Error modeling method and system based on CCD camera pair assembly system

Abstract

The application provides an error modeling method and system based on a CCD camera alignment assembly system, and relates to the technical field of high-precision electronic manufacturing assembly, and comprises the following steps: obtaining the internal and external parameters of the CCD camera through calibration, establishing the conversion relationship between the camera and the mechanical coordinate system, and constructing a collaborative calibration error tree; controlling the movement of the motion platform, synchronously collecting the pose and environmental temperature data, decomposing the vibration and thermal deformation error components through time-frequency analysis and superimposing them into dynamic errors; extracting the positioning error based on the pose data, combining the distortion parameters to construct a mechanical-optical coupling error map; and finally, fusing the collaborative calibration error tree, the dynamic errors and the coupling error map to generate a global error map, thereby completing the error modeling of the CCD camera-based alignment assembly system. The application improves the precision and applicability of error modeling.

Description

Technical Field

[0001] This invention relates to the field of high-precision electronic manufacturing and assembly technology, specifically to an error modeling method and system based on a CCD camera alignment and assembly system. Background Technology

[0002] With the development of modern industrial automation and precision manufacturing technologies, CCD cameras, due to their high resolution and real-time imaging capabilities, are widely used in alignment and assembly systems to achieve high-precision automated assembly. However, in practical applications, the accuracy of CCD camera alignment and assembly systems is affected by various factors, including camera calibration errors, positioning errors of the mechanical motion platform, and interference from environmental factors. Traditional error analysis typically focuses on a single error source, such as compensating for imaging errors through the calibration of the intrinsic and extrinsic parameters of a single camera, or using mechanical correction methods to reduce platform motion errors. However, these methods fail to fully consider the coupling effect between the optical and mechanical systems, resulting in limitations in error compensation that make it difficult to meet the requirements of high-precision assembly.

[0003] Furthermore, mechanical motion platforms are subject to vibration and thermal deformation during operation, generating dynamic errors. These dynamic errors are time-varying and complex, making them difficult to describe using static calibration methods. Simultaneously, the correlation between camera distortion parameters and mechanical errors has not been fully studied, resulting in insufficient overall error modeling. This is particularly true when multi-camera collaboration is involved, as the relative pose errors between cameras and their propagation paths are not effectively quantified, thus limiting the system's ability to predict and compensate for global errors. Therefore, existing technologies urgently require a method that can comprehensively consider multi-source errors and quantify their interactions to improve the accuracy and reliability of CCD camera alignment and assembly systems.

[0004] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to provide an error modeling method and system based on a CCD camera alignment and assembly system, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] An error modeling method for a CCD camera alignment and assembly system includes the following steps:

[0008] The intrinsic and extrinsic parameters of each CCD camera in the alignment and assembly system are obtained by calibrating the target. The intrinsic parameters include focal length, principal point coordinates, pixel size and distortion parameters, and the distortion parameters include radial distortion coefficient and tangential distortion coefficient. The extrinsic parameters are the rotation matrix and translation vector of the camera relative to the mechanical coordinate system.

[0009] Based on the intrinsic and extrinsic parameters, the transformation relationship between each camera coordinate system and the machine coordinate system is established, and a collaborative calibration error tree between cameras is constructed. The collaborative calibration error tree includes the relative pose parameters and error propagation paths between cameras.

[0010] Based on the aforementioned conversion relationship, the motion platform is controlled to perform alignment motion, and real-time pose data and ambient temperature data of the motion platform are collected simultaneously. The pose data includes platform position, velocity, and acceleration data.

[0011] Time-frequency analysis is performed on the pose data to decompose it into vibration error components and thermal deformation error components. The vibration error components are quantified by establishing an acceleration-vibration response mapping relationship, and the thermal deformation error components are characterized by constructing a linear relationship between temperature and thermal deformation. The two types of error components are superimposed to form a dynamic error.

[0012] Based on the pose data, the positioning error data of the mechanical motion platform is extracted, and a mechanical-optical coupling error map is constructed by combining the distortion parameters.

[0013] The collaborative calibration error tree, dynamic error, and mechanical-optical coupling error map are fused to generate a global error map, thereby completing the error modeling of the CCD camera-based alignment and assembly system.

[0014] Furthermore, the intrinsic and extrinsic parameters of each CCD camera are obtained by calibrating the target. The specific logic behind this is as follows:

[0015] A high-precision checkerboard calibration target is selected and fixed on a flat platform for adjusting its posture. A CCD camera is controlled to capture at least 10 sets of clear images containing the complete target from different angles, distances, and orientations, ensuring that the target covers different areas of the camera's field of view in the images. The acquired images are preprocessed, and the pixel coordinates of the checkerboard corner points are extracted using the Harris corner detection algorithm. A world coordinate system is established with a corner point on the target plane as the origin, and the world coordinate system coordinates of each corner point are determined based on the actual physical size of the target. Using the Zhang calibration algorithm, with the pixel coordinates of the corner points and the world coordinate system coordinates as input, a perspective projection equation is constructed. The camera's intrinsic parameters and the corresponding extrinsic parameters for each image are obtained by solving the least squares method. The solved parameters are verified, and the reprojection error is calculated. If the reprojection error is within a preset threshold, the calibration result is considered valid; otherwise, images are reacquired and parameters are solved again. The reprojection error refers to the difference between the pixel coordinates of the corner points in the world coordinate system projected onto the image using intrinsic and extrinsic parameters and the actual detected pixel coordinates.

[0016] The preprocessing includes grayscale correction and edge enhancement, based on the following formula:

[0017] ;

[0018] In the formula, For the original image in grayscale value at that location The corrected grayscale value. , These are the gain coefficient and the offset, respectively, which are determined by fitting the image gray-level distribution characteristics using the least squares method.

[0019] Edge enhancement using the Sobel operator:

[0020] ;

[0021] ;

[0022] ;

[0023] In the formula, For the enhanced edge response value, This represents the convolution operation. This indicates that the Sobel operator in the horizontal direction is connected to... The horizontal gradient value obtained after convolution is used to detect vertical edge changes in the image; It is through the Sobel operator in the vertical direction and The vertical gradient value obtained from convolution is used to detect horizontal edge changes in the image.

[0024] Furthermore, based on the intrinsic and extrinsic parameters, the transformation relationship between each camera coordinate system and the mechanical coordinate system is established through the camera imaging model. That is, the three-dimensional coordinates in the camera coordinate system are converted into image pixel coordinates using the intrinsic parameter matrix, and then the rigid transformation between the camera coordinate system and the mechanical coordinate system is achieved through the rotation matrix and translation vector of the extrinsic parameters.

[0025] Using the extrinsic parameters of each camera as a reference, the relative pose parameters between cameras are determined by analyzing the rotation matrix and translation vector between different camera extrinsic parameters. At the same time, based on the error propagation theory, the propagation path from the single-camera calibration error to the relative pose error between cameras is analyzed, and a collaborative calibration error tree containing the relative pose parameters and their error sources is constructed. The root node and intermediate nodes of the collaborative calibration error tree are error sources, the branches are error propagation directions, and the leaf nodes are the final relative pose errors between cameras. The relative pose parameters include the relative rotation matrix and the relative translation vector, and the relative pose error includes the relative rotation angle error and the relative translation vector error.

[0026] The conversion of 3D coordinates in the camera coordinate system to image pixel coordinates using an intrinsic parameter matrix is ​​based on the following formula:

[0027] ;

[0028] In the formula, For image pixel coordinates, ( () represents the three-dimensional coordinates in the camera coordinate system. This is the intrinsic parameter matrix; Indicates the focal length in the horizontal direction. Indicates the focal length in the vertical direction, ( The coordinates of the main points are obtained through the calibration process.

[0029] The rigid transformation between the camera coordinate system and the machine coordinate system is achieved by using the rotation matrix and translation vector of the extrinsic parameters. The formula used is as follows:

[0030] ;

[0031] In the formula, ( () represents the three-dimensional coordinates in the machine coordinate system. For rotation matrix, It is a translation vector. , and These represent the translation components of the camera coordinate system origin in the X, Y, and Z axes of the machine coordinate system, respectively, all obtained through the calibration process.

[0032] Furthermore, the formula for calculating the relative rotation matrix is ​​as follows:

[0033] ;

[0034] In the formula, Indicates camera Compared to a camera The relative rotation matrix, and Cameras ,camera The rotation matrix relative to the machine coordinate system is obtained through a calibration process; for The inverse matrix, and For the index of the CCD camera in the alignment assembly system, and ;

[0035] The formula for calculating the relative translation vector is as follows:

[0036] ;

[0037] In the formula, Indicates camera Compared to a camera The relative translation vector, and Cameras ,camera The translation vector relative to the machine coordinate system is obtained through the calibration process;

[0038] Based on error propagation theory, the propagation path from single-camera calibration error to relative pose error between cameras is analyzed, and its mathematical representation is as follows:

[0039] Rotation error propagation: Assume the camera The rotation angle error is ,camera The rotation angle error is The formula for calculating the relative rotation angle error is as follows:

[0040] ;

[0041] in, Indicates camera With camera The relative rotation angle error, The Jacobian matrix is ​​used to transfer rotational errors by the camera. rotation matrix It is derived that;

[0042] Translation error propagation: Assume the camera The translation vector error is ,camera The translation vector error is The formula for calculating the relative translation vector error is as follows:

[0043] ;

[0044] In the formula, Indicates camera With camera The relative translation vector error.

[0045] Furthermore, based on the established transformation relationship between the camera coordinate system and the mechanical coordinate system, the motion controller controls the motion platform to perform assembly and alignment movements according to a preset alignment trajectory; the platform position data is collected in real time, and velocity and acceleration data are obtained from the position data through differential operations; at the same time, the ambient temperature data at the motion platform is collected, and the sampling frequency is consistent with the pose data; the time stamp synchronization technology ensures that the timestamps of the pose data and the ambient temperature data are accurately aligned.

[0046] Furthermore, the pose data is decomposed in the frequency domain using the Fast Fourier Transform method:

[0047] ;

[0048] In the formula, For the frequency domain representation of the pose signal, This is the time-domain representation of the pose signal. For frequency, Represents a time variable. Represents the imaginary unit;

[0049] Set frequency threshold ,Will middle The high-frequency components are identified as vibration error components. middle The low-frequency components are identified as thermal deformation error components; the frequency threshold Based on the platform's vibration characteristics;

[0050] The vibration error component is inversely transformed to obtain the time-domain vibration signal, and a mapping relationship between acceleration and vibration amplitude is established. The thermal deformation error component is inversely transformed to obtain the time-domain thermal deformation signal, and a linear relationship between temperature and thermal deformation is established. The vibration error component and the thermal deformation error component are superimposed to form the dynamic error, and the dynamic error is smoothed by the sliding window averaging method. Finally, the optimized dynamic error is output. The size of the sliding window is set according to the system response time.

[0051] The logic behind establishing the mapping relationship between acceleration and vibration amplitude is as follows: for each acceleration... Calculate the corresponding vibration amplitude. The formula is as follows:

[0052] ;

[0053] In the formula, For the index of acceleration, Indicates acceleration Frequency domain representation of the generated vibration signal;

[0054] A polynomial fitting method is used to establish the mapping relationship between acceleration and vibration amplitude, as shown in the following formula:

[0055] ;

[0056] In the formula, Indicates acceleration The vibration amplitude below, Let be the order of the polynomial. Indicates the order index of the polynomial. The fitting coefficients are obtained by using the least squares method on ( Data was obtained through fitting.

[0057] The logic behind establishing a linear relationship between temperature and thermal deformation is as follows: based on the collected ambient temperature data... Data analysis was constructed by combining thermal deformation error components. ],in This is the index of the sampling time. Indicates at the sampling time The corresponding thermal deformation error component; the thermal deformation amount refers to the thermal deformation amount, which is obtained by converting the frequency domain signal back to the time domain through inverse Fourier transform, and obtaining the time domain value of the thermal deformation error component corresponding to the sampling time.

[0058] The following linear model is fitted using the least squares method:

[0059] ;

[0060] In the formula, The temperature coefficient is used to characterize the degree of thermal deformation caused by temperature changes. For ambient temperature, The initial temperature, The intercept is the thermal deformation at the initial temperature. and Through [ The data was obtained through linear regression calculations.

[0061] The accuracy of the linear model is verified by calculating the fitting residuals. If the root mean square of the residuals is within the preset range, the linear relationship is determined to be valid; otherwise, the temperature sampling range is expanded, data is collected again, and the model is fitted.

[0062] Furthermore, positioning error data of the mechanical motion platform is extracted based on the pose data, and the positioning error data includes platform backlash error, straightness error, and multi-axis non-orthogonality error;

[0063] Among them, platform return back clearance error The position deviation is calculated by moving in the forward and reverse directions at the same command position, based on the following formula:

[0064] ;

[0065] In the formula, , These are the actual positions during forward and reverse movement, respectively;

[0066] Straightness error The deviation between the actual trajectory and the ideal straight line is calculated using the root mean square formula, as follows:

[0067] ;

[0068] In the formula, For the first The actual trajectory offset of each sampling point For the first The ideal straight line fit value for each sampling point The number of sampling points. This is the index of the sampling points distributed along the measurement trajectory;

[0069] Multiaxial nonorthogonality error The two axes are determined by measuring the deviation of the actual included angle between the two axes from 90°. The two axes refer to two motion axes that are nominally orthogonal to each other in the alignment assembly system.

[0070] Sure The formula used is as follows:

[0071] ;

[0072] In the formula, This is the actual included angle between the two axes;

[0073] By combining the camera's distortion parameters, a mechanical-optical coupling error map is constructed. This map quantifies the platform's backlash error, straightness error, and multi-axis non-orthogonality error in matrix form; where the matrix... The expression is as follows:

[0074] ;

[0075] in, and These are the first-order and second-order coefficients of radial distortion, respectively. and denoted as the tangential distortion coefficient.

[0076] Furthermore, the collaborative calibration error tree, dynamic error, and mechanical-optical coupling error map are fused together. The collaborative calibration error tree provides the static transmission relationship of relative pose error between cameras, the dynamic error provides the time-varying error of vibration and thermal deformation, and the mechanical-optical coupling error map provides the quantitative correlation between platform positioning error and camera distortion. The three types of error sources are mapped to a unified mechanical coordinate system through a weighted fusion algorithm. After fusion, a comprehensive error evaluation index of the alignment and assembly system under the mechanical coordinate system is generated, thereby constructing a global error map. The global error map is stored in the form of a quantitative model, which includes the comprehensive error evaluation index of the alignment and assembly system and the contribution weight of each error, thereby completing the overall error modeling of the system.

[0077] The formula for calculating the comprehensive error evaluation index is as follows:

[0078] ;

[0079] In the formula, This is a comprehensive error assessment index. To define the relative pose error scalar of the collaborative calibration error tree, For dynamic error, For the error scalar of the mechanical-optical coupling error spectrum, based on the matrix Obtain by performing norm calculation. , and These are reference values ​​for the error scalars of relative pose error, dynamic error, and mechanical-optical coupling error map, respectively. , and The preset proportionality coefficient, and satisfies ;

[0080] The relative pose error scalar is calculated by: taking the relative rotation angle error... Multiply by characteristic length Convert it into a linearized rotation error; calculate this linearized rotation error and the relative translation vector error. The Euclidean norm yields a single scalar value, with length as its dimension, that comprehensively characterizes the relative pose deviation between cameras. ;in, Determined based on the working distance of the assembly system.

[0081] The present invention also provides an error modeling system based on a CCD camera alignment and assembly system. This error modeling system is used to execute the aforementioned error modeling method based on a CCD camera alignment and assembly system, including:

[0082] The camera calibration module is used to obtain the intrinsic and extrinsic parameters of each CCD camera in the alignment and assembly system through the calibration target. The intrinsic parameters include focal length, principal point coordinates, pixel size and distortion parameters. The distortion parameters include radial distortion coefficient and tangential distortion coefficient. The extrinsic parameters are the rotation matrix and translation vector of the camera relative to the mechanical coordinate system.

[0083] The coordinate transformation module is used to establish the transformation relationship between each camera coordinate system and the machine coordinate system based on the intrinsic and extrinsic parameters, and to construct a collaborative calibration error tree between cameras. The collaborative calibration error tree includes the relative pose parameters and error propagation paths between cameras.

[0084] The data acquisition module is used to control the motion platform to perform alignment motion based on the conversion relationship, and to simultaneously acquire the real-time pose data and ambient temperature data of the motion platform. The pose data includes platform position, velocity and acceleration data.

[0085] The error decomposition module is used to perform time-frequency analysis on the pose data, decomposing the pose data into vibration error components and thermal deformation error components; the vibration error components are quantified by establishing an acceleration-vibration response mapping relationship, and the thermal deformation error components are characterized by constructing a linear relationship between temperature and thermal deformation, and the two types of error components are superimposed to form a dynamic error.

[0086] A coupling map module is constructed to extract positioning error data of the mechanical motion platform based on the pose data, and to construct a mechanical-optical coupling error map by combining the distortion parameters.

[0087] The error fusion module is used to fuse the collaborative calibration error tree, dynamic error, and mechanical-optical coupling error map to generate a global error map, thereby completing the error modeling of the CCD camera alignment and assembly system.

[0088] Compared with the prior art, the beneficial effects of the present invention are:

[0089] This invention achieves quantitative analysis of error propagation relationships between multi-camera coordinate systems by constructing a collaborative calibration error tree, significantly improving the calibration accuracy of multi-camera systems. It employs time-frequency analysis to decompose pose data into vibration and thermal deformation error components, generating dynamic errors and effectively solving the modeling challenge of time-varying errors under high-speed motion. By constructing a mechanical-optical coupling error map, the interaction between mechanical positioning errors and camera distortion is systematically analyzed, providing a more comprehensive basis for error compensation. Finally, the global error map generated through multi-source error fusion accurately reflects the comprehensive error distribution of the system under various operating conditions. This invention not only improves the accuracy and applicability of error modeling but also enhances the overall reliability and stability of CCD camera alignment and assembly systems. Attached Figure Description

[0090] Figure 1 This is a schematic diagram of the overall method flow of the present invention;

[0091] Figure 2 This is a schematic diagram of the overall system modules of the present invention;

[0092] Figure 3 A bar chart showing the relative pose error scalar and the comprehensive error evaluation index;

[0093] Figure 4 This is a 3D bar chart of the relative pose error scalar, dynamic error, and comprehensive error evaluation index. Detailed Implementation

[0094] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0095] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0096] Example:

[0097] Please see Figure 1 The present invention provides a technical solution:

[0098] An error modeling method for a CCD camera alignment and assembly system includes the following steps:

[0099] Step 1: Obtain the intrinsic and extrinsic parameters of each CCD camera in the alignment and assembly system by calibrating the target. The intrinsic parameters include focal length, principal point coordinates, pixel size and distortion parameters. The distortion parameters include radial distortion coefficient and tangential distortion coefficient. The extrinsic parameters are the rotation matrix and translation vector of the camera relative to the mechanical coordinate system.

[0100] In this embodiment, the intrinsic and extrinsic parameters of each CCD camera are obtained by calibrating the target. The specific logic is as follows:

[0101] A high-precision checkerboard calibration target is selected and fixed on a flat platform for adjusting its posture. A CCD camera is controlled to capture at least 10 sets of clear images containing the complete target from different angles, distances, and orientations, ensuring that the target covers different areas of the camera's field of view in the images. The acquired images are preprocessed, and the pixel coordinates of the checkerboard corner points are extracted using the Harris corner detection algorithm. A world coordinate system is established with a corner point on the target plane as the origin, and the world coordinate system coordinates of each corner point are determined based on the actual physical size of the target. Using the Zhang calibration algorithm, with the pixel coordinates of the corner points and the world coordinate system coordinates as input, a perspective projection equation is constructed. The camera's intrinsic parameters and the corresponding extrinsic parameters for each image are obtained by solving the least squares method. The solved parameters are verified, and the reprojection error is calculated. If the reprojection error is within a preset threshold, the calibration result is considered valid; otherwise, images are reacquired and parameters are solved again. The reprojection error refers to the difference between the pixel coordinates of the corner points in the world coordinate system projected onto the image using intrinsic and extrinsic parameters and the actual detected pixel coordinates.

[0102] The preprocessing includes grayscale correction and edge enhancement, based on the following formula:

[0103] ;

[0104] In the formula, For the original image in grayscale value at that location The corrected grayscale value. , These are the gain coefficient and the offset, respectively, which are determined by fitting the image gray-level distribution characteristics using the least squares method.

[0105] Edge enhancement using the Sobel operator:

[0106] ;

[0107] ;

[0108] ;

[0109] In the formula, For the enhanced edge response value, This represents the convolution operation. This indicates that the Sobel operator in the horizontal direction is connected to... The horizontal gradient value obtained after convolution is used to detect vertical edge changes in the image; It is through the Sobel operator in the vertical direction and The vertical gradient value obtained from convolution is used to detect horizontal edge changes in the image.

[0110] Step 1 involves accurately obtaining the intrinsic and extrinsic parameters of each CCD camera using a calibration target. The intrinsic parameters include focal length, principal point coordinates, pixel size, and distortion parameters, while the extrinsic parameters are the camera's rotation matrix and translation vector relative to the mechanical coordinate system. Combining a high-precision calibration target with Zhang's calibration algorithm significantly improves calibration accuracy, ensuring the accuracy of both intrinsic and extrinsic parameters. Simultaneously, the reliability of the calibration results is verified through reprojection error verification, effectively reducing the generation of error sources. This step provides reliable parameter support for establishing the subsequent transformation relationship between the camera and the mechanical coordinate system, laying the foundation for the entire error modeling process.

[0111] Compared with existing technologies, this invention employs a multi-view calibration method based on a high-precision checkerboard target during the calibration process, and utilizes the Harris corner detection algorithm to extract checkerboard corners, improving corner detection accuracy. Simultaneously, the Zhang calibration algorithm is optimized using the least squares method, and the effectiveness of the calibration parameters is verified through reprojection error, ensuring the accuracy and reliability of the calibration results. Furthermore, grayscale correction and edge enhancement during preprocessing further enhance the accuracy of corner extraction. Therefore, this invention has significant advantages in calibration accuracy and error control, and can better meet the needs of high-precision alignment assembly systems. Step 1 provides accurate basic data support for error modeling, including the intrinsic and extrinsic parameters of the camera, ensuring the accuracy of subsequent transformation relationships between each camera and the mechanical coordinate system. At the same time, the high-precision calibration in this step can significantly reduce the accumulation of system errors caused by parameter errors, reducing uncertainty in the error propagation path from the source. Furthermore, accurate calibration results of intrinsic and extrinsic parameters provide a reliable data foundation for dynamic error analysis, construction of collaborative calibration error trees, and generation of mechanical-optical coupling error maps, ultimately ensuring the accuracy and effectiveness of the global error map, which is an important part of the entire error modeling method.

[0112] Step 2: Based on the intrinsic and extrinsic parameters, establish the transformation relationship between each camera coordinate system and the machine coordinate system, and construct a collaborative calibration error tree between cameras. The collaborative calibration error tree includes the relative pose parameters and error propagation paths between cameras.

[0113] In this embodiment, based on the intrinsic parameters and the extrinsic parameters, the transformation relationship between each camera coordinate system and the mechanical coordinate system is established through the camera imaging model. That is, the three-dimensional coordinates under the camera coordinate system are converted into image pixel coordinates using the intrinsic parameter matrix, and then the rigid transformation between the camera coordinate system and the mechanical coordinate system is achieved through the rotation matrix and translation vector of the extrinsic parameters.

[0114] Using the extrinsic parameters of each camera as a reference, the relative pose parameters between cameras are determined by analyzing the rotation matrix and translation vector between different camera extrinsic parameters. At the same time, based on the error propagation theory, the propagation path from the single-camera calibration error to the relative pose error between cameras is analyzed, and a collaborative calibration error tree containing the relative pose parameters and their error sources is constructed. The root node and intermediate nodes of the collaborative calibration error tree are error sources, the branches are error propagation directions, and the leaf nodes are the final relative pose errors between cameras. The relative pose parameters include the relative rotation matrix and the relative translation vector, and the relative pose error includes the relative rotation angle error and the relative translation vector error.

[0115] Specifically, using the extrinsic parameters (rotation matrix and translation vector) of each camera as a benchmark, the relative pose parameters between cameras are determined by calculating the relative rotation matrix (obtained by multiplying the inverses of the corresponding camera rotation matrices) and the relative translation vector (obtained by the difference between the corresponding camera translation vectors after transformation by the relative rotation matrix) between different camera extrinsic parameters. Simultaneously, based on error propagation theory, the propagation path of rotation angle error and translation vector error to relative rotation angle error and relative translation vector error between cameras during single-camera calibration is analyzed (achieved through the derivation of the error propagation Jacobian matrix and the formula for relative pose parameters), thereby constructing a collaborative calibration error tree. In this error tree, the root node and intermediate nodes represent error sources at various levels, branches indicate the direction of error propagation from the source to the terminal, and leaf nodes represent the final relative pose error between cameras (including relative rotation angle error and relative translation vector error) formed after propagation and superposition. This comprehensively characterizes the error composition and propagation logic of relative pose parameters in a multi-camera system.

[0116] The conversion of 3D coordinates in the camera coordinate system to image pixel coordinates using an intrinsic parameter matrix is ​​based on the following formula:

[0117] ;

[0118] In the formula, For image pixel coordinates, ( () represents the three-dimensional coordinates in the camera coordinate system. This is the intrinsic parameter matrix; Indicates the focal length in the horizontal direction. Indicates the focal length in the vertical direction, ( The coordinates of the main points are obtained through the calibration process.

[0119] The rigid transformation between the camera coordinate system and the machine coordinate system is achieved by using the rotation matrix and translation vector of the extrinsic parameters. The formula used is as follows:

[0120] ;

[0121] In the formula, ( () represents the three-dimensional coordinates in the machine coordinate system. For rotation matrix, It is a translation vector. , and These represent the translation components of the camera coordinate system origin in the X, Y, and Z axes of the machine coordinate system, respectively, all obtained through the calibration process.

[0122] The formula for calculating the relative rotation matrix is ​​as follows:

[0123] ;

[0124] In the formula, Indicates camera Compared to a camera The relative rotation matrix, and Cameras ,camera The rotation matrix relative to the machine coordinate system is obtained through a calibration process; for The inverse matrix, and For the index of the CCD camera in the alignment assembly system, and ;

[0125] The formula for calculating the relative translation vector is as follows:

[0126] ;

[0127] In the formula, Indicates camera Compared to a camera The relative translation vector, and Cameras ,camera The translation vector relative to the machine coordinate system is obtained through the calibration process;

[0128] Based on error propagation theory, the propagation path from single-camera calibration error to relative pose error between cameras is analyzed, and its mathematical representation is as follows:

[0129] Rotation error propagation: Assume the camera The rotation angle error is ,camera The rotation angle error is The formula for calculating the relative rotation angle error is as follows:

[0130] ;

[0131] in, Indicates camera With camera The relative rotation angle error, The Jacobian matrix is ​​used to transfer rotational errors by the camera. rotation matrix It is derived that;

[0132] Translation error propagation: Assume the camera The translation vector error is ,camera The translation vector error is The formula for calculating the relative translation vector error is as follows:

[0133] ;

[0134] In the formula, Indicates camera With camera The relative translation vector error.

[0135] Step 2 establishes the transformation relationship between the coordinate systems of each camera and the machine coordinate system based on intrinsic and extrinsic parameters, and constructs a collaborative calibration error tree among the cameras. This effectively achieves spatial coordinate unification and error propagation path modeling for the multi-camera system. The collaborative calibration error tree accurately describes the relative pose parameters between cameras and their error sources and propagation paths, systematically linking single-camera calibration errors with multi-camera system errors, making error analysis hierarchical and traceable. This method not only accurately quantifies the error propagation process of the multi-camera system but also provides a structured error representation for subsequent global error modeling.

[0136] Compared with existing technologies, this invention significantly improves the accuracy and interpretability of multi-camera system error modeling by introducing a collaborative calibration error tree. Traditional technologies typically focus only on single-camera calibration or simple inter-camera transformation relationships, lacking analysis of error propagation paths and their cumulative effects. This invention, however, analyzes the relative pose parameters of extrinsic parameters between cameras and, combined with error propagation theory, systematically analyzes the propagation path from single-camera calibration errors to relative pose errors between cameras. It also precisely quantifies the error propagation process through a mathematical model, effectively reducing the impact of multi-camera system error accumulation and achieving higher calibration accuracy and error analysis capabilities. Step 2 is the core of the entire error modeling method. By constructing a collaborative calibration error tree, it achieves global modeling of the sources and propagation processes of multi-camera system errors, providing a basic framework for subsequent dynamic error analysis and the generation of mechanical-optical coupling error maps. Simultaneously, the precise camera-machine coordinate system transformation relationship ensures the spatial consistency of the multi-camera system, and the hierarchical structure and clear error propagation path of the collaborative calibration error tree provide high-precision static error input for the final fusion of the global error map, ultimately improving the overall accuracy and reliability of the entire system error modeling.

[0137] Step 3: Based on the transformation relationship, control the motion platform to perform alignment motion, and simultaneously collect the real-time pose data and ambient temperature data of the motion platform. The pose data includes platform position, velocity and acceleration data.

[0138] In this embodiment, based on the established transformation relationship between the camera coordinate system and the machine coordinate system, the motion controller controls the motion platform to perform assembly and alignment movements according to a preset alignment trajectory; the platform position data is collected in real time, and velocity and acceleration data are obtained from the position data through differential operations; at the same time, the ambient temperature data at the motion platform is collected, and the sampling frequency is consistent with the pose data; the time stamp synchronization technology ensures that the timestamps of the pose data and the ambient temperature data are accurately aligned.

[0139] Step 3 controls the motion platform to perform alignment movements based on the transformation relationship between the camera and the machine coordinate system, while simultaneously collecting real-time pose data and ambient temperature data of the motion platform. This step comprehensively considers the dynamic behavior of the motion platform and changes in the external ambient temperature, providing crucial data for subsequent error analysis. Simultaneous collection of pose and temperature data, ensuring timestamp alignment, effectively avoids data deviation and distortion of error quantification results, thereby ensuring the reliability and accuracy of error modeling. Furthermore, by controlling the motion platform to move along a preset trajectory, the dynamic error performance of the assembly system in a real-world scenario can be systematically tested, improving the ability to model and describe errors under actual working conditions.

[0140] Compared with existing technologies, this invention accurately integrates dynamic data of the motion platform and ambient temperature data in step 3. Traditional technologies often ignore the impact of environmental factors on system errors or only collect static data without dynamic error quantification. Through time-stamping synchronization technology, this invention can ensure the temporal consistency of pose data and temperature data, effectively improving the accuracy and reliability of error quantification. Furthermore, this invention further refines the sources of platform dynamic errors, enabling independent analysis and quantification of vibration errors and thermal deformation errors. Existing technologies typically cannot distinguish or accurately characterize these complex error sources, thereby improving the comprehensiveness and applicability of error modeling. Step 3 is the core of dynamic error modeling. By collecting pose data and ambient temperature data of the motion platform in real time, it provides high-quality input for subsequent time-frequency analysis. This step not only accurately extracts and quantifies the system's vibration response and thermal deformation behavior but also tests the platform's motion error performance through a preset trajectory, thereby constructing an error model adaptable to real-world scenarios. Furthermore, the real-time data acquisition results from step 3 will be combined with the collaborative calibration error tree and the mechanical-optical coupling error map, providing an important basis for the dynamic analysis and fusion of the final global error map, ensuring the comprehensiveness and dynamic adaptability of error modeling.

[0141] Step 4: Perform time-frequency analysis on the pose data to decompose the pose data into vibration error components and thermal deformation error components; the vibration error components are quantified by establishing an acceleration-vibration response mapping relationship, and the thermal deformation error components are characterized by constructing a linear relationship between temperature and thermal deformation amount, and the two types of error components are superimposed to form dynamic error;

[0142] In this embodiment, the pose data is decomposed in the frequency domain using the Fast Fourier Transform method:

[0143] ;

[0144] In the formula, For the frequency domain representation of the pose signal, This is the time-domain representation of the pose signal. For frequency, Represents a time variable. Represents the imaginary unit;

[0145] Set frequency threshold ,Will middle The high-frequency components are identified as vibration error components. middle The low-frequency components are identified as thermal deformation error components; the frequency threshold Based on the platform's vibration characteristics;

[0146] Set frequency threshold and will The low-frequency components are determined to be thermal deformation errors. The high-frequency components are identified as vibration errors, based on the fundamental difference in physical characteristics between the two types of errors: thermal deformation, caused by changes in ambient temperature, involves slow temperature conduction and material expansion and contraction, resulting in low-frequency fluctuations that change gradually over time in the time-domain pose signal, corresponding to low-frequency components in the frequency domain; while vibration errors are caused by the mechanical vibration of the moving platform, exhibiting instantaneous, periodic, and high-frequency responses, manifesting as rapidly fluctuating signals in the time domain, corresponding to high-frequency components in the frequency domain. This is combined with pre-defined platform vibration characteristics. It can accurately distinguish the frequency domain distribution of the two types of errors and achieve effective decomposition.

[0147] The vibration error component is inversely transformed to obtain the time-domain vibration signal, and a mapping relationship between acceleration and vibration amplitude is established. The thermal deformation error component is inversely transformed to obtain the time-domain thermal deformation signal, and a linear relationship between temperature and thermal deformation is established. The vibration error component and the thermal deformation error component are superimposed to form the dynamic error, and the dynamic error is smoothed by the sliding window averaging method. Finally, the optimized dynamic error is output. The size of the sliding window is set according to the system response time.

[0148] The logic behind establishing the mapping relationship between acceleration and vibration amplitude is as follows: for each acceleration... Calculate the corresponding vibration amplitude. The formula is as follows:

[0149] ;

[0150] In the formula, For the index of acceleration, Indicates acceleration Frequency domain representation of the generated vibration signal;

[0151] Dependent variable This reflects the motion platform at a specific acceleration value. The maximum amplitude of the vibration signal generated under the excitation of [the system] in the high-frequency band, its physical meaning is a quantitative index of the vibration intensity of the system under the acceleration condition. The technical advantages are: by extracting the peak value in the frequency domain instead of the mean value in the time domain, it is possible to more sensitively capture the resonance effect and impact response caused by acceleration changes, providing characteristic data for establishing a high-precision vibration model; at the same time, using the maximum value instead of the average value can ensure the conservatism of error compensation and avoid positioning deviation caused by underestimation of amplitude.

[0152] A polynomial fitting method is used to establish the mapping relationship between acceleration and vibration amplitude, as shown in the following formula:

[0153] ;

[0154] In the formula, Indicates acceleration The vibration amplitude below, Let be the order of the polynomial. Indicates the order index of the polynomial. The fitting coefficients are obtained by using the least squares method on ( Data was obtained through fitting.

[0155] Dependent variable It is a continuous mapping function established through polynomial fitting, meaning that for any acceleration input, it predicts the amplitude of vibration that may be caused. The technical effect of this function is reflected in: firstly, it transforms discrete experimental data ( The first method transforms the acceleration into a continuous function to predict vibration at points where acceleration is not measured; the second method uses polynomial coefficients. It reveals the nonlinear relationship between vibration amplitude and acceleration; thirdly, it provides a calculation basis for real-time error compensation, and the system can dynamically estimate the vibration error based on the current acceleration a.

[0156] The logic behind establishing a linear relationship between temperature and thermal deformation is as follows: based on the collected ambient temperature data... Data analysis was constructed by combining thermal deformation error components. ],in This is the index of the sampling time. Indicates at the sampling time The corresponding thermal deformation error component; the thermal deformation amount refers to the thermal deformation amount, which is obtained by converting the frequency domain signal back to the time domain through inverse Fourier transform, and obtaining the time domain value of the thermal deformation error component corresponding to the sampling time.

[0157] The following linear model is fitted using the least squares method:

[0158] ;

[0159] In the formula, The temperature coefficient is used to characterize the degree of thermal deformation caused by temperature changes. For ambient temperature, The initial temperature, The intercept is the thermal deformation at the initial temperature. and Through [ The data was obtained through linear regression calculations.

[0160] The accuracy of the linear model is verified by calculating the fitting residuals. If the root mean square of the residuals is within the preset range, the linear relationship is determined to be valid; otherwise, the temperature sampling range is expanded, data is collected again, and the model is fitted.

[0161] Step 4 involves time-frequency analysis of the motion platform's pose data to decompose the error components into vibration error components and thermal deformation error components, which are then modeled and quantified separately. The core advantage of this step lies in accurately distinguishing dynamic errors from different sources and extracting the characteristics of vibration and thermal deformation from both frequency and time domain perspectives. By establishing a mapping relationship between acceleration and vibration response, and a linear relationship between temperature and thermal deformation, the variation law of dynamic errors can be effectively characterized and expressed quantitatively. Furthermore, superimposing the two types of dynamic error components to form the overall dynamic error and employing smoothing techniques to optimize the error results helps reduce the impact of data noise on error modeling, ensuring more accurate dynamic error analysis.

[0162] Compared with existing technologies, this invention employs a more systematic and refined analysis method in dynamic error modeling. Traditional techniques often only model the overall error, lacking independent analysis and separation of vibration and thermal deformation errors, resulting in unclear error sources and limited accuracy and applicability of the error model. This invention uses Fast Fourier Transform to perform frequency domain decomposition on pose data, scientifically dividing high-frequency vibration errors and low-frequency thermal deformation errors, and quantifying them separately using acceleration-vibration response mapping and temperature-thermal deformation relationships, thus more accurately characterizing the behavioral features of dynamic errors. Furthermore, combining the sliding window averaging method to smooth dynamic errors effectively reduces random noise interference, further improving the accuracy of error modeling. Step 4 plays a crucial role in the overall error modeling scheme, providing technical support for the accurate extraction and modeling of dynamic errors. By separating and independently quantifying vibration and thermal deformation error components, not only is the hierarchy and refinement of error modeling enhanced, but the analysis of error sources in dynamic environments is also supplemented, compensating for the shortcomings of static error analysis in the collaborative calibration error tree. Furthermore, the quantification results of dynamic errors provide dynamic compensation data for the construction of the mechanical-optical coupling error map, laying a solid foundation for the generation of the global error map. This step, in synergy with other steps, effectively improves the comprehensiveness of error modeling and its applicability in complex scenarios, providing a scientific basis for system error optimization and compensation.

[0163] Step 5: Extract positioning error data of the mechanical motion platform based on the pose data, and construct a mechanical-optical coupling error map by combining the distortion parameters;

[0164] In this embodiment, positioning error data of the mechanical motion platform is extracted based on the pose data. The positioning error data includes platform backlash error, straightness error, and multi-axis non-orthogonality error.

[0165] Among them, platform return back clearance error The position deviation is calculated by moving in the forward and reverse directions at the same command position, based on the following formula:

[0166] ;

[0167] In the formula, , These are the actual positions during forward and reverse movement, respectively;

[0168] Straightness error The deviation between the actual trajectory and the ideal straight line is calculated using the root mean square formula, as follows:

[0169] ;

[0170] In the formula, For the first The actual trajectory offset of each sampling point For the first The ideal straight line fit value for each sampling point The number of sampling points. This is the index of the sampling points distributed along the measurement trajectory;

[0171] Multiaxial nonorthogonality error The two axes are determined by measuring the deviation of the actual included angle between the two axes from 90°. The two axes refer to two motion axes that are nominally orthogonal to each other in the alignment assembly system.

[0172] Sure The formula used is as follows:

[0173] ;

[0174] In the formula, This is the actual included angle between the two axes;

[0175] By combining the camera's distortion parameters, a mechanical-optical coupling error map is constructed. This map quantifies the platform's backlash error, straightness error, and multi-axis non-orthogonality error in matrix form; where the matrix... The expression is as follows:

[0176] ;

[0177] in, and These are the first-order and second-order coefficients of radial distortion, respectively. and denoted as the tangential distortion coefficient.

[0178] Step 5 extracts positioning error data from the mechanical motion platform based on pose data and constructs a mechanical-optical coupling error map by combining it with camera distortion parameters. This map quantitatively characterizes the correlation between platform positioning error and camera imaging distortion in matrix form. The advantage of this step is that it comprehensively considers the inherent errors of the mechanical motion platform and optical imaging errors, establishing the mutual influence relationship between the mechanical and optical systems. This coupling analysis method can comprehensively reflect the impact of mechanical motion errors on image quality, thus providing more accurate data support for system error compensation. Furthermore, the matrix-form error map construction makes error quantification more intuitive and structured, making it more suitable for subsequent fusion of the global error map.

[0179] Compared with existing technologies, this invention proposes a coupled modeling method for mechanical and optical errors for the first time in step 5. Traditional technologies generally analyze mechanical or optical errors separately, making it difficult to fully reflect the complex interaction between the two. This invention not only extracts multiple key positioning errors of the mechanical motion platform but also constructs a unified mechanical-optical coupled error map by combining camera distortion parameters, which can more accurately describe the comprehensive impact of mechanical motion errors on optical imaging. This map-based error quantification method provides the possibility for multi-factor correlation analysis, making up for the shortcomings of existing error analysis methods. In addition, the use of matrix form to store error information improves the structure of error modeling, which is conducive to the iterative update and dynamic compensation of the error map. Step 5 is the key step in realizing the coupled error modeling of the mechanical-optical system. It combines the positioning error data of the mechanical platform with the distortion error of camera imaging to construct a mechanical-optical coupled error map, laying the foundation for dynamic error compensation in global error modeling. This step can not only quantitatively analyze the impact of the mechanical platform positioning error on the overall system accuracy but also provide important input data for the subsequent fusion of the collaborative calibration error tree, dynamic error, and mechanical-optical coupled error map. Furthermore, the results of this step provide a scientific basis for optimizing the error distribution of the system and improving the alignment accuracy, ultimately enhancing the error modeling accuracy and robustness of the entire alignment assembly system.

[0180] Step 6: The collaborative calibration error tree, dynamic error and mechanical-optical coupling error map are fused to generate a global error map, thereby completing the error modeling of the CCD camera alignment and assembly system.

[0181] In this embodiment, the collaborative calibration error tree, dynamic error, and mechanical-optical coupling error map are fused. The collaborative calibration error tree provides the static transmission relationship of relative pose error between cameras, the dynamic error provides the time-varying error of vibration and thermal deformation, and the mechanical-optical coupling error map provides the quantitative correlation between platform positioning error and camera distortion. The three types of error sources are mapped to a unified mechanical coordinate system through a weighted fusion algorithm. After fusion, a comprehensive error evaluation index of the alignment and assembly system under the mechanical coordinate system is generated, thereby constructing a global error map. The global error map is stored in the form of a quantitative model, which includes the comprehensive error evaluation index of the alignment and assembly system and the contribution weight of each error, thereby completing the overall error modeling of the system.

[0182] The formula for calculating the comprehensive error evaluation index is as follows:

[0183] ;

[0184] In the formula, This is a comprehensive error assessment index. To define the relative pose error scalar of the collaborative calibration error tree, For dynamic error, For the error scalar of the mechanical-optical coupling error spectrum, based on the matrix Obtain by performing norm calculation. , and These are reference values ​​for the error scalars of relative pose error, dynamic error, and mechanical-optical coupling error map, respectively. , and The preset proportional coefficient satisfies ,and The reasons are as follows: Dynamic error is a time-varying disturbance that exists in real time during the operation of the alignment and assembly system. It directly affects the alignment accuracy of the motion platform and the stability of the assembly action, and has the most significant impact on the final assembly quality of the system. Therefore, it is given the largest weight. The relative pose error scalar of the collaborative calibration error tree determines the reference accuracy of multi-camera collaborative alignment. It is the core source of the system's static error. Its impact is second only to dynamic error but higher than mechanical-optical coupling error. Therefore, it is given a medium weight. Although the mechanical-optical coupling error scalar is related to the platform positioning error and camera distortion, its impact can be weakened through early calibration optimization. Its contribution to the overall system error is the lowest. Therefore, it is given the smallest weight.

[0185] Among them, reference value , and The determination method is as follows: The scalar mean of the relative pose error obtained by the system under standard operating conditions through collaborative calibration experiments with multiple sets of cameras; The average dynamic error statistics collected when the motion platform is running unloaded along a preset trajectory; This is a theoretical threshold for the coupled error scalar, calculated based on the system design accuracy requirements, the allowable range of mechanical positioning error, and camera distortion parameters. All three parameters were determined through calibration experiments and performance tests before the system left the factory, and are used to unify the error dimensions of different dimensions into comparable relative error values.

[0186] The relative pose error scalar is calculated by: taking the relative rotation angle error... Multiply by characteristic length Convert it into a linearized rotation error; calculate this linearized rotation error and the relative translation vector error. The Euclidean norm yields a single scalar value, with length as its dimension, that comprehensively characterizes the relative pose deviation between cameras. ;in, Determined based on the working distance of the assembly system.

[0187] For matrix Obtain norm by performing norm calculation The formula used is as follows:

[0188] ;

[0189] In the formula, Representation matrix The Middle Line number Column elements, Represents a matrix Perform norm calculation. Specifically, in the calculation, first... Squaring each element, summing all the squared values, and finally taking the square root of the sum gives the error scalar of the mechanical-optical coupling error map. By using this norm calculation, the coupled error information in matrix form can be transformed into a single scalar, which facilitates subsequent weighted fusion with other error sources.

[0190] Table 1: Statistics of Comprehensive Error Assessment Index

[0191]

[0192] Analysis of the 15 sets of experimental data shows that the overall comprehensive error assessment index fluctuates accordingly with changes in the relative pose error scalar, dynamic error, and mechanical-optical coupling error scalar of the collaborative calibration error tree. The numerical changes of the three error sources have a correlated impact on the comprehensive error assessment index through weighted calculation. When the overall levels of the three error sources are low, the comprehensive error assessment index is generally small; however, when two or three error sources increase simultaneously, the comprehensive error assessment index rises accordingly. This reflects that the weighted fusion logic in the formula effectively integrates the contributions of each error source, allowing the comprehensive error assessment index to reasonably characterize the changing state of the overall system error level.

[0193] From the data distribution, the fluctuation range of the comprehensive error assessment index matches the fluctuation range of the values ​​of each error source. No outliers that contradict the changing trends of the error sources have appeared, indicating that the preset proportional coefficient and reference value settings are reasonable. This ensures that after normalization and weighting, the error sources of different dimensions can form a comprehensive assessment result that is consistent with the actual error state of the system, providing a reliable quantitative basis for subsequent system error analysis and optimization.

[0194] In the above formula, the dependent variable It reflects the overall error level of the alignment and assembly system, and its physical meaning is the weighted synthesis result of all error sources in the mechanical coordinate system. The core value lies in unifying and quantifying multi-source heterogeneous errors into a comparable comprehensive index. The technical benefits are reflected in: firstly, providing a direct basis for error compensation, allowing the control system to... The system adjusts the motion trajectory in real time based on the distribution of errors; secondly, it balances the impact of different error sources on system accuracy by optimizing the weight coefficients globally, ultimately improving assembly positioning accuracy.

[0195] Independent variables include , and These represent error components from different physical sources. These independent variables and dependent variables... There is a linear weighted relationship between them, and the influence mechanism is as follows: each independent variable is a component of the comprehensive error, and the weight coefficient reflects the importance of the error source to the overall accuracy of the system. The value of is directly determined by the algebraic sum of these independent variables, and their correlation is reflected in the fact that an increase in any independent variable will lead to . Increase, therefore, the independent variable in the formula , and It is positively correlated with the dependent variable, meaning that an increase in any error component will lead to an increase in the overall error.

[0196] Step 6 generates a global error map by fusing the collaborative calibration error tree, dynamic error, and mechanical-optical coupling error map, thereby achieving comprehensive error modeling of the CCD camera alignment and assembly system. The advantage of this step lies in its comprehensive consideration of multiple error sources in the system, including static errors between cameras, dynamic errors during platform movement, and the coupling error between mechanical platform positioning errors and optical distortion. This fusion method can map multiple errors to the mechanical coordinate system in a unified form, thus forming a more comprehensive and intuitive error map, improving the accuracy and applicability of error modeling, and laying the foundation for subsequent error compensation and system optimization.

[0197] Compared with existing technologies, the innovation of step 6 lies in the joint analysis and fusion of multiple error sources. Traditional error modeling methods typically focus only on a single error type, neglecting the correlation and comprehensive effects between different error types. This invention provides static error propagation relationships through a collaboratively calibrated error tree, provides time-varying error quantities through dynamic errors, analyzes the correlation between mechanical platform errors and camera distortion through a mechanical-optical coupling error map, and represents the comprehensive error evaluation index in a unified mechanical coordinate system using a weighted fusion algorithm. This integrated analysis method not only improves the comprehensiveness and robustness of error modeling but also more accurately characterizes the overall error distribution characteristics of the assembly system, thereby significantly improving modeling accuracy and the effectiveness of practical applications. Step 6 is a key step in realizing global error modeling. By fusing multiple error sources, a complete global error map is generated, providing a precise basis for error analysis, optimization, and compensation of the alignment assembly system. This step organically combines the data from the collaboratively calibrated error tree, dynamic errors, and mechanical-optical coupling error map, improving the systematic nature and operability of error modeling. The global error map can not only guide the accuracy optimization of the assembly system but also provide reliable data support for error prediction and compensation in complex working environments. All other steps in the overall scheme provide input data for step 6, and the result of step 6 ultimately determines the overall effect of error modeling, which is the core foundation for realizing error optimization and compensation.

[0198] Please see Figure 2 An error modeling system based on a CCD camera alignment and assembly system includes:

[0199] The camera calibration module is used to obtain the intrinsic and extrinsic parameters of each CCD camera in the alignment and assembly system through the calibration target. The intrinsic parameters include focal length, principal point coordinates, pixel size and distortion parameters. The distortion parameters include radial distortion coefficient and tangential distortion coefficient. The extrinsic parameters are the rotation matrix and translation vector of the camera relative to the mechanical coordinate system.

[0200] The coordinate transformation module is used to establish the transformation relationship between each camera coordinate system and the machine coordinate system based on the intrinsic and extrinsic parameters, and to construct a collaborative calibration error tree between cameras. The collaborative calibration error tree includes the relative pose parameters and error propagation paths between cameras.

[0201] The data acquisition module is used to control the motion platform to perform alignment motion based on the conversion relationship, and to simultaneously acquire the real-time pose data and ambient temperature data of the motion platform. The pose data includes platform position, velocity and acceleration data.

[0202] The error decomposition module is used to perform time-frequency analysis on the pose data, decomposing the pose data into vibration error components and thermal deformation error components; the vibration error components are quantified by establishing an acceleration-vibration response mapping relationship, and the thermal deformation error components are characterized by constructing a linear relationship between temperature and thermal deformation, and the two types of error components are superimposed to form a dynamic error.

[0203] A coupling map module is constructed to extract positioning error data of the mechanical motion platform based on the pose data, and to construct a mechanical-optical coupling error map by combining the distortion parameters.

[0204] The error fusion module is used to fuse the collaborative calibration error tree, dynamic error, and mechanical-optical coupling error map to generate a global error map, thereby completing the error modeling of the CCD camera alignment and assembly system.

[0205] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0206] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0207] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0208] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. An error modeling method for a CCD camera-based alignment and assembly system, characterized in that, The specific steps include: Obtain the intrinsic and extrinsic parameters of each CCD camera in the alignment assembly system through the calibration target, wherein the intrinsic parameters include focal length, principal point coordinates, pixel size and distortion parameters, the distortion parameters include radial distortion coefficient and tangential distortion coefficient, and the extrinsic parameters are the rotation matrix and translation vector of the camera relative to the mechanical coordinate system; Establish the conversion relationship between the camera coordinate system and the mechanical coordinate system based on the intrinsic and extrinsic parameters, and construct a cooperative calibration error tree among the cameras, wherein the cooperative calibration error tree includes the relative pose parameters and error transmission paths among the cameras; Based on the conversion relationship, control the motion platform to perform alignment movement, and synchronously collect real-time pose data and environmental temperature data of the motion platform, wherein the pose data includes platform position, speed and acceleration data; Perform time-frequency analysis on the pose data to decompose the pose data into vibration error component and thermal deformation error component; the vibration error component is quantified by establishing an acceleration-vibration response mapping relationship, the thermal deformation error component is represented by constructing a temperature-thermal deformation amount linear relationship, and the two types of error components are superimposed to form a dynamic error; Extract positioning error data of the mechanical motion platform based on the pose data, and construct a mechanical-optical coupling error map in combination with the distortion parameters; The positioning error data includes a stage back-lash error , straightness error , multi-axis non-orthogonality error ; In combination with the distortion parameters of the camera, a mechanical-optical coupling error map is constructed, which quantitatively represents the platform back-lash gap error, straightness error and multi-axis non-orthogonality error in the form of a matrix The expression of the matrix is as follows: wherein and are the first and second order coefficients of radial distortion, respectively, and are tangential distortion coefficients; Fuse the cooperative calibration error tree, the dynamic error and the mechanical-optical coupling error map to generate a global error map, so as to complete the error modeling of the alignment assembly system based on the CCD camera; The cooperative calibration error tree provides the static transmission relationship of the relative pose error among the cameras, the dynamic error provides the time-varying error amount of vibration and thermal deformation, and the mechanical-optical coupling error map provides the quantitative correlation between the platform positioning error and the camera distortion; the three types of error sources are mapped to the unified mechanical coordinate system through a weighted fusion algorithm, and a comprehensive error evaluation index of the alignment assembly system in the mechanical coordinate system is generated after fusion, so as to construct a global error map, wherein the global error map is stored in the form of a quantitative model, and includes the comprehensive error evaluation index of the alignment assembly system and the contribution weight of each error.

2. The method of claim 1, wherein: The intrinsic and extrinsic parameters of each CCD camera are obtained through the calibration target, and the specific logic is as follows: The high-precision checkerboard calibration target is selected, fixed on a flat platform for adjusting its attitude, and at least 10 groups of clear images containing the complete target are captured by the CCD camera from different angles, distances and positions to ensure that the target covers different areas of the camera field of view in the images; the collected images are preprocessed, the pixel coordinates of the checkerboard corner points are extracted by the Harris corner detection algorithm, and a world coordinate system is established with a corner point of the target plane as the origin, and the world coordinate system coordinates of each corner point are determined in combination with the actual physical size of the target; the Zhang calibration algorithm is used to construct the perspective projection equation by taking the pixel coordinates and the world coordinate system coordinates of the corner points as inputs, and the internal parameters of the camera and the external parameters corresponding to each image are solved by the least square method; the solved parameters are verified, the re-projection error is calculated, and if the re-projection error is within a preset threshold, the calibration result is considered valid, otherwise the images are re-collected and the parameters are solved; the re-projection error refers to comparing the pixel coordinates of the corner points in the world coordinate system projected onto the image through the internal parameters and the external parameters with the actually detected pixel coordinates, and the deviation value is the re-projection error; The preprocessing includes gray correction and edge enhancement, and the formula is: In the formula, is the gray value of the original image at , is the corrected gray value, , are the gain coefficient and the offset, respectively, which are determined by fitting the image gray distribution characteristics by the least square method. The Sobel operator is used for edge enhancement: In the formula, is an enhanced edge response value, represents a convolution operation, represents a horizontal gradient value obtained after a convolution operation of the horizontal Sobel operator and is used to detect a vertical edge change in the image; is a vertical gradient value obtained by a convolution of the vertical Sobel operator and is used to detect a horizontal edge change in the image.

3. The method of claim 2, wherein: Based on the internal parameters and the external parameters, the conversion relationship between the camera coordinate system and the mechanical coordinate system is established through the camera imaging model, that is, the three-dimensional coordinates in the camera coordinate system are converted into image pixel coordinates by using the internal parameter matrix, and then the rigid transformation between the camera coordinate system and the mechanical coordinate system is realized by the rotation matrix and the translation vector of the external parameters; Taking the external parameters of each camera as the reference, the relative pose parameters between the cameras are determined by analyzing the rotation matrix and the translation vector between the external parameters of different cameras, and based on the error propagation theory, the transmission path from the single camera calibration error to the relative pose error between the cameras is analyzed, and then a collaborative calibration error tree containing the relative pose parameters and the error sources thereof is constructed, the root node and the intermediate node of the collaborative calibration error tree are error sources, the branches are error transmission directions, and the leaf nodes are the final relative pose errors between the cameras; the relative pose parameters include the relative rotation matrix and the relative translation vector, and the relative pose error includes the relative rotation angle error and the relative translation vector error; The three-dimensional coordinates in the camera coordinate system are converted into image pixel coordinates by using the internal parameter matrix, and the formula is as follows: wherein, is the image pixel coordinate, is the three-dimensional coordinate in the camera coordinate system, is the intrinsic matrix; denotes the focal length in the horizontal direction, denotes the focal length in the vertical direction, is the principal point coordinate, all of which are obtained through a calibration process; The rigid transformation between the camera coordinate system and the mechanical coordinate system is realized by the rotation matrix and the translation vector of the external parameters, and the formula is as follows: In the formula, is a three-dimensional coordinate in a mechanical coordinate system, is a rotation matrix, is a translation vector, , and respectively represent the translation components of the camera coordinate system origin in the X-axis, Y-axis and Z-axis directions of the mechanical coordinate system, and are obtained through the calibration process.

4. The method of claim 3, wherein: The calculation formula of the relative rotation matrix is as follows: wherein, denotes the camera with respect to the camera , the relative rotation matrix, and are the camera , the camera with respect to the mechanical coordinate system, which is obtained by a calibration process; is the inverse matrix of , and are the indices of the CCD cameras in the alignment system, and ; The calculation formula of the relative translation vector is as follows: wherein denotes the camera with respect to the camera a relative translation vector, and are the translation vectors of the camera , the camera with respect to the mechanical coordinate system, which are obtained by a calibration process; Based on the error propagation theory, the transmission path from the single camera calibration error to the relative pose error between the cameras is analyzed, and the mathematical representation of the error transmission path is as follows: Rotation error propagation: Let the rotation angle error of camera be , and the rotation angle error of camera be , then the formula for the relative rotation angle error is as follows: wherein, represents a camera with a camera a relative rotation angle error of the camera, is a rotation error propagation Jacobian matrix derived from a rotation matrix of the camera ; Translation error propagation: Let the translation vector error of camera be , and the translation vector error of camera be , then the relative translation vector error is calculated as follows: In the formula, represents the camera and the relative translation vector error of the camera .

5. The method of claim 4, wherein: Based on the established camera coordinate system and mechanical coordinate system conversion relationship, the motion platform is controlled by the motion controller to move according to the preset alignment track; real-time platform position data is collected, and velocity and acceleration data are obtained from the position data through differential operation, and the environmental temperature data at the motion platform is collected at the same sampling frequency as the pose data; the time stamp of the pose data and the environmental temperature data is accurately aligned through time stamp synchronization technology.

6. The method of claim 1, wherein: The pose data is decomposed in the frequency domain by using the fast Fourier transform method: wherein is a frequency domain representation of the pose signal, is a time domain representation of the pose signal, is a frequency, denotes a time variable, denotes the imaginary unit; Setting a frequency threshold The high frequency component in the error signal is determined as a vibration error component, and the low frequency component in the error signal is determined as a thermal deformation error component; the frequency threshold is set according to the vibration characteristics of the platform ; The high frequency component in the error signal is determined as a vibration error component, and the low frequency component in the error signal is determined as a thermal deformation error component; the frequency threshold is set according to the vibration characteristics of the platform ; The high frequency component in the error signal is determined as a vibration error component, and the low frequency component in the error signal is determined as a thermal deformation error component; the frequency threshold is set according to the vibration characteristics of the platform The vibration error component is inversely transformed to obtain a time-domain vibration signal, and a mapping relationship between acceleration and vibration amplitude is established; the thermal deformation error component is inversely transformed to obtain a time-domain thermal deformation signal, and a linear relationship between temperature and thermal deformation is established; the vibration error component and the thermal deformation error component are superimposed to form a dynamic error, and a sliding window average method is used to smooth the dynamic error, and finally the optimized dynamic error is output; the size of the sliding window is set according to the system response time; Wherein, the mapping relationship between acceleration and vibration amplitude is established, and the logic is that for each acceleration , the corresponding vibration amplitude is calculated , and the formula is as follows: In the formula, is an index of acceleration, represents a frequency domain expression corresponding to the vibration signal generated by the acceleration ​ A polynomial fitting is used to establish the mapping relationship between acceleration and vibration amplitude, and the formula is as follows: In the formula, Indicates acceleration The vibration amplitude below, Let be the order of the polynomial. Indicates the order index of the polynomial. The fitting coefficients are obtained by using the least squares method on ( Data was obtained through fitting. A linear relationship between temperature and thermal deformation is established, and the logic is as follows: according to the collected environmental temperature data , combined with the thermal deformation error component, a data pair is constructed ], wherein is the index of the sampling time, represents the corresponding thermal deformation error component at the sampling time ; the thermal deformation amount refers to the thermal deformation error component time domain value corresponding to the sampling time, which is obtained by converting the frequency domain signal back to the time domain through inverse Fourier transform, that is, the thermal deformation amount; A least squares method is used to fit the following linear model: wherein represents the temperature coefficient, used to characterize the degree of thermal distortion caused by temperature change, is the ambient temperature, is the initial temperature, is the intercept, i.e. the amount of thermal distortion at the initial temperature, and is obtained by linear regression calculation on the data pairs of ]. The accuracy of the linear model is verified by calculating the fitting residual, and if the root mean square of the residual is within the preset range, the linear relationship is effective, otherwise the temperature sampling range is expanded and the data is collected again and fitted.

7. The error modeling method of the CCD camera alignment assembly system according to claim 1, characterized in that: where platform back lash error The position deviation of the forward and reverse direction movements at the same instruction position is calculated, and the formula is as follows: wherein , are the actual positions during forward and reverse motion, respectively; Straightness error The straightness error is obtained by root mean square calculation of the deviation of the actual motion trajectory from the ideal straight line, and the formula is as follows: wherein is the actual trajectory offset of the th sampling point, is the ideal straight line fit value of the th sampling point, is the number of sampling points, is the index of the sampling point distributed along the measurement trajectory. Multi-axis non-orthogonality error By measuring the deviation of the actual included angle between two axes from 90°, the two axes being two mutually nominally orthogonal movement axes in a positioning assembly system; determined The formula on which this is based is as follows: In the formula, is the actual included angle between the two axes.

8. A method of modeling errors in a CCD camera alignment system according to claim 1, characterized in that: The calculation formula of the comprehensive error evaluation index is as follows: In the formula, is a comprehensive error evaluation index, is a relative pose error scalar of the cooperative calibration error tree, is a dynamic error, is an error scalar of the mechanical-optical coupling error map, and is calculated according to the norm calculation on the matrix , , and are reference values of the relative pose error scalar, the dynamic error, and the error scalar of the mechanical-optical coupling error map, respectively; , and are preset proportional coefficients, and satisfy ; The relative pose error scalar is computed by converting the relative rotation angle error φ to a linearized rotation error; computing the Euclidean norm of the linearized rotation error and the relative translation vector error , resulting in a single scalar value in units of length that comprehensively characterizes the relative pose deviation between the cameras, i.e. ; where is determined from the working distance of the assembly system. is determined from the working distance of the assembly system.

9. A system for error modeling of a system for aligning components based on a CCD camera, the system comprising: The error modeling system of the CCD camera alignment assembly system is used to execute the error modeling method of the CCD camera alignment assembly system according to any one of claims 1-8, comprising: A camera calibration module is configured to obtain the intrinsic and extrinsic parameters of each CCD camera in the alignment assembly system through a calibration target, wherein the intrinsic parameters include focal length, principal point coordinates, pixel size, and distortion parameters, the distortion parameters include radial distortion coefficients and tangential distortion coefficients, and the extrinsic parameters are the rotation matrix and translation vector of the camera relative to the mechanical coordinate system; A coordinate conversion module is configured to establish the conversion relationship between the camera coordinate system and the mechanical coordinate system based on the intrinsic and extrinsic parameters, and to construct a collaborative calibration error tree between the cameras, wherein the collaborative calibration error tree includes the relative pose parameters and error transmission paths between the cameras; A data acquisition module is configured to control the motion platform to move based on the conversion relationship, and to synchronously collect real-time pose data and environmental temperature data of the motion platform, wherein the pose data includes platform position, velocity, and acceleration data; An error decomposition module is configured to perform time-frequency analysis on the pose data, to decompose the pose data into vibration error components and thermal deformation error components, to quantify the vibration error components by establishing an acceleration-vibration response mapping relationship, to represent the thermal deformation error components by constructing a temperature-thermal deformation amount linear relationship, and to superimpose the two types of error components to form a dynamic error. A coupling graph module is constructed to extract positioning error data of the mechanical motion platform based on the pose data and to construct a mechanical-optical coupling error graph in combination with distortion parameters; An error fusion module is configured to fuse the collaborative calibration error tree, the dynamic error and the mechanical-optical coupling error graph to generate a global error graph, thereby completing error modeling of the position assembly system based on the CCD camera pair.

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