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

Abstract

The invention 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 the method comprises the steps: obtaining internal parameters and external parameters of a CCD camera through calibration, building a camera and mechanical coordinate system conversion relation, and constructing a collaborative calibration error tree; controlling the motion platform to move, synchronously acquiring pose and environment temperature data, decomposing vibration and thermal deformation error components through time-frequency analysis, and superposing the vibration and thermal deformation error components into dynamic errors; extracting a positioning error based on the pose data, and constructing a mechanical-optical coupling error spectrum in combination with the distortion parameters; and finally, fusing the collaborative calibration error tree, the dynamic error and the coupling error atlas to generate a global error atlas, and completing alignment assembly system error modeling based on the CCD camera. According to the invention, the precision and applicability of error modeling are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of high-precision electronic manufacturing assembly technology, in particular to an error modeling method and system based on a CCD camera alignment assembly system. BACKGROUND

[0002] With the development of modern industrial automation and precision manufacturing technology, CCD cameras are widely used in alignment assembly systems due to their high resolution and real-time imaging capabilities, for realizing high-precision automated assembly. However, in practical applications, the precision of the CCD camera alignment assembly system is affected by various factors, including camera calibration errors, positioning errors of the mechanical motion platform, and environmental disturbances. Traditional error analysis usually only focuses on a single error source, such as compensating for imaging errors through single-camera internal and external parameter calibration, or reducing platform motion errors through mechanical correction. However, these methods fail to fully consider the coupling effect of optical and mechanical systems, resulting in limitations in error compensation that are difficult to meet the needs of high-precision assembly.

[0003] In addition, the mechanical motion platform is affected by vibration and thermal deformation during operation, resulting in dynamic errors that are time-varying and complex, making it difficult to describe them through static calibration methods. At the same time, the correlation between camera distortion parameters and mechanical errors has not been fully studied, resulting in insufficient overall error modeling, especially when multiple cameras are involved. The relative pose errors between cameras and their transmission paths in the system have not been effectively quantified, limiting the system's ability to predict and compensate for global errors. Therefore, there is an urgent need for a method that can consider multiple error sources and quantify their interactions to improve the precision and reliability of the CCD camera alignment assembly system.

[0004] The above information disclosed in the background section is only intended to strengthen the understanding of the background of the present disclosure, and therefore it can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0005] The present application aims to provide an error modeling method and system based on a CCD camera alignment assembly system to solve the problems raised in the background.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions: An error modeling method based on a CCD camera alignment assembly system, comprising the following specific steps: Obtaining the internal and external parameters of each CCD camera in the alignment assembly system through a calibration target, the internal parameters including focal length, principal point coordinates, pixel size, and distortion parameters, the distortion parameters including radial distortion coefficients and tangential distortion coefficients, and the external parameters being the rotation matrix and translation vector of the camera relative to the mechanical coordinate system; establish a conversion relationship between the camera coordinate system and the mechanical coordinate system based on the intrinsic parameters and the extrinsic parameters, and construct a cooperative calibration error tree between the cameras, the cooperative calibration error tree including relative pose parameters and error transmission paths between the cameras; based on the conversion relationship, control the motion platform to perform alignment motion, and synchronously collect real-time pose data and environmental temperature data of the motion platform, the pose data including platform position, speed and acceleration data; perform time-frequency analysis on the pose data, 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, the thermal deformation error components are represented by constructing a temperature-thermal deformation amount linear relationship, and the two types of error components are superimposed to form dynamic errors; 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 distortion parameters; fuse the cooperative calibration error tree, the dynamic errors and the mechanical-optical coupling error map to generate a global error map, so as to complete error modeling of the alignment assembly system based on the CCD cameras.

[0007] Further, the intrinsic parameters and the extrinsic parameters of each CCD camera are obtained by calibrating a target, and the specific logic is as follows: select a high-precision checkerboard calibration target, fix it on a flat platform for adjusting its attitude; control the CCD camera to shoot at least 10 groups of clear images containing the complete target from different angles, distances and directions, to ensure that the target covers different areas of the camera field of view in the images; pre-process the collected images, extract the pixel coordinates of the checkerboard corner points by the Harris corner detection algorithm, and establish a world coordinate system with a corner point of the target plane as the origin, and determine the world coordinate system coordinates of each corner point in combination with the actual physical size of the target; use Zhang's calibration algorithm to construct a perspective projection equation with the pixel coordinates and the world coordinate system coordinates of the corner points as inputs, and solve the camera intrinsic parameters and the extrinsic parameters corresponding to each image by the least squares method; verify the solved parameters, calculate the re-projection error, if the re-projection error is within a preset threshold, the calibration result is considered valid, otherwise, re-collect images and solve the parameters; 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 intrinsic parameters and the extrinsic parameters with the actually detected pixel coordinates, and the deviation value is the re-projection error; The pre-processing includes gray correction and edge enhancement, and the formula is as follows: ; In the formula, is the gray value of the original image at , is the corrected gray value, is the corrected gray 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. Edge enhancement using the Sobel operator: ; ; ; 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.

[0008] 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. 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. 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: ; 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. 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: ; 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.

[0009] Furthermore, the formula for calculating the relative rotation matrix is ​​as follows: ; 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 ; The formula for calculating the relative translation vector is as follows: ; 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; 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: 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: ; 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; 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: ; In the formula, Indicates camera With camera The relative translation vector error.

[0010] 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.

[0011] Furthermore, the pose data is decomposed in the frequency domain using the Fast Fourier Transform method: ; 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; 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; The time-domain vibration signal is obtained by inverse transformation of the vibration error component, and a mapping relationship between acceleration and vibration amplitude is established; the time-domain thermal deformation signal is obtained by inverse transformation of the thermal deformation error component, 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 the 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; The mapping relationship between acceleration and vibration amplitude is established, and the logic is as follows: for each acceleration , the corresponding vibration amplitude is calculated , wherein is the index of acceleration, represents the frequency domain expression of the vibration signal generated by the acceleration ; The mapping relationship between acceleration and vibration amplitude is established by polynomial fitting, and the formula is as follows: , wherein represents the vibration amplitude under the acceleration , is the order of the polynomial, represents the order index of the polynomial, is the fitting coefficient, which is obtained by fitting the data pair by the least square method; The linear relationship between temperature and thermal deformation is established, and the logic is as follows: according to the collected environmental temperature data , a data pair is constructed by combining the thermal deformation error component, wherein is the index of the sampling time, represents the corresponding thermal deformation error component at the sampling time ; the thermal deformation is converted back to the time domain by inverse Fourier transform, and the thermal deformation error component time domain value corresponding to the sampling time is obtained, which is the thermal deformation; The following linear model is fitted by the least square method: , wherein represents the temperature coefficient, which is used to represent the degree of thermal deformation caused by temperature change, is the environmental temperature, is the initial temperature, is the intercept, i.e. the thermal deformation at the initial temperature, and are obtained by fitting the data pair​​​ The data was obtained through linear regression calculations. 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.

[0012] 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; Among them, platform return back clearance error The positional deviation is calculated by moving in opposite directions at the same command position, based on the following formula: ; In the formula, , These are the actual positions during forward and reverse movement, respectively; Straightness error The deviation between the actual trajectory and the ideal straight line is calculated using the root mean square formula, as follows: ; 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 refers to the index of the sampling points distributed along the measurement trajectory; 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. Sure The formula used is as follows: ; In the formula, This is the actual included angle between the two axes; 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: ; in, and These are the first-order and second-order coefficients of radial distortion, respectively. and denoted as the tangential distortion coefficient.

[0013] Further, the cooperative calibration error tree, the dynamic error and the mechanical-optical coupling error map are fused, wherein the cooperative calibration error tree provides a static transmission relationship of relative pose errors between cameras, the dynamic error provides time-varying error amounts of vibration and thermal deformation, and the mechanical-optical coupling error map provides quantitative correlation of platform positioning errors and camera distortion; the three types of error sources are mapped to a 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, the global error map is stored in the form of a quantitative model, and contains the comprehensive error evaluation index of the alignment assembly system and contribution weights of each error, so as to complete system overall error modeling; The calculation formula of the comprehensive error evaluation index is as follows: ; In the formula, is the 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 obtained according to norm calculation on a 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 calculated by the following method: the relative rotation angle error is multiplied by a feature length , and is converted into a linearized rotation error; the Euclidean norm of the linearized rotation error and a relative translation vector error is calculated, to obtain a single scalar value with a length dimension, which comprehensively represents the relative pose deviation between cameras, that is, ; wherein, is determined according to the working distance of the assembly system.

[0014] The application further provides an error modeling system of a CCD camera alignment assembly system, which is used for executing the error modeling method of the CCD camera alignment assembly system, and comprises: a camera calibration module, configured to acquire internal parameters and external parameters of each CCD camera in the alignment assembly system through a calibration target, the internal parameters including focal length, principal point coordinates, pixel size and distortion parameters, the distortion parameters including radial distortion coefficients and tangential distortion coefficients, and the external parameters being a rotation matrix and a translation vector of the camera relative to a mechanical coordinate system; a coordinate conversion module, configured to establish a conversion relationship between each camera coordinate system and the mechanical coordinate system based on the internal parameters and the external parameters, and to construct a cooperative calibration error tree among the cameras, the cooperative calibration error tree including relative pose parameters and error transmission paths among the cameras; a data acquisition module, configured to control a motion platform to perform alignment movement based on the conversion relationship, and to synchronously acquire real-time pose data and environmental temperature data of the motion platform, the pose data including platform position, speed and acceleration data; an error decomposition module, configured to perform time-frequency analysis on the pose data, decompose the pose data into vibration error components and thermal deformation error components, quantify the vibration error components by establishing an acceleration-vibration response mapping relationship, represent the thermal deformation error components by constructing a temperature-thermal deformation amount linear relationship, and superimpose the two types of error components to form dynamic errors; a coupling graph construction module, configured to extract positioning error data of the mechanical motion platform based on the pose data, and construct a mechanical-optical coupling error graph in combination with the distortion parameters; an error fusion module, configured to fuse the cooperative calibration error tree, the dynamic errors and the mechanical-optical coupling error graph to generate a global error graph, so as to complete error modeling of the CCD camera alignment assembly system.

[0015] Compared with the prior art, the present application has the following advantages: The present application realizes quantitative analysis of error transmission relationships among multiple camera coordinate systems by constructing a cooperative calibration error tree, significantly improves the calibration accuracy of the multi-camera system, decomposes the pose data into vibration and thermal deformation error components by using a time-frequency analysis method, generates dynamic errors, effectively solves the modeling problem of time-varying errors under high-speed motion, constructs a mechanical-optical coupling error graph, analyzes the interaction between mechanical positioning errors and camera distortion, provides a more comprehensive basis for error compensation, and finally generates a global error graph through multi-source error fusion, which can accurately reflect the comprehensive error distribution of the system under various working conditions. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a schematic diagram of the overall method flow of the present application; Figure 2 is a schematic diagram of the overall system module of the present application; Figure 3 is a bar chart of relative pose error scalar and comprehensive error evaluation index; Figure 4 is a 3D bar chart of relative pose error scalar, dynamic error and comprehensive error evaluation index. DETAILED DESCRIPTION

[0017] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present application should be understood as the common meanings understood by those skilled in the art to which the present application belongs. The terms "first", "second" and similar terms used in the present application do not represent any order, number or importance, but are only used to distinguish different components. The terms "include" or "contain" and similar terms mean that the elements or objects before the terms cover the elements or objects listed after the terms and their equivalents, and do not exclude other elements or objects. The terms "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. The terms "up", "down", "left", "right" and the like only represent relative positional relationships, and when the absolute positions of the described objects change, the relative positional relationships may also change accordingly.

[0019] Embodiment: Please refer to Figure 1 The present application provides a technical solution: A method for error modeling of a CCD camera-based alignment assembly system, comprising the following specific steps: Step 1: 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; In this embodiment, the intrinsic and extrinsic parameters of each CCD camera are obtained through a calibration target, and the specific logic is as follows: The high-precision checkerboard calibration target is selected and fixed on a flat platform for adjusting its attitude; at least 10 groups of clear images containing the complete target are captured by the CCD camera from different angles, distances and positions, so as 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 a perspective projection equation with 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, if the re-projection error is within a preset threshold, the calibration result is considered to be effective, 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 the position, is the corrected gray value, , are gain coefficient and offset respectively, which are determined by fitting the image gray distribution characteristics by the least square method; Sobel operator is used for edge enhancement: ; ; ; In the formula, is the enhanced edge response value, represents convolution operation, represents the horizontal gradient value obtained by convolution operation of the horizontal Sobel operator and, is used for detecting the vertical edge change in the image; is the vertical gradient value obtained by convolution of the vertical Sobel operator and, is used for detecting the horizontal edge change in the image.

[0020] ​The internal parameters and external parameters of each CCD camera are accurately obtained by calibrating the target, the internal parameters including focal length, principal point coordinates, pixel size and distortion parameters, and the external parameters being a rotation matrix and a translation vector of the camera relative to the mechanical coordinate system. The high-precision calibration target is combined with Zhang's calibration algorithm to significantly improve the calibration accuracy and ensure the accuracy of the camera internal parameters and external parameters. The reliability of the calibration result is verified by the re-projection error to effectively reduce the error sources. Through this step, reliable parameter support is provided for the subsequent conversion relationship between the camera and the mechanical coordinate system, laying the foundation for the entire error modeling.

[0021] Compared with the prior art, the high-precision chessboard target-based multi-view calibration method is used in the calibration process, and the Harris corner point detection algorithm is used to extract the chessboard corner points, thereby improving the corner point detection accuracy. At the same time, Zhang's calibration algorithm is combined with the least square method for optimization and solution, and the effectiveness of the calibration parameters is verified by the re-projection error to ensure the accuracy and reliability of the calibration result. In addition, the gray correction and edge enhancement in the preprocessing process further improve the accuracy of the corner point extraction. Therefore, the present application has significant advantages in calibration accuracy and error control, and can better adapt to the needs of high-precision alignment assembly systems. Step 1 provides accurate basic data support for error modeling, including the internal and external parameters of the camera, to ensure the accuracy of the conversion relationship between the cameras and the mechanical coordinate system. At the same time, the high-precision calibration of this step can significantly reduce the accumulation of system errors caused by parameter errors, and reduce the uncertainty in the error transmission path from the source. In addition, the accurate internal and external parameter calibration results provide a reliable data basis for dynamic error analysis, collaborative calibration error tree construction and mechanical-optical coupling error map generation, ultimately ensuring the accuracy and effectiveness of the global error map, which is an important part of the entire error modeling method.

[0022] Step 2: establishing the conversion relationship between the camera coordinate system and the mechanical coordinate system based on the internal and external parameters, and constructing a collaborative calibration error tree between the cameras, the collaborative calibration error tree including the relative pose parameters and error transmission paths between the cameras; In this embodiment, 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 using the rotation matrix and the translation vector of the external parameters; With each camera external parameter as a benchmark, relative pose parameters between cameras are determined by analyzing rotation matrix and translation vector between different camera external parameters, and based on error propagation theory, a propagation path from single camera calibration error to relative pose error between cameras is analyzed, and then a collaborative calibration error tree containing relative pose parameters and error sources thereof is constructed, wherein root nodes and intermediate nodes of the collaborative calibration error tree are error sources, branches are error propagation directions, and leaf nodes are final relative pose errors between cameras; the relative pose parameters include relative rotation matrix and relative translation vector, and the relative pose error includes relative rotation angle error and relative translation vector error; Specifically, with each camera external parameter (rotation matrix and translation vector) as a benchmark, relative rotation matrix (obtained by multiplying inverse matrices of corresponding camera rotation matrices) and relative translation vector (obtained by subtracting the difference of corresponding camera translation vectors after conversion by the relative rotation matrix) between different camera external parameters are calculated to determine the relative pose parameters between cameras; and based on error propagation theory, a propagation path (achieved by error propagation Jacobian matrix and relative pose parameter formula derivation) of rotation angle error and translation vector error in the single camera calibration process to relative rotation angle error and relative translation vector error between cameras is analyzed, and then a collaborative calibration error tree is constructed. In the error tree, root nodes and intermediate nodes represent error sources at each level, branches represent the propagation direction of errors from the source to the terminal, and leaf nodes are the relative pose errors (including relative rotation angle error and relative translation vector error) between cameras finally formed after propagation and superposition, so as to completely represent the error composition and propagation logic of the relative pose parameters in the multi-camera system.

[0023] Wherein, the three-dimensional coordinates in the camera coordinate system are converted into image pixel coordinates by using the intrinsic parameter matrix, and the formula is as follows: ; In the formula, is the image pixel coordinate, is the three-dimensional coordinate in the camera coordinate system, is the intrinsic parameter matrix; represents the focal length in the horizontal direction, represents the focal length in the vertical direction, is the principal point coordinate, which is obtained through the 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 parameter, and the formula is as follows: ; In the formula, is the three-dimensional coordinate in the mechanical coordinate system, is the rotation matrix, is the translation vector, , and respectively, which are obtained by the calibration process.

[0024] The calculation formula of the relative rotation matrix is as follows: ; In the formula, denotes the relative rotation matrix of the camera with respect to the camera ; and are the rotation matrices of the camera and the camera with respect to the mechanical coordinate system, which are obtained by the calibration process; is the inverse matrix of ; and are the indices of the CCD cameras in the alignment assembly system, and ; The calculation formula of the relative translation vector is as follows: ; In the formula, denotes the relative translation vector of the camera with respect to the camera ; and are the translation vectors of the camera and the camera with respect to the mechanical coordinate system, which are obtained by the calibration process; 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 the mathematical representation of the error propagation path is as follows: Rotation error propagation: let the rotation angle error of the camera be , and the rotation angle error of the camera be , then the calculation formula of the relative rotation angle error is as follows: ; wherein, denotes the relative rotation angle error of the camera and the camera , is the rotation error propagation Jacobian matrix, which is derived from the rotation matrix of the camera ; Translation error propagation: let the translation vector error of the camera be , and the translation vector error of the camera be , the calculation formula of the relative translation vector error is as follows: ; In the formula, indicates the relative translation vector error of the camera and the camera .

[0025] Step 2 effectively realizes the spatial coordinate unification of the multi-camera system and the error transmission path modeling by establishing the conversion relationship between the camera coordinate system and the mechanical coordinate system based on the intrinsic parameters and the extrinsic parameters, and constructing the collaborative calibration error tree between the cameras. The collaborative calibration error tree accurately describes the relative pose parameters between the cameras, the error sources and the transmission paths, systematically associates the single-camera calibration error with the multi-camera system error, and makes the error analysis hierarchical and traceable. This method not only accurately quantifies the error transmission process of the multi-camera system, but also provides a structured error expression for subsequent global error modeling.

[0026] Compared with the prior art, the present application significantly improves the accuracy and interpretability of the error modeling of the multi-camera system by introducing the collaborative calibration error tree. The traditional technology usually only focuses on single-camera calibration or simple conversion relationship between cameras, and lacks analysis of the transmission path and cumulative effect of the error. The present application analyzes the relative pose parameters of the extrinsic parameters between the cameras, combines the error transmission theory, systematically analyzes the transmission path from the single-camera calibration error to the relative pose error between the cameras, and accurately quantifies the error transmission process through the mathematical model, thereby effectively reducing the influence of error accumulation of the multi-camera system, achieving higher calibration accuracy and error analysis capability. Step 2 is the core link of the whole error modeling method, which realizes the global modeling of the error sources and transmission process of the multi-camera system by constructing the collaborative calibration error tree, and provides a basic framework for subsequent dynamic error analysis and generation of mechanical-optical coupling error atlas. At the same time, the accurate conversion relationship between the camera and the mechanical coordinate system ensures the spatial consistency of the multi-camera system, and the hierarchical structure of the collaborative calibration error tree and the clear error transmission path provide high-precision static error input for the fusion of the final global error atlas, and finally improve the overall accuracy and reliability of the whole system error modeling.

[0027] Step 3: based on the conversion relationship, controlling the motion platform to perform alignment movement, and synchronously collecting real-time pose data and environmental temperature data of the motion platform, the pose data including platform position, speed and acceleration data; In this embodiment, based on the established conversion relationship between the camera coordinate system and the mechanical coordinate system, the motion platform is controlled to perform assembly alignment motion according to the preset alignment track through the motion controller; the platform position data is collected in real time, and the speed and acceleration data are obtained from the position data through differential operation, and the environmental temperature data at the motion platform are 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 the time stamp synchronization technology.

[0028] In step 3, the motion platform is controlled to perform alignment motion based on the conversion relationship between the camera and the mechanical coordinate system, and the real-time pose data and environmental temperature data of the motion platform are collected synchronously. This step can comprehensively consider the dynamic behavior of the motion platform and the external environmental temperature change, and provide key data for subsequent error analysis. Synchronous collection of pose data and temperature data and ensuring timestamp alignment can effectively avoid data deviation and distortion of error quantization results, thereby ensuring the reliability and accuracy of error modeling. In addition, by controlling the motion platform to move according to the preset track, the dynamic error performance of the assembly system in the actual scene can be systematically tested, and the model description ability of the error in the real working state is improved.

[0029] Compared with the prior art, the motion platform dynamic data and environmental temperature data are accurately fused in step 3 of the present application, while the traditional technology often ignores the influence of environmental factors on system error, or only collects static data and lacks dynamic error quantization. Through the time stamp synchronization technology, the present application can ensure the time consistency of the pose data and the temperature data, effectively improve the accuracy and reliability of the error quantization. In addition, the present application further refines the source of the platform dynamic error, and can independently analyze and quantify the vibration error and the thermal deformation error, while the prior art usually cannot distinguish or accurately represent these complex error sources, thereby improving the comprehensiveness and applicability of error modeling. Step 3 is the core link of dynamic error modeling, which collects the pose data and environmental temperature data of the motion platform in real time to provide high-quality input for subsequent time-frequency analysis. This link not only can accurately extract and quantify the vibration response and thermal deformation behavior of the system, but also can test the error performance of the platform motion through the preset track, thereby constructing an error model with actual scene adaptability. In addition, the real-time data collection results of step 3 will be combined with the collaborative calibration error tree and the mechanical-optical coupling error map to provide an important basis for dynamic analysis and fusion of the final global error map, ensuring the comprehensiveness and dynamic adaptability of error modeling.

[0030] Step 4: performing 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, the thermal deformation error components are represented by constructing a temperature-thermal deformation amount linear relationship, and the two types of error components are superimposed to form a dynamic error; In the embodiment, the pose data is decomposed in frequency domain by using fast Fourier transform method. ; In the formula, is the frequency domain expression of the pose signal, is the time domain expression of the pose signal, is the frequency, denotes the time variable, denotes the imaginary unit; A frequency threshold is set , the high-frequency component of is determined as the vibration error component, and the low-frequency component of is determined as the thermal deformation error component; the frequency threshold is set according to the vibration characteristics of the platform; A frequency threshold is set , and the low-frequency component of is determined as the thermal deformation error, and the high-frequency component of is determined as the vibration error. The core basis is the difference in physical characteristics of the two types of errors: thermal deformation is caused by changes in ambient temperature, and the temperature conduction and material thermal expansion and contraction process is slow, which is reflected in the time domain pose signal as low-frequency fluctuations changing slowly over time, corresponding to the low-frequency component in the frequency domain; and the vibration error is caused by mechanical vibration of the motion platform, and the vibration response has instantaneousness, periodicity and high change frequency, which is reflected in the time domain as a rapidly fluctuating signal, corresponding to the high-frequency component in the frequency domain. In combination with the vibration characteristics of the platform , the frequency domain distribution of the two types of errors can be accurately distinguished to achieve effective decomposition. The inverse transform of the vibration error component is performed to obtain the time domain vibration signal, and the mapping relationship between the acceleration and the vibration amplitude is established. The inverse transform of the thermal deformation error component is performed to obtain the time domain thermal deformation signal, and the linear relationship between the temperature and the thermal deformation is established. The vibration error component and the thermal deformation error component are superimposed to form a dynamic error, and the 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; The mapping relationship between the acceleration and the vibration amplitude is established, and the logic is that for each acceleration

[0031] , the corresponding vibration amplitude is calculated, and the formula is as follows: ; ; In the formula, is the index of the acceleration, denotes the frequency domain expression corresponding to the vibration signal generated by the acceleration ;​ 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.

[0032] A polynomial fitting method is used to establish the mapping relationship between acceleration and vibration amplitude, as shown in the following formula: ; 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. Dependent variable It is a continuous mapping function established through polynomial fitting, meaning that for any acceleration input, it predicts the amplitude of the 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.

[0033] 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. The following linear model is fitted using the least squares method: ; In the formula, The temperature coefficient is used to characterize the degree of thermal deformation caused by temperature changes. ambient temperature, initial temperature, intercept, i.e. the amount of thermal deformation at the initial temperature, and 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, it is determined that the linear relationship is valid, otherwise the temperature sampling range is expanded to re-collect data and fit.

[0034] Step 4 decomposes the error components into vibration error components and thermal deformation error components by time-frequency analysis of the pose data of the motion platform, and models and quantifies them respectively. The core advantage of this step is to accurately distinguish dynamic errors from different sources, and to extract the characteristics of vibration and thermal deformation from the frequency and time domains. By establishing the mapping relationship between acceleration and vibration response and the linear relationship between temperature and thermal deformation, the change law of dynamic error can be effectively characterized and expressed in a quantitative form. In addition, the two types of dynamic error components are superimposed to form the overall dynamic error, and the smoothing processing technology is used to optimize the error result, which helps to reduce the influence of data noise on error modeling and provides protection for more accurate dynamic error analysis.

[0035] Compared with the prior art, the present application adopts a more systematic and refined analysis method in dynamic error modeling. Traditional techniques often only model the error as a whole, lack independent analysis and separation of vibration error and thermal deformation error, and lead to unclear error sources, limited accuracy and applicability of the error model. The present application decomposes the pose data in the frequency domain by fast Fourier transform, scientifically divides high-frequency vibration error and low-frequency thermal deformation error, and quantifies them by acceleration-vibration response mapping and temperature-thermal deformation relationship respectively, which can more accurately characterize the behavior characteristics of dynamic error. In addition, the sliding window average method is used to smooth the dynamic error, which can effectively reduce random noise interference and further improve the error modeling accuracy. Step 4 plays a key role in the overall error modeling scheme, providing technical support for accurate extraction and modeling of dynamic error. By separating and independently quantifying vibration and thermal deformation error components, not only the hierarchy and refinement of error modeling are enhanced, but also the error source analysis in dynamic environment is supplemented, making up for the deficiency of static error analysis in the collaborative calibration error tree. In addition, the quantization result of dynamic error provides dynamic compensation data for the construction of mechanical-optical coupling error map, and lays a solid foundation for the generation of global error map. This step and other steps work together to effectively improve the comprehensiveness and applicability in complex scenarios of error modeling, and provide a scientific basis for system error optimization and compensation.

[0036] 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; 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. Among them, platform return back clearance error The positional deviation is calculated by moving in opposite directions at the same command position, based on the following formula: ; In the formula, , These are the actual positions during forward and reverse movement, respectively; Straightness error The deviation between the actual trajectory and the ideal straight line is calculated using the root mean square formula, as follows: ; 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; 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. Sure The formula used is as follows: ; In the formula, This is the actual included angle between the two axes; 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: ; in, and These are the first-order and second-order coefficients of radial distortion, respectively. and denoted as the tangential distortion coefficient.

[0037] Step 5, by extracting the positioning error data of the mechanical motion platform based on the pose data, and combining the distortion parameters of the camera to construct a mechanical-optical coupling error map, the correlation between the platform positioning error and the camera imaging distortion is quantitatively characterized in the form of a matrix. The advantage of this step is that the inherent error of the mechanical motion platform and the optical imaging error are considered comprehensively, and the mutual influence relationship between the mechanical and optical systems is established. This coupling analysis method can comprehensively reflect the influence of mechanical motion error on imaging quality, thereby providing more accurate data support for system error compensation. In addition, through the construction of the error map in the form of a matrix, the error quantification is more intuitive and structured, which is more suitable for the fusion of subsequent global error maps.

[0038] Compared with the prior art, the coupling modeling method of mechanical error and optical error is first proposed in step 5 of the present application, while the traditional technology generally analyzes mechanical error or optical error separately, and it is difficult to comprehensively reflect the complex interaction between the two. The present application not only extracts various key positioning errors of the mechanical motion platform, but also constructs a unified mechanical-optical coupling error map combined with the distortion parameters of the camera, which can more accurately describe the comprehensive influence of mechanical motion error on optical imaging. This graph-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 structuralization degree of error modeling, which is conducive to the iterative updating and dynamic compensation of error maps. Step 5 is the key link to realize the coupling error modeling of mechanical-optical system, which combines the positioning error data of the mechanical platform with the distortion error of the camera imaging, and constructs a mechanical-optical coupling error map, laying a foundation for dynamic error compensation in global error modeling. This step not only can quantitatively analyze the influence of mechanical platform positioning error on the overall precision of the system, but also provides important input data for the subsequent fusion of collaborative calibration error tree, dynamic error and mechanical-optical coupling error map. In addition, the results of this step provide a scientific basis for optimizing the error distribution of the system and improving the positioning accuracy, ultimately improving the error modeling accuracy and robustness of the entire positioning assembly system.

[0039] Step 6: 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 positioning assembly system; In this embodiment, the collaborative calibration error tree, dynamic error and mechanical-optical coupling error map are fused, wherein the collaborative calibration error tree provides the static transmission relationship of the relative pose error between 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 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, 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, and the global error map is stored in the form of a quantitative model, and contains the comprehensive error evaluation index of the alignment assembly system and the contribution weight of each error, so as to complete the system overall error modeling. The calculation formula of the comprehensive error evaluation index is as follows: ; In the formula, is the comprehensive error evaluation index, is the relative pose error scalar of the collaborative calibration error tree, is the dynamic error, is the error scalar of the mechanical-optical coupling error map, which is obtained by performing 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, which satisfy , and The reasons are as follows: the dynamic error is a time-varying disturbance existing in the running process of the alignment assembly system, directly affecting the motion platform alignment accuracy and assembly action stability, and having the most significant influence on the final assembly quality of the system, so the maximum weight is given; the relative pose error scalar of the collaborative calibration error tree determines the reference accuracy of the multi-camera collaborative alignment, and is the core source of the system static error, so the intermediate weight is given; the mechanical-optical coupling error scalar is related to the platform positioning error and the camera distortion, but its influence can be weakened through early calibration optimization, and the contribution degree to the overall error of the system is the lowest, so the minimum weight is given.

[0040] The determination method of the reference values , and is as follows: is the average value of the relative pose error scalar obtained by calibrating the same sample through multiple groups of cameras under standard working conditions; is the statistical average value of the dynamic error collected when the motion platform runs empty according to the 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.

[0041] 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.

[0042] For matrix Obtain the norm by performing norm calculation The formula used is as follows: ; 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.

[0043] Table 1: Statistics of Comprehensive Error Assessment Index

[0044] 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.

[0045] From the data distribution, the fluctuation range of the comprehensive error evaluation index matches the numerical fluctuation range of each error source, and there is no abnormal value contrary to the trend of error source change, which shows that the preset proportion coefficient and reference value setting are reasonable, and can ensure that the error sources of different dimensions can form a comprehensive evaluation result consistent with the actual error state of the system after normalization and weighting, providing a reliable quantitative basis for subsequent system error analysis and optimization.

[0046] In the above formula, the dependent variable reflects the overall error level of the positioning assembly system, and its physical meaning is the weighted synthesis result of all error sources in the mechanical coordinate system. The core value of is to quantify multiple heterogeneous error sources into a comparable comprehensive index, and the technical effect is reflected in: first, providing a direct basis for error compensation, and the control system can adjust the motion trajectory in real time according to the distribution of ; second, through global optimization of weight coefficients, the influence of different error sources on system accuracy is balanced, and finally the assembly positioning accuracy is improved.

[0047] The independent variables include , and , which respectively represent error components of different physical sources. There is a linear weighted relationship between these independent variables and the dependent variable , and the influence mechanism is: each independent variable is a constituent element 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 the correlation is reflected in: the increase of any independent variable will cause to rise, therefore, the independent variables , and are positively correlated with the dependent variable, that is, the increase of any error component will cause the comprehensive error to increase.

[0048] Step 6 generates a global error map by fusing the collaborative calibration error tree, dynamic error and mechanical-optical coupling error map, thereby realizing the comprehensive error modeling of the CCD camera positioning assembly system. The advantage of this step is that it comprehensively considers multiple error sources in the system, including static errors between cameras, dynamic errors in the platform motion process, and coupling errors between mechanical platform positioning errors and optical distortion. This fusion method can map multiple errors in a unified form to the mechanical coordinate system, thereby forming a more comprehensive and intuitive error map, improving the accuracy and applicability of error modeling, and laying a foundation for subsequent error compensation and system optimization.

[0049] Compared with the prior art, the innovation of step 6 lies in the joint analysis and fusion of multiple error sources. Traditional error modeling methods usually only focus on a single error type, ignoring the correlation and comprehensive effect between different error types. The present application provides a static error transmission relationship through a collaborative calibration error tree, a time-varying error quantity through a dynamic error, a correlation between mechanical platform errors and camera distortion through a mechanical-optical coupling error map, and a comprehensive error evaluation index in a unified mechanical coordinate system through a weighted fusion algorithm. This integrated analysis method not only improves the comprehensiveness and robustness of error modeling, but also more accurately represents the overall error distribution characteristics of the assembly system, thereby significantly improving the modeling accuracy and effectiveness of practical applications. Step 6 is a key link to achieve global error modeling, which generates a complete global error map by fusing multiple error sources, providing accurate basis for error analysis, optimization and compensation of the alignment assembly system. This link organically combines the data of collaborative calibration error tree, dynamic error and mechanical-optical coupling error map, improving the systematicness and operability of error modeling. The global error map not only guides the precision optimization of the assembly system, but also provides reliable data support for error prediction and compensation in complex working environments. The 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 of error optimization and compensation.

[0050] Please refer to Figure 2 , the error modeling system of the alignment assembly system based on the CCD camera, comprising: a camera calibration module for obtaining the intrinsic and extrinsic parameters of each CCD camera in the alignment assembly system through a calibration target, the intrinsic parameters including focal length, principal point coordinates, pixel size and distortion parameters, the distortion parameters including radial distortion coefficients and tangential distortion coefficients, and the extrinsic parameters being the rotation matrix and translation vector of the camera relative to the mechanical coordinate system; a coordinate conversion module for establishing the conversion relationship between the camera coordinate system and the mechanical coordinate system based on the intrinsic and extrinsic parameters, and constructing a collaborative calibration error tree between the cameras, the collaborative calibration error tree containing the relative pose parameters and error transmission paths between the cameras; a data acquisition module for controlling the motion platform to perform alignment motion based on the conversion relationship, and synchronously acquiring real-time pose data and environmental temperature data of the motion platform, the pose data including platform position, velocity and acceleration data; an error decomposition module for performing 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, the thermal deformation error components are characterized by constructing a temperature-thermal deformation amount linear relationship, and the two types of error components are superimposed to form a dynamic error; The coupling graph module is configured to extract positioning error data of the mechanical motion platform based on the pose data, and construct a mechanical-optical coupling error graph in combination with distortion parameters; The 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, so as to complete error modeling of the assembly system based on the CCD camera pair.

[0051] The above formulas are all dimensionless numerical calculations, the formulas are obtained by software simulation of a large amount of data to obtain a formula closest to the actual situation, and the preset parameters in the formulas are set by a person skilled in the art according to the actual situation.

[0052] The above embodiments can be realized wholly or partially by software, hardware, firmware or any other combination. When realized by software, the above embodiments can be realized wholly or partially in the form of a computer program product. Those skilled in the art can realize that the units and algorithm steps of the examples described in combination with the embodiments disclosed herein can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software methods depends on the specific application and design constraints of the technical solutions.

[0053] The units described as separate components can or can not be physically separated, and the components shown as units can or can not be physical units, which can be located in one place or distributed on multiple network units. Part or all of the units can be selected according to actual needs to achieve the purpose of the embodiments.

[0054] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present 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 parameters and extrinsic parameters of each CCD camera in the alignment assembly system through the calibration target, the intrinsic parameters including focal length, principal point coordinates, pixel size and distortion parameters, the distortion parameters including radial distortion coefficient and tangential distortion coefficient, and the extrinsic parameters being 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 parameters and the extrinsic parameters, and construct a cooperative calibration error tree between the cameras, the cooperative calibration error tree containing the relative pose parameters and error transmission paths between the cameras; Based on the conversion relationship, control the motion platform to perform alignment motion, and synchronously collect real-time pose data and environmental temperature data of the motion platform, the pose data including platform position, velocity and acceleration data; 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, the thermal deformation error components are characterized by constructing a temperature-thermal deformation amount linear relationship, and the two types of error components are superimposed to form 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; 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 error modeling of the alignment assembly system based on the CCD camera.

2. The method of claim 1, wherein: The specific logic for obtaining the intrinsic parameters and extrinsic parameters of each CCD camera through the calibration target is as follows: A high-precision checkerboard calibration target is selected, which is fixed on a flat platform for adjusting its attitude; control the CCD camera to shoot at least 10 groups of clear images containing the complete target from different angles, distances and directions, ensuring that the target in the image covers different areas of the camera field of view; preprocess the collected images, extract the pixel coordinates of the checkerboard corner points through the Harris corner detection algorithm, and establish a world coordinate system with a corner point of the target plane as the origin, and determine the world coordinate system coordinates of each corner point in combination with the actual physical size of the target; use Zhang's calibration algorithm to construct a perspective projection equation with the pixel coordinates and world coordinate system coordinates of the corner points as inputs, and solve the camera intrinsic parameters and the extrinsic parameters corresponding to each image through the least squares method; verify the solved parameters, calculate the re-projection error, if the re-projection error is within a preset threshold, the calibration result is considered valid, otherwise, re-collect images and solve the parameters; 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 intrinsic parameters and the extrinsic 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, , respectively, the gain coefficient and the offset, are determined by fitting the image gray distribution characteristics by the least square method. Sobel operator is used for edge enhancement: ； ； ； wherein is an enhanced edge response value, denotes a convolution operation, denotes a horizontal gradient value obtained by performing a convolution operation on the image data with a Sobel operator in the horizontal direction and is used to detect a change in the vertical direction of the edge in the image; denotes a vertical gradient value obtained by performing a convolution operation on the image data with a Sobel operator in the vertical direction and is used to detect a change in the horizontal direction of the edge in the image. is an enhanced edge response value, denotes a convolution operation, denotes a horizontal gradient value obtained by performing a convolution operation on the image data with a Sobel operator in the horizontal direction and is used to detect a change in the vertical direction of the edge in the image; denotes a vertical gradient value obtained by performing a convolution operation on the image data with a Sobel operator in the vertical direction and is used to detect a change in the horizontal direction of the edge in the image. < 3. The method of claim 2, wherein: Based on the intrinsic parameters and the extrinsic 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 through the intrinsic parameter matrix, and then the rigid transformation between the camera coordinate system and the mechanical coordinate system is realized through the rotation matrix and the translation vector of the extrinsic parameters; The relative pose parameters between the cameras are determined by analyzing the rotation matrix and the translation vector between different camera extrinsic parameters, and based on error propagation theory, the transmission path from single camera calibration error to the relative pose error between the cameras is analyzed, and 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 branch is the error transmission direction, and the leaf node is the final relative pose error between the cameras; the relative pose parameters include a relative rotation matrix and a relative translation vector, and the relative pose error includes a relative rotation angle error and a relative translation vector error; The three-dimensional coordinates in the camera coordinate system are converted into image pixel coordinates by using the intrinsic 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 extrinsic parameter, 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 of the camera and are the camera , the camera the rotation matrix with respect to the mechanical coordinate system, which is obtained by a calibration process; is the inverse matrix of , and are indices of the CCD cameras in the alignment system, and ; The calculation formula of the relative translation vector is as follows: ； wherein represents the camera with respect to the camera a relative translation vector, and are the camera , the camera translation vectors with respect to the mechanical coordinate system, obtained through a calibration process; Based on the error propagation theory, the transmission path from 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 of 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 , the translation vector error of camera be , then the relative translation vector error is calculated as follows: ； In the formula, represents the relative translation vector error of the camera with the camera .

5. The method of claim 4, wherein: Based on the established conversion relationship between the camera coordinate system and the mechanical coordinate system, the motion platform is controlled to move according to the preset alignment trajectory by the motion controller; the platform position data is collected in real time, and the speed and acceleration data are obtained from the position data by differential operation, and the environmental temperature data at the motion platform are collected, and the sampling frequency is consistent with the pose data; the time stamp of the pose data and the environmental temperature data is accurately aligned by the 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; 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; The vibration error component is inversely transformed to obtain the time domain vibration signal, and the 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 the 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 the 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 acceleration of the vehicle. The mapping relationship between acceleration and vibration amplitude is established by polynomial fitting, 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, data pairs are constructed ] where is the index of the sampling time, represents the corresponding thermal deformation error component at the sampling time . The thermal deformation amount is converted from the frequency domain signal to the time domain by inverse Fourier transform, and the time domain value of the thermal deformation error component corresponding to the sampling time is obtained, that is, the thermal deformation amount; The following linear model is fitted by using the least square method: ； wherein represents the temperature coefficient, which is 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, if the root mean square of the residual is within the preset range, it is determined that the linear relationship is effective, otherwise the temperature sampling range is expanded and the data is collected again and fitted.

7. The method of claim 1, wherein: The positioning error data of the mechanical motion platform is extracted based on the pose data, and the positioning error data includes platform back gap error, straightness error and multi-axis non-orthogonality error; 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 The deviation of the actual included angle between two axes, which are nominally orthogonal to each other in a positioning system, from 90° is determined by measurement. determined The formula on which this is based is as follows: ； In the formula, is the actual included angle between the two axes; 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.

8. The method of claim 1, wherein: The cooperative calibration error tree, the dynamic error and the mechanical-optical coupling error map are fused, wherein the cooperative calibration error tree provides a static transmission relationship of relative pose errors between cameras, the dynamic error provides time-varying error amounts of vibration and thermal deformation, and the mechanical-optical coupling error map provides quantitative correlation of platform positioning errors and camera distortion; three types of error sources are mapped to a 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 in the form of a quantitative model, wherein the comprehensive error evaluation index of the alignment assembly system and the contribution weights of each error are contained, so as to complete system overall error modeling; 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 obtained according to norm calculation on a 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 to a linearized rotation error by multiplying it with a characteristic length and computing the Euclidean norm of the linearized rotation error and the relative translation vector error resulting in a single scalar value in length dimension that comprehensively characterizes the relative pose deviation between the cameras, i.e. ; where is determined according to 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 based on the CCD camera alignment assembly system is used to execute the error modeling method based on the CCD camera alignment assembly system according to any one of claims 1-8, comprising: A camera calibration module is configured to obtain intrinsic parameters 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 a rotation matrix and a translation vector of the camera relative to the mechanical coordinate system; A coordinate conversion module is configured to establish a conversion relationship between each camera coordinate system and the mechanical coordinate system based on the intrinsic parameters and the extrinsic parameters, and to construct a cooperative calibration error tree between the cameras, wherein the cooperative calibration error tree contains relative pose parameters and error transmission paths between the cameras; A data acquisition module is configured to control the motion platform to perform alignment motion based on the conversion relationship, and to synchronously acquire real-time pose data and environmental temperature data of the motion platform, wherein the pose data includes platform position, speed 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 dynamic errors; A coupling map construction module is configured to extract positioning error data of the mechanical motion platform based on the pose data, and to construct a mechanical-optical coupling error map in combination with distortion parameters; An error fusion module is configured to 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 error modeling of the CCD camera alignment assembly system.

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