, fit the coordinates of the measuring point S1 into a spatial rectangular coordinate system to represent the spatial pose information of the target ball tool, obtain the target ball tool coordinate system, and determine the coordinate axes of the target ball tool coordinate system with different directional accuracies in turn, with the X-axis being the coordinate axis direction with the highest accuracy; S3, determine the homogeneous coordinate transformation matrix between the target ball tool coordinate system and the binocular camera; S4 obtains the complete coordinate transformation relationship from the laser tracker coordinate system to the binocular camera coordinate system, thereby establishing a combined measurement system composed of the laser tracker and the binocular camera. In the combined measurement system, error compensation is used to improve the overall error of the system and improve the accuracy of the measurement system.

[0046] The error propagation and evolution mechanism in an optical 3D chain measurement system can be represented by three stages: "condensation-mapping-coupling". In the error condensation stage, the measurement error of the preceding measuring device is first condensed into the position and attitude errors of the tool coordinate system through the observed coordinate values ​​of a spatially distributed set of measuring points. In the error mapping stage, the data from the preceding stage is synchronously mapped to the coordinate system of the following measuring device through the spatial pose transformation process. The magnitude and nature of the error remain unchanged during the mapping stage; only the value and direction change. The data from the preceding stage, combined with the measurement error of the following measuring device itself, ultimately manifests as the composite error value of the coordinate points in the measurement space of the following measuring device, geometrically represented by an error ellipsoidal distribution, thus completing the entire error propagation process between adjacent measuring devices. Therefore, in the combined measurement system composed of a laser tracker and a binocular camera, the target sphere tool coordinate system obtained by S2 fitting... The inherent uncertainty will be mapped and transferred to the stereo camera coordinate system. In the process of measurement, the error is coupled and superimposed with the measurement error of the binocular camera, thus converging to form the measurement error of the entire measurement system. The optimization method proposed in this invention employs a specific error compensation mechanism to effectively improve the measurement accuracy of the coupled system.

[0047] As another specific implementation method, S2 fits the coordinates of the measurement point S1 into a spatial rectangular coordinate system based on the principal component analysis method, and obtains the pose relationship of the fitted coordinate system.

[0048] Principal Component Analysis (PCA) aims to transform a set of interrelated index variables into a few independent principal components through linear combination, thereby achieving dimensionality reduction and information condensation. Each principal component is a linear combination of the original variables; the larger the variance, the more information the principal component contains.

[0049] As another specific implementation method, S21, for the n measurement points in S1 Principal component analysis was used to fit the coordinate system and establish a rectangular coordinate system. Its origin is denoted as ; Origin of coordinates The coordinates are

[0050] Furthermore, the covariance matrix along the coordinate axes is calculated.

[0051]

[0052] In the above formula, It is a 3×3 symmetric positive semi-definite matrix. Eigenvalue decomposition of this matrix yields three eigenvalues. and eigenvectors , .

[0053]

[0054] Among them, eigenvalues The corresponding unit eigenvector , , They are orthogonal to each other in pairs.

[0055] S22, the rectangular coordinate system obtained from S21 by principal component analysis. Assign a coordinate system to the target ball tool .in, The origin of the coordinate system is eigenvectors As a coordinate system The X-axis, eigenvectors As a coordinate system Y-axis, eigenvector As a coordinate system The Z-axis. A coordinate system is established based on this. Not only do the coordinate axes have excellent directional accuracy, but the eigenvalue corresponding to the X-axis is the largest, making it the coordinate axis with the highest accuracy among the three coordinate axes.

[0056] The coordinate system thus established Not only do the coordinate axes have excellent directional accuracy, but the eigenvalue corresponding to the X-axis is the largest, making it the coordinate axis with the highest accuracy among the three coordinate axes.

[0057] As another specific implementation method, in S4, in Towards When performing coordinate system transformation, X-axis and Align the Z-axis with axial constraints.

[0058] Due to coordinate system The errors along the three coordinate axes are different (the X-axis has the highest accuracy), therefore, different coupling methods between coordinate systems will lead to changes in the final system measurement accuracy. In the measurement error model of a stereo camera, the error growth rate in the depth direction (Z-axis) is significantly higher than that in the other two coordinate axes (X and Y directions). That is to say, in the stereo camera's own measurement coordinate system, when the target point is measured from near to far, the measurement error will increase significantly, mainly the Z-axis error will increase sharply. Combined with the coordinate system discussed in step two... The distribution characteristics of the coordinate axis direction uncertainty, in Towards When performing coordinate system transformation, if X-axis and By aligning the Z-axis with axial constraints, the low-precision directional error growth of the binocular coordinate system can be compensated by a high-precision fitted coordinate system, thereby improving the overall accuracy of the combined measurement system.

[0059] As another specific implementation, in S4, let the initial state be represented by the measurement coordinate system of the binocular camera as... , Towards The rotation matrix in the homogeneous transformation matrix of the transformation is The corresponding translation vector is Based on the requirements of coupling compensation, it is necessary to... X-axis and The Z-axis, after a homogeneous transformation, satisfies the collinearity requirement (the direction axes can be the same or opposite). Let... ,represent The X-axis direction; let ,represent The Z-axis direction. Then the final optimized rotation matrix. R Must meet

[0060] calculate The column vector of the first column

[0061]

[0062] Further calculations R The minimum required rotation angle. Let the axis of rotation be... k The rotation angle is Then there is

[0063] The Rodriguez formula can be used to calculate

[0064]

[0065] In the above formula, K yes k The cross product matrix has .pass It can achieve the original The first column is transformed as follows However, further optimization is needed to minimize the alignment residual. Let's assume that after... The transformed matrix is ,but

[0066] In the above formula already satisfied Towards After coordinate system transformation X-axis and Alignment is achieved along the Z-axis, but a winding is still needed. rotation angle getting closer To minimize coordinate system transformation deviation. Let's assume... The rotation matrix is

[0067]

[0068] The final rotation matrix is

[0069] To minimize alignment error, it is equivalent to... Maximize the trace

[0070] Maximize the above expression. ( (It is the arctangent function in the fourth quadrant), at which point the following equation holds.

[0071] Therefore, the final rotation matrix R have

[0072] Determining the rotation matrix R Then, the translation vector t It can be obtained by minimizing the alignment error.

[0073] By combining all the formulas in S4, the original coordinate system transformation matrix is ​​optimized to achieve coordinate system transformation based on error coupling compensation, thereby improving the overall accuracy of the combined measurement system.

[0074] A combined measurement method consisting of a laser tracker and a binocular camera includes the two methods described above. As another specific embodiment, Example Step 1: To verify the optimization effect of the target sphere distribution using the "flattened elongated ellipsoid" configuration proposed in this scheme, this embodiment proposes three different point set configurations: "quasi-spherical," "cuboid," and "flattened elongated ellipsoid." The dimensional ratio of the three perpendicular coordinate directions of the quasi-spherical is 1.01:1:0.99; the length-width-height ratio of the cuboid is 2:1.05:1; and the dimensional ratio of the three axes of the flattened elongated ellipsoid is 3.2:1:0.5. Based on the same envelope volume, and using the same number of target spheres (12), the spatial distribution of the three point set configurations is as follows... Figure 3 As shown, the corresponding coordinate distribution is shown in Table 1.

[0075] Table 1. Distribution of measuring point coordinates for three typical spatial configurations.

[0076] Step 2: A real measurement system consisting of a laser tracker and a binocular camera is used to physically verify the target ball distribution listed in Step 1. The structural and error parameters of the laser tracker and binocular camera used in this invention are derived from real measurement equipment, as detailed below. The measurement system error parameters of the laser tracker are as follows: angle measurement error is 1.238'', and distance measurement error is 15µm + 0.3µm / m. The structural parameters and measurement error parameters of the binocular camera are as follows: it adopts a symmetrical configuration, and the baseline distance is... Both cameras have a focal length of 100mm. The angle of intersection of the optical axes of the two cameras is The pixel error of the imaging plane is .

[0077] Step 3, use Figure 4 The experimental environment shown was used with a robot having an arm span of 1.6m to perform measurements according to the three target ball distributions shown in Table 1. Simultaneously, pose calibration was performed using tracker #1 to determine... Towards The coordinate system homogeneous transformation matrix was determined; system error verification was performed using tracker #2 to determine the magnitude of the system measurement error generated after using the calibrated matrix. The straight-line distance between tracker #1 and the binocular camera was approximately 2m, and the straight-line distance between tracker #2 and the binocular camera was approximately 7m. The calibration and verification error values ​​measured for the three spatial distributions are listed in Table 2. As can be seen from Table 2, after adopting the ellipsoidal distribution configuration, both the calibration and verification errors show a significant improvement in the overall accuracy of the measurement system.

[0078] Table 2. Measured error values ​​for three target ball distribution configurations.

[0079] Step 4: Further, firstly, only calibration methods without coupling compensation constraints (such as the widely used "Levenberg–Marquardt" algorithm) are used for... Figure 4 The experiment shown was calibrated and verified, and the average error obtained is shown in Table 2, with the corresponding coordinate system. To coordinate system homogeneous pose transformation matrix as follows

[0080] Furthermore, based on the "Levenberg–Marquardt" algorithm, the coupled compensation axis constraint alignment optimization algorithm proposed in this invention is used, and the average error values ​​obtained are shown in Table 2. At this time, the coordinate system... To coordinate system homogeneous pose transformation matrix as follows:

[0081] As can be seen from the data comparison in Table 2 above, the optimization method proposed in this invention results in a loss of calibration accuracy for the combined measurement system (from 0.15 to 0.17), but by... High-precision coordinate axis orientation and By constraining and aligning the low-precision coordinate axes, the overall measurement accuracy of the measurement system can be significantly improved (from 0.45 to 0.33). Therefore, compared with existing technologies, the accuracy optimization method proposed in this invention achieves a significant breakthrough in technical approach and implementation, possessing distinct technical advantages and broad application value.

[0082] Existing optimization methods are limited to improving single-machine accuracy or optimizing common point matching algorithms, but neither deeply analyzes the underlying mechanisms of error propagation, accumulation, and amplification in chained systems. This invention, for the first time, shifts the optimization focus from "single-machine accuracy" and "post-processing registration" to the error propagation process itself. It systematically suppresses the inherent "condensation-mapping-coupling" chained error propagation mechanism in coordinate system transformation, intervening at the source and propagation path of error generation, thus overcoming the limitations of previous methods that only compensated for the results.

[0083] By optimizing the spatial geometric layout of common target points, the numerical stability of coordinate system fitting is improved, reducing uncertainty in the error aggregation stage from the source. Constraints are introduced during the coordinate mapping stage to suppress the leverage effect of errors in specific directions and control the growth trend of errors during propagation. These two measures work together to achieve systematic suppression of error propagation throughout the entire process.

[0084] Because transmission errors in chained systems often exhibit a geometric amplification effect, even small suppression of these errors can lead to a multiplicative improvement in the final system accuracy. Experiments show that this method can significantly reduce the error component introduced by coordinate transmission without changing hardware performance, thus overcoming the bottleneck encountered by simply improving single-machine accuracy or modifying matching algorithms.

[0085] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. The invention extends to any new features or combinations disclosed in this specification, and any modifications, equivalent substitutions, and improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention. It is obvious to those skilled in the art that the invention is not limited to the details of the above exemplary embodiments, and that detailed technical features not disclosed in this embodiment, such as specific structures, are all prior art and can be obtained by those skilled in the art from the prior art. The connection method can be a fixed connection, a detachable connection, or an integral part; it can be a fixed connection, a movable connection, or a hinged connection; it can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific manner of the above terms in the embodiments of the present invention according to the specific circumstances, and this disclosure does not specifically limit this aspect.

Claims

1. A combined measurement method consisting of a laser tracker and a binocular camera, characterized in that: Includes the following steps: S1, the laser tracker measures the spatial coordinates of multiple target spheres, with at least 3 measurement points that cannot be collinear. The spatial distribution configuration of the target spheres has different lengths along all three axes. The measured coordinates are marked as follows: n is the number of measurement points; S2, fit the coordinates of the measuring point S1 into a spatial rectangular coordinate system to represent the spatial pose information of the target ball tool, and obtain the target ball tool coordinate system; S3, determine the homogeneous coordinate transformation matrix between the target ball tool coordinate system and the binocular camera; S4 obtains the complete coordinate transformation relationship from the laser tracker coordinate system to the binocular camera coordinate system, thereby establishing a combined measurement system composed of the laser tracker and the binocular camera.

2. The method as described in claim 1, characterized in that: The target sphere has a spatial distribution configuration of an elongated ellipsoid.

3. The method as described in claim 2, characterized in that: In the spatial distribution configuration of the target sphere, which is an oblate ellipsoid, the dimensional ratio of the major and minor semi-axis and the thickness direction is 3.2:1:0.

5.

4. A combined measurement method consisting of a laser tracker and a binocular camera, characterized in that: Includes the following steps: S1, the laser tracker measures the spatial coordinates of multiple target spheres, with at least 3 measurement points that are not collinear. The measured coordinates are then marked as follows: n is the number of measurement points; S2, fit the coordinates of the measuring point S1 into a spatial rectangular coordinate system to represent the spatial pose information of the target ball tool, obtain the target ball tool coordinate system, and determine the coordinate axes of the target ball tool coordinate system with different directional accuracies in turn, with the X-axis being the coordinate axis direction with the highest accuracy; S3, determine the homogeneous coordinate transformation matrix between the target ball tool coordinate system and the binocular camera; S4 obtains the complete coordinate transformation relationship from the laser tracker coordinate system to the binocular camera coordinate system, thereby establishing a combined measurement system composed of the laser tracker and the binocular camera. In the combined measurement system, error compensation is used to improve the overall error of the system and improve the accuracy of the measurement system.

5. The method as described in claim 4, characterized in that: S2 uses principal component analysis to fit the coordinates of the S1 measurement point into a spatial rectangular coordinate system, thereby obtaining the pose relationship of the fitted coordinate system.

6. The method as described in claim 5, characterized in that: S21, for the n measurement points in S1 Principal component analysis was used to fit the coordinate system and establish a rectangular coordinate system. Its origin is denoted as ; Origin of coordinates The coordinates are Furthermore, the covariance matrix along the coordinate axes is calculated. In the above formula, It is a 3×3 symmetric positive semi-definite matrix; Eigenvalue decomposition of this matrix yields three eigenvalues. and eigenvectors , ; Among them, eigenvalues The corresponding unit eigenvector , , Each pair of objects is orthogonal; S22, the rectangular coordinate system obtained from S21 by principal component analysis. Assign a coordinate system to the target ball tool .in, The origin of the coordinate system is eigenvectors As a coordinate system The X-axis, eigenvectors As a coordinate system Y-axis, eigenvector As a coordinate system The Z-axis. A coordinate system is established based on this. Not only do the coordinate axes have excellent directional accuracy, but the eigenvalue corresponding to the X-axis is the largest, making it the coordinate axis with the highest accuracy among the three coordinate axes.

7. The method as described in claim 6, characterized in that: In S4, Towards When performing coordinate system transformation, X-axis and Align the Z-axis with axial constraints.

8. The method as described in claim 7, characterized in that: In S4, let the initial state be represented by the measurement coordinate system of the stereo camera as . , Towards The rotation matrix in the homogeneous transformation matrix of the transformation is The corresponding translation vector is ; Based on the requirements of coupling compensation, X-axis and The Z-axis satisfies the collinearity requirement after homogeneous transformation; let ,represent The X-axis direction; let ,represent The Z-axis direction is then the final optimized rotation matrix. R satisfy calculate The column vector of the first column Further calculations R The minimum required rotation angle, assuming the axis of rotation is... k The rotation angle is Then there is The Rodriguez formula can be used to calculate In the above formula, K is the cross product matrix of k, and we have ;pass The original The first column is transformed as follows Then, further optimization is performed to achieve the minimum alignment residual. Let's assume that after... The transformed matrix is ,but In the above formula accomplish Towards After coordinate system transformation X-axis and Alignment is achieved along the Z-axis, and then a rotation is obtained. rotation angle getting closer To minimize coordinate system transformation deviation, let's assume... The rotation matrix is The final rotation matrix is To minimize alignment error, it is equivalent to... Maximize the trace Maximize the above expression. ( (It is the arctangent function in the four quadrants), the following equation holds. Therefore, the final rotation matrix R have Determining the rotation matrix R Then, the translation vector t It can be obtained by minimizing the alignment error. By combining all the formulas in S4, the original coordinate system transformation matrix is ​​optimized to achieve coordinate system transformation based on error coupling compensation, thereby improving the overall accuracy of the combined measurement system.

9. A combined measurement method consisting of a laser tracker and a binocular camera, characterized in that: This includes any of the methods described in 1-3 and any of the methods described in 4-8.

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