Articulated arm measuring machine error correction method based on Laguerre polynomial error representation
By combining Laguerre polynomial error modeling and the sparrow-peacock algorithm for collaborative optimization, the problem of insufficient accuracy of articulated arm measuring machines in the measurement of large-size workpieces is solved, achieving efficient and reliable error correction, which is suitable for high-precision three-dimensional measurement in modern manufacturing.
Patent Information
- Application Number
- CN202511437356.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-09
- Publication Date
- 2026-02-27
AI Technical Summary
Existing articulated arm measuring machines suffer from insufficient accuracy in measuring large workpieces, including small angular errors in arm length magnification, sensor drift, and splicing errors, resulting in low measurement efficiency, high cost, and increased safety risks.
Laguerre polynomial error modeling is adopted, and the sparrow and peacock algorithms are combined to perform servo correction of the error. The joint angle is obtained through the angle sensor to establish the position transfer model. The nonlinear error is represented by Laguerre polynomial expansion. The collaborative mechanism of sparrow search algorithm and peacock optimization algorithm is introduced to solve the coefficients of the Laguerre polynomial and output the three-dimensional coordinates after error correction.
It significantly suppresses error accumulation, improves measurement accuracy and efficiency, reduces calibration frequency, enhances long-term reliability, and reduces production and safety risks. It is suitable for engineering scenarios such as wind turbine blades, ship hull panels, and heavy machine tools.
Smart Images
Figure CN121572282A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of mechanical arm control and measurement and control, and particularly relates to a joint arm measuring machine error correction method based on Laguerre polynomial error representation. BACKGROUND
[0002] In engineering practice, there are many problems affecting the accuracy of the joint arm measuring machine due to the lack of precision compensation method and sensor itself. For example, the long arm length amplifies the small angle error of each joint, resulting in a remote position error; optical encoders and magnetic encoders are prone to drift and nonlinearity in dusty, oily, light and vibrating environments; large workpieces often need to be measured by segmenting and repositioning, and the lack of absolute and repeatability of traditional sensors leads to splicing errors and frequent calibration, thereby reducing the efficiency of on-site measurement and increasing the risk of rework. The innovation of the joint arm coordinate measuring machine based on capacitive grid sensors is to address these engineering pain points. The high-density grid realizes higher resolution and linearity, lower zero drift and stronger anti-pollution ability, providing absolute and stable joint angle readings. The error compensation technology based on Laguerre polynomial can identify and correct high-frequency and nonlinear error components online, significantly suppress error accumulation, reduce repositioning and splicing errors, and reduce calibration frequency. This scheme not only improves the remote measurement accuracy and long-term reliability in engineering scenarios such as wind turbine blades, ship hulls and heavy machine tools, but also improves the measurement efficiency, reduces the maintenance cost and reduces the production and safety risks caused by measurement errors, and plays an important role in the digitization of ancient artifacts, medical bone digital twin and industrial intelligent detection. SUMMARY
[0003] The present application is aimed at the urgent need for on-site high-precision three-dimensional measurement of large-size workpieces in modern manufacturing industry, and provides a joint arm measuring machine error correction method based on Laguerre polynomial error representation. By using Laguerre polynomial error modeling and sparrow algorithm and peacock algorithm for error servo correction, it is beneficial to high-precision identification of error function parameters in high-order high-dimensional space, and provides an accurate and controllable mathematical basis for precision compensation of coordinate measuring machines.
[0004] The technical solution of the present application is as follows: The joint arm measuring machine error correction method based on Laguerre polynomial error representation comprises the following steps: Step 1, angle sensors are configured at each joint of the joint arm measuring machine to obtain joint angles, and a terminal capacitive probe is used to realize real-time acquisition of the spatial coordinates of the measured workpiece; Step 2, a homogeneous transformation matrix is used to establish a position transmission model; Step 3, a kinematic model of the coordinate measuring machine is established, each joint angle is taken as an input variable, and a Laguerre polynomial is used to represent the non-linear error characteristics. Step 4, combine the original coordinates with the Laguerre error characteristics to generate a modified data set containing error information, introduce the synergy mechanism of sparrow search algorithm and peacock optimization algorithm to solve the optimal solution of the Laguerre polynomial coefficients to be solved, and then obtain the final Laguerre error correction coefficient, and apply the Laguerre error correction coefficient to the kinematic model of the coordinate measuring machine, and output the error corrected three-dimensional coordinates.
[0005] Step 2 includes the following expression: Wherein represents the total position transformation matrix from the base coordinate system to the end capillary grid measuring head coordinate system, represents the rotation and translation transformation matrix of the i th joint, i is a positive integer, and n is the number of joints, is the i th joint angle, is the micro displacement error at the i th joint.
[0006] Step 3 includes the following expression: Wherein represents the joint angle corresponding term geometric error value, is the k th order Laguerre polynomial, k is an integer greater than or equal to 0, and m is a positive integer, is the coefficient to be solved.
[0007] Step 4 includes the following expression: Wherein is the sparrow global search operator, is the peacock local optimization operator, is the Laguerre polynomial coefficient to be solved generated by the t th group, t is a positive integer, is the Laguerre polynomial coefficient to be solved generated by the t+1 th group.
[0008] includes the following expression: Wherein is the micro rotation error vector generated by the i th joint when rotating to the angle , is the rotation error component around the X axis in , is the rotation error component around the Y axis in , is the rotation error component around the Z axis in ; in Is the i-th joint rotating to the angle? The tiny displacement error that occurs at that time yes x-axis component, yes The y-axis component, yes z-axis component; in Let n be the k-th Laguerre basis function, where k is an integer greater than or equal to 0, and n is the order of the function. , These are all parameter coefficients to be determined, i.e., the fitting coefficients of the error function.
[0009] Including the following expressions: in It is the positional error of the end in the j-th data set, where j is a positive integer. It is the actual end position obtained by the laser measurement system in the j-th data set. It is the ideal position calculated using the ideal kinematic model in the j-th set of data. It is a small disturbance at the end. It is the Jacobian matrix of the end-effector position with respect to the joint variables. It is a tiny disturbance in the joint. It is a higher-order error term or other interference. It refers to the position at the end.
[0010] Step 4 involves fitting the measured data to the model output using the least squares method. The least squares fitting equation is as follows: , in It is the translation error component of the i-th joint in the j-th dataset. It is the k-th order Laguerre basis function in the j-th dataset. It is a higher-order error term or other disturbance in the j-th dataset; Stacking all j sets of data results in the following matrix equation: Where E is the residual vector and D is the error observation vector. M is the number of dataset groups, and L is the basis function matrix. U is the order of the Laguerre polynomial, and A is the vector of coefficients to be determined. .
[0011] Including the following expressions: in It is a cost function constructed by minimizing the sum of squared residuals. This is the final Laguerre error correction factor. The Laguerre coefficients after identification. Let be the unit direction vector of the error at the i-th joint.
[0012] Step 4 includes the following update rule expression for global optimization of the population using the sparrow search algorithm: in Let be the position of the i-th joint in the (t+1)-th iteration, where t is a positive integer. Here, T is the adjustment factor, Q is the maximum number of iterations, Q is the random perturbation, and L is the position increment. Let i be the position of the i-th joint in the t-th iteration; The position update formula for local development using the Peacock Optimization Algorithm combined with the Lévy Flight Strategy is as follows: in Let i be the position of the i-th joint in the (t+1)-th candidate solution. Let be the position of the i-th joint in the t-th candidate solution. This is the step size coefficient. and All are random variables that follow a normal distribution. The Lévy distribution index; The Sparrow Search algorithm and the Peacock Optimization algorithm form a collaborative mechanism through alternating iterations. That is, the global candidate solution output by the Sparrow Search algorithm serves as the initial solution set for the Peacock Optimization algorithm, and the local optimal solution obtained by the Peacock Optimization algorithm is then fed back to update the sparrow population. This achieves coupled optimization of global exploration and local development, thereby improving the accuracy and stability of optimization.
[0013] The technical effects of this invention are as follows: This invention is based on an error correction method for articulated arm measuring machines (CMMs) using Laguerre polynomial error characterization. It employs Laguerre polynomial error modeling and uses the sparrow and peacock algorithms for servo error correction. In terms of error modeling, an orthogonal polynomial expansion model is used with joint angles as input variables. A higher-order Laguerre function is used to fit the six-dimensional error of each joint. Furthermore, a sparrow-peacock two-layer optimization framework with weight initialization capability and error backpropagation tuning mechanism is constructed. An optimization system is built with multiple sets of joint angles and corresponding real end-effector error outputs, achieving high-precision identification of error function parameters in high-order, high-dimensional space, providing an accurate and controllable mathematical basis for CMM accuracy compensation.
[0014] This invention is based on an articulated arm measuring machine with Laguerre polynomial error characterization, and innovatively integrates the sparrow algorithm and the peacock algorithm to correct the error coefficients. Attached Figure Description
[0015] Figure 1 This is a flowchart illustrating the error correction method for articulated arm measuring machines based on Laguerre polynomial error characterization of the present invention. Figure 1 The process includes: Step 1, establishing a coordinate measuring machine model; Step 2, characterizing joint errors using Laguerre polynomials; Step 3, obtaining error characterization results through error source analysis, error term inversion, and least squares fitting; Step 4, combining the error characterization results with the original 3D coordinate data and inputting them into the sparrow-peacock algorithm optimization module to find the optimal coefficient matrix; Step 5, updating individual positions through fitness iteration calculation to obtain the correction matrix; and Step 6, multiplying the correction matrix with the original coordinates to obtain the corrected coordinates.
[0016] Figure 2 This is a schematic diagram of the coordinate measuring machine system structure involved in the articulated arm measuring machine error correction method based on Laguerre polynomial error characterization of the present invention.
[0017] Figure 3 This is a schematic diagram of the operation flowchart of a coordinate measuring machine system. Figure 3 The process includes: Step 1, zeroing the robotic arm; Step 2, starting the human-machine interface; Step 3, receiving data; Step 4, processing data; and Step 5, generating corrected coordinates.
[0018] The attached diagram is labeled as follows: 1-Coordinate measuring machine model (model building module); 2-Laguerre polynomial characterization of joint errors (model building module); 3-Error source analysis; 4-Error term inversion; 5-Least squares fitting; 6-Obtaining original 3D coordinates (data input module); 7-Combining error characterization results with original 3D coordinate data; 8-Sparrow-Peacock algorithm optimization module; 9-Fitness calculation; 10-Individual position update; 11-Corrected coordinates; 12-Base; 13-Rotating support; 14-First angle sensor; 15-Second angle sensor; 16-Third robotic arm joint; 17-Third angle sensor; 18-Micrometer; 19-Fourth angle sensor; 20-Second robotic arm joint; 21-First robotic arm joint; 22-Computer; 23-Data cable; 24-Zeroing robotic arm; 25-Starting human-machine interface; 26-Data reception; 27-Data processing; 28-Generating corrected coordinates. Detailed Implementation
[0019] The following is in conjunction with the attached diagram ( Figures 1-3 The present invention will be described below.
[0020] Figure 1 This is a flowchart illustrating the error correction method for articulated arm measuring machines based on Laguerre polynomial error characterization of the present invention. Figure 2 This is a schematic diagram of the coordinate measuring machine system structure involved in the articulated arm measuring machine error correction method based on Laguerre polynomial error characterization of the present invention. Figure 3 This is a schematic diagram of the operation flowchart of a coordinate measuring machine system. (Reference) Figures 1 to 3 As shown, an error correction method for an articulated arm measuring machine based on Laguerre polynomial error characterization is proposed. A multi-degree-of-freedom articulated arm structure is constructed, with angle sensors configured at each joint to acquire joint angles. This is combined with an end-effector capacitive probe to achieve real-time acquisition of the spatial coordinates of the workpiece. The system's pose transfer is modeled using a homogeneous transformation matrix.
[0021]
[0022] in, This represents the total pose transformation matrix from the base coordinate system to the end probe coordinate system. Let the rotation and translation transformation matrix of the i-th joint be represented. Let i be the angle of the i-th joint. This represents the small displacement error at the i-th joint.
[0023] Subsequently, a kinematic model of the coordinate measuring machine was established, with the angles of each joint as input variables. The nonlinear error characteristics were characterized using Laguerre polynomial expansion. For each joint error component, Laguerre basis functions of order 13 were used for expansion. , in, This represents the geometric error value corresponding to the joint angle. For the k-th order Laguerre polynomial, The coefficients are to be determined. This modeling method can improve the stability and accuracy of fitting high-dimensional error components while ensuring the orthogonality of the functions. During the modeling process, the least squares method is used to fit the measurement data and the model output.
[0024] In the data processing stage, the system combines the original coordinates with Laguerre error characteristics to generate a corrected dataset containing error information. Subsequently, a collaborative mechanism of the Sparrow Search algorithm and the Peacock Optimization algorithm is introduced to solve for the optimal solution of the Laguerre polynomial coefficients. The Sparrow algorithm handles the global search, maintaining the diversity of the solution space; the Peacock algorithm, combined with Lévy flight, performs local optimization to improve convergence accuracy. Its iterative relationship can be expressed as: , in, For the global search operator for sparrows, For the peacock local optimization operator, The coefficients of the Laguerre polynomial generated for the t-th group are to be determined. Through alternating iterations, the final Laguerre error correction coefficients are obtained and applied to the kinematic model to output the error-corrected 3D coordinates.
[0025] The coordinate measuring machine system mainly consists of a robotic arm and sensors. The robotic arm can perform translational and rotational movements to measure objects. The sensors are responsible for collecting data on the robotic arm's rotational and translational movements. If smart sensors are used, the algorithm of this invention can be embedded.
[0026] The robotic arm can be (or not) composed of highly modular joint units. Each joint module can include a deceleration module (such as a reducer) to control the rotation speed of the robotic arm. Modularization greatly simplifies the assembly, maintenance, and upgrade process, and supports the rapid replacement of modules with different arm lengths or specifications according to task requirements. The robotic arm probe sensor can be a capacitive micrometer (or other similar functional modules).
[0027] The minute deviations in the motion of each joint of the robot can be decomposed into the following in the three spatial axes: Rotational errors about the X, Y, and Z axes: , For the i-th joint when it rotates to the angle At that time, the small rotation error vector generated, For the i-th joint at angle , At that time, the rotational error component about the X-axis, For the i-th joint at angle , At that time, the rotational error component about the Y-axis, For the i-th joint at angle , When, the rotational error component around the Z-axis.
[0028] Small displacement errors along the X, Y, and Z axes:
[0029] Characterizing the nonlinear mapping relationship between rotation and displacement error at each joint: , in: The k-th order Laguerre basis function has orthogonality and recursiveness. The parameters to be determined are the fitting coefficients of the error function. The continuous nonlinear error is expressed with finite parameters to establish a computable error model for real-time compensation.
[0030] n: Function order. In one embodiment of this invention, based on existing calculation results, it is selected as 13 to balance accuracy and stability. Other values can be selected in other cases.
[0031] The Laguerre parameters are calculated through a process of "data acquisition - error inversion - least squares fitting". The core logic lies in the progressive and synergistic effect of these three steps, which can build a rigorous physical relationship from measured data to theoretical models. Ultimately, this ensures that the Laguerre parameters not only meet the fitting accuracy in mathematics, but also have clear physical meaning and practical effectiveness.
[0032] To accurately construct the error model during data acquisition, it is necessary to collect the robot end-effector positions (M is a positive integer) under M different joint angle configurations: : The angle value of the i-th joint in the j-th data set The actual position of the end effector obtained by the laser measurement system in this group. Position calculated using an ideal kinematic model Error between measured value and ideal value By using an error inverse mapping algorithm, the actual position of the end effector is differed from its ideal position to obtain the pose error of the end effector. By using the Jacobian moment of the robot's forward kinematics model, the end effector error is mapped to the error components of each joint.
[0033] set up The Jacobian matrix of the end-effector pose with respect to joint variables, and the small perturbation at the end. It can be represented as: , in, This refers to minute perturbations of the joint (including rotational and translational errors). This refers to higher-order error terms or other disturbances.
[0034] Ultimately, this is achieved by solving for the Jacobian inverse or pseudo-inverse: , This allows the end-point error to be reflected back into the equivalent error term of each joint, providing the necessary data foundation for subsequent function modeling based on Laguerre polynomials.
[0035] Establish the least squares fitting equation and construct the fitting relationship in the following form:
[0036] Stack all j datasets to form a matrix equation: E is the residual vector.
[0037] in: D is the error observation vector. ; L is the basis function matrix. ; A is the vector of coefficients to be determined. .
[0038] Design the final cost function and solve for the final error coefficient.
[0039] Minimize the sum of squared residuals to construct the cost function:
[0040] Find the minimum value to obtain the parameter coefficients. Other error terms, such as rotational error, are handled similarly.
[0041] The final model can be represented as: , in, Let be the unit direction vector of the error at the i-th joint. The Laguerre coefficients after identification. This is the final error correction value.
[0042] The sparrow search algorithm is used to perform global optimization of the population, and its update rule is as follows: , in: Let i be the position of the i-th individual in the t-th iteration; As a regulating factor; T is the maximum number of iterations; Q represents a random perturbation; L is the position increment, used to maintain population diversity and avoid getting trapped in local optima; Secondly, the peacock optimization algorithm is introduced and combined with the Lévy flight strategy for local development. Its position update formula is as follows: , in: The position of the j-th candidate solution; This is the step size coefficient; Let be a random variable that follows a normal distribution; The Lévy distribution index is used to enhance local search capabilities and convergence speed.
[0043] The two algorithms form a collaborative mechanism through alternating iterations. The global candidate solutions output by the Sparrow Search algorithm serve as the initial solution set for the Peacock Algorithm, and the local optimal solutions obtained by the Peacock Algorithm are then fed back to update the sparrow population. This achieves coupled optimization of global exploration and local development, thereby improving the accuracy and stability of the optimization process.
[0044] This system realizes a closed-loop process from hardware acquisition to software error compensation. The original angle signal of the workpiece under test is obtained by the angle sensor at the joint, and the three-dimensional point acquisition is completed by the end probe. Then, the system error is modeled and least squares fitted by establishing a kinematic model and using Laguerre polynomial expansion to obtain the parameter matrix characterizing the error. The original coordinates and the error model results are then input into the optimization module. The optimal correction coefficient is obtained by iteratively using the global optimization of the sparrow search algorithm and the local refinement of the peacock optimization algorithm. This correction coefficient is then fed back to the model to generate the error-corrected three-dimensional coordinates.
[0045] This project addresses the urgent need in modern manufacturing for high-precision 3D measurement of large-sized workpieces on-site. It designs and manufactures an articulated arm measuring machine based on Laguerre polynomial error characterization and innovatively integrates the sparrow algorithm and peacock algorithm to correct the error coefficients.
[0046] This embodiment provides an error correction method for articulated arm measuring machines based on Laguerre polynomial error characterization. For example... Figure 1As shown, after establishing the coordinate measuring machine model (1), the error at the joint is represented by Laguerre polynomial (2). The overall trend of the error is captured by the low-order term, and the local dynamic fluctuation is captured by the high-order term. Then, in the error characterization process, the source of the error is identified (3), the error term is inverted (4), and the least squares method is fitted (5). Then, the original coordinate data is input (6), the error characterization result formula is combined with the original data (7), and the sparrow-peacock algorithm (8) is input to optimize and find the best coefficient matrix. The fitness is calculated iteratively (9) to update the individual position (10). Finally, the corrected matrix is multiplied by the original coordinates to obtain the corrected coordinates (11). The coordinate measuring machine system mainly consists of two parts: a robotic arm and sensors. The robotic arm can realize translation and rotation functions, so as to measure the object by operating the robotic arm; the sensors are responsible for collecting data on the rotation and translation of the robotic arm. The overall robotic arm is built on the base (12), and the robotic arm realizes rotation in the horizontal plane through the rotating support (13); through the rotation of the first robotic arm joint (21), the second robotic arm joint (20), and the third robotic arm joint (15), the robotic arm realizes bending and twisting in the vertical plane to contact the object to be measured; the first angle sensor (14) measures the rotation angle and angular acceleration of the robotic arm in the horizontal plane to obtain measurement data, and the second angle sensor (15), the third angle sensor (17), and the fourth angle sensor (19) measure the rotation angle and angular acceleration of the robotic arm joints respectively to obtain measurement data; the micrometer (18) directly contacts the object to be measured and obtains relevant measurement data such as linear displacement by moving on the object.
[0047] The coordinate measuring machine (CMM) and the computer (22) are connected via a data cable to form a human-machine measurement system (23). The angle data from the angle sensor and the linear displacement data from the micrometer obtained in the CMM are transmitted to the computer (22) via the data cable, and then the coordinate measurement can begin. After zeroing all the sensors of the robotic arm (24), the human-machine interaction program (25) is opened, the front-end interface is entered, and the “Start Measurement” button is clicked to start data reception (26). After the measurement is completed, the “Stop” button is clicked, and then the “Data Processing” button is clicked (27) to obtain the original coordinate values. Finally, the “Coordinate Generation” button is clicked to generate the three-dimensional coordinates after Laguerre polynomial correction (28).
[0048] The coordinate measuring machine (CMM) system mainly consists of two parts: a robotic arm and sensors. The robotic arm can perform translational and rotational movements, allowing for the measurement of objects by manipulating the robotic arm; the sensors are responsible for collecting data on the rotation and translational movements of the robotic arm.
[0049] The robotic arm is composed of highly modular joint units. Each joint module contains a reducer to control the rotation speed of the robotic arm. Modularity greatly simplifies the assembly, maintenance, and upgrade process, and supports the rapid replacement of modules with different arm lengths or specifications according to task requirements. The robotic arm probe sensor adopts a capacitive micrometer, which can achieve the 1μm accuracy required by the platform at low cost, and has a simple structure that is easy to maintain and repair.
[0050] The minute deviations in the motion of each joint of the robot can be decomposed into the following in the three spatial axes: Rotational errors about the X, Y, and Z axes: , For the i-th joint when it rotates to the angle At that time, the small rotation error vector generated, For the i-th joint at angle , At that time, the rotational error component about the X-axis, For the i-th joint at angle , At that time, the rotational error component about the Y-axis, For the i-th joint at angle , When, the rotational error component around the Z-axis.
[0051] Small displacement errors along the X, Y, and Z axes:
[0052] Characterizing the nonlinear mapping relationship between rotation and displacement error at each joint: , in: The k-th order Laguerre basis function has orthogonality and recursiveness. The parameters to be determined are the fitting coefficients of the error function. The continuous nonlinear error is expressed with finite parameters to establish a computable error model for real-time compensation.
[0053] n: Function order. In one embodiment of this invention, based on existing calculation results, it is selected as 13 to balance accuracy and stability. Other values can be selected in other cases.
[0054] The Laguerre parameters are calculated through a process of "data acquisition - error inversion - least squares fitting". The core logic lies in the progressive and synergistic effect of these three steps, which can build a rigorous physical relationship from measured data to theoretical models. Ultimately, this ensures that the Laguerre parameters not only meet the fitting accuracy in mathematics, but also have clear physical meaning and practical effectiveness.
[0055] To accurately construct the error model during data acquisition, it is necessary to collect the robot end-effector positions (M is a positive integer) under M different joint angle configurations: : The angle value of the i-th joint in the j-th data set The actual position of the end effector obtained by the laser measurement system in this group. Position calculated using an ideal kinematic model Error between measured value and ideal value By using an error inverse mapping algorithm, the actual position of the end effector is differed from its ideal position to obtain the pose error of the end effector. By using the Jacobian moment of the robot's forward kinematics model, the end effector error is mapped to the error components of each joint.
[0056] set up The Jacobian matrix of the end-effector pose with respect to joint variables, and the small perturbation at the end. It can be represented as: , in, This refers to minute perturbations of the joint (including rotational and translational errors). This refers to higher-order error terms or other disturbances.
[0057] Ultimately, this is achieved by solving for the Jacobian inverse or pseudo-inverse: , This allows the end-point error to be reflected back into the equivalent error term of each joint, providing the necessary data foundation for subsequent function modeling based on Laguerre polynomials.
[0058] Establish the least squares fitting equation and construct the fitting relationship in the following form:
[0059] Stack all j datasets to form a matrix equation: E is the residual vector.
[0060] in: D is the error observation vector.
[0061] L is the basis function matrix.
[0062] A is the vector of coefficients to be determined.
[0063] Design the final cost function and solve for the final error coefficient.
[0064] Minimize the sum of squared residuals to construct the cost function:
[0065] Find the minimum value to obtain the parameter coefficients. Other error terms, such as rotational error, are handled similarly.
[0066] The final model can be represented as: , in, Let be the unit direction vector of the error at the i-th joint. The Laguerre coefficients after identification. This is the final error correction value.
[0067] The sparrow search algorithm is used to perform global optimization of the population, and its update rule is as follows: , in: Let i be the position of the i-th individual in the t-th iteration. As a regulatory factor T is the maximum number of iterations. Q is a random perturbation. L is the position increment, used to maintain population diversity and avoid getting trapped in local optima; Secondly, the peacock optimization algorithm is introduced and combined with the Lévy flight strategy for local development. Its position update formula is as follows: , in: The position of the j-th candidate solution Step size coefficient A random variable that follows a normal distribution The Lévy distribution index is used to enhance local search capabilities and convergence speed. The two algorithms form a collaborative mechanism through alternating iterations. The global candidate solutions output by the Sparrow Search algorithm serve as the initial solution set for the Peacock Algorithm, and the local optimal solutions obtained by the Peacock Algorithm are then fed back to update the sparrow population. This achieves coupled optimization of global exploration and local development, thereby improving the accuracy and stability of the optimization process.
[0068] The technical solutions of the present invention have been clearly and completely described above with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.
[0069] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.
Claims
1. An error correction method for articulated arm measuring machines based on Laguerre polynomial error characterization, characterized in that, Includes the following steps: Step 1: Configure angle sensors at each joint of the articulated arm measuring machine to obtain the joint angle, and use the end capacitive probe to realize the real-time acquisition of the spatial coordinates of the workpiece being measured. Step 2: Establish the position transfer model using a homogeneous transformation matrix; Step 3: Establish the kinematic model of the coordinate measuring machine, using the angles of each joint as input variables, and characterize the nonlinear error characteristics through Laguerre polynomial expansion; Step 4: Combine the original coordinates with the Laguerre error features to generate a corrected dataset containing error information. Introduce the collaborative mechanism of the Sparrow Search algorithm and the Peacock Optimization algorithm to solve for the optimal solution of the coefficients to be determined in the Laguerre polynomial, thereby obtaining the final Laguerre error correction coefficients. Apply the Laguerre error correction coefficients to the kinematic model of the coordinate measuring machine and output the error-corrected three-dimensional coordinates.
2. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Step 2 includes the following expression: in This represents the total position transformation matrix from the base coordinate system to the end capacitive probe coordinate system. Let n represent the rotation and translation transformation matrix of the i-th joint, where i is a positive integer and n is the number of joints. Let i be the angle of the i-th joint. This represents the small displacement error at the i-th joint.
3. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Step 3 includes the following expression: in Indicates joint angle The corresponding geometric error value, Let m be the k-th order Laguerre polynomial, where k is an integer greater than or equal to 0, and m is a positive integer. The coefficients to be determined are denoted as .
4. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Step 4 includes the following expression: in For the global search operator for sparrows, For the peacock local optimization operator, Let be the coefficients to be determined for the Laguerre polynomials generated in the t-th group, where t is a positive integer. These are the coefficients to be determined for the Laguerre polynomials generated by group t+1.
5. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Including the following expressions: in For the i-th joint when it rotates to the angle The small rotational error vector generated at that time, yes The rotational error component about the X-axis, yes The rotational error component about the Y-axis, yes Rotational error component around the Z-axis; in Is the i-th joint rotating to the angle? The tiny displacement error that occurs at that time yes x-axis component, yes The y-axis component, yes The z-axis component; in Let n be the k-th Laguerre basis function, where k is an integer greater than or equal to 0, and n is the order of the function. , These are all parameter coefficients to be determined, i.e., the fitting coefficients of the error function.
6. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Including the following expressions: in It is the positional error of the end in the j-th data set, where j is a positive integer. It is the actual end position obtained by the laser measurement system in the j-th data set. It is the ideal position calculated using the ideal kinematic model in the j-th set of data. It is a small disturbance at the end. It is the Jacobian matrix of the end-effector position with respect to the joint variables. It's a tiny disturbance in the joint. It is a higher-order error term or other interference. It refers to the position at the end.
7. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Step 4 involves fitting the measured data to the model output using the least squares method. The least squares fitting equation is as follows: ， in It is the translation error component of the i-th joint in the j-th dataset. It is the k-th order Laguerre basis function in the j-th dataset. It is a higher-order error term or other disturbance in the j-th dataset; Stacking all j datasets together yields the following matrix equation: Where E is the residual vector and D is the error observation vector. M is the number of dataset groups, and L is the basis function matrix. U is the order of the Laguerre polynomial, and A is the vector of coefficients to be determined. .
8. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Including the following expressions: in It is a cost function constructed by minimizing the sum of squared residuals. This is the final Laguerre error correction factor. The Laguerre coefficients after identification. Let be the unit direction vector of the error at the i-th joint.
9. The method for error correction of articulated arm measuring machines based on Laguerre polynomial error characterization according to claim 1, characterized in that, Step 4 includes the following update rule expression for global optimization of the population using the sparrow search algorithm: in Let be the position of the i-th joint in the (t+1)-th iteration, where t is a positive integer. Here, T is the adjustment factor, Q is the maximum number of iterations, Q is the random perturbation, and L is the position increment. Let i be the position of the i-th joint in the t-th iteration; The position update formula for local development using the Peacock Optimization Algorithm combined with the Lévy Flight Strategy is as follows: in Let i be the position of the i-th joint in the (t+1)-th candidate solution. Let be the position of the i-th joint in the t-th candidate solution. This is the step size coefficient. and All are random variables that follow a normal distribution. The Lévy distribution index; The Sparrow Search algorithm and the Peacock Optimization algorithm form a collaborative mechanism through alternating iterations. That is, the global candidate solution output by the Sparrow Search algorithm serves as the initial solution set for the Peacock Optimization algorithm, and the local optimal solution obtained by the Peacock Optimization algorithm is then fed back to update the sparrow population. This achieves coupled optimization of global exploration and local development, thereby improving the accuracy and stability of optimization.