Geometric error-based satellite antenna reflector component pose coordination method and system

Abstract

The invention relates to a geometric error-based satellite antenna reflector part pose coordination method and system, and the method comprises the steps: building a global coordinate system, scanning original point cloud data, carrying out the multi-scale filtering and voxelization processing, dividing the processed point cloud data into molded surface effective points and edge feature points, and obtaining coordinates under the global coordinate system, and establishing a joint regulation and control objective function containing a profile approximation error term and a gap uniformity error term, locking the pose of the central fixed reflecting surface, sequentially solving the rigid body transformation matrix of each reflecting surface sub-block to be assembled according to a spatial adjacency relation, physically assembling each reflecting surface sub-block to be assembled, and obtaining the assembled reflecting surface. And pose coordination of the satellite antenna reflecting surface component is realized. According to the method, the problems that the molded surface precision is difficult to control and edge gaps are not uniform in the assembling process of the reflecting surface of the large satellite antenna are solved, and high-precision virtual assembling and pose correction of the reflecting surface sub-blocks are achieved.

Description

Technical Field

[0001] This invention relates to the field of precision manufacturing and assembly technology for spacecraft, and in particular to a method and system for attitude coordination of satellite antenna reflector components based on geometric errors. Background Technology

[0002] High-gain parabolic antennas are core payloads for modern communication satellites, remote sensing satellites, and deep space probes. The surface accuracy of their reflectors directly determines key electrical performance indicators such as antenna gain and sidelobe levels. Due to limitations in the envelope size of launch vehicle fairings, large-aperture antennas typically cannot be manufactured as a single unit and are instead widely produced in modular form, using folding / assembly deployment. This structure usually consists of a fixed central reflector and multiple rings of deployable or splicable reflector sub-blocks (panels). Currently, ground assembly of such antenna reflectors mainly relies on high-precision tooling and laser trackers for assisted positioning. Physical adjustment mechanisms are used to repeatedly fine-tune the position and attitude of each sub-block to approximate the theoretical parabolic surface.

[0003] With the rapid development of aerospace technology, extremely stringent requirements have been placed on the error of reflective surfaces, often needing to be controlled at the micrometer level. Traditional physical trial assembly methods usually rely on repeated "measurement-adjustment-remeasurement" iterations based on manual experience. This is not only time-consuming and labor-intensive with long production cycles, but also prone to physical damage to the mirror surface made of fragile materials such as carbon fiber honeycomb sandwich during repeated adjustments. This makes it difficult to meet the requirements of "full-cycle digital precision manufacturing" for next-generation high-performance satellite antennas.

[0004] In the precision assembly process based on measured data, there exists a complex "error coupling" problem, namely, an inherent contradiction and constraint between "surface fit accuracy" and "joint gap uniformity". Due to manufacturing limitations, each reflective surface has varying degrees of inherent distortion or deformation relative to the theoretical model. Existing single-objective optimization methods or simple weighted averaging methods struggle to find the globally optimal solution under the dual constraints of the theoretical parabolic surface and edge gaps, leading to unstable assembly quality.

[0005] In summary, to address the problems of low efficiency, large errors, and difficulty in controlling multi-source error coupling in the assembly of large-aperture modular satellite antennas, there is an urgent need for a virtual docking and pose coordination method based on high-precision three-dimensional scanning data. This method constructs a joint constraint model that includes surface geometric features and edge gap features using measured data in a virtual environment. The optimal pose of each component is calculated through an iterative optimization strategy, thereby achieving the optimal balance of assembly quality under manufacturing error conditions. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method and system for coordinating the pose of satellite antenna reflector components based on geometric errors, which solves the problems faced in the assembly process of large satellite antenna reflectors, such as difficulty in controlling surface accuracy, uneven edge gaps, and easy accumulation of assembly errors.

[0007] To achieve the above technical objectives, the present invention provides the following technical solution: a method for coordinating the pose of satellite antenna reflector components based on geometric errors, comprising the following steps: S1. Use a laser tracker to establish a global coordinate system, and use a scanner to scan the original point cloud data of the central fixed reflector of the satellite antenna and each reflector sub-block to be assembled. S2. Perform multi-scale filtering and voxelization uniform resampling on the original point cloud data. Based on the boundary detection algorithm, divide the processed point cloud data into effective points of the surface and edge feature points, and obtain the coordinates of the effective points of the surface and edge feature points in the global coordinate system. S3. Establish a joint control objective function; the joint control objective function includes a surface approximation error term based on effective points of the surface and a gap uniformity error term based on edge feature points; S4. Lock the pose of the central fixed reflector, use the joint control objective function, and solve the rigid body transformation matrix and virtually assemble each reflector sub-block to be assembled in sequence according to the spatial adjacency relationship, so as to obtain the rigid body transformation matrix of all reflector sub-blocks to be assembled. S5. Use the rigid body transformation matrix obtained by solving to physically assemble each reflector sub-block to achieve pose coordination of the satellite antenna reflector components.

[0008] Optionally, in step S3, establishing the joint regulatory objective function includes: S31. Construct the theoretical parabolic equation for the reflecting surface sub-block, defined as follows: ; in, , , These represent the x, y, and z coordinates of a point in the original point cloud data of the reflective surface sub-block in the global coordinate system. The focal length of the parabolic surface; S32. Define the rigid body transformation matrix of the reflective surface sub-block to be assembled. The rigid body transformation matrix Including rotation matrix Translation vector , Represents the real number space; for any point in the original point cloud data The new point after transformation Represented as: ; S33. Constructing the surface approximation error term based on the theoretical parabolic equation. The definition is as follows: ; in, Indicates the total number of valid points on the surface; , , They represent the first Effective points of individual surfaces After rigid body transformation matrix The effective points of the transformed new surface The x, y, and z coordinates; S34. Constructing the gap uniformity error term The definition is as follows: ; in, This represents the total number of feature points on the upper edge of the reflective surface sub-block to be assembled; Indicates the first reflective surface sub-block to be assembled Edge feature points After rigid body transformation matrix The transformed new edge feature points; This represents all points on the edge of the fixed reflecting surface, which consists of the central fixed reflecting surface and the fixed reflecting surface sub-blocks, and intersecting with... The closest point in space is obtained using the KD-tree nearest neighbor search algorithm. and This forms a pair of edge-matching points; Represents the calculation of the Euclidean norm; This represents the theoretical gap value. If the design requires seamless splicing of all reflective sub-blocks, then... If the design requires a allowance for thermal expansion gaps or adhesive layer thickness, then Set it to a constant greater than 0; S35, Introducing surface approximation weighting coefficient Gap constraint weight coefficient By linearly combining the surface approximation error term and the gap uniformity error term, a joint control objective function is obtained, mathematically represented as follows: ; in This represents the joint control objective function.

[0009] Optionally, step S4 includes: S41. Using the central fixed reflective surface as a reference block, lock the pose of the reference block and set all its edge feature points. Store the set of rigid boundaries in the local area ; S42. Construct the topological adjacency matrix between the central fixed reflective surface and each reflective surface sub-block. Based on the breadth-first search algorithm, generate a spiral or ring-shaped assembly sequence including each reflective surface sub-block to be assembled, with the reference block as the root node. S43. Based on the assembly sequence, select the reflective surface sub-blocks to be assembled as the current optimization objects, and substitute the current rigid boundary set into the joint control objective function. Solve for the rigid body transformation matrix of the current optimization object; S44. After solving the rigid body transformation matrix, the reflective surface sub-block is virtually assembled and marked as fixed. All edge feature points of the virtually assembled reflective surface sub-block are stored in the local rigid boundary set. ; S45. Repeat steps S43-S44 to solve the rigid body transformation matrix of each reflective surface sub-block to be assembled, until all reflective surface sub-blocks are virtually assembled.

[0010] Optionally, step S42 includes: S421. Construct the topological adjacency matrix between the central fixed reflector and each reflector sub-block. If the center is a fixed reflective surface With reflective surface sub-block If there is a common edge, then ,otherwise Similarly, if the reflective surface sub-block With reflective surface sub-block If there is a common edge, then ,otherwise ; S422. Based on the breadth-first search algorithm, with the reference block as the root node, the topological adjacency matrix is ​​queried. Elements with a median value of 1 are used to identify the next ring of reflective sub-blocks that are physically adjacent to the current reflective sub-block, thereby generating a spiral or ring-shaped assembly sequence. ,in Indicates the first A reflective surface sub-block to be assembled. This represents the total number of reflective surface sub-blocks to be assembled.

[0011] Optionally, in step S43, solving the rigid body transformation matrix of the current optimization object includes: S431. Define the state vector of the current optimization object. ;in, Indicates the transpose operation; , , These represent the translation vectors along the x, y, and z axes, respectively, and constitute the translation components of the rigid body transformation matrix of the current optimization object. , , These represent the rotation angles about the x-axis, y-axis, and z-axis, respectively, forming the rotation angle components of the rigid body transformation matrix of the current optimization object. Represent the space of real numbers; S432. Using the Levenberg-Marquardt algorithm to jointly regulate the objective function. Perform iterative minimization to obtain the state increment for each iteration. The joint control objective function is dynamically adjusted during the solution process. Surface approximation weighting coefficient With gap constraint weight coefficient ; S433, In each iteration, based on the acquired state increment The state vector of the current optimization object Incremental updates are performed. When the iteration stops, the translation and rotation components of the state vector saved after the last update are extracted, and the translation vector and rotation matrix are constructed respectively. Then, the final rigid body transformation matrix of the reflective surface sub-block is synthesized.

[0012] Optionally, in step S432, the Levenberg-Marquardt algorithm is used to jointly regulate the objective function. Perform iterative minimization to obtain the state increment for each iteration. ,include: S4321. Perform a geometric consistency check on the edge matching point pairs. If the edge matching point... If the included angle of the normal vectors is greater than a preset threshold or the distance is greater than a preset value, it is determined to be a mismatch, and the edge matching point pair is temporarily removed from the solution process of the current iteration. S4322. Calculate the objective function of joint regulation. Jacobian matrix The Jacobian matrix The mathematical representation is as follows: ; in, Represents the surface approximation error term Jacobian matrix, Indicates the gap uniformity error term The Jacobian matrix; S4323. Solve the following system of linear equations within the framework of the Levenberg-Marquardt algorithm to obtain the state increment. : ; in, For approximate Hessian matrix, It is a diagonal weight matrix. The gradient vector, The current residual vector is a vector composed of the scalar differences between all points on the current reflective surface sub-block and the theoretical target. It is the damping factor; S4324, When the joint control objective function The decrease in the function value is less than the set threshold. or state increment The modulus is less than the preset threshold. When, or when the number of iterations reaches the preset maximum number of iterations. Stop iterating when the time is right.

[0013] Optionally, in step S432, the surface approximation weight coefficients are dynamically adjusted during the solution process. Gap constraint weight coefficient ,include: Set large gap constraint weight coefficients in the initial stage. Approximation weighting coefficients for small surfaces As the number of iterations increases or the residual decreases, the surface area gradually approaches the weighting coefficient. The residual is the residual vector in step S4323. The Euclidean norm or modulus.

[0014] The present invention also provides a satellite antenna reflector component pose coordination system based on geometric errors, for applying the aforementioned satellite antenna reflector component pose coordination method based on geometric errors, comprising: The coordinate system establishment and point cloud data acquisition module is used to establish a global coordinate system and acquire the original point cloud data of the central fixed reflector and each reflector sub-block of the satellite antenna. The point cloud data preprocessing module is used to perform multi-scale filtering and voxelization on the raw point cloud data and divide it into effective points of the surface and edge feature points, and take the coordinates of the effective points of the surface and edge feature points in the global coordinate system. The registration and solving module is used to establish a joint control objective function and solve the rigid body transformation matrix of each reflective surface sub-block to be assembled in sequence according to the spatial adjacency relationship. The solved rigid body transformation matrix is ​​then sent to the physical assembly module. The physical assembly module is used to decompose the transformation matrices of each rigid body to be assembled obtained by solving into translation vectors and Euler angles, and output them to the human-machine interface or automatic assembly control system to guide technicians or robotic arms to complete the physical assembly.

[0015] The present invention also provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the aforementioned geometric error-based satellite antenna reflector component pose coordination method.

[0016] The present invention also provides a computer-readable storage medium storing computer instructions for causing a processor to execute the aforementioned method for coordinating the pose of satellite antenna reflector components based on geometric errors.

[0017] By employing the above technical solution, the present invention provides a method and system for coordinating the pose of satellite antenna reflector components based on geometric errors, which has at least the following beneficial effects: (1) By combining the global reference control of the laser tracker with the high-density detail acquisition of the handheld scanner, this invention effectively solves the problems of accuracy attenuation and splicing accumulation error in the cross-scale measurement of large antenna reflectors, and realizes high-precision positioning of the central fixed surface and the sub-block to be assembled in a unified coordinate system, providing reliable data support with full coverage and low noise for subsequent pose calculation. (2) The present invention constructs a joint control objective function including "surface approximation degree" and "gap uniformity", and introduces dynamic weight adjustment and mismatch elimination strategy. In the optimization process, a smooth transition from priority edge alignment to fine surface attitude adjustment is achieved, which not only ensures the final electrical performance of the antenna, but also ensures the mechanical assembly safety between sub-blocks, and solves the problem that a single constraint is difficult to take into account multiple physical field indicators. (3) The present invention adopts a serialized recursive assembly strategy from the inside out, and uses topological adjacency to construct a dynamically extended rigid boundary. By locking the pose of the converged reflective surface sub-blocks one by one, the high-dimensional global optimization problem is degraded into a series of low-dimensional local optimization problems, which effectively suppresses the error propagation and accumulation effect in the multi-sub-block collaborative assembly process, and significantly improves the computational efficiency and final convergence stability of the virtual assembly of large-scale reflective surface arrays. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of the satellite antenna reflector component pose coordination method and system based on geometric errors according to the present invention; Figure 2This is a schematic diagram illustrating the division of the edge feature point set and the effective point set of the surface in an embodiment of the present invention; Figure 3 This is a schematic diagram of the physically assembled satellite antenna reflector component in an embodiment of the present invention. Detailed Implementation

[0019] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0020] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0021] Please refer to Figures 1-3 This illustration shows a specific implementation of the present embodiment. In this embodiment, a global coordinate system is established, the original point cloud data is scanned and multi-scale filtering and voxelization are performed, the processed point cloud data is divided into effective points of the surface and edge feature points and the coordinates under the global coordinate system are obtained, a joint control objective function including the surface approximation error term and the gap uniformity error term is established, the pose of the central fixed reflector is locked, and the rigid body transformation matrix of each reflector sub-block to be assembled is solved in sequence according to the spatial adjacency relationship. The reflector sub-blocks to be assembled are physically assembled, which alleviates the problems of difficult surface accuracy control and uneven edge gap in the assembly of large satellite antenna reflectors, and realizes high-precision virtual assembly and pose correction of reflector sub-blocks.

[0022] Please refer to Figure 1 This embodiment proposes a pose coordination method for satellite antenna reflector components based on geometric errors. The method includes the following steps: S1. Use a laser tracker to establish a global coordinate system, and use a scanner to scan the original point cloud data of the central fixed reflector of the satellite antenna and each reflector sub-block to be assembled.

[0023] As a preferred embodiment of step S1, the specific process includes: S11. Set up a global control network at the assembly site and establish a global coordinate system using a laser tracker. Attach the laser tracker target ball mount to the non-functional surfaces of the central fixed reflective surface and each reflective surface sub-block to be assembled. Measure and record the feature point coordinates of each component in the global coordinate system, which will serve as the rigid skeleton for subsequent point cloud stitching.

[0024] S12. Using a high-resolution handheld 3D laser scanner or a structured light scanner mounted on the end of a robotic arm, perform a full-coverage scan of each reflective surface sub-block to be assembled. During the scanning process, the scanner automatically identifies and locks the target points set in step S11, i.e., the feature points represented by the laser tracker target ball mount pasted on the non-functional surface of the component. Utilizing the global coordinate constraints of the target points, the local spatial pose matrix of the scanner is aligned to the known global absolute coordinates, thereby preventing pose drift during multi-frame point cloud stitching, eliminating accumulated errors in real time during the scanning process, and directly outputting high-density point cloud data in the global coordinate system as the original point cloud data.

[0025] This invention effectively solves the problems of accuracy attenuation and splicing accumulation error in cross-scale measurement of large antenna reflectors by combining global reference control of a laser tracker with high-density detail acquisition of a handheld scanner. It achieves high-precision positioning of the central fixed surface and the sub-block to be assembled in a unified coordinate system, providing reliable data support with full coverage and low noise for subsequent pose calculation.

[0026] S2. Perform multi-scale filtering and voxelization uniform resampling on the original point cloud data. Based on the boundary detection algorithm, divide the processed point cloud data into effective points of the surface and edge feature points, and obtain the coordinates of the effective points of the surface and edge feature points in the global coordinate system.

[0027] As a preferred embodiment of step S2, the specific process includes: S21. Perform multi-scale filtering on the original point cloud data to remove background noise and outliers.

[0028] S22. Calculate the point cloud normal vector using principal component analysis (PCA), and then perform voxelization uniform resampling of the point cloud density to improve computational efficiency.

[0029] S23. Based on the curvature abrupt change feature, using a boundary detection algorithm and setting a curvature threshold, the edge feature points of the central fixed reflective surface and each reflective surface sub-block to be assembled are accurately extracted to form an edge feature point set. The remaining point set is then marked as the effective points of the surface, forming the effective point set of the surface. This is used for subsequent parabolic surface fitting calculations. The edge feature point set defined in this embodiment... With the effective point set of the profile For reference Figure 2 , Figure 2 The red dots are edge feature points (some edge feature points are connected to form a line), and the blue dots are effective points of the surface.

[0030] S24. Extract the feature corner points or artificial marker points of the central fixed reflective surface and each reflective surface sub-block to be assembled. Through random sampling and RANSAC iteration, use the coarse registration algorithm to calculate the initial rigid body transformation matrix of the central fixed reflective surface and each reflective surface sub-block to be assembled relative to the global coordinate system. Transform all data into a unified computational domain to obtain the coordinates of the effective points of the surface and the edge feature points in the global coordinate system.

[0031] S3. Establish a joint control objective function; the joint control objective function includes a surface approximation error term based on effective points of the surface and a gap uniformity error term based on edge feature points.

[0032] As a preferred embodiment of step S3, the establishment of the joint regulatory objective function specifically includes: S31. Based on the optical design parameters of the satellite antenna, construct a theoretical parabolic equation for the reflective sub-block as an absolute geometric reference. This theoretical parabolic equation is defined as follows: ; in, , , These represent the x, y, and z coordinates of a point in the original point cloud data of the reflective surface sub-block in the global coordinate system. The focal length is the parabolic focal length.

[0033] This equation defines the spatial surface that all reflective sub-blocks should ideally adhere to, and is the only metric for evaluating "surface approximation".

[0034] S32. Define the rigid body transformation matrix of the reflective surface sub-block to be assembled. The rigid body transformation matrix Including rotation matrix Translation vector , recorded as , Represents the real number space; for any point in the original point cloud data The new point after transformation Represented as: .

[0035] S33. Constructing the surface approximation error term based on the theoretical parabolic equation. This is used to constrain the reflector sub-blocks to conform to the theoretical parabolic equation, ensuring the antenna's electrical performance (such as gain and phase consistency). The surface approximation error term... Defined as the following least squares objective function: ; in, Indicates the total number of valid points on the surface; , , They represent the first Effective points of individual surfaces After rigid body transformation matrix The effective points of the transformed new surface The x, y, and z coordinates; where Indicates the effective point based on this surface type. Current horizontal coordinate The calculated theoretical z-coordinate.

[0036] This formula calculates the axial deviation from the theoretical surface rather than the normal distance, because in parabolic antenna design, the phase error in the z-direction (optical axis direction) has the most significant impact on electrical performance.

[0037] S34. Constructing the gap uniformity error term This is used to constrain the relative positions of the reflective sub-blocks to be assembled with their adjacent fixed reflective sub-blocks (or the center-fixed reflective surface), ensuring mechanical assembly accuracy and preventing collisions or excessive gaps. Gap uniformity error item. The definition is as follows: ; in, This represents the total number of feature points on the upper edge of the reflective surface sub-block to be assembled; Indicates the first reflective surface sub-block to be assembled Edge feature points After rigid body transformation matrix The transformed new edge feature points; This represents all points on the edge of the fixed reflecting surface, which consists of the central fixed reflecting surface and the fixed reflecting surface sub-blocks, and intersecting with... The closest point in space is obtained using the KD-tree nearest neighbor search algorithm. and This forms a pair of edge-matching points; This indicates the calculation of the Euclidean norm, which is the calculation of the straight-line distance between two points; This represents the theoretical gap value. If the design requires seamless splicing of all reflective sub-blocks, then... If the design requires a allowance for thermal expansion gaps or adhesive layer thickness, then Set to a constant greater than 0 (in this embodiment, it is set to 0.05 mm).

[0038] Gap uniformity error term Used to constrain the relative position between the sub-block to be assembled and the fixed adjacent sub-block, ensuring mechanical assembly accuracy and preventing collisions or excessive gaps.

[0039] S35, Introducing surface approximation weighting coefficient Gap constraint weight coefficient By linearly combining the surface approximation error term and the gap uniformity error term, a joint control objective function is obtained, mathematically represented as follows: ; in This represents the joint control objective function. When this value approaches 0, it indicates that the assembly state simultaneously meets the requirements for both the surface and clearance. This is achieved by adjusting the weighting coefficients. , This can balance the relationship between antenna gain performance (shape-dominated) and mechanical assembly safety (gap-dominated): Shape approximation weighting coefficient Used to adjust the dominant role of surface accuracy in optimization, increasing This forces the system to prioritize parabolic focusing performance, but may result in slight deviations in edge gaps; gap constraint weighting coefficient (Dimensionless), used to adjust the dominance of edge stitching accuracy in optimization, increasing... This will force the system to prioritize ensuring a tight fit of the mechanical structure, but may cause the overall shape to deviate slightly from the theoretical equation. and The value of is not fixed, but is used as an adjustable hyperparameter, which is dynamically adjusted according to the current residual convergence during the iterative solution process in the subsequent step S4.

[0040] S4. Employing an "inside-out" sequential iterative optimization strategy, the pose of the central fixed reflector is prioritized and used as a rigid boundary constraint. A joint control objective function is then used to solve for the rigid body transformation matrix and virtually assemble each reflector sub-block to be assembled, according to spatial adjacency relationships, thereby obtaining the rigid body transformation matrix of all reflector sub-blocks to be assembled. This step proposes a recursive assembly strategy based on topological adjacency relationships. By "freezing" the optimized reflector sub-blocks one by one, the rigid boundary range is gradually expanded, effectively suppressing the propagation and accumulation of assembly errors.

[0041] As a preferred embodiment of step S4, the specific process includes: S41. Using the fixed central reflector located at the geometric center of the antenna as a reference block, lock the pose of the reference block as the starting rigid boundary constraint for the entire assembly sequence, and set all its edge feature points... Store the set of rigid boundaries in the local area Local rigid boundary set It represents all the fixed physical boundaries that can be used as references at the current moment.

[0042] S42. Determine the assembly sequence according to the spatial adjacency relationship, construct the topological adjacency matrix between the central fixed reflective surface and each reflective surface sub-block, and generate a spiral or ring-shaped assembly sequence including each reflective surface sub-block to be assembled based on the breadth-first search algorithm with the reference block as the root node.

[0043] As a preferred embodiment of step S42, the specific process includes: S421. Based on the CAD model of the satellite antenna reflector design, construct the topological adjacency matrix between the central fixed reflector and each reflector sub-block. If the center is a fixed reflective surface With reflective surface sub-block If there is a common edge, then ,otherwise Similarly, if the reflective surface sub-block With reflective surface sub-block If there is a common edge, then ,otherwise .

[0044] S422. Using the constructed topological adjacency matrix as the input to the underlying data structure of the graph traversal, and based on the breadth-first search algorithm, with the reference block as the root node, the next ring of blocks physically adjacent to the current node (the current reflective surface sub-block) is identified layer by layer by querying the elements with a value of 1 in the matrix, thereby generating a spiral or ring-shaped assembly sequence. ,in Indicates the first A reflective surface sub-block to be assembled. This represents the total number of reflective surface sub-blocks to be assembled. This assembly sequence ensures that each reflective surface sub-block to be assembled... It has an adjacency relationship with at least one fixed preceding reflective surface sub-block (or a central fixed reflective surface), which ensures the completeness of the constraints.

[0045] S43. Based on the assembly sequence, select the reflective surface sub-blocks to be assembled as the current optimization objects, and substitute the current rigid boundary set into the joint control objective function. Solve for the rigid body transformation matrix of the current optimization object.

[0046] As a preferred embodiment of step S43, the specific process of solving the rigid body transformation matrix of the current optimization object includes: S431. Define the state vector of the current optimization object. ;in, Indicates the transpose operation; , , These represent the translation vectors along the x, y, and z axes, respectively, and constitute the translation components of the rigid body transformation matrix of the current optimization object. , , These represent the rotation angles about the x-axis, y-axis, and z-axis, respectively, forming the rotation angle components of the rigid body transformation matrix of the current optimization object. Represents the space of real numbers.

[0047] S432. The Levenberg-Marquardt (LM) algorithm is used to jointly regulate the objective function. Perform iterative minimization to obtain the state increment for each iteration. The joint control objective function is dynamically adjusted during the solution process. Surface approximation weighting coefficient With gap constraint weight coefficient .

[0048] As a preferred embodiment of step S432, the Levenberg-Marquardt (LM) algorithm is used to jointly regulate the objective function. Perform iterative minimization to obtain the state increment for each iteration. The specific process includes: S4321. Perform a geometric consistency check on the edge matching point pairs. If the edge matching point... If the included angle of the normal vector is greater than a preset threshold (30° in this embodiment) or the distance is greater than a preset value (5mm in this embodiment), it is determined to be a mismatch. The edge matching point pair is temporarily removed from the solution process of the current iteration to prevent measurement noise from destroying the optimization direction.

[0049] S4322. Calculate the objective function of joint regulation. Jacobian matrix The Jacobian matrix The mathematical representation is as follows: ;

[0050] in, Represents the surface approximation error term The Jacobian matrix describes the partial derivatives of the effective point coordinates of the profile with respect to the axial residuals. Indicates the gap uniformity error term The Jacobian matrix describes the partial derivative of the coordinate changes of the edge feature points with respect to the gap distance.

[0051] S4323. Dynamically adjust the trust region radius or damping factor based on the current error residual, and solve the following linear equations within the Levenberg-Marquardt algorithm framework to obtain the state increment. : ; in, Approximate Hessian matrix; It is a diagonal weight matrix; The gradient vector, The current residual vector is a vector composed of the scalar differences between the actual pose and the ideal pose of all points on the current reflective surface sub-block. Damping factor; state increment During the acquisition process, the approximate model descent amount corresponding to the current step size and the actual joint control objective function are calculated. The ratio of the decrease in function value. Here, the step size refers to the state increment obtained in this iteration. This refers to the magnitude and direction of the vector that the current reflector sub-block moves in the pose parameter space; the approximate model descent refers to the expected reduction in the error of the objective function predicted only based on the local quadratic approximation model. If the ratio is greater than zero, it indicates a good approximation effect, and the step size is accepted, while the damping factor is reduced. If the ratio is less than zero, it indicates a poor approximation effect; therefore, the step size should be rejected, and the damping factor should be increased. Recalculate the state increment .

[0052] S4324, When the joint control objective function The decrease in the function value is less than the set threshold. or state increment The modulus is less than the preset threshold. When, or when the number of iterations reaches the preset maximum number of iterations. Stop iterating when the time is right.

[0053] In this invention, the threshold The convergence criterion for the function is to monitor the joint control objective function in two consecutive iterations. change in function value , This represents the number of iterations, when it is less than a threshold. (In this embodiment, it is set to) When the error reaches a certain level, it is considered that it can no longer be significantly reduced. The magnitude of the monitored state increment is used as the convergence criterion for step size. When it is less than the threshold (e.g., translation amount) Rotation amount When the position of the reflective surface sub-block is considered stable, the maximum number of iterations is considered to be [number missing]. To prevent the program from going into an infinite loop in extreme cases.

[0054] As a preferred embodiment of step S432, the surface approximation weight coefficients are dynamically adjusted during the solution process. Gap constraint weight coefficient Specifically, it includes the following two stages: Initial Phase (Phase I): Set larger gap constraint weight coefficients. and smaller surface approximation weighting coefficient (For example At this point, the algorithm primarily focuses on pulling the reflective surface sub-blocks to the correct edge splicing positions, quickly eliminating large positional deviations.

[0055] Fine-tuning phase (Phase II): As the number of iterations increases or the residual (the residual vector in step S4323) deteriorates, the fine-tuning phase continues. The Euclidean norm or modulus transforms the discrete errors at each point in vector form into a single scalar, thus macroscopically characterizing the comprehensive geometric deviation between the actual pose of the current reflector sub-block and the ideal target. This gradually increases the surface approximation weighting coefficient. At this point, the algorithm focuses on fine-tuning the attitude angle of the reflective surface sub-blocks to ensure they closely conform to the theoretical parabola, thereby guaranteeing that the final electrical performance meets the standards.

[0056] S433, In each iteration, based on the acquired state increment The state vector of the current optimization object Incremental updates are performed. When the iteration stops, the translation and rotation components of the state vector saved after the last update are extracted, and the translation vector and rotation matrix are constructed respectively. Then, the final rigid body transformation matrix of the reflective surface sub-block is synthesized.

[0057] S44. After solving the rigid body transformation matrix, perform virtual assembly on the reflector sub-block (that is, transform the pose data of the reflector sub-block based on the solved rigid body transformation matrix, save the new pose data, but do not change its actual pose) and mark it as "fixed". Store all edge feature points of the reflector sub-block after virtual assembly into the local rigid boundary set. Mathematically, it is represented as: ; in Indicates the first Edge feature points of the reflective surface sub-blocks to be assembled after virtual assembly The set of points formed by this. The pose data of the virtually assembled reflective surface sub-block remains unchanged throughout the entire rigid body transformation matrix solution process. This operation means that the first... The edges of each reflective surface sub-block are transformed from "object to be adjusted" to "reference benchmark", providing new constraint support for subsequent reflective surface sub-blocks.

[0058] S45. Repeat steps S43-S44 to solve the rigid body transformation matrix of each reflective surface sub-block to be assembled, until all reflective surface sub-blocks are virtually assembled.

[0059] This invention constructs a joint control objective function encompassing "surface approximation degree" and "gap uniformity," and introduces dynamic weight adjustment and mismatch elimination strategies. During the optimization process, it achieves a smooth transition from priority edge alignment to fine-grained surface orientation adjustment, ensuring both the final electrical performance of the antenna and the mechanical assembly safety between sub-blocks. This solves the problem of single constraints failing to simultaneously address multiple physics indicators. Furthermore, this invention employs an "inside-out" sequential recursive assembly strategy, utilizing topological adjacency relationships to construct dynamically expanding rigid boundaries. By locking the poses of converged reflector sub-blocks one by one, the high-dimensional global optimization problem is degraded into a series of low-dimensional local optimization problems. This effectively suppresses error propagation and accumulation effects during multi-sub-block collaborative assembly, significantly improving the computational efficiency and final convergence stability of large-scale reflector array virtual assembly.

[0060] S5. Use the rigid body transformation matrix obtained by solving to physically assemble each reflector sub-block to achieve pose coordination of the satellite antenna reflector components.

[0061] In this embodiment, the physically assembled satellite antenna reflector component can be referred to... Figure 3 .

[0062] This application also provides a satellite antenna reflector component pose coordination system based on geometric errors, used to apply the aforementioned satellite antenna reflector component pose coordination method based on geometric errors, including: The coordinate system establishment and point cloud data acquisition module is used to establish a global coordinate system and acquire the original point cloud data of the central fixed reflector and each reflector sub-block of the satellite antenna. The point cloud data preprocessing module is used to perform multi-scale filtering and voxelization on the raw point cloud data and divide it into effective points of the surface and edge feature points, and take the coordinates of the effective points of the surface and edge feature points in the global coordinate system. The registration and solving module is used to establish a joint control objective function and solve the rigid body transformation matrix of each reflective surface sub-block to be assembled in sequence according to the spatial adjacency relationship. The solved rigid body transformation matrix is ​​then sent to the physical assembly module. The physical assembly module is used to decompose the transformation matrices of each rigid body to be assembled obtained by solving into translation vectors and Euler angles, and output them to the human-machine interface or automatic assembly control system to guide technicians or robotic arms to complete the physical assembly.

[0063] This application also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the aforementioned satellite antenna reflector component pose coordination method based on geometric errors.

[0064] This application also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the aforementioned satellite antenna reflector component pose coordination method based on geometric errors.

[0065] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0066] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0067] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A method for pose coordination of satellite antenna reflector components based on geometric errors, characterized in that, include: S1. Use a laser tracker to establish a global coordinate system, and use a scanner to scan the original point cloud data of the central fixed reflector of the satellite antenna and each reflector sub-block to be assembled. S2. Perform multi-scale filtering and voxelization uniform resampling on the original point cloud data. Based on the boundary detection algorithm, divide the processed point cloud data into effective surface points and edge feature points, and obtain the coordinates of the effective surface points and edge feature points in the global coordinate system. S3. Establish a joint control objective function; the joint control objective function includes a surface approximation error term based on effective points of the surface and a gap uniformity error term based on edge feature points; S4. Lock the pose of the central fixed reflector, use the joint control objective function, and solve the rigid body transformation matrix and virtually assemble each reflector sub-block to be assembled in sequence according to the spatial adjacency relationship, so as to obtain the rigid body transformation matrix of all reflector sub-blocks to be assembled. S5. Use the rigid body transformation matrix obtained by solving to physically assemble each reflector sub-block to achieve pose coordination of the satellite antenna reflector components.

2. The method for coordinate the pose of satellite antenna reflector components based on geometric errors according to claim 1, characterized in that: In step S3, establishing the joint control objective function includes: S31. Construct the theoretical parabolic equation for the reflecting surface sub-block, defined as follows: ； in, , , These represent the x, y, and z coordinates of a point in the original point cloud data of the reflective surface sub-block in the global coordinate system. The focal length of the parabolic surface; S32. Define the rigid body transformation matrix of the reflective surface sub-block to be assembled. The rigid body transformation matrix Including rotation matrix Translation vector , Represents the real number space; for any point in the original point cloud data The new point after transformation Represented as: ； S33. Constructing the surface approximation error term based on the theoretical parabolic equation. The definition is as follows: ； in, Indicates the total number of valid points on the surface; , , They represent the first Effective points of individual surfaces After rigid body transformation matrix The effective points of the transformed new surface The x, y, and z coordinates; S34. Constructing the gap uniformity error term The definition is as follows: ； in, This represents the total number of feature points on the upper edge of the reflective surface sub-block to be assembled; Indicates the first reflective surface sub-block to be assembled Edge feature points After rigid body transformation matrix The transformed new edge feature points; This represents all points on the edge of the fixed reflecting surface, which consists of the central fixed reflecting surface and the fixed reflecting surface sub-blocks, and intersecting with... The closest point in space is obtained using the KD-tree nearest neighbor search algorithm. and This forms a pair of edge-matching points; Represents the calculation of the Euclidean norm; This represents the theoretical gap value. If the design requires seamless splicing of all reflective sub-blocks, then... If the design requires a allowance for thermal expansion gaps or adhesive layer thickness, then Set it to a constant greater than 0; S35, Introducing surface approximation weighting coefficient Gap constraint weight coefficient By linearly combining the surface approximation error term and the gap uniformity error term, a joint control objective function is obtained, mathematically represented as follows: ； in This represents the joint control objective function.

3. The method for coordinate the pose of satellite antenna reflector components based on geometric errors according to claim 2, characterized in that: Step S4 includes: S41. Using the central fixed reflective surface as a reference block, lock the pose of the reference block and set all its edge feature points. Store the set of rigid boundaries in the local area ; S42. Construct the topological adjacency matrix between the central fixed reflective surface and each reflective surface sub-block. Based on the breadth-first search algorithm, generate a spiral or ring-shaped assembly sequence including each reflective surface sub-block to be assembled, with the reference block as the root node. S43. Based on the assembly sequence, select the reflective surface sub-blocks to be assembled as the current optimization objects, and substitute the current rigid boundary set into the joint control objective function. Solve for the rigid body transformation matrix of the current optimization object; S44. After solving the rigid body transformation matrix, the reflective surface sub-block is virtually assembled and marked as fixed. All edge feature points of the virtually assembled reflective surface sub-block are stored in the local rigid boundary set. ; S45. Repeat steps S43-S44 to solve the rigid body transformation matrix of each reflective surface sub-block to be assembled, until all reflective surface sub-blocks are virtually assembled.

4. The method for coordinate the pose of satellite antenna reflector components based on geometric errors according to claim 3, characterized in that: Step S42 includes: S421. Construct the topological adjacency matrix between the central fixed reflector and each reflector sub-block. If the center is a fixed reflective surface With reflective surface sub-block If there is a common edge, then ,otherwise Similarly, if the reflective surface sub-block With reflective surface sub-block If there is a common edge, then ,otherwise ; S422. Based on the breadth-first search algorithm, with the reference block as the root node, the topological adjacency matrix is ​​queried. Elements with a median value of 1 are used to identify the next ring of reflective sub-blocks that are physically adjacent to the current reflective sub-block, thereby generating a spiral or ring-shaped assembly sequence. ,in Indicates the first A reflective surface sub-block to be assembled. This represents the total number of reflective surface sub-blocks to be assembled.

5. The method for coordinate the pose of satellite antenna reflector components based on geometric errors according to claim 3, characterized in that: In step S43, solving the rigid body transformation matrix of the current optimization object includes: S431. Define the state vector of the current optimization object. ;in, Indicates the transpose operation; , , These represent the translation vectors along the x, y, and z axes, respectively, and constitute the translation components of the rigid body transformation matrix of the current optimization object. , , These represent the rotation angles about the x-axis, y-axis, and z-axis, respectively, forming the rotation angle components of the rigid body transformation matrix of the current optimization object. Represent the space of real numbers; S432. Using the Levenberg-Marquardt algorithm to jointly regulate the objective function. Perform iterative minimization to obtain the state increment for each iteration. The joint control objective function is dynamically adjusted during the solution process. Surface approximation weighting coefficient With gap constraint weight coefficient ; S433, In each iteration, based on the obtained state increment The state vector of the current optimization object Incremental updates are performed. When the iteration stops, the translation and rotation components of the state vector saved after the last update are extracted, and the translation vector and rotation matrix are constructed respectively. Then, the final rigid body transformation matrix of the reflective surface sub-block is synthesized.

6. The method for coordinate the pose of satellite antenna reflector components based on geometric errors according to claim 5, characterized in that: In step S432, the Levenberg-Marquardt algorithm is used to jointly regulate the objective function. Perform iterative minimization to obtain the state increment for each iteration. ,include: S4321. Perform a geometric consistency check on the edge matching point pairs. If the edge matching point... If the included angle of the normal vectors is greater than a preset threshold or the distance is greater than a preset value, it is determined to be a mismatch, and the edge matching point pair is temporarily removed from the solution process of the current iteration. S4322. Calculate the objective function of joint regulation. Jacobian matrix The Jacobian matrix The mathematical representation is as follows: ； in, Represents the surface approximation error term Jacobian matrix, Indicates the gap uniformity error term The Jacobian matrix; S4323. Solve the following system of linear equations within the framework of the Levenberg-Marquardt algorithm to obtain the state increment. : ； in, For approximate Hessian matrix, It is a diagonal weight matrix. The gradient vector, The current residual vector is a vector composed of the scalar differences between all points on the current reflective surface sub-block and the theoretical target. It is the damping factor; S4324, When the joint control objective function The decrease in the function value is less than the set threshold. or state increment The modulus is less than the preset threshold. When, or when the number of iterations reaches the preset maximum number of iterations. Stop iterating when the time is right.

7. The method for coordinate the pose of satellite antenna reflector components based on geometric errors according to claim 6, characterized in that: In step S432, the surface approximation weight coefficients are dynamically adjusted during the solution process. Gap constraint weight coefficient ,include: Set large gap constraint weight coefficients in the initial stage. Approximation weighting coefficients for small surfaces As the number of iterations increases or the residual decreases, the surface area gradually approaches the weighting coefficient. The residual is the residual vector in step S4323. The Euclidean norm or modulus.

8. A satellite antenna reflector component pose coordination system based on geometric errors, used to apply the satellite antenna reflector component pose coordination method based on geometric errors as described in any one of claims 1-7, characterized in that, include: The coordinate system establishment and point cloud data acquisition module is used to establish a global coordinate system and acquire the original point cloud data of the central fixed reflector and each reflector sub-block of the satellite antenna. The point cloud data preprocessing module is used to perform multi-scale filtering and voxelization on the raw point cloud data and divide it into effective points of the surface and edge feature points, and take the coordinates of the effective points of the surface and edge feature points in the global coordinate system. The registration and solving module is used to establish a joint control objective function and solve the rigid body transformation matrix of each reflective surface sub-block to be assembled in sequence according to the spatial adjacency relationship. The solved rigid body transformation matrix is ​​then sent to the physical assembly module. The physical assembly module is used to decompose the transformation matrices of each rigid body to be assembled obtained by solving into translation vectors and Euler angles, and output them to the human-machine interface or automatic assembly control system to guide technicians or robotic arms to complete the physical assembly.

9. An electronic device, characterized in that, The electronic device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the satellite antenna reflector component pose coordination method based on geometric errors as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the pose coordination method for satellite antenna reflector components based on geometric errors, as described in any one of claims 1-7.

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