Laser tracking based alignment positioning system and method

Abstract

The application relates to the technical field of large structure space pose online compensation, and discloses a laser tracking-based assembling and adjusting positioning system and method, wherein the laser tracking-based assembling and adjusting positioning method comprises the following steps: arranging a plurality of laser tracking targets, and establishing an observation model separating pose from deformation; obtaining rigid body pose estimation and deformation state estimation; updating an actuator instruction and driving a posture adjusting actuator to perform pose adjustment; detecting the length of the deformation state estimation, and triggering an unloading force balancing fine adjustment process; determining whether assembling and adjusting reaches target precision; through the arrangement of the laser tracking targets and the introduction of the observation model, the application models the measurement points collected by the laser tracker as the superposition of rigid body pose and limited dimension deformation, estimates rigid body rotation, rigid body translation and deformation modal coefficients, realizes the separation of the pose and the deformation from the mechanism, and improves the positioning precision and assembling and adjusting reliability of a high-precision optical assembling and adjusting station.

Description

Technical Field

[0001] This invention relates to the field of online spatial pose compensation technology for large structures, and more specifically, to a laser tracking-based assembly and positioning system and method. Background Technology

[0002] In the assembly and adjustment of large-scale precision equipment (such as the assembly and positioning of large optical components, spacecraft structural parts, precision platforms and their tooling systems), it is usually necessary to complete high-precision spatial position and attitude adjustments within a limited space, and to monitor and correct deviations in real time during the assembly and adjustment process. Laser tracking measurement technology has advantages such as long measurement distance, high accuracy, and the ability to acquire three-dimensional coordinates in real time, and is therefore widely used in the assembly, positioning and online inspection of large components.

[0003] Chinese Patent CN118500364B discloses a system and method for online spatial pose compensation of large structures based on multiple laser trackers. The system includes a numerically controlled positioner (CNC) locator, a laser tracker, a reflective target ball, a ball joint, and a large structure. Each laser tracker corresponds to one reflective target ball and is installed close to it. The CNC locator is connected to the large structure via a ball joint. Multiple reflective target balls are distributed and installed on the large structure. At least three sets of CNC locators and laser trackers are provided. The system also provides a method that avoids the inefficiency of single-point measurement and iterative pose adjustment in traditional large structure pose adjustment and positioning methods. Furthermore, it allows for real-time detection and compensation of the pose adjustment trajectory, ensuring the positioning accuracy of the large structure.

[0004] However, existing pose calculation methods based on rigid body assumptions often fail to achieve optimal performance in assembly scenarios involving heavy loads, flexible supports, or unloading / contact constraints. Taking vertical mirror assembly as an example, under conditions of multi-point spring unloading on the mirror back and parallel unloading via the mirror edge ring support, during rotation, tilting, and lifting adjustments, changes in support point reaction force distribution, friction state, soft pad compression and rebound, and connector preload can cause elastic deformation, contact nonlinearity, and micro-slippage in the mirror body and tooling structure. In this case, the target ball coordinate changes measured by the laser tracker contain two components: one originating from the rigid body motion of the entire object, and the other from the elastic deformation and local relative displacement of the object or tooling. When a rigid body model is still used to fit the target ball data, the algorithm equates the deformation term to pose changes, leading to inconsistencies between the calculated pose and the actual assembly state of the object. This can result in problems such as pose alignment without shape / surface conformation, and non-repeatable results under different orientations. Summary of the Invention

[0005] The purpose of this invention is to provide a laser-tracking-based assembly and positioning system and method to solve the above-mentioned problems.

[0006] This invention provides a laser-tracking-based assembly and positioning method, comprising the following steps:

[0007] Multiple laser tracking targets are deployed on the surface of the object being tracked and its supporting structure. The reference coordinates of the targets are calibrated, and an observation model separating pose and deformation is established based on the reference coordinates.

[0008] The unloading force vector of the current sampling period is obtained from the gravity unloading system. Based on the observation model and the unloading force vector, a weighted least squares optimization problem is constructed to solve the rigid body pose estimate and deformation state estimate, thereby realizing the joint estimation and separation of pose and deformation.

[0009] The pose error is calculated based on the rigid body pose estimation value. The pose error is mapped to the actuator fine-tuning vector. The actuator command is updated based on the fine-tuning vector and the attitude adjustment actuator is driven to perform pose adjustment.

[0010] The modulus of the deformation state estimate is detected. When the Euclidean norm of the deformation state estimate exceeds the preset deformation threshold for a consecutive preset number of durations, the unloading force equalization fine-tuning process is triggered.

[0011] The system determines whether the setup has reached the target accuracy based on the pose error. If the target accuracy is reached, the setup process ends; otherwise, it returns to continue executing the process of solving the rigid body pose estimate and deformation state estimate.

[0012] Furthermore, an observation model separating pose and deformation is established, including:

[0013] Establish a global coordinate system and a structural local coordinate system;

[0014] For each target, establish reference coordinates in the local structural coordinate system;

[0015] The deformation mode basis is pre-set and a mode matrix is ​​set for each target. The mode matrix has 3 rows and the number of columns is the deformation mode dimension.

[0016] An observation model is established, in which the measurement coordinates of each target are the result of the rigid body rotation matrix acting on the coordinate terms and then superimposed with the rigid body translation vector and measurement noise. The coordinate terms are the sum of the reference coordinates and deformation displacement of the target, and the deformation displacement is the modal matrix multiplied by the deformation modal coefficient vector.

[0017] Furthermore, the rigid body rotation matrix describes the rotation relationship between the local coordinate system and the global coordinate system of the structure;

[0018] The rigid body translation vector describes the position of the origin of the local coordinate system in the global coordinate system;

[0019] The deformation mode coefficient vector is a column vector whose dimension is equal to the deformation mode dimension. Each component in the deformation mode coefficient vector corresponds to a deformation mode.

[0020] Furthermore, the estimated values ​​of the rigid body pose and deformation state are obtained as follows:

[0021] The gravity unloading system includes setting multiple unloading points on the back of the object being unloaded, and each unloading point is equipped with an unloading force sensor. The dimension of the unloading force vector is equal to the number of unloading force sensors.

[0022] Set a reference unloading force vector, which is the unloading force value at each unloading point under the calibration state;

[0023] A mapping matrix from force to deformation mode is constructed, wherein the number of rows in the mapping matrix is ​​equal to the deformation mode dimension and the number of columns is equal to the number of unloading force sensors;

[0024] The a priori predicted values ​​of the forces in the deformation mode are calculated by multiplying the mapping matrix by the unloading force difference term, which is the difference between the current unloading force vector and the reference unloading force vector.

[0025] Set a deformation force consistency regularization term, which is the square of the Euclidean norm of the difference between the deformation modal coefficient vector to be estimated and the force prior prediction value;

[0026] A weighted least squares optimization problem is constructed, and the estimated values ​​of the rigid body rotation matrix, rigid body translation vector, and deformation mode coefficient vector are obtained by solving the problem. The estimated values ​​of the rigid body rotation matrix and rigid body translation vector together constitute the rigid body pose estimate, and the deformation mode coefficient vector constitutes the deformation state estimate.

[0027] Furthermore, the objective function of the weighted least squares optimization problem is set as the sum of the data fitting term, the force consistency constraint term, and the deformation sparsity constraint term:

[0028] The data fitting term represents the weighted sum of squared residuals between all target measured coordinates and model predicted coordinates. The model predicted coordinates are the estimated values ​​of the rigid body rotation matrix acting on the coordinate term and then superimposed with the rigid body translation vector.

[0029] The force consistency constraint term is equal to the preset force consistency regularization coefficient multiplied by the deformation force consistency regularization term;

[0030] The deformation sparsity constraint term is equal to the preset deformation sparsity regularization coefficient multiplied by the square of the Euclidean norm of the deformation modal coefficient vector.

[0031] Furthermore, the weighted least squares optimization problem is solved using the incremental Gauss-Newton method, including:

[0032] For the optimization and update of the rigid body rotation matrix, the Lie algebra parameterization method is adopted. The current rigid body rotation matrix is ​​converted into a three-dimensional rotation vector through logarithmic mapping. The increment of the rotation vector is calculated in the Lie algebra space. The increment of the rotation vector is converted into an incremental rotation matrix through exponential mapping. The current rigid body rotation matrix is ​​multiplied by the incremental rotation matrix to obtain the updated rigid body rotation matrix.

[0033] For rigid body translation vectors and deformation mode coefficient vectors, a direct addition update method is used, that is, the current vector value is added to the increment vector obtained by the current iteration calculation;

[0034] Use the estimation result of the previous sampling period as the initial value of the current sampling period;

[0035] The iteration termination condition is that the norm of the parameter update is less than the preset convergence threshold or the preset maximum number of iterations is reached.

[0036] Furthermore, updating the executor instructions based on the fine-tuning vector includes:

[0037] The target pose is set as the target rotation matrix and the target translation vector;

[0038] Calculate the rotation error vector, which is obtained by logarithmic transformation of the relative rotation matrix. The relative rotation matrix is ​​the product of the target rotation matrix and the transpose of the estimated rigid body rotation matrix.

[0039] Calculate the translation error vector, which is the difference between the target translation vector and the estimated value of the rigid body translation vector;

[0040] The rotation error vector and translation error vector are merged into a pose error vector, which is then mapped to the fine-tuning vector of the actuator. The pseudo-inverse of the actuator's Jacobian matrix is ​​calculated using the damped least squares method, and the fine-tuning vector of the actuator is calculated based on the pseudo-inverse.

[0041] The calculated fine-tuning vector is subjected to safety limiting, and the limiting function independently performs saturation limiting on each component of the fine-tuning vector.

[0042] The update of the executor instruction adopts a smoothing strategy. The executor instruction vector of the next sampling period is equal to the executor instruction vector of the current sampling period plus the fine-tuning term. The fine-tuning term is a preset smoothing coefficient multiplied by the current fine-tuning vector.

[0043] The updated actuator command vector is sent to the attitude adjustment actuator.

[0044] Furthermore, the pseudo-inverse of the actuator Jacobian matrix is ​​calculated by multiplying the transpose of the actuator Jacobian matrix by the inverse of the matrix. The matrix is ​​the product of the actuator Jacobian matrix and the transpose of the actuator Jacobian matrix plus a unit term, where the unit term is a preset damping factor multiplied by the identity matrix.

[0045] The actuator fine-tuning vector is calculated by multiplying the pseudo-inverse of the actuator Jacobian matrix by the pose error vector.

[0046] In the aforementioned safety limiting process, for each actuator, a preset lower limit and a preset upper limit for the fine-tuning vector are set. If the calculated fine-tuning vector is less than the preset lower limit, the fine-tuning vector is changed to the preset lower limit value. If the calculated fine-tuning vector is greater than the preset upper limit, the fine-tuning vector is changed to the preset upper limit value. Otherwise, the original value remains unchanged.

[0047] Furthermore, the unloading force balancing fine-tuning process includes:

[0048] The unloading force fine-tuning direction vector is calculated. The unloading force fine-tuning direction vector is the difference between the zero vector and the current deformation mode coefficient vector estimate multiplied by the mapping matrix from the deformation mode coefficient space to the unloading force space. The dimension of the zero vector is equal to the deformation mode dimension.

[0049] Apply static balance constraints to the unloading force fine-tuning direction vector, including: the sum of the total unloading forces at each unloading point after the unloading force adjustment remains within the preset total unloading force range, and the unloading force adjustment amount at each unloading point satisfies the single-point unloading force change range constraint;

[0050] For systems equipped with unloading force adjustment actuators, the unloading force adjustment command vector is sent to the unloading force adjustment actuator. The unloading force adjustment command vector is the unloading force vector of the current sampling period plus an adjustment term. The adjustment term is the preset unloading force adjustment step size coefficient multiplied by the unloading force fine-tuning direction vector.

[0051] This invention provides a laser-tracking-based assembly and positioning system for storing computer-readable instructions, which, when read, can execute the aforementioned laser-tracking-based assembly and positioning method; the system includes:

[0052] The deformation observation module deploys multiple laser tracking targets on the surface of the object being monitored and its supporting structure, calibrates the reference coordinates of the targets, and establishes an observation model that separates pose and deformation based on the reference coordinates.

[0053] The joint estimation module obtains the unloading force vector of the current sampling period from the gravity unloading system, constructs a weighted least squares optimization problem based on the observation model and the unloading force vector, and solves it to obtain the rigid body pose estimate and deformation state estimate, thereby realizing the joint estimation and separation of pose and deformation.

[0054] The pose adjustment module calculates the pose error based on the rigid body pose estimation value, maps the pose error to the actuator fine-tuning vector, updates the actuator command based on the fine-tuning vector, and drives the pose adjustment actuator to perform pose adjustment.

[0055] The deformation adjustment module detects the modulus of the deformation state estimate. When the Euclidean norm of the deformation state estimate exceeds the preset deformation threshold for a continuous preset number of cycles, the unloading force balancing fine-tuning process is triggered.

[0056] The assembly and adjustment determination module determines whether the assembly and adjustment has reached the target accuracy based on the pose error. When the target accuracy is reached, the assembly and adjustment process ends; otherwise, it returns to continue executing the process of solving the rigid body pose estimation value and deformation state estimation value.

[0057] The beneficial effects of this invention are as follows: By deploying a laser tracking target on the plane mirror assembly and introducing a low-order deformation mode model, the measurement points collected by the laser tracker are uniformly modeled as a superposition of rigid body pose and finite-dimensional deformation. In the optimization solution, the rigid body rotation, rigid body translation, and deformation mode coefficients are estimated simultaneously, achieving mechanistic separability between pose and deformation. Compared to traditional assembly methods that only consider measurement results as rigid body motion, this invention can extract the true rigid body pose even under conditions of uneven gravity unloading and structural flexibility, avoiding the misinterpretation of structural deformation as pose error for compensation. This significantly improves the positioning accuracy and assembly reliability of high-precision optical assembly stations.

[0058] This invention incorporates the unloading force measurement of a gravity unloading system into the deformation estimation process, constructs a mapping matrix from force to deformation modes and a deformation force consistency regularization term, and fuses the unloading force prior with laser tracking observations within a weighted least squares framework. This achieves robust estimation and suppression of deformation modes, effectively reducing the impact of sensor noise and local nonlinearities on the results. The system adaptively adjusts the deformation mode dimension, measurement weights, and damping factors by monitoring the condition number of the observation matrix and the actuator Jacobian matrix. Furthermore, it introduces damped least squares, amplitude limiting, and command smoothing strategies in the actuator fine-tuning calculation, ensuring good numerical stability and dynamic safety of the pose closed-loop adjustment even under heavy-load scenarios at the tower top. Simultaneously, this invention uses the deformation state estimation results to guide the unloading force equalization fine-tuning and forms a digital fingerprint with the deformation mode coefficients and unloading force vector at convergence, enabling traceability and process reproducibility of the assembly and adjustment process. This endows the system with integrated collaborative capabilities for deformation monitoring, pose control, and unloading optimization, demonstrating significant engineering application value. Attached Figure Description

[0059] Figure 1 This is a flowchart illustrating the laser tracking-based assembly and positioning method of the present invention.

[0060] Figure 2 This is an example diagram showing the rigid body pose estimation and deformation state estimation obtained in the laser tracking-based assembly and positioning method of the present invention;

[0061] Figure 3 This is an example diagram of pose adjustment in the laser tracking-based assembly and positioning method of the present invention;

[0062] Figure 4 This is a module example diagram of the laser tracking-based assembly and positioning system of the present invention. Detailed Implementation

[0063] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, features described in some examples may be combined in other examples.

[0064] The assembly and positioning system and method based on laser tracking include the following embodiments:

[0065] Example 1:

[0066] A laser-tracking-based assembly and positioning method was applied to a high-precision assembly and adjustment station on a vertical assembly and adjustment test tower. In this scenario, the object being adjusted is a plane mirror assembly, which has the ability to rotate 360 ​​degrees around its optical axis and can be tilted in two dimensions within a range of approximately ±1.5 degrees. The gravity unloading system of the plane mirror assembly includes approximately 30 spring unloading points on the back of the mirror and a ring support on the mirror edge. Each unloading point is equipped with an unloading force sensor, with an unloading resolution on the order of approximately 1 Newton. A laser tracker is installed and provides a global reference point for coordinate unification. The assembly and adjustment control system operates in closed-loop mode, capable of driving the attitude adjustment mechanism and the rotation mechanism, and receiving sensor data in real time.

[0067] The laser tracking-based assembly and positioning method in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0068] Step 100: Deploy multiple laser tracking targets on the surface of the object being tracked and its supporting structure, calibrate the reference coordinates of the targets, and establish an observation model that separates pose and deformation based on the reference coordinates.

[0069] First, a global coordinate system and a structural local coordinate system are established. The global coordinate system takes the reference point of the assembly and testing tower as its origin, and its three coordinate axes are defined along the east, north, and vertically upward directions, respectively. The structural local coordinate system takes the geometric center of the plane mirror assembly as its origin, and its three coordinate axes are bound to the structural features of the assembly. The reason for adopting a dual coordinate system design is that the global coordinate system provides a unified reference benchmark for all equipment within the assembly and testing tower, ensuring the comparability and traceability of measurement results between different assembly and testing stations. The structural local coordinate system is directly related to the physical structure of the plane mirror assembly, making the attitude description and deformation analysis of the assembly more intuitive and matching the mechanical properties of the assembly itself. The two coordinate systems are linked through rigid body transformation, ensuring both global consistency and facilitating local analysis.

[0070] Multiple laser tracking targets are deployed on the surface of the plane mirror assembly and its supporting structure. The total number of targets ranges from 4 to 12. The number of targets is determined by comprehensively considering measurement redundancy and system complexity. When the diameter of the plane mirror assembly is less than one meter, 4 to 6 targets can be selected; when the diameter is greater than one meter, 8 to 12 targets can be selected to improve measurement coverage. The reason for choosing this range of target numbers is that too few targets will result in insufficient measurement information to accurately estimate the rigid body pose and deformation state simultaneously. In particular, when there are fewer than 4 targets, it is impossible to uniquely determine the rigid body pose in three-dimensional space. On the other hand, too many targets will increase the measurement time and data processing burden of the laser tracker, reduce the real-time response capability of the system, and also increase the calibration workload and system maintenance costs. For each target, its reference coordinates are pre-calibrated in the local coordinate system of the structure. These reference coordinates are three-dimensional vectors obtained under the nominally undeformed state. The purpose of pre-calibrating the reference coordinates is to establish the baseline state of the target position, so that in subsequent measurements, the positional changes caused by rigid body motion and deformation can be identified by comparing the difference between the current measured coordinates and the reference coordinates, thus providing the necessary reference benchmark for separating pose and deformation.

[0071] A pre-defined deformation modal basis is established, which can be obtained through finite element analysis, empirical measurement, or online learning. The reason for using a deformation modal basis is that the deformation of a plane mirror assembly during gravity unloading typically exhibits a regular spatial distribution pattern. These patterns can be approximated by a few dominant deformation modes, such as overall bending, torsion, and local concavity. Using a low-order modal basis not only significantly reduces the parameter dimension of the deformation description, improving the computational efficiency and numerical stability of the estimation algorithm, but also effectively suppresses the influence of measurement noise on deformation estimation. This is because high-order modes often correspond to small local deformation features, which are easily confused with measurement noise, while low-order modes correspond to macroscopic overall deformation features and have stronger noise resistance. For each target point, a corresponding modal matrix is ​​set, with three rows. This number of rows is because the position of each target point in three-dimensional space is described by three coordinate components, corresponding to the east, north, and vertically upward directions of the global coordinate system. Therefore, the deformation displacement of the target point also needs to be expressed in these three directions, thus giving the modal matrix a three-row structure. The number of columns in the modal matrix represents the deformation modal dimension, which is determined based on the structural complexity of the plane mirror assembly. For simple symmetrical structures, it can be 2 to 3, while for complex asymmetrical structures, it can be 5 to 6. Generally, a value of 4 is chosen to balance deformation description capability and computational efficiency. Each column of the modal matrix represents an independent deformation modal direction, describing the displacement components of the target under the corresponding deformation mode.

[0072] This establishes a unified observation model where the measured coordinates of each target in the current sampling period are equal to the result of the rigid body rotation matrix acting on the coordinate terms, plus the rigid body translation vector and measurement noise. The coordinate terms are the sum of the target's reference coordinates and deformation displacement. This unified observation model is established to decompose the actual measured position of the target into the superposition of three physical processes: first, the position change caused by the rigid body motion of the target along with the plane mirror assembly; second, the position offset caused by local deformation due to factors such as uneven unloading force; and finally, the unavoidable random errors during laser tracker measurement. This decomposition method conforms to the actual physical process, allowing subsequent mathematical optimization methods to separate two different types of physical quantities—rigid body pose and deformation state—from the measurement data. The rigid body rotation matrix belongs to a three-dimensional special orthogonal group. A three-dimensional special orthogonal group is defined as a set of third-order square matrices whose product of the matrix and its transpose equals the identity matrix and whose determinant is one. This rotation matrix describes the rotation relationship of the structure's local coordinate system relative to the global coordinate system. The rigid body translation vector is a three-dimensional column vector describing the position of the origin of the structure's local coordinate system in the global coordinate system. The deformation displacement is equal to the modal matrix multiplied by the deformation mode coefficient vector. The deformation mode coefficient vector is a column vector with dimensions equal to the deformation mode dimension. Each component in the deformation mode coefficient vector corresponds to a specific deformation mode. The magnitude of this component indicates the intensity of the deformation mode being excited within the current sampling period. Specifically, when the absolute value of a certain deformation mode coefficient vector component is large, it indicates that the plane mirror component has undergone significant deformation under the deformation mode described by that deformation mode. For example, the first deformation mode may correspond to overall bending deformation, the second deformation mode may correspond to torsional deformation, and the third deformation mode may correspond to local concave deformation. The positive values ​​of each deformation mode coefficient vector component... The negative sign indicates the deformation direction of the deformation mode; a positive value indicates deformation along the positive direction of the mode, and a negative value indicates deformation along the negative direction. The deformation mode coefficient vector, through a linear combination of the contributions of each deformation mode, fully characterizes the non-rigid deformation state induced by factors such as uneven unloading force. The physical dimension of this vector is length, usually in millimeters. Its numerical range depends on the stiffness characteristics of the plane mirror assembly and the uniformity of the unloading force distribution. For high-stiffness assemblies or those with uniform unloading force distribution, the absolute values ​​of each component of the deformation mode coefficient vector are usually less than 0.5 mm. For low-stiffness assemblies or those with uneven unloading force distribution, the absolute values ​​of each component of the deformation mode coefficient vector may reach 1 to 3 mm. The measurement noise vector follows a Gaussian distribution with zero mean, and its covariance matrix is ​​determined by the measurement accuracy of the laser tracker.

[0073] The established observation model and corresponding parameters are used as inputs for subsequent steps. This observation model provides a mathematical framework for subsequent joint estimation, clarifies the relationship between the measurement data and the parameters to be estimated, and enables the optimization algorithm to effectively extract rigid body pose and deformation state information from the measurement data. The accuracy of the observation model directly affects the quality of the estimation results; therefore, in practical applications, it is necessary to ensure the accuracy of the model parameters through thorough calibration and verification.

[0074] Step 200: Obtain the unloading force vector for the current sampling period from the gravity unloading system. Based on the observation model and the unloading force vector, construct a weighted least squares optimization problem to solve for the rigid body pose estimate and deformation state estimate, thus achieving joint estimation and separation of pose and deformation. Specifically, as follows... Figure 2 As shown.

[0075] The unloading force vector for the current sampling period is obtained from the gravity unloading system. The dimension of this vector is equal to the number of unloading force sensors. The number of unloading force sensors is determined based on the size and weight distribution of the plane mirror assembly. For lightweight assemblies with a diameter less than 0.8 meters, 15 to 20 sensors can be configured, while for heavy-duty assemblies with a diameter greater than 1.2 meters, 30 to 40 sensors can be configured to ensure the uniformity of the unloading force distribution. Each component of the unloading force vector represents the measured unloading force at the corresponding spring unloading point in the current sampling period. The reason for introducing the unloading force vector as input is that there is a direct physical causal relationship between the distribution of unloading force and the deformation state of the plane mirror assembly. When the unloading force at some unloading points deviates from the ideal value, it will generate an uneven stress distribution inside the mirror, leading to observable deformation. By incorporating the unloading force information into the estimation algorithm, an independent physical prior constraint can be provided for the estimation of the deformation state, improving the accuracy and robustness of the deformation estimation. Especially when the number of targets is limited or the measurement noise is high, the unloading force information can effectively compensate for the insufficiency of laser tracking measurement information and avoid large drift in deformation estimation.

[0076] A reference unloading force vector is set, which represents the unloading force value at each unloading point under calibration conditions. Calibration conditions refer to the ideal state where the plane mirror assembly is in its nominal attitude and with minimal deformation. This reference unloading force vector is pre-calibrated during the system initialization phase. The purpose of setting the reference unloading force vector is to establish a baseline state for the unloading force distribution. This baseline state corresponds to the ideal unloading configuration with minimal deformation. By comparing the difference between the current unloading force and the reference unloading force, it can be determined whether the current unloading force distribution deviates from the ideal state, thereby predicting the possible deformation. At the same time, the reference unloading force vector also provides a target reference for subsequent unloading force adjustments, giving unloading force optimization a clear direction. The accurate calibration of this reference vector is crucial to the effectiveness of the entire method. Typically, the optimal reference unloading force distribution is determined through multiple experiments and optimizations during the system installation and commissioning phase.

[0077] A force-to-deformation mode mapping matrix is ​​constructed, where the number of rows equals the deformation mode dimension and the number of columns equals the number of unloading force sensors. The mapping matrix is ​​obtained through offline calibration. During the calibration phase, several sets of known force changes are applied to the unloading system, and the corresponding deformation mode coefficient changes are measured. The elements of the mapping matrix are determined using the least squares regression method. The reason for using offline calibration is that the force-to-deformation mapping relationship is influenced by a combination of factors, including the material properties, geometry, and support method of the plane mirror assembly, making it difficult to obtain accurately through purely theoretical calculations. However, by actually applying known force changes and measuring the corresponding deformation response, the true mapping relationship can be learned directly from the experimental data. This data-driven calibration method automatically incorporates the combined effects of all actual physical effects without requiring detailed modeling of complex mechanical processes. Considering the friction, gap, and hysteresis effects at the spring unloading point, as well as the coupling effect between the mirror edge ring support and the back spring, the force-to-deformation mapping relationship may exhibit nonlinear characteristics under different operating conditions. To improve mapping accuracy, a piecewise linear mapping strategy is adopted, dividing the unloading force amplitude range into several working intervals, each corresponding to an independently calibrated mapping matrix; alternatively, a gain-adaptive approach is used, dynamically adjusting the scaling factor of the mapping matrix based on the magnitude of the current unloading force vector and the historical deformation residuals. These adaptive strategies aim to approximate the true nonlinear mapping relationship as closely as possible while maintaining the algorithm's real-time performance. The piecewise linear strategy approximates the overall nonlinear characteristics by using different linear mappings in different working intervals, while the gain-adaptive approach dynamically corrects the mapping strength based on the actually observed deformation residuals. Both methods significantly improve mapping accuracy while keeping computational complexity under control. When the measurement noise from the unloading force sensor is high, the weight of prior force information in the joint estimation is reduced to avoid amplifying noise and misleading deformation estimation. During the assembly and adjustment process, the mapping matrix can be calibrated online based on accumulated measurement data, gradually improving the accuracy of force-to-deformation prediction.

[0078] Multiplying the above mapping matrix by the unloading force difference term, which is the difference between the current unloading force vector and the reference unloading force vector, shows that the difference between the current and reference unloading force vectors can be linearly transformed into a prior estimate of the deformation mode coefficients through the mapping matrix. The reason for using the unloading force difference instead of the absolute unloading force value is that deformation is mainly caused by the non-uniformity of the unloading force distribution, rather than the absolute magnitude of the unloading force. When the unloading force at each unloading point is consistent with the reference unloading force, even if the absolute value of the unloading force is large, as long as the distribution is uniform, the deformation will be small. However, when the unloading force distribution deviates from the reference state, even if the total unloading force remains unchanged, the non-uniform distribution will cause significant deformation. Therefore, using the unloading force difference as input can more accurately reflect the true cause of deformation and improve the accuracy of force prior prediction.

[0079] A deformation force consistency regularization term is introduced, which is the square of the Euclidean norm of the difference between the vector of deformation modal coefficients to be estimated and the prior force prediction. The Euclidean norm is set as the square root of the sum of the squares of the vector components. This regularization term characterizes the degree of deviation between the estimated deformation modal coefficients and the prior force prediction, serving as a constraint in the joint estimation to prevent deformation estimation drift. The reason for introducing the deformation force consistency regularization term is to provide physical constraints for deformation estimation during the optimization solution process. Since the number of targets measured by laser tracking is limited and the measurement is noisy, relying solely on measurement data fitting may lead to multiple solutions or instability in deformation estimation. However, unloading force information provides independent physical clues about the deformation state. By requiring the estimated deformation modal coefficients to be consistent with the deformation modal coefficients predicted by the unloading force, the solution space can be effectively constrained, making the estimation results more consistent with actual physical laws and improving the reliability and stability of deformation estimation.

[0080] In each sampling period, a weighted least squares optimization problem is constructed based on the consistency constraints between the observation model established in step 100 and the aforementioned structure. The variables to be solved in this optimization problem include three types of parameters: rigid body rotation matrix, rigid body translation vector, and deformation mode coefficient vector. By solving this optimization problem, the estimated values ​​of these three types of parameters can be obtained simultaneously. The rigid body rotation matrix and rigid body translation vector together constitute the rigid body pose estimate, and the deformation mode coefficient vector constitutes the deformation state estimate, thereby achieving joint estimation and separation of pose and deformation. The reason for adopting the weighted least squares optimization problem is that this method can process measurement data of multiple targets simultaneously within a unified mathematical framework. It finds the optimal parameter estimate by minimizing the weighted sum of squares of the measurement residuals. The weighting mechanism allows different confidence levels to be assigned based on the measurement quality of different targets, so that targets with better measurement quality have a greater impact on the estimation results, while targets with poorer measurement quality have a smaller impact on the estimation results, thereby improving the robustness of the overall estimation. At the same time, the least squares method has clear statistical significance and can provide maximum likelihood estimation under the assumption that the measurement noise follows a Gaussian distribution, ensuring the statistical optimality of the estimation results.

[0081] The objective function is set as the sum of a data fitting term, a force consistency constraint term, and a deformation sparsity constraint term. This multi-terminal objective function design aims to achieve a balance among various optimization objectives. The data fitting term ensures that the estimation results match the laser tracking measurement data; the force consistency constraint term ensures that the deformation estimation matches the unloading force measurement information; and the deformation sparsity constraint term ensures that the deformation estimation is physically reasonable and avoids overfitting noise. The combined effect of these three terms ensures that the final estimation result accurately reflects the measurement data, satisfies physical constraints, and maintains numerical stability.

[0082] The data fitting term represents the weighted sum of squared residuals between the measured coordinates and the model predicted coordinates of all targets. For each target, the square of the Euclidean norm of the difference between its measured coordinates and the model predicted coordinates is calculated, multiplied by the preset measurement weight corresponding to that target, and finally summed over all targets. The model predicted coordinates are the result of the rigid body rotation matrix acting on the coordinate term and then superimposed with the rigid body translation vector. The rigid body rotation matrix and the rigid body translation vector are the optimization variables to be solved. The coordinate term is the sum of the target's reference coordinates and the deformation displacement. The deformation displacement is obtained by multiplying the modal matrix by the deformation modal coefficient vector to be solved. The preset measurement weights are adaptively given based on the measurement quality indicators, which include quantifiable parameters such as valid measurement marks returned by the laser tracker, the magnitude of measurement residuals, or the variance of repeated measurements. The initial preset measurement weight value is 1. When the measurement quality indicators indicate high measurement reliability, the corresponding preset measurement weight is set to a larger value of 1.2 to 1.5 times. When the measurement quality indicators indicate low measurement reliability, the corresponding preset measurement weight is set to a smaller value of 0.5 to 0.8 times, thereby improving the robustness of the estimation.

[0083] The reason for adopting adaptive measurement weights is that, in the actual measurement process of laser trackers, the measurement quality of different target points may vary. For example, the measurement accuracy of some targets may decrease due to occlusion, poor reflection conditions, or excessive distance. If all targets are given the same weight, targets with poor measurement quality will have an adverse effect on the estimation results, reducing the overall estimation accuracy. However, by adaptively adjusting the weights according to the measurement quality index, the estimation algorithm can trust the data with good measurement quality more and reduce the impact of data with poor measurement quality, thereby improving the robustness and accuracy of the estimation. This adaptive weighting strategy has important value in practical engineering applications and can effectively cope with the challenges brought by complex measurement environments.

[0084] The force consistency constraint term is equal to the preset force consistency regularization coefficient multiplied by the deformation force consistency regularization term. The preset force consistency regularization coefficient is a non-negative value used to control the strength of the force consistency constraint. The default value of the preset force consistency regularization coefficient is 0.1, which is determined through offline calibration experiments. When the unloading force sensor has high accuracy, a larger value of 0.2 to 0.5 can be used to make the deformation estimation more dependent on the unloading force measurement information. When the unloading force sensor has low accuracy, a smaller value of 0.01 to 0.05 can be used to reduce the influence of force measurement error. The reason for setting an adjustable force consistency regularization coefficient is to balance the laser tracking measurement information and the unloading force measurement information. When the unloading force sensor has high accuracy, increasing the regularization coefficient can make full use of the constraint effect of the force measurement information on deformation estimation and improve the accuracy of deformation estimation. When the unloading force sensor has low accuracy or large noise, decreasing the regularization coefficient can reduce the adverse effect of force measurement error on deformation estimation and avoid erroneous force prior information from misleading the estimation results. This adjustable regularization mechanism enables the algorithm to adapt to different sensor configurations and measurement conditions, and has good adaptability and robustness. The deformation sparsity constraint term is equal to the preset deformation sparsity regularization coefficient multiplied by the square of the Euclidean norm of the deformation mode coefficient vector. The preset deformation sparsity regularization coefficient is non-negative. This term applies a L2 penalty to the deformation mode coefficients to suppress overfitting and ensure the physical reasonableness of the estimation results. The default value of the preset deformation sparsity regularization coefficient is 0.01. This default value is determined based on the ratio of the deformation mode dimension to the number of targets. When the ratio is less than 0.5, a smaller value of 0.005 to 0.01 can be used. When the ratio is greater than 0.7, a larger value of 0.02 to 0.05 can be used to enhance the deformation suppression effect. The reason for introducing the deformation sparsity constraint term is that, when the number of targets is limited, the estimation of deformation mode coefficients may suffer from overfitting. That is, in order to better fit the measurement data, the estimation algorithm may give physically unreasonable large deformation coefficients. These excessively large deformation coefficients are actually fitting measurement noise rather than the actual deformation. By applying the L2 penalty, the magnitude of the deformation mode coefficient vector is encouraged to be as small as possible. Under the premise of meeting the measurement data fitting requirements, the solution with smaller deformation amplitude is preferred. This is consistent with the actual physical situation, because under normal unloading conditions, the deformation of the plane mirror component is usually small. This constraint term can effectively suppress overfitting and improve the physical rationality and generalization ability of deformation estimation.

[0085] The aforementioned optimization problem is solved iteratively using the incremental Gauss-Newton method. The Gauss-Newton method is an iterative optimization algorithm for nonlinear least squares problems. Its core idea is to linearize the nonlinear objective function in each iteration and then solve the linearized least squares subproblem to obtain the parameter update step size. The Gauss-Newton method is chosen because it is particularly suitable for solving nonlinear least squares problems. Compared to the general gradient descent method, the Gauss-Newton method utilizes the special structure of the least squares problem, avoiding the direct calculation of the second derivative by constructing an approximate Hessian matrix, thus reducing computational complexity while maintaining convergence speed. Compared to Newton's method, the Gauss-Newton method does not require calculating the complete Hessian matrix of the objective function, avoiding numerical problems caused by the Hessian matrix potentially being nondefinite. This is particularly suitable for the case where the rigid body rotation matrix has nonlinear constraints in this invention. The incremental implementation utilizes the time continuity of the setup process, using the estimation result of the previous sampling period as the initial value of the current sampling period, ensuring that the initial point of each iteration is close to the true solution, significantly reducing the number of iterations required for convergence and meeting the requirements of real-time control. Suppose that the parameter vector of the current iteration point includes the parameterized representation of the rigid body rotation matrix, the rigid body translation vector, and the deformation mode coefficient vector, and the residual vector is composed of the difference between the measured value and the predicted value.

[0086] For the optimization and updating of the rigid body rotation matrix, Lie algebra parameterization is employed. The rigid body rotation matrix is ​​a third-order square matrix describing the overall rotational attitude of the plane mirror assembly. This matrix belongs to a special three-dimensional orthogonal group and satisfies the constraint that the product of the matrix and its transpose equals the identity matrix and has a determinant of one. Because the rigid body rotation matrix has orthogonality constraints, it cannot be directly updated using unconstrained optimization methods; therefore, Lie algebra parameterization is introduced. The reason for using Lie algebra parameterization is that although the rigid body rotation matrix has nine matrix elements, due to the orthogonality constraints, it actually only has three independent degrees of freedom. Directly optimizing these nine matrix elements would not only introduce redundant parameters and increase computational cost, but more importantly, it would be impossible to guarantee that the updated matrix still satisfies the orthogonality constraints during the optimization process. This could lead to the accumulation of numerical errors, causing the rotation matrix to gradually deviate from the orthogonality group. Lie algebra parameterization, by introducing a three-dimensional rotation vector as an optimization variable, transforms the constrained rotation matrix optimization problem into an unconstrained vector optimization problem. This reduces the parameter dimension, improves computational efficiency, and automatically ensures that the updated rotation matrix always satisfies the orthogonality constraints through exponential mapping, avoiding additional orthogonalization processing and the accumulation of numerical errors. Lie algebras are vector spaces corresponding to Lie groups. For a three-dimensional rotation group, its corresponding Lie algebra can be represented as a three-dimensional rotation vector. A three-dimensional rotation vector is a three-dimensional column vector whose direction represents the rotation axis and whose magnitude represents the rotation angle about that axis. Through Lie algebra parameterization, constrained rigid body rotation matrices can be converted into unconstrained three-dimensional rotation vectors for optimization.

[0087] The 3D rotation vector and rigid body rotation matrix are mutually converted through exponential and logarithmic mappings. The exponential mapping is a mapping from Lie algebra space to Lie group space, converting the 3D rotation vector into a rigid body rotation matrix. The logarithmic mapping is the inverse of the exponential mapping, converting the rigid body rotation matrix back into a 3D rotation vector. During the optimization iteration process, the current rigid body rotation matrix is ​​first converted into a 3D rotation vector using the logarithmic mapping. Then, the increment of the rotation vector is calculated in Lie algebra space; this increment represents the rotation correction to be applied in this iteration. Next, the increment of the rotation vector is converted into an incremental rotation matrix using the exponential mapping. The incremental rotation matrix is ​​also a third-order orthogonal matrix, describing the relative rotation relationship from the current rotation state to the updated rotation state. Finally, the current rigid body rotation matrix is ​​left-multiplied by the incremental rotation matrix to obtain the updated rigid body rotation matrix. The advantage of this update method is that it automatically maintains the orthogonality constraint of the rigid body rotation matrix, ensuring that the updated rigid body rotation matrix still belongs to a 3D special orthogonal group without requiring additional orthogonalization processing.

[0088] For rigid body translation vectors and deformation mode coefficient vectors, since they are both unconstrained vector parameters, a direct addition update method is adopted, that is, the current vector value is added to the increment vector obtained by the current iteration to obtain the updated vector value.

[0089] The residual Jacobian matrix is ​​the partial derivative matrix of the residual vector with respect to the parameter vector, describing the sensitivity of the residual to parameter changes. The Jacobian matrix of the rigid body rotation matrix is ​​calculated using the adjoint representation of Lie algebras, a linear transformation in Lie algebra theory used to describe the effects of Lie algebra elements. The parameter update for each iteration is solved using the normal equation, where the left-hand side is the transpose of the residual Jacobian matrix multiplied by the residual Jacobian matrix itself, and the right-hand side is the transpose of the residual Jacobian matrix multiplied by the negative of the residual vector.

[0090] During the iteration process, the estimation result of the previous sampling period is used as the initial value of the current sampling period. The temporal continuity of the assembly and adjustment process is utilized to accelerate convergence and ensure real-time performance. The iteration terminates when the norm of the parameter update is less than a preset convergence threshold or when a preset maximum number of iterations is reached. This incremental iteration strategy is adopted because the time interval between adjacent sampling periods during the assembly and adjustment process is usually short, and the pose and deformation state of the plane mirror component do not change drastically. Therefore, the estimation result of the previous sampling period is necessarily close to the true state of the current sampling period. Using it as the initial value allows the optimization algorithm to start iterating from a position close to the optimal solution, significantly reducing the number of iterations required for convergence. This approach satisfies the requirements of real-time control while ensuring estimation accuracy. This strategy is particularly suitable for closed-loop control scenarios, enabling high-frequency state estimation and control updates with limited computational resources. The preset convergence threshold is determined based on the measurement accuracy of the laser tracker. When the measurement accuracy is better than 10 micrometers, it can be taken as 0.0000005 to 0.000001; when the measurement accuracy is 20 to 50 micrometers, it can be taken as 0.000005 to 0.00001. The maximum number of preset iterations is determined based on real-time requirements and sampling period. When the sampling period is greater than 100 milliseconds, 20 to 30 iterations can be used to achieve sufficient convergence. When the sampling period is less than 50 milliseconds, 10 to 15 iterations can be used to ensure real-time response.

[0091] When the iteration termination condition is met, the optimization solution process ends, at which point the optimal estimates of the three types of parameters are obtained. The rigid body rotation matrix estimate and the rigid body translation vector estimate together constitute the rigid body pose estimate for the current sampling period. This rigid body pose estimate describes the rotational attitude and translational position of the plane mirror assembly as a rigid body in the global coordinate system, without including any deformation component influence. The deformation mode coefficient vector estimate constitutes the deformation state estimate for the current sampling period. This deformation state estimate uses low-dimensional mode coefficients to characterize the non-rigid body deformation of the plane mirror assembly caused by factors such as uneven unloading force. Through the above optimization solution process, the rigid body pose and deformation state are simultaneously separated and estimated from the target coordinates measured by the laser tracker. The rigid body pose estimate serves as the input for pose error calculation and actuator command generation in subsequent step 300, while the deformation state estimate serves as the input for deformation monitoring and unloading force adjustment in subsequent step 400. The significance of achieving this separation estimation lies in decoupling two different types of physical quantities that were originally coupled in the measurement data, so that pose control and deformation suppression can be optimized for their respective objectives. This avoids the problem of mutual interference between pose adjustment and deformation change in traditional methods. This decoupling strategy is the key technical foundation for achieving high-precision assembly and adjustment in this invention, and provides accurate and reliable state information for subsequent dual-objective cooperative control.

[0092] Step 300: Calculate the pose error based on the rigid body pose estimation value, map the pose error to an actuator fine-tuning vector, update the actuator command based on the fine-tuning vector, and drive the attitude adjustment actuator to perform pose adjustment, specifically as follows: Figure 3 As shown.

[0093] The target pose is set as the target rotation matrix and the target translation vector. This target pose is determined by the optical axis alignment requirements or other assembly indicators and is given in advance before the assembly task begins.

[0094] Based on the rigid body pose estimation value obtained in step 200, the pose error is calculated. The rigid body pose estimation value obtained by optimization in step 200 includes two parts: the rigid body rotation matrix estimation value and the rigid body translation vector estimation value. This rigid body pose estimation value has been separated from the deformation state estimation value during the optimization process, so it can be directly used for pose error calculation without being disturbed by deformation components. The reason for using the separated rigid body pose estimate to calculate the pose error is to ensure that the pose control loop is not affected by deformation factors. In traditional assembly and adjustment methods, if the pose and deformation are not separated, the measured target position change includes both rigid body motion and deformation. The pose error calculated directly based on the measured position will mistakenly identify deformation as pose deviation, causing the control system to attempt to compensate for the actual position deviation caused by deformation by adjusting the attitude actuator. This erroneous compensation not only fails to eliminate the true pose error but also introduces new pose deviations, and may even lead to oscillation or divergence of the control system. However, this invention separates and estimates the rigid body pose and deformation state in step 200, so that the pose error calculated in step 300 only reflects the true rigid body pose deviation, thereby ensuring the accuracy of pose adjustment and the stability of the control system. For rotation error, Lie algebra is used. Lie algebra is a vector space corresponding to a Lie group. For a three-dimensional rotation group, its corresponding Lie algebra can be represented as a three-dimensional vector, called a rotation vector. The mapping from the rotation matrix to the rotation vector is called a logarithmic mapping. The reason for using Lie algebras to represent rotation error is that rotation error is essentially a relative rotation from the current attitude to the target attitude. If represented directly by a rotation matrix, nine elements would be required, which is inconvenient for subsequent error compensation calculations. A rotation vector, however, only needs three components to fully describe the rotation error: its direction represents the rotation axis that needs correction, and its magnitude represents the rotation angle that needs correction. This representation not only has low parameter dimensionality but also clear physical meaning, facilitating the establishment of a linear mapping relationship with the actuator's adjustment. Furthermore, the Lie algebra space possesses the properties of a vector space, allowing direct addition, subtraction, and linear transformations, simplifying subsequent control algorithm design. Specifically, for the rotation matrix, its rotation angle is obtained by subtracting one from the trace of the matrix, dividing by two, and then taking the inverse cosine, where the trace is the sum of the diagonal elements of the matrix. The rotation axis is a unit vector, extracted from the antisymmetric part of the rotation matrix. The result of the logarithmic mapping is equal to the product of the rotation angle and the rotation axis.

[0095] Based on the above settings, the rotation error vector is calculated as follows: First, the product of the target rotation matrix and the transpose of the rigid body rotation matrix estimate obtained in step 200 is calculated to obtain the relative rotation matrix from the current attitude to the target attitude. Then, it is converted into a rotation vector form through logarithmic mapping. The direction of the rotation error vector represents the correction rotation axis, and its magnitude represents the rotation angle that needs to be corrected.

[0096] The translation error vector is directly calculated from the difference between the target translation vector and the estimated rigid body translation vector obtained in step 200.

[0097] The rotation error vector and translation error vector are combined into a 6-dimensional pose error vector, with the first three components representing rotation errors and the last three components representing translation errors. This pose error vector is calculated solely based on the rigid body pose estimate obtained through optimization in step 200, excluding the influence of the deformation state estimate. This mechanism avoids miscompensating deformation errors as pose adjustments, ensuring the accuracy of the compensation. The reason for using a 6-dimensional pose error vector is that the pose of a rigid body in three-dimensional space is fully described by six degrees of freedom, including three rotational degrees of freedom and three translational degrees of freedom. Combining rotation and translation errors into a unified 6-dimensional vector facilitates establishing a unified mapping relationship with the actuator's adjustment capabilities, simplifying subsequent control algorithm design. Furthermore, the 6-dimensional vector representation conforms to standard practices in robotics and multibody dynamics, possessing a sound theoretical foundation and engineering experience.

[0098] The calculated pose error vector is mapped to the fine-tuning vector of the actuator. The system has a known actuator Jacobian matrix, which describes the differential relationship between the actuator displacement change and the end-effector pose change. The number of rows is 6, corresponding to the pose degrees of freedom, and the number of columns is equal to the number of actuators. The actuator Jacobian matrix is ​​obtained through system kinematic calibration.

[0099] The pseudo-inverse of the actuator Jacobian matrix is ​​calculated using the damped least squares method. The calculation involves multiplying the transpose of the actuator Jacobian matrix by the inverse of a matrix. This matrix is ​​equal to the product of the actuator Jacobian matrix and its transpose, plus an identity term. The identity term is a preset damping factor multiplied by the identity matrix. The preset damping factor is set to a small positive value to improve numerical stability. The preset damping factor is determined based on the condition number of the actuator Jacobian matrix. When the condition number is less than 100, a smaller value between 0.001 and 0.01 can be used to reduce the impact on the solution. When the condition number is greater than 1000, a larger value between 0.1 and 1 can be used to enhance numerical stability. The reason for using damped least squares instead of direct pseudo-inverse is that the actuator Jacobian matrix may have a large condition number or be close to singular. In particular, when the actuator is configured in a near-singular configuration or the controllability of some pose degrees of freedom is weak, direct calculation of pseudo-inverse will lead to numerical instability, and the obtained actuator adjustment may have an abnormally large value, causing actuator saturation or system instability. The damped least squares method adds a damping term during the matrix inversion process, which is equivalent to applying a regularization constraint to the solution space. While ensuring that the pose error is effectively compensated, it limits the magnitude of the actuator adjustment, so that even in near-singular configurations, numerically stable and physically reasonable actuator commands can be obtained, thus improving the robustness of the control system.

[0100] The fine-tuning vector of the actuator is calculated based on the pseudo-inverse. It is calculated by multiplying the pseudo-inverse of the actuator's Jacobian matrix by a 6-dimensional pose error vector, which is formed by vertically concatenating the rotation error vector and the translation error vector.

[0101] The calculated fine-tuning vector is subjected to safety limiting. The limiting function independently saturates and limits each component of the fine-tuning vector. For each actuator, a preset lower limit and a preset upper limit for the fine-tuning vector are set. If the calculated fine-tuning vector is less than the preset lower limit, the value of the fine-tuning vector is changed to the preset lower limit value; if the calculated fine-tuning vector is greater than the preset upper limit, the value of the fine-tuning vector is changed to the preset upper limit value; otherwise, the original value remains unchanged. The preset lower limit and preset upper limit of the fine-tuning vector are determined based on the actuator's stroke range and safety margin. For small actuators with a stroke range of less than 20 mm, a value of -2 mm to +2 mm can be used; for large actuators with a stroke range of more than 50 mm, a value of -10 mm to +10 mm can be used to prevent system instability caused by excessive single adjustment. The reason for implementing safety limiting is that under certain abnormal conditions, such as large noise in the measurement data, temporary non-convergence of the estimation algorithm, or near-singularity of the actuator's Jacobian matrix, the calculated fine-tuning amount may be abnormally large. If these abnormal values ​​are sent directly to the actuator, it may cause the actuator to exceed its stroke range and cause mechanical collision, or cause structural vibration or even damage to the equipment due to excessive movement. By setting a reasonable limiting range, the single adjustment amount of the actuator can be constrained within a safe and controllable range, ensuring the safety of the system even under abnormal conditions. At the same time, limiting can also play a role in smooth control, avoiding violent actuator movements caused by sudden changes in pose error, and improving the stability of the assembly and adjustment process.

[0102] The actuator command update adopts a smoothing strategy. The actuator command vector for the next sampling period is equal to the actuator command vector for the current sampling period plus a fine-tuning term. The fine-tuning term is a preset smoothing coefficient multiplied by the current fine-tuning vector. The preset smoothing coefficient ranges from greater than 0 to no more than 1. The preset smoothing coefficient is determined based on the inertia of the assembly object and the actuator response speed. For light-load, fast-response systems, a larger value of 0.5 to 0.8 can be used to accelerate the convergence speed. For heavy-load, slow-response systems, a smaller value of 0.1 to 0.3 can be used to make the actuator action smoother, which can suppress the jitter risk during the assembly process and is suitable for heavy-load assembly scenarios at the top of the tower. The reason for adopting a smoothing strategy to update actuator instructions is that directly applying all the calculated fine-tuning amount to the actuator may lead to an overly aggressive system response, especially in heavy-load assembly and adjustment scenarios. Plane mirror components have a large inertia, and sudden large-amplitude movements of the actuator can excite structural vibrations, which not only prolongs the assembly and adjustment time but may also damage delicate optical components or mechanical structures. By introducing a smoothing coefficient, only a portion of the fine-tuning amount is applied each time, allowing the actuator to gradually approach the target pose in a progressive manner. This can effectively suppress vibration and overshoot, improve the smoothness and safety of the assembly and adjustment process, and at the same time, the smoothing strategy can also filter out high-frequency disturbances caused by measurement noise and estimation errors to a certain extent, thereby improving the robustness of the control system.

[0103] The updated actuator command vector is sent to the attitude adjustment actuator, which drives the electric cylinder or three-point support adjuster to perform the corresponding displacement adjustment.

[0104] Step 400: Detect the modulus of the deformation state estimate. When the Euclidean norm of the deformation state estimate exceeds the preset deformation threshold for a consecutive preset number of durations, trigger the unloading force balancing fine-tuning process.

[0105] In each sampling cycle, the modulus of the deformation state estimate obtained in step 200 is detected. A preset deformation threshold is set as the criterion for judging the degree of deformation. This preset deformation threshold is determined based on calibration experiments, and its default value is 0.5 mm. This default value is determined according to the stiffness and assembly accuracy requirements of the plane mirror assembly. For high-stiffness components or high-precision assembly tasks, a smaller value of 0.1 to 0.3 mm can be used to strictly control deformation. For low-stiffness components or general-precision assembly tasks, a larger value of 0.5 to 1 mm can be used to avoid frequent triggering of unloading force adjustments. The reason for setting a deformation threshold judgment mechanism is to achieve a balance between deformation control and system stability. If no threshold is set and unloading force is adjusted for any small deformation, it will lead to excessively frequent unloading force adjustments, which will not only increase the wear and energy consumption of the actuator, but may also worsen the assembly effect due to the dynamic disturbance introduced during the adjustment process. By setting a reasonable deformation threshold, unloading force adjustment is only triggered when the degree of deformation exceeds the acceptable range, which ensures the assembly accuracy requirements and avoids unnecessary frequent adjustments, thereby improving the overall efficiency and stability of the system.

[0106] A preset duration period is set as the time criterion for determining deformation exceeding the limit. This preset duration period is determined based on the dynamic characteristics of the assembly and adjustment process, with a default value of 5 sampling periods. For fast-response systems, 3 to 5 sampling periods can be used, and for slow-response systems, 8 to 10 sampling periods can be used. When the Euclidean norm of the estimated deformation modal coefficient vector exceeds the preset deformation threshold for consecutive preset duration periods, it indicates that the current deformation degree is large and is not a transient fluctuation caused by instantaneous disturbance, but a steady-state deformation caused by the persistent factor of uneven unloading force distribution. At this time, the unloading force balancing fine-tuning process is triggered. This persistence determination mechanism can effectively avoid false triggering caused by measurement noise or transient disturbances, and improve the reliability of unloading force adjustment decisions. The reason for introducing the continuous period number determination is that the deformation estimate may briefly exceed the limit within a single sampling period due to measurement noise, environmental vibration, or transient response during attitude adjustment. If the unloading force adjustment is triggered based on only a single exceedance, the false trigger rate will be too high. Frequent unloading force adjustments not only waste time and resources, but may also affect the stability of the assembly due to disturbances introduced during the adjustment process. By requiring the deformation exceedance phenomenon to occur continuously over multiple consecutive sampling periods, transient disturbances and steady-state deformations can be effectively distinguished. This ensures that only deformations caused by persistent factors such as uneven distribution of unloading force will trigger the adjustment process, thereby improving the targeting and effectiveness of unloading force adjustment.

[0107] The unloading force fine-tuning direction vector is calculated by multiplying the difference between the zero vector and the current estimated value of the deformation mode coefficient vector by a mapping matrix from the deformation mode coefficient space to the unloading force space. The dimension of the zero vector is equal to the deformation mode dimension, representing the desired zero deformation state. The number of rows in this mapping matrix is ​​equal to the number of unloading force sensors, and the number of columns is equal to the deformation mode dimension. This mapping matrix can be the transpose of the force-to-deformation mode mapping matrix in step 200, or determined through a dedicated calibration experiment. The calculated unloading force fine-tuning direction vector represents the unloading force adjustment direction and relative magnitude required to reduce deformation. The dimension of this vector is equal to the number of unloading force sensors, and each component in the vector corresponds to the unloading force adjustment amount that needs to be applied at an unloading point. The reason for adopting this method of calculating the unloading force fine-tuning direction based on the mapping matrix is ​​to establish a reverse mapping relationship from the deformation state to the unloading force adjustment. Since the forward mapping from the unloading force to the deformation has been established in step 200, by solving this mapping relationship in reverse, it can be determined how to adjust the unloading force at each unloading point in order to eliminate the currently observed deformation. Using the transpose of the mapping matrix as an approximate inverse mapping is a simple and effective method in most cases. When the forward mapping matrix is ​​close to orthogonal, its transpose is the exact inverse mapping. When the mapping matrix does not satisfy orthogonality, a more accurate inverse mapping matrix can be determined through special calibration experiments. This adjustment strategy based on physical mapping relationship is more scientific and efficient than simple trial and error or empirical adjustment.

[0108] To ensure the safety and controllability of unloading force adjustment, static balance constraints are applied to the unloading force fine-tuning direction vector. The reason for applying static balance constraints is that the plane mirror assembly must remain in a stable supported state throughout the unloading force adjustment process. If the adjusted unloading force distribution does not meet the static balance conditions, it may lead to dangerous situations such as assembly overturning, support point disengagement, or excessive local stress. This would not only fail to improve the deformation state but could also cause assembly failure or even equipment damage. Therefore, static constraints must be considered when calculating the unloading force adjustment amount to ensure the safety and feasibility of the adjustment. First, the sum of the total unloading forces at all unloading points after unloading force adjustment should remain within a preset total unloading force range. This preset total unloading force range is determined based on the weight and safety margin of the plane mirror assembly. Its lower limit is 0.95 to 0.98 times the weight of the plane mirror assembly, and its upper limit is 1.02 to 1.05 times the weight of the plane mirror assembly. This range ensures that the plane mirror assembly remains in a stable supported state throughout the unloading force adjustment process, preventing support failure due to insufficient total unloading force or structural overload due to excessive total unloading force.

[0109] Secondly, the adjustment of the unloading force at each unloading point must meet the constraints of the single-point unloading force variation range to avoid pull-out or overcompression at local unloading points. For each unloading point, a preset lower limit and a preset upper limit for the single-point unloading force are set. The preset lower limit is determined based on the preload of the spring unloading mechanism and the risk of pull-out, with a default value of 0.5 to 0.7 times the reference unloading force at that unloading point. When the unloading force at the unloading point is lower than this lower limit, the spring may lose its preload or the support contact surface may detach, leading to local support failure. The preset upper limit is determined based on the maximum load-bearing capacity and structural strength of the spring unloading mechanism, with a default value of 1.3 to 1.5 times the reference unloading force at that unloading point. When the unloading force at the unloading point exceeds this upper limit, the spring may be over-compressed or the local structural stress may exceed the limit, causing mechanical damage or plastic deformation. After calculating the unloading force fine-tuning direction vector, each component is checked. If the unloading force after adjustment at a certain unloading point exceeds the safe range defined by the preset single-point unloading force lower limit and the preset single-point unloading force upper limit at that unloading point, then the component is limited to restrict its adjustment amount within the safe range, ensuring that the unloading force at all unloading points is always within a reasonable working range.

[0110] Secondly, the unloading force adjustment must consider the coupling effect between the mirror edge ring support and the spring unloading point to ensure that the adjustment process does not disrupt the overall support stability. Since the mirror edge ring support and the mirror back spring unloading point share the weight of the plane mirror assembly, changes in the unloading force at the spring unloading point will correspondingly alter the contact force at the mirror edge ring support, creating a mechanical coupling between the two. When calculating the unloading force fine-tuning direction vector, the change in contact force at the mirror edge ring support is predicted using finite element analysis or empirical models to ensure that the contact force distribution of the mirror edge ring support remains uniform after adjustment and does not exceed the allowable contact stress. This avoids damage to the mirror edge due to excessive local contact force or additional deformation caused by uneven contact force distribution.

[0111] After satisfying the above constraints, an unloading force adjustment command vector is generated. This vector is calculated by adding an adjustment term to the unloading force vector of the current sampling period. The adjustment term is a preset unloading force adjustment step size coefficient multiplied by the unloading force fine-tuning direction vector. The preset unloading force adjustment step size coefficient ranges from greater than 0 to no more than 0.3. The preset unloading force adjustment step size coefficient is determined based on the response speed of the unloading force adjusting actuator and the stability requirements of the adjustment process. For fast-response electric adjusting actuators, a larger value of 0.2 to 0.3 can be used to accelerate deformation suppression. For slow-response manual adjusting mechanisms, a smaller value of 0.05 to 0.1 can be used to avoid dynamic disturbances caused during the adjustment process. This step size coefficient setting allows the unloading force adjustment to proceed gradually, applying only a partial correction each time. Through cumulative adjustments over multiple sampling periods, the unloading force distribution gradually becomes more uniform, thus ensuring the adjustment effect while avoiding system oscillations or instability caused by excessively large single adjustment amplitudes. The reason for adopting a gradual adjustment strategy is that although the mapping relationship between unloading force and deformation can be approximated as linear in a small range, it may exhibit nonlinear characteristics when adjusted over a large range. At the same time, the unloading force adjustment process will cause slight changes in the attitude of the plane mirror assembly, which will affect the laser tracking measurement and pose control loop. If a large unloading force adjustment is applied at once, it may cause coupled oscillations between the pose control and deformation suppression loops. By setting a small step size coefficient, the unloading force changes at a slow rate, which can give the pose control loop enough time to compensate, maintaining the decoupling of the two control loops and the stability of the overall system.

[0112] For systems equipped with unloading force adjustment actuators, the unloading force adjustment command vector is sent to the actuator, driving the electric or hydraulic adjustment mechanism at each unloading point to perform the corresponding unloading force adjustment. The unloading force adjustment actuator responds to the adjustment command at a relatively slow rate, gradually making the unloading force distribution more uniform and reducing deformation-inducing factors from the source. For systems without automatic adjustment capabilities, unloading force adjustment suggestions are output to the operating interface for manual reference. Operators can manually adjust the spring preload or support shim thickness at each unloading point based on the displayed unloading force adjustment suggestions to achieve manual equalization of the unloading force.

[0113] This step applies the deformation state estimate inversely to the unloading strategy optimization, enabling the assembly and adjustment system to simultaneously possess pose closed-loop control and deformation suppression capabilities, forming a dual-objective collaborative working mode. The reason for adopting this dual-objective collaborative working mode is that traditional assembly and adjustment methods typically only focus on pose control, treating deformation as an uncontrollable interference factor. This leads to situations where, even if the pose reaches the target accuracy, the component may still have significant deformation affecting the final assembly and adjustment quality. However, this invention, by achieving separate estimation of pose and deformation in step 200, not only provides accurate rigid body pose information for pose control but also obtains a quantitative description of the deformation state. Furthermore, in step 400, the deformation state information is used to guide the adjustment of the unloading force, suppressing deformation at its source. This dual-objective collaborative control strategy allows for simultaneous optimization of pose accuracy and deformation control, significantly improving the overall quality of assembly and adjustment, and is particularly suitable for high-precision optical component assembly and adjustment scenarios that are sensitive to deformation.

[0114] Step 500: Determine whether the assembly and adjustment have reached the target accuracy based on the pose error. If the target accuracy is reached, the assembly and adjustment process ends; otherwise, return to continue executing the process of solving the rigid body pose estimation value and deformation state estimation value.

[0115] In each sampling cycle, the pose error vector calculated in step 300 is used to determine whether the assembly has reached the target accuracy. Preset rotation convergence thresholds and preset translation convergence thresholds are set, and these two thresholds are predetermined based on the accuracy requirements of the assembly task. The preset rotation convergence threshold is determined based on the optical axis alignment accuracy requirements; for high-precision optical systems, it can be 0.005 degrees to 0.01 degrees, and for general-precision optical systems, it can be 0.02 degrees to 0.05 degrees. The preset translation convergence threshold is determined based on the position positioning accuracy requirements; for high-precision positioning tasks, it can be 0.05 mm to 0.1 mm, and for general-precision positioning tasks, it can be 0.2 mm to 0.5 mm.

[0116] The convergence criterion is that the pose is considered to have reached the target when the Euclidean norm of the rotation error vector is less than or equal to the preset rotation convergence threshold and the Euclidean norm of the translation error vector is less than or equal to the preset translation convergence threshold.

[0117] When the above conditions are met, the assembly and adjustment process ends. The system records the estimated value of the deformation modal coefficient vector and the unloading force vector of the current sampling period, forming the digital fingerprint data of this assembly and adjustment. This digital fingerprint data is stored in the assembly and adjustment database and can be used for subsequent assembly and adjustment reset or process reproduction, realizing the traceability of the assembly and adjustment process. The reason for recording digital fingerprint data is to establish a complete data archive for the assembly and adjustment process. The deformation modal coefficient vector and the unloading force vector together describe the internal stress state and support force distribution of the plane mirror assembly when it reaches the target pose. This information has important reference value for subsequent maintenance, reset or assembly and adjustment of similar components. When the same component needs to be reassembled and adjusted, historical digital fingerprint data can be directly loaded as the initial unloading force distribution, which can significantly shorten the assembly and adjustment time. When other components with similar structures need to be assembled and adjusted, the initial parameters can be set with reference to historical digital fingerprint data to improve the assembly and adjustment efficiency. At the same time, digital fingerprint data also provides a data foundation for continuous improvement of the assembly and adjustment process. By analyzing the digital fingerprints of a large number of assembly and adjustment cases, the deformation laws and optimal unloading strategies of different types of components can be summarized, and the level of assembly and adjustment technology can be gradually improved.

[0118] If the above conditions are not met, return to step 200 to continue the process of solving for the rigid body pose estimate and deformation state estimate until the convergence condition is met or the preset maximum number of iterations is reached. The preset maximum number of iterations is determined based on the time limit and convergence speed of the assembly and adjustment task. For fast assembly and adjustment tasks, it can be 50 to 100 iterations, and for precision assembly and adjustment tasks, it can be 150 to 200 iterations to ensure sufficient convergence.

[0119] Example 2

[0120] See Figure 4 As shown, a laser-tracking-based assembly and positioning system is provided, which stores computer-readable instructions that, when read, can execute the aforementioned laser-tracking-based assembly and positioning method. The system includes:

[0121] The deformation observation module 101 deploys multiple laser tracking targets on the surface of the object being monitored and its supporting structure, calibrates the reference coordinates of the targets, and establishes an observation model that separates pose and deformation based on the reference coordinates.

[0122] The joint estimation module 102 obtains the unloading force vector of the current sampling period from the gravity unloading system, constructs a weighted least squares optimization problem based on the observation model and the unloading force vector, and solves the rigid body pose estimate and deformation state estimate to achieve joint estimation and separation of pose and deformation.

[0123] The pose adjustment module 103 calculates the pose error based on the rigid body pose estimation value, maps the pose error to the actuator fine-tuning vector, updates the actuator command based on the fine-tuning vector, and drives the pose adjustment actuator to perform pose adjustment.

[0124] The deformation adjustment module 104 detects the modulus of the deformation state estimate. When the Euclidean norm of the deformation state estimate exceeds the preset deformation threshold for a continuous preset number of cycles, the unloading force balancing fine-tuning process is triggered.

[0125] The assembly and adjustment determination module 105 determines whether the assembly and adjustment has reached the target accuracy based on the pose error. When the target accuracy is reached, the assembly and adjustment process ends; otherwise, it returns to continue executing the process of solving the rigid body pose estimation value and deformation state estimation value.

[0126] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method of alignment positioning based on laser tracking, characterized in that, Includes the following steps: Multiple laser-tracking targets are deployed on the surface of the target object and its supporting structure. Reference coordinates of the targets are calibrated. Based on these reference coordinates, an observation model separating pose and deformation is established, including: Establish a global coordinate system and a structural local coordinate system; For each target, establish reference coordinates in the local structural coordinate system; The deformation mode basis is pre-set and a mode matrix is ​​set for each target. The mode matrix has 3 rows and the number of columns is the deformation mode dimension. An observation model is established, in which the measured coordinates of each target are the result of the rigid body rotation matrix acting on the coordinate terms, superimposed with the rigid body translation vector and measurement noise. The coordinate terms are the sum of the reference coordinates and deformation displacement of the target, and the deformation displacement is the modal matrix multiplied by the deformation modal coefficient vector. The rigid body rotation matrix describes the rotation relationship between the local coordinate system and the global coordinate system, the rigid body translation vector describes the position of the origin of the local coordinate system in the global coordinate system, and the deformation modal coefficient vector is a column vector whose dimension is equal to the deformation modal dimension. Each component in the deformation modal coefficient vector corresponds to a deformation mode. Obtain the unloading force vector of the current sampling period from the gravity unloading system, construct a weighted least squares optimization problem based on the observation model and the unloading force vector, and solve it to obtain the rigid body pose estimate and deformation state estimate. The pose error is calculated based on the rigid body pose estimation value. The pose error is mapped to the actuator fine-tuning vector. The actuator command is updated based on the fine-tuning vector and the attitude adjustment actuator is driven to perform pose adjustment. The modulus of the deformation state estimate is detected. When the Euclidean norm of the deformation state estimate exceeds the preset deformation threshold for a consecutive preset number of durations, the unloading force equalization fine-tuning process is triggered. The system determines whether the setup has reached the target accuracy based on the pose error. If the target accuracy is reached, the setup process ends; otherwise, it returns to continue executing the process of solving the rigid body pose estimate and deformation state estimate.

2. The laser tracker-based alignment positioning method of claim 1, wherein, The obtained rigid body pose estimate and deformation state estimate include: The gravity unloading system includes setting multiple unloading points on the back of the object being unloaded, and each unloading point is equipped with an unloading force sensor. The dimension of the unloading force vector is equal to the number of unloading force sensors. Set a reference unloading force vector, which is the unloading force value at each unloading point under the calibration state; A mapping matrix from force to deformation mode is constructed, wherein the number of rows in the mapping matrix is ​​equal to the deformation mode dimension and the number of columns is equal to the number of unloading force sensors; The a priori predicted values ​​of the forces in the deformation mode are calculated by multiplying the mapping matrix by the unloading force difference term, which is the difference between the current unloading force vector and the reference unloading force vector. Set a deformation force consistency regularization term, which is the square of the Euclidean norm of the difference between the deformation modal coefficient vector to be estimated and the force prior prediction value; A weighted least squares optimization problem is constructed, and the estimated values ​​of the rigid body rotation matrix, rigid body translation vector, and deformation mode coefficient vector are obtained by solving the problem. The estimated values ​​of the rigid body rotation matrix and rigid body translation vector together constitute the rigid body pose estimate, and the deformation mode coefficient vector constitutes the deformation state estimate.

3. The laser tracker-based alignment positioning method of claim 2, wherein, The objective function of the weighted least squares optimization problem is set as the sum of the data fitting term, the force consistency constraint term, and the deformation sparsity constraint term: The data fitting term represents the weighted sum of squared residuals between all target measured coordinates and model predicted coordinates. The model predicted coordinates are the estimated values ​​of the rigid body rotation matrix acting on the coordinate term and then superimposed with the rigid body translation vector. The force consistency constraint term is equal to the preset force consistency regularization coefficient multiplied by the deformation force consistency regularization term; The deformation sparsity constraint term is equal to the preset deformation sparsity regularization coefficient multiplied by the square of the Euclidean norm of the deformation modal coefficient vector.

4. The laser tracking-based assembly and positioning method according to claim 2, characterized in that, The weighted least squares optimization problem is solved using the incremental Gauss-Newton method, including: For the optimization and update of the rigid body rotation matrix, the Lie algebra parameterization method is adopted. The current rigid body rotation matrix is ​​converted into a three-dimensional rotation vector through logarithmic mapping. The increment of the rotation vector is calculated in the Lie algebra space. The increment of the rotation vector is converted into an incremental rotation matrix through exponential mapping. The current rigid body rotation matrix is ​​multiplied by the incremental rotation matrix to obtain the updated rigid body rotation matrix. For rigid body translation vectors and deformation mode coefficient vectors, a direct addition update method is used, that is, the current vector value is added to the increment vector obtained by the current iteration calculation; Use the estimation result of the previous sampling period as the initial value of the current sampling period; The iteration termination condition is that the norm of the parameter update is less than the preset convergence threshold or the preset maximum number of iterations is reached.

5. The laser tracking-based assembly and positioning method according to claim 1, characterized in that, The executor instructions updated based on the fine-tuning vector include: The target pose is set as the target rotation matrix and the target translation vector; Calculate the rotation error vector, which is obtained by logarithmic transformation of the relative rotation matrix. The relative rotation matrix is ​​the product of the target rotation matrix and the transpose of the estimated rigid body rotation matrix. Calculate the translation error vector, which is the difference between the target translation vector and the estimated value of the rigid body translation vector; The rotation error vector and translation error vector are merged into a pose error vector, which is then mapped to the fine-tuning vector of the actuator. The pseudo-inverse of the actuator's Jacobian matrix is ​​calculated using the damped least squares method, and the fine-tuning vector of the actuator is calculated based on the pseudo-inverse. The calculated fine-tuning vector is subjected to safety limiting, and the limiting function independently performs saturation limiting on each component of the fine-tuning vector. The update of the executor instruction adopts a smoothing strategy. The executor instruction vector of the next sampling period is equal to the executor instruction vector of the current sampling period plus the fine-tuning term. The fine-tuning term is a preset smoothing coefficient multiplied by the current fine-tuning vector. The updated actuator command vector is sent to the attitude adjustment actuator.

6. The laser tracking-based assembly and positioning method according to claim 5, characterized in that, The pseudo-inverse of the actuator Jacobian matrix is ​​calculated by multiplying the transpose of the actuator Jacobian matrix by the inverse of the matrix. The matrix is ​​the product of the actuator Jacobian matrix and the transpose of the actuator Jacobian matrix plus a unit term, where the unit term is a preset damping factor multiplied by the identity matrix. The actuator fine-tuning vector is calculated by multiplying the pseudo-inverse of the actuator Jacobian matrix by the pose error vector. In the aforementioned safety limiting process, for each actuator, a preset lower limit and a preset upper limit for the fine-tuning vector are set. If the calculated fine-tuning vector is less than the preset lower limit, the fine-tuning vector is changed to the preset lower limit value. If the calculated fine-tuning vector is greater than the preset upper limit, the fine-tuning vector is changed to the preset upper limit value. Otherwise, the original value remains unchanged.

7. The laser tracking-based assembly and positioning method according to claim 1, characterized in that, The unloading force balancing fine-tuning process includes: The unloading force fine-tuning direction vector is calculated. The unloading force fine-tuning direction vector is the difference between the zero vector and the current deformation mode coefficient vector estimate multiplied by the mapping matrix from the deformation mode coefficient space to the unloading force space. The dimension of the zero vector is equal to the deformation mode dimension. Apply static balance constraints to the unloading force fine-tuning direction vector, including: the sum of the total unloading forces at each unloading point after the unloading force adjustment remains within the preset total unloading force range, and the unloading force adjustment amount at each unloading point satisfies the single-point unloading force change range constraint; For systems equipped with unloading force adjustment actuators, the unloading force adjustment command vector is sent to the unloading force adjustment actuator. The unloading force adjustment command vector is the unloading force vector of the current sampling period plus an adjustment term. The adjustment term is the preset unloading force adjustment step size coefficient multiplied by the unloading force fine-tuning direction vector.

8. A laser-tracking-based assembly and positioning system, characterized in that, The system is used to store computer-readable instructions, which, when read, execute the laser-tracking-based assembly and positioning method according to any one of claims 1-7; the system includes: The deformation observation module deploys multiple laser tracking targets on the surface of the object being monitored and its supporting structure, calibrates the reference coordinates of the targets, and establishes an observation model that separates pose and deformation based on the reference coordinates. The joint estimation module obtains the unloading force vector of the current sampling period from the gravity unloading system, constructs a weighted least squares optimization problem based on the observation model and the unloading force vector, and solves it to obtain the rigid body pose estimate and deformation state estimate. The pose adjustment module calculates the pose error based on the rigid body pose estimation value, maps the pose error to the actuator fine-tuning vector, updates the actuator command based on the fine-tuning vector, and drives the pose adjustment actuator to perform pose adjustment. The deformation adjustment module detects the modulus of the deformation state estimate. When the Euclidean norm of the deformation state estimate exceeds the preset deformation threshold for a continuous preset number of cycles, the unloading force balancing fine-tuning process is triggered. The assembly and adjustment determination module determines whether the assembly and adjustment has reached the target accuracy based on the pose error. When the target accuracy is reached, the assembly and adjustment process ends; otherwise, it returns to continue executing the process of solving the rigid body pose estimation value and deformation state estimation value.

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