SCARA robot arm length and zero point calibration method based on support vector regression

Abstract

The invention discloses an SCARA robot arm length and zero point calibration method based on support vector regression. The method comprises the following steps: establishing an SCARA robot kinematics model, recording joint angle data at a preset point of a calibration plate, constructing an overdetermined homogeneous linear equation set, and preliminarily resolving an offset value of the arm length and the zero point. Aiming at nonlinear errors which are difficult to process by a traditional calibration method, an SVR model is introduced, error modeling and compensation are carried out by utilizing a radial basis function (RBF), and dynamic error correction of the robot in different environments is realized. According to the method, the actual error data in the working space of the robot is collected in real time, the calibration precision is remarkably improved, human intervention is reduced, and the precision stability of the robot in high-speed operation and long-time operation is guaranteed. Compared with the prior art, by means of the automatic calibration and error compensation process, nonlinear errors in a complex environment are effectively processed, the industrial production efficiency is improved, the downtime is shortened, and the method has high robustness and wide application prospects.

Description

Technical Field

[0001] The invention relates to the technical field of robots, and in particular to a SCARA robot arm length and zero point calibration method based on support vector regression. Background Art

[0002] The SCARA (Selective Compliance Assembly Robot Arm) robot is an industrial robot designed for fast and precise horizontal operations. It is widely used in industrial fields such as electronic product assembly, material handling, precision packaging and dispensing. The design features of the SCARA robot are a highly rigid vertical axis and a highly flexible horizontal axis. It can move flexibly in a two-dimensional plane while maintaining vertical rigidity. It is suitable for industrial operation scenarios that require high precision and high speed. The accuracy and repeatability of the SCARA robot's operation directly depend on the calibration of its arm length and zero position. However, due to slight errors in the manufacturing and assembly process, the robot is prone to arm length deviation and zero position offset during operation, resulting in inconsistency between its actual working path and the theoretical trajectory, which seriously affects the operation accuracy.

[0003] In order to ensure the operating accuracy of SCARA robots, the industry usually uses several calibration methods to calibrate the arm length and zero point position. The more common methods in the prior art include: 1. Laser rangefinder calibration method: The robot arm length and zero point are calibrated by a laser rangefinder. This method has the advantages of high precision and non-contact measurement, but its disadvantages are that it requires high-precision measurement equipment, the equipment cost is expensive, and it is easily disturbed by the laser path in a complex industrial environment, resulting in unstable measurement results.

[0004] 2. Mechanical alignment calibration method: manually or semi-automatically adjust the arm length and zero point of the SCARA robot. This method is simple and easy to operate, but because it relies on manual operation, the accuracy is low, and the calibration process is time-consuming and easily affected by human factors, resulting in poor consistency and repeatability.

[0005] 3. Based on mathematical modeling and simulation: The deviation between the arm length and the zero position is inferred from the known motion trajectory and the expected position, and the model is used for error correction. However, this method depends on the accuracy of the model and the performance of the simulation software. Once there is an error in the simulation model, the actual effect is often difficult to meet the high-precision requirements. In addition, this method requires high computing power and the calibration process is complicated.

[0006] In addition, the disadvantages of the existing technology are that the laser ranging method is costly and sensitive to the environment, and the measurement results are easily affected by external interference; the mechanical alignment method has low accuracy and efficiency, and is easily affected by human operation errors, and cannot meet the high-precision industrial needs; although the mathematical modeling and simulation methods can partially solve the errors, they are limited by the accuracy of the model and the simulation conditions, and it is difficult to handle complex nonlinear errors, and the calculation burden is heavy.

[0007] In order to solve the above problems, the industry has gradually tried to adopt a calibration method based on error compensation, which compensates for the deviation of the robot arm length and zero position through data collection and modeling. However, the existing error compensation methods are usually based on linear models and cannot effectively deal with the nonlinear errors caused by factors such as joint wear and assembly errors in actual robot operations. At the same time, the existing compensation methods are usually only effective under static conditions after calibration and lack the ability to adjust dynamically, resulting in the inability to maintain stable accuracy when the robot is running at high speed.

[0008] Therefore, how to improve the accuracy of SCARA robot arm length and zero point calibration and handle dynamic and nonlinear error compensation has become the technical problem to be solved by the present invention. Summary of the invention

[0009] The technical problem solved by the present invention is to provide a SCARA robot arm length and zero point calibration method based on support vector regression in response to the defects existing in the above-mentioned prior art, so as to solve the problems of low calibration accuracy, insufficient error compensation, and inability to handle nonlinear and dynamic errors proposed in the above-mentioned background technology.

[0010] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows: A SCARA robot arm length and zero point calibration method based on support vector regression, the method comprising the following steps: Step 1, the establishment of the kinematic equation of the SCARA robot: Based on the structure of the upper arm and lower arm of the SCARA robot, its kinematic model is defined, where: The length of the upper arm is L1, and the length of the lower arm is L2; The first joint angle is θ1, and the second joint angle is θ2; The position of the SCARA robot end in the workspace is determined by the following equation: Step 2, calibration point selection and data collection: Align the calibration pin at the end of the SCARA robot to the preset points M and N on the calibration board, record the joint angles θ1 and θ2 at different positions, and establish the error model of arm length and zero offset based on the measured angles; Step 3: Preliminary solution based on overdetermined homogeneous linear equations: Based on the collected multiple calibration point positions and the corresponding joint angles, construct an overdetermined homogeneous linear equation system: Ax=0 Among them, the matrix A is composed of the coordinates and angle information of each calibration point. By solving the eigenvector corresponding to the minimum eigenvalue of the equation group, the arm length error and zero offset value of the SCARA robot are preliminarily estimated; Step 4: Construction and training of support vector regression SVR model: Using multiple sets of data points randomly collected in the workspace of the SCARA robot, the error between the actual position and the ideal position is recorded, and the error is the residual error after the calibration is completed; The error data set is divided into a training set and a test set, and regression analysis is performed using the support vector regression SVR model. The model uses the radial basis kernel function RBF, and its loss function is defined as: in, is the weight vector, is the regularization parameter, and is a slack variable, representing the prediction error; Step 5, error compensation: Based on the training results of the SVR model, the position error of the SCARA robot is predicted in real time when the robot is moving, and the target position of the SCARA robot is compensated according to the predicted error value. The compensation formula is: in, is the error value predicted by the SVR model; Step 6, calculation and adjustment: According to the compensated SCARA robot end position, further adjust the arm length and zero point position to ensure high-precision operation of the robot in different working environments.

[0011] As a further solution of the present invention, the calibration points include at least two preset points in the workspace of the SCARA robot, and the calibration process is performed by aligning the calibration needle with the preset points in sequence and recording the joint angles.

[0012] As a further solution of the present invention, the overdetermined homogeneous linear equations are solved by the Jacobi method to obtain the eigenvector corresponding to the minimum eigenvalue, which is used to preliminarily calculate the arm length error and the zero point offset.

[0013] As a further solution of the present invention, the support vector regression model uses a radial basis kernel function RBF to process the nonlinear error of the SCARA robot in the workspace.

[0014] As a further solution of the present invention, the data in the error data set is obtained by random sampling to ensure the diversity and representativeness of the data.

[0015] As a further solution of the present invention, the SVR model is trained by a sequential minimum optimization (SMO) algorithm to minimize the error and determine the optimal support vector.

[0016] Compared with the prior art, the present invention has the following beneficial effects: 1. Accurate arm length and zero point calibration: This invention introduces the support vector regression (SVR) method and uses the radial basis kernel function (RBF) to deal with nonlinear error problems, which greatly improves the calibration accuracy of the SCARA robot arm length and zero point. Compared with traditional laser ranging or mechanical alignment calibration methods, this invention can automatically adapt to complex nonlinear error distributions, especially when the robot is running for a long time, wear or assembly errors accumulate, it can still maintain high accuracy. Through accurate error modeling and regression, this invention not only reduces the interference of human factors, but also reduces the dependence on high-precision hardware equipment and reduces the overall cost.

[0017] 2. Dynamic error compensation capability: In actual industrial application scenarios, SCARA robots are often in high-speed and dynamic operating environments, and traditional calibration methods are difficult to adapt to dynamic errors caused by environmental changes. The present invention uses the SVR model, combined with real-time data acquisition, to perform dynamic error compensation during robot operation. This real-time compensation mechanism ensures high-precision positioning of the robot under high-speed operation or different environmental changes (such as temperature and vibration), effectively reduces the accumulation and transmission of errors, and significantly improves the accuracy of the robot's task execution.

[0018] 3. Support nonlinear error correction and strong robustness: The present invention constructs an overdetermined homogeneous linear equation system and combines the Jacobi method to solve the eigenvector corresponding to the minimum eigenvalue to achieve preliminary calibration of the arm length and zero offset. Then, through the error correction of SVR, complex nonlinear errors can be adaptively processed. Compared with the traditional linear error model, the present invention has stronger robustness, especially when facing nonlinear errors such as robot mechanical wear and joint axis offset, it can still ensure high-precision operation and has wider adaptability.

[0019] 4. High degree of automation, improving industrial production efficiency: The present invention greatly reduces the reliance on manual operations and reduces the interference of human errors through the automated calibration and error compensation process. Especially in modern industrial scenarios, such as electronic component assembly, precision machining and other occasions that require extremely high positioning accuracy, the present invention can automatically adapt to different tasks and working environments, reduce downtime, and improve production efficiency. In particular, after the present invention introduces SVR model training and automatic compensation mechanism, the robot does not need to be frequently recalibrated, can operate stably for a long time, and further reduces maintenance costs.

[0020] 5. Data-driven error compensation and strong model generalization ability: The present invention adopts a data-driven error compensation method and randomly collects actual error data from multiple points to train the SVR model, so that the model can cover the diverse error distribution in the workspace and ensure the generalization ability of the model.

[0021] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0023] Figure 1 It is the kinematics positive solution diagram of the SCARA robot of the present invention; Figure 2 It is a schematic diagram of the calibration plate of the present invention; Figure 3 It is a schematic diagram of the process of the present invention; Figure 4 It is a schematic diagram of the calibration steps of the present invention; Figure 5 It is a diagram of the calculation results of the present invention; Figure 6 Table 1 Experimental data diagram of the present invention; Figure 7 Table 2 is a graph showing the experimental results of the present invention. DETAILED DESCRIPTION

[0024] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0025] See also Figure 1 —7. In an embodiment of the present invention, a method for calibrating arm length and zero point of a SCARA robot using support vector regression is provided, the method comprising the following steps: Step 1, the establishment of the kinematic equation of the SCARA robot: Based on the structure of the upper arm and lower arm of the SCARA robot, its kinematic model is defined, where: The length of the upper arm is L1, and the length of the lower arm is L2; The first joint angle is θ1, and the second joint angle is θ2; The position of the SCARA robot end in the workspace is determined by the following equation: Step 2, calibration point selection and data collection: Align the calibration pin at the end of the SCARA robot to the preset points M and N on the calibration board, record the joint angles θ1 and θ2 at different positions, and establish the error model of arm length and zero offset based on the measured angles; Step 3: Preliminary solution based on overdetermined homogeneous linear equations: Based on the collected multiple calibration point positions and the corresponding joint angles, construct an overdetermined homogeneous linear equation system: Ax=0 Among them, the matrix A is composed of the coordinates and angle information of each calibration point. By solving the eigenvector corresponding to the minimum eigenvalue of the equation group, the arm length error and zero offset value of the SCARA robot are preliminarily estimated; Step 4: Construction and training of support vector regression SVR model: Using multiple sets of data points randomly collected in the workspace of the SCARA robot, the error between the actual position and the ideal position is recorded, and the error is the residual error after the calibration is completed; The error data set is divided into a training set and a test set, and regression analysis is performed using the support vector regression SVR model. The model uses the radial basis kernel function RBF, and its loss function is defined as: in, is the weight vector, is the regularization parameter, and is a slack variable, representing the prediction error; Step 5, error compensation: Based on the training results of the SVR model, the position error of the SCARA robot is predicted in real time when the robot is moving, and the target position of the SCARA robot is compensated according to the predicted error value. The compensation formula is: in, is the error value predicted by the SVR model; Step 6, calculation and adjustment: According to the compensated SCARA robot end position, further adjust the arm length and zero point position to ensure high-precision operation of the robot in different working environments.

[0026] As a further solution of the present invention, the calibration points include at least two preset points in the workspace of the SCARA robot, and the calibration process is performed by aligning the calibration needle with the preset points in sequence and recording the joint angles.

[0027] As a further solution of the present invention, the overdetermined homogeneous linear equations are solved by the Jacobi method to obtain the eigenvector corresponding to the minimum eigenvalue, which is used to preliminarily calculate the arm length error and the zero point offset.

[0028] As a further solution of the present invention, the support vector regression model uses a radial basis kernel function RBF to process the nonlinear error of the SCARA robot in the workspace.

[0029] As a further solution of the present invention, the data in the error data set is obtained by random sampling to ensure the diversity and representativeness of the data.

[0030] As a further solution of the present invention, the SVR model is trained by a sequential minimum optimization (SMO) algorithm to minimize the error and determine the optimal support vector.

[0031] Embodiment 1: The SCARA robot arm length and zero point calibration and error compensation method supporting vector regression of the present invention is particularly suitable for precision industrial scenarios, especially in high-precision and high-speed operations such as electronic product assembly and medical device manufacturing, and can significantly improve the robot's operating accuracy and stability. Taking electronic component assembly as an example, SCARA robots usually need to complete the assembly of multiple precision components in a very short time. Due to the high operating frequency, complex movements, and the small size of the electronic components themselves, if there is any positioning deviation during the operation, it may cause assembly failure or product quality problems, which will have a significant impact on production efficiency and yield rate.

[0032] In order to solve these problems, the present invention first calculates the initial error between the arm length and the zero point by establishing a kinematic model of the SCARA robot. The SCARA robot has two joints, the length of its upper arm is L1, and the length of its lower arm is L2. The position of the end in the workspace is determined by the joint angles θ1 and θ2. Under ideal conditions, the theoretical position calculation formula of the robot end is: in, Indicates the deviation of the joint angle.

[0033] In actual applications, due to mechanical assembly errors during the manufacturing process, wear of parts after long-term use, and environmental changes (such as temperature fluctuations, vibrations, etc.), the robot's joint angles and arm lengths may deviate from the theoretical values, causing the zero position to drift. This drift will accumulate errors, thus affecting the accuracy of the entire production process.

[0034] To solve this problem, the present invention first selects calibration points and collects data, installs a calibration needle at the end of the SCARA robot, and records the joint angles θ1 and θ2 at different positions through multiple preset points M and N on the calibration board. Through the collected multiple calibration points, an overdetermined homogeneous linear equation group is constructed, and the eigenvector corresponding to the minimum eigenvalue of the equation group is solved using the Jacobi method to preliminarily estimate the robot arm length error and zero point offset value. This process ensures that the length deviation of the upper arm and the lower arm can be corrected during the preliminary calibration process, and the zero point position is corrected, laying the foundation for the subsequent dynamic error compensation.

[0035] Existing calibration methods often do not work well in such complex operating environments. Although laser ranging methods can provide high-precision measurements, they require expensive equipment and have harsh environmental requirements and are easily affected by external interference. Mechanical alignment methods are limited by manual operation, have low calibration accuracy and are time-consuming, and cannot meet the needs of modern high-speed production lines. Although mathematical modeling and simulation methods can simulate and calibrate, they have difficulty in handling complex nonlinear errors, are complex to calculate, and rely on the accuracy of the model.

[0036] In order to overcome these technical bottlenecks, the present invention introduces a support vector regression (SVR) model to dynamically compensate for the residual error after calibration. The specific implementation method is: after the SCARA robot completes the preliminary calibration, 200 sets of point data in the workspace are randomly collected, and the difference between the actual position and the ideal position is recorded to form a training set and a test set. The support vector regression (SVR) model is adopted, and the radial basis kernel function (RBF) is used for regression analysis to establish an error compensation model, and its loss function is: By optimizing this objective function, the model can minimize the residual error in robot operation and significantly improve the calibration accuracy.

[0037] In actual use, when the SCARA robot performs assembly tasks, its sensors collect the robot's motion parameters in real time, including characteristic data such as position, speed, and acceleration. Through the SVR model, the system can dynamically predict the robot's error value in different environments and automatically compensate the robot's end position based on the predicted error. The compensation formula is: in, is the error value predicted by the SVR model; Application Example 1: In the assembly process of high-precision electronic components, the SCARA robot needs to repeatedly grasp and accurately place tiny components in a very short time. Due to long-term operation, the wear of the joint bearings and the fluctuation of ambient temperature will cause the actual position of the robot to deviate from the theoretical trajectory. Through the SVR model of the present invention, the system can automatically identify and correct these errors, ensuring that the robot can achieve the expected accuracy every time it places components and avoid assembly misalignment.

[0038] Application Example 2: In medical device production lines, SCARA robots are used to assemble precision parts, which requires avoiding any slight deviation during operation. Traditional calibration methods are difficult to adapt to such high-precision scenarios, especially when the robot is operating at high speed, which will generate a large inertial force and cause position deviation. Through the dynamic error compensation mechanism of the present invention, the robot can adjust the zero point position in real time during the operation process, ensuring that stable high precision can be maintained during high-speed operation.

[0039] The present invention can not only adapt to complex error conditions in different environments, but also ensure the continuous and efficient operation of the robot in various industrial scenarios through dynamic compensation mechanisms, especially in tasks involving high precision and high speed. Compared with the prior art, the present invention realizes adaptive processing of nonlinear errors by introducing the support vector regression (SVR) model, significantly improves the robustness and accuracy of robot operation, and reduces the long-term impact caused by assembly errors, wear and other factors. Through automated, data-driven calibration and error compensation, the present invention greatly improves the efficiency of the production line and product quality.

[0040] Embodiment 2: In an electronic equipment production workshop, SCARA robots are used for precision assembly operations in a small space. Such operations require robots to complete the grasping and assembly of electronic components with high precision and efficiency in an extremely limited operating space. Traditional SCARA robots often have operational errors due to inaccurate arm length and zero position calibration, especially in a small operating environment, which makes it impossible to meet high-precision operation requirements. These errors usually come from geometric deviations during the robot manufacturing and assembly process, as well as mechanical wear after long-term use, resulting in zero position offset.

[0041] To solve this problem, the present invention proposes a SCARA robot arm length and zero point calibration and error compensation method based on support vector regression (SVR). In the precision assembly scenario in a small space, the robot needs to repeatedly perform grabbing and placing operations between multiple preset points. First, using the calibration method of the present invention, a calibration pin is installed at the end of the SCARA robot, and the preset points M and N on the calibration plate are aligned in turn. The joint angle data of the calibration point is collected, and the robot arm length and zero point deviation are preliminarily calculated to ensure that the length difference and zero point offset of the upper arm and the lower arm are corrected during the basic calibration.

[0042] However, the calibration process can only eliminate some static errors in robot assembly and manufacturing, but cannot deal with dynamic errors in the robot operation process, especially in a small space. Any slight error accumulation will lead to inaccurate positioning of the robot end, affecting its grasping and assembly accuracy. Therefore, the present invention introduces a support vector regression (SVR) model to perform error compensation by collecting dynamic parameters of the robot in real time during operation. The system continuously collects data such as the end position, speed, acceleration, etc. of the robot during high-speed operation, and predicts the error distribution of the robot in a specific environment through the SVR model.

[0043] For example, in a precision assembly process in a small space, a SCARA robot needs to grab tiny electronic components and place them accurately on an assembly board. Since the assembly position is very compact, during repeated operations, the robot will gradually deviate from its originally set path due to the accumulation of tiny errors caused by vibration and temperature changes in the environment. Through the SVR dynamic compensation model of the present invention, the system can identify these deviations in real time and adjust the target position according to the predicted error value, thereby ensuring the accuracy of each grab and placement and avoiding poor assembly due to errors.

[0044] In this embodiment, the method of the present invention successfully solves the problem of inaccurate operation caused by environmental restrictions and accumulated errors in the operation of the robot in a small space, and ensures the positioning accuracy of the robot in high-speed operation through real-time error compensation. Compared with the traditional calibration method, the present invention not only improves the adaptability of the robot in complex environments, but also effectively reduces the accumulated errors in operation, greatly improving the consistency and production efficiency of product assembly.

[0045] Embodiment 3: See also Figure 1 , Figure 1 This is the positive solution diagram of SCARA robot kinematics.

[0046] Since the calibration of the SCARA robot arm length and zero point is only related to the first and second axes, its kinematics can be simplified to a planar two-axis robot.

[0047] like Figure 1 As shown, the robot's base coordinate system xOy is established at the base coordinate origin O. Point O and point A are the robot's rotation joints, point B is the robot's end, OA is the robot's arm, length L1, and AB is the robot's forearm, length L2. θ1 is the angle between the x-axis and OA; θ2 is the angle between OA and AB; Δθ2 is the angle deviation between the theoretical value and the actual value of the robot's arm and forearm. From this, the positive kinematics equation of the SCARA robot can be written: In addition, it is stipulated that when θ2 is between 0° and 180°, the SCARA robot is on the left hand side; when θ2 is between 0° and -180°, the SCARA robot is on the right hand side. The theoretical values ​​of L1 and L2 are 100mm, and the theoretical value of Δθ2 is 0°.

[0048] See also Figure 2 , Figure 2 is a schematic diagram of the calibration plate, assuming that the length between point M and point N on it is d, and the length of d is 150 mm.

[0049] See also Figure 3 , Figure 3 It is a schematic diagram of the process of the present invention.

[0050] The end calibration needle of the SCARA robot measures the corresponding angles of the two preset points on the calibration plate. The calibration steps are as follows: (1) The calibration pin is fixed at the end of the robot. Drag the robot from the left hand side so that the calibration pin coincides with point M and record the angle θ1 of the two joints at this time. (1) ,θ2 (1) .

[0051] (2) The calibration pin is fixed at the end of the robot. Drag the robot from the right hand side so that the calibration pin coincides with point M and record the angle θ1 of the two joints at this time. (2) 、 θ2 (2) .

[0052] (3) The calibration pin is fixed at the end of the robot. Drag the robot from the left hand side so that the calibration pin coincides with point N and record the angle θ1 of the two joints at this time. (3) 、 θ2 (3) .

[0053] (4) The calibration pin is fixed at the end of the robot. Drag the robot from the right hand side so that the calibration pin coincides with point N and record the angle θ1 of the two joints at this time. (4) 、 θ2 (4) .

[0054] See also Figure 4 , Figure 4 Schematic diagram of the calibration steps.

[0055] According to the measured angle and the kinematics of the SCARA robot, the equations for the arm length and zero offset are constructed. According to the measured angle at point M and the positive kinematics equation of the SCARA robot, we can obtain: According to the measured angle at point N and the SCARA robot forward kinematics equation, we can get: Connecting the above two equations and simplifying them, we can get: By using methods such as variable substitution, we can simplify the overdetermined homogeneous linear equations: make , then: The problem of solving an overdetermined homogeneous linear system of equations is transformed into the problem of solving the eigenvalues ​​and eigenvectors of the corresponding real symmetric matrix, and the Jacobi method is used to find the eigenvector corresponding to the minimum eigenvalue.

[0056] Obviously, the above equations belong to an overdetermined homogeneous linear equations, that is, Ax=0, A is an m×n matrix with full column rank, and m > n. It is known that the condition for Ax=0 to have an exact solution is: rank(A) < n, so the above equations do not have an exact solution.

[0057] Since there is no exact solution, we can find a set of approximate solutions x + So that: At this point, in order to obtain a non-zero solution that satisfies the above equation, some restrictions need to be added so that the minimum x is obtained while satisfying the conditions. + If it is a solution to the equation A = 0, then kx is obviously also (k is an arbitrary scalar), so we can restrict . Then we can construct a constrained least squares problem: The unconstrained optimization can then be constructed via the Lagrange multiplier method: To obtain The extreme values ​​of x and Find partial derivatives: make ,have to: It follows that in order to obtain The extreme value of Satisfies the above formula. It is easy to get that x and They are The eigenvalues ​​and eigenvectors of .

[0058] There are There are many eigenvalues ​​and eigenvectors, and they all satisfy the above formula. Then Substitution We can get: Obviously, the solution to the overdetermined homogeneous linear system is The eigenvector corresponding to the smallest eigenvalue.

[0059] From the previous point, we can simplify the overdetermined homogeneous linear equations and know that: but It must be a real symmetric matrix. The following describes a method for solving the eigenvector corresponding to the minimum eigenvalue of a real symmetric matrix.

[0060] For a real symmetric matrix A, there must be an orthogonal matrix Q such that Q T AQ=D. D is a diagonal matrix, the elements on the main diagonal are the eigenvalues ​​of matrix A, and each column of the orthogonal matrix Q corresponds to the eigenvector of the corresponding element on the main diagonal of the diagonal matrix D.

[0061] The Jacobi method uses plane rotation to perform similarity transformation on matrix A, transforming A into a diagonal matrix, thereby solving for eigenvalues ​​and eigenvectors. pq, is a unit matrix with cosφ in row p, column p, row q, column q, -sinφ in row p and column q, and sinφ in row q and column p. For such a plane rotation matrix, it is not difficult to verify that it is an orthogonal matrix. Therefore, for vector x,U pq x is equivalent to rotating the plane defined by the pth and qth coordinate axes by φ degrees. Let the matrix A1 = U pq T AU pq is a rotation matrix and also an orthogonal matrix, so in fact matrix A1 is similar to matrix A, so their eigenvalues ​​are the same.

[0062] Let the element in the i-th row and j-th column of matrix A1 be b ij , the element in the i-th row and j-th column of matrix A is a ij (i=0,1,2,…,n−1, j=0,1,2,...,n-1). The following formula gives the operation relationship between the two matrix elements: The specific steps of Jacobi method to solve matrix eigenvalues ​​and eigenvectors are summarized as follows: (1) Initialize the eigenvector to a diagonal matrix V, with the main diagonal elements being 1 and the other elements being 0 (2) Find the element a with the largest absolute value among the elements on the non-main diagonal of A. pq (3) Usage , calculate the rotation matrix (4) Calculate matrix A1 and multiply the rotation matrix by the current matrix V to get the current feature matrix V (5) If the maximum value of the non-main diagonal elements of the current iteration of matrix A is less than the given threshold, stop the calculation, otherwise execute the above process. When the calculation stops, the eigenvalue is the main diagonal element of matrix A, and the characteristic matrix is ​​the matrix V (6) Extract the eigenvector corresponding to the minimum eigenvalue According to the solution results, the zero offset value can be obtained, from which the actual arm length of the SCARA robot can be calculated. Using the above Jacobi method, we can calculate .

[0063] according to So, the zero point offset is: , The ratio of the length of the upper arm to the length of the lower arm is: .

[0064] The actual arm length is: Similarly, the measured angle of point M and the measured angle of point N are subtracted to obtain: .

[0065] Then we have: Embodiment 4: The key point of the present invention is to transform the problem of solving an overdetermined homogeneous linear equation system into the problem of solving the eigenvalues ​​and corresponding eigenvectors of the corresponding real symmetric matrix, and use the Jacobi method to find the eigenvector corresponding to its minimum eigenvalue.

[0066] The present invention uses the "derivation method" to derive the solution of the overdetermined homogeneous linear equation system, which is The eigenvector corresponding to the minimum eigenvalue. Compared with the "SVD decomposition method", the method used in the present invention is more concise and efficient.

[0067] The present invention uses the "Jacobi method" to solve the eigenvector corresponding to the minimum eigenvalue of a complex matrix. Compared with other methods such as the bisection method and the least squares method, the method used in the present invention has fewer iterations and more accurate calculation results.

[0068] The main source of robot error is geometric error, that is, during the manufacturing and assembly process of the robot, due to factors such as clearance error in the assembly itself, low assembly accuracy, machining error, or wear of parts caused by long-term use, the relative position relationship between the position of the upper arm joint axis and the lower arm joint axis of the SCARA robot will produce errors. Generally, such geometric errors are avoided as much as possible by improving the accuracy of processing and assembly, but due to the processing accuracy of the CNC machine tools themselves and inevitable manual operation errors, this method obviously cannot completely avoid such errors. Therefore, it is necessary to improve the accuracy of the SCARA robot through the method of zero point calibration, that is, first find out the key geometric error parameters, and then use the kinematic calibration method to find the actual value of the parameters.

[0069] However, the method of obtaining the actual value of the parameter through the kinematic calibration method is also limited by the accuracy of the obtained data. Therefore, it is necessary to introduce a regression analysis method based on the support vector machine (SVM) to compensate for the error of the calibrated data. The specific method is as follows: 1. Data collection: After the robot is calibrated, randomly select 200 groups of points in the workspace. These points should cover the entire working area of ​​the robot to ensure the representativeness and diversity of the sample. Let the robot move in sequence according to the positions of these points, and record the difference between the actual position and the ideal position of the robot each time it reaches the point, that is, the residual position error. This error will be used as sample data.

[0070] The sample data is divided into 200 sets of position error data collected into training samples and test samples. Usually, the ratio is 80-20: training samples: 160 sets of data, used for model training. Test samples: 40 sets of data, used for model verification and evaluation.

[0071] 2. Feature extraction: Determine the features used for regression analysis, which may include the robot's position coordinates (such as X, Y, Z), the distance between the target point and the actual point, the robot's movement speed, acceleration, etc.

[0072] 3. Build a support vector regression (SVR) model: The goal of SVR is to find a hyperplane so that the distance between most data points and the plane is within a certain range (i.e., the ε-insensitive interval) while minimizing the complexity of the model. Unlike traditional regression, SVR focuses on the support vector, that is, the data point closest to the hyperplane.

[0073] SVR uses an ε-insensitive loss function. For each data point, if the error between its predicted value and the true value is less than ε, it is not counted in the loss; otherwise, it is penalized according to the absolute value of the error. This method can tolerate a certain prediction error, thereby reducing overfitting.

[0074] Then, by introducing the Lagrange multiplier, the loss function is transformed into an optimization problem, the goal is to minimize the following function: in, is the weight vector, C is the regularization parameter, ξ i is the slack variable, representing the prediction error at each point.

[0075] SVR can use kernel functions (such as linear kernels, polynomial kernels, or radial basis function kernels) to map data to a high-dimensional space to capture nonlinear relationships. The choice of kernel function is crucial to model performance. Choose a suitable kernel function (such as the radial basis function) to capture the nonlinear characteristics of the data. Set the hyperparameters of SVR: the regularization parameter C and the threshold ε of the tolerance error. These parameters can be optimized through cross-validation.

[0076] Model training: Using 160 sets of training samples, the sequential minimum optimization algorithm (SMO) is used to minimize the loss function and find the best support vector and weight. In this process, SVR will learn how to map input features to output errors to achieve effective error compensation.

[0077] Model testing and evaluation: 40 sets of test samples were used to verify the trained SVR model, input the test data, and predict the corresponding error value. The performance of the model was evaluated, and indicators such as root mean square error (RMSE) and mean absolute error (MAE) were used to check the difference between the predicted results and the actual position error.

[0078] Error compensation: Once the model is tested and verified, the robot can use the model to compensate for errors in future movements. During each movement, the current feature data is input, the error of the current position is predicted through the SVR model, and the robot's target position is adjusted accordingly to improve the accuracy of the movement.

[0079] Result analysis: Analyze the effects before and after error compensation, compare the actual position after compensation with the ideal position, and evaluate the effectiveness of the compensation strategy. If necessary, further optimize the model or retrain it to adapt to different working environments or tasks.

[0080] Through the above steps, the SVR method can be effectively used to compensate for the position error of the robot and improve its accuracy and reliability in practical applications.

[0081] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, the embodiments should be considered exemplary and non-restrictive in all respects, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims be included in the present invention.

Claims

1. A SCARA robot arm length and zero point calibration method based on support vector regression, characterized in that: The method comprises the following steps: Step 1, the establishment of the kinematic equation of the SCARA robot: Based on the structure of the upper arm and lower arm of the SCARA robot, its kinematic model is defined, where: The length of the upper arm is L1, and the length of the lower arm is L2; The first joint angle is θ1, and the second joint angle is θ2; The position of the SCARA robot end in the workspace is determined by the following equation: Step 2, calibration point selection and data collection: Align the calibration pin at the end of the SCARA robot to the preset points M and N on the calibration board, record the joint angles θ1 and θ2 at different positions, and establish the error model of arm length and zero offset based on the measured angles; Step 3: Preliminary solution based on overdetermined homogeneous linear equations: Based on the collected multiple calibration point positions and the corresponding joint angles, construct an overdetermined homogeneous linear equation system: Ax=0 Among them, the matrix A is composed of the coordinates and angle information of each calibration point. By solving the eigenvector corresponding to the minimum eigenvalue of the equation group, the arm length error and zero offset value of the SCARA robot are preliminarily estimated; Step 4: Construction and training of support vector regression SVR model: Using multiple sets of data points randomly collected in the workspace of the SCARA robot, the error between the actual position and the ideal position is recorded, and the error is the residual error after the calibration is completed; The error data set is divided into a training set and a test set, and regression analysis is performed using the support vector regression SVR model. The model uses the radial basis kernel function RBF, and its loss function is defined as: in, is the weight vector, is the regularization parameter, and is a slack variable, representing the prediction error; Step 5, error compensation: Based on the training results of the SVR model, the position error of the SCARA robot is predicted in real time when the robot is moving, and the target position of the SCARA robot is compensated according to the predicted error value. The compensation formula is: in, is the error value predicted by the SVR model; Step 6, calculation and adjustment: According to the compensated SCARA robot end position, further adjust the arm length and zero point position to ensure high-precision operation of the robot in different working environments.

2. The SCARA robot arm length and zero point calibration method based on support vector regression according to claim 1 is characterized in that: The calibration points include at least two preset points in the workspace of the SCARA robot. During the calibration process, the calibration needle is aligned with the preset points in sequence and the joint angles are recorded.

3. The SCARA robot arm length and zero point calibration method based on support vector regression according to claim 1 is characterized in that: The overdetermined homogeneous linear equations are solved by the Jacobi method to obtain the eigenvector corresponding to the minimum eigenvalue, which is used to preliminarily calculate the arm length error and the zero point offset.

4. The SCARA robot arm length and zero point calibration method based on support vector regression according to claim 1 is characterized in that: The support vector regression model adopts radial basis kernel function RBF to process the nonlinear error of the SCARA robot in the workspace.

5. The SCARA robot arm length and zero point calibration method based on support vector regression according to claim 1 is characterized in that: The data in the error data set are obtained by random sampling to ensure the diversity and representativeness of the data.

6. The SCARA robot arm length and zero point calibration method based on support vector regression according to claim 1 is characterized in that: The SVR model is trained by the sequential minimal optimization (SMO) algorithm to minimize the error and determine the optimal support vector.

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