A 2pru-psr kinematics calibration method fusing ball bar and circular grating

Abstract

The present application relates to the technical field of parallel robot, especially a kind of 2PRU-PSR kinematics calibration method fusing ball bar and circular grating, which aims to solve the problem that existing calibration technology is high in cost or cannot guarantee end trajectory roundness and absolute pose accuracy simultaneously.The core is to establish a kind of fusion error mapping model, which combines ball bar error mapping model and circular grating error mapping model based on mechanism kinematics.When calibrating, control mechanism end moves along the preset spatial conical bottom surface trajectory, and synchronously collects ball bar rod length data and circular grating angle data installed at rotary joint;By substituting the measured data into the fusion model, the structural parameter error of the mechanism can be identified;Finally, the kinematics model is corrected using the identification result to realize error compensation.The present application can significantly improve the end absolute positioning accuracy while ensuring the motion roundness through dual-sensor information fusion and double constraints.

Description

Technical Field

[0001] This invention relates to the field of parallel robot technology, specifically to a 2PRU-PSR kinematic calibration method that integrates a ballbar and a circular grating. Background Technology

[0002] The motion accuracy of parallel robots is a key performance indicator, with geometric parameter errors being the most significant factor affecting end-effector accuracy. Kinematic calibration is a core technology for improving this accuracy. Currently, high-precision calibration mainly relies on equipment such as laser trackers, identifying parameters by measuring end-effector position errors. However, this method is expensive, complex to operate, and difficult to implement after the equipment is installed. Another common method is calibration using a ballbar, which is lower in cost and easier to use in the field. However, traditional methods primarily focus on optimizing the circularity of the end-effector's trajectory, making it difficult to effectively guarantee the absolute pose accuracy of the end-effector. Therefore, existing technologies suffer from a contradiction between cost and convenience in calibration schemes, and single-sensor calibration cannot simultaneously address both trajectory shape accuracy and absolute position / attitude accuracy. Developing a method that can comprehensively utilize low-cost measurement equipment to achieve high-precision calibration of the end-effector's pose has become an urgent technical problem to be solved. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention aims to provide a 2PRU-PSR kinematic calibration method that integrates a ballbar and a circular grating.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a kinematic calibration method for a 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating, comprising the following steps: S1. Establish a kinematic error mapping model for the 2PRU-PSR parallel mechanism. The model includes at least a first mapping relationship from the mechanism structure parameter error to the moving platform pose error, and a second mapping relationship from the moving platform pose error to the tool end pose error. S2. Establish a ballbar error mapping model, wherein the model establishes a third mapping relationship between the measured change in the length of the ballbar and the position error of the cutter end; S3. Establish a circular grating error mapping model, which includes an installation error model and a measurement error model; the measurement error model establishes a fourth mapping relationship between the measured angle change of the circular grating and the attitude error of the moving platform. S4. Merge the ballbar error mapping model with the circular grating error mapping model, and combine the third mapping relationship and the fourth mapping relationship to construct a fused error parameter mapping model; S5. Plan and control the end effector of the parallel mechanism to drive the ball bar to move along a preset spatial circular trajectory, while collecting the bar length measurement data of the ball bar and the angle measurement data of the circular grating installed at the rotary joint of the parallel mechanism; S6. Based on the measurement data collected in step S5 and the fusion error parameter mapping model constructed in step S4, parameter identification is performed to obtain the actual structural parameter error of the parallel mechanism. S7. The theoretical kinematic model of the parallel mechanism is corrected by using the identified actual structural parameter errors, and the parallel mechanism is controlled based on the corrected kinematic model.

[0005] In some embodiments, in step S1, the first mapping relationship is obtained by performing a first-order perturbation derivation on the inverse kinematic equations of the parallel mechanism, specifically as follows: ,in Let be the pose error vector of the moving platform. The Jacobian matrix represents the structural parameter error. This is a structural parameter error vector that includes the installation error of the fixed platform, the installation position error of the moving platform, and the rod length error.

[0006] In some embodiments, in step S1, the second mapping relationship is characterized by the following formula: ,in For the tool tip position error, For the position error of the moving platform, For the attitude matrix of the moving platform, For tool size error, The angular velocity vector of the moving platform. The vector of the tool in the moving coordinate system.

[0007] In some embodiments, in step S2, the ballbar error mapping model is determined by applying geometric constraint equations to the ballbar. The first-order perturbation derivation yields the final form as follows: ,in The roundness error vector is composed of the measurements from the ballbar. Identify the Jacobian matrix for the ballbar error parameters.

[0008] In some embodiments, in step S3, the installation error model includes at least measurement error components caused by eccentricity error, tilt error, and null position error.

[0009] In some embodiments, in step S3, there are two circular gratings, which are respectively installed at the U-axis and S-axis of the 2PRU-PSR parallel mechanism to measure the rotation angle of the corresponding joints.

[0010] In some embodiments, in step S4, the fusion error parameter mapping model is: ,in This is the measurement error vector for the circular grating. This is the Jacobian matrix for mapping the error of the circular grating.

[0011] In some embodiments, in step S5, the preset spatial circular trajectory is the circumference of the base of a cone with the fixed center of the ball bar as the cone apex and the ball bar shaft as the generatrix. The apex angle of the cone is adjusted by changing the angle between the ball bar shaft and the horizontal plane, thereby realizing the measurement of the circular trajectory on different spatial planes.

[0012] In some embodiments, step S6, the parameter identification process includes: based on the fusion error parameter mapping model, using the least squares method or iterative optimization algorithm to analyze the structural parameter error vector. Solve the problem.

[0013] In some embodiments, step S5 further includes: synchronously recording the joint drive value of the parallel mechanism during data acquisition; in step S6, using the joint drive value and the positive kinematic model of the parallel mechanism to calculate the theoretical position of the tool tip, which is used to construct the roundness error vector together with the ballbar measurement data. .

[0014] Compared with the prior art, the beneficial effects of the present invention are: 1. A balance between accuracy and cost is achieved: By integrating the relatively inexpensive ballbar and high-precision circular grating, an efficient calibration system is constructed. This method avoids the use of high-cost equipment such as laser trackers, lowering the calibration threshold and cost. Simultaneously, through multi-sensor information fusion, it achieves comprehensive calibration accuracy approaching or even surpassing that of a single high-cost device. 2. Breakthroughs in traditional calibration methods: The innovative fusion error mapping model, while ensuring the roundness of the end effector trajectory in the traditional ballbar model, introduces a circular grating for direct measurement and constraint of the end effector attitude. This dual constraint mechanism fundamentally solves the problem that traditional ballbar calibration methods cannot guarantee the absolute pose accuracy of the end effector, and achieves simultaneous tracing and compensation of position and attitude errors; 3. Improved the completeness and accuracy of the calibration model: By establishing a complete circular grating error model that includes installation and measurement errors, and deeply integrating it with the mechanism kinematic model and ballbar model, a more complete error parameter mapping relationship was constructed. This effectively reduced the coupling between parameters and the uncertainty of the model, making the identified structural parameters closer to the true values, and improving the reliability of the kinematic model and the accuracy of the calibration results; 4. Enhanced practicality and applicability: The ballbar and circular grating used are easy to integrate and install on-site. The calibration process is rationally designed and can be performed after the equipment is installed, making it highly practical. This method is not only applicable to the 2PRU-PSR configuration, but its multi-source information fusion and dual-constraint approach also provides an effective technical reference for high-precision, low-cost calibration of other types of parallel or hybrid robots.

[0015] Details of one or more embodiments of this application are set forth in the following drawings and description to make other features, objects and advantages of this application more readily apparent. The embodiments of this application will provide a detailed description and understanding of the application. Attached Figure Description

[0016] Figure 1 This is a physical diagram of the parallel mechanism in this invention; Figure 2 This is a schematic diagram of the parallel module in this invention; Figure 3 This is a schematic diagram showing the installation position and angle of the circular grating in this invention; Figure 4 This is a schematic diagram of the eccentric model of the circular grating in this invention; Figure 5 This is a schematic diagram of the tilted circular grating model in this invention; Figure 6 This is a flowchart illustrating the overall process for calibrating the error parameters of the parallel mechanism of the present invention.

[0017] In the diagram: 1. Three-axis parallel module; 2. Circular grating angle measuring device II; 3. Circular grating angle measuring device I; 4. Ball bar length measuring device. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1 This embodiment provides an overall implementation plan for a kinematic calibration method of a 2PRU-PSR parallel mechanism that integrates a ballbar and a circular grating. Addressing the technical deficiency of traditional ballbar calibration methods in existing technologies, which can only guarantee the roundness of the end effector trajectory but struggle to ensure absolute pose accuracy, this method proposes a novel error parameter calibration scheme that integrates the ballbar and the circular grating. This scheme combines the angular error model of the circular grating with a basic ballbar error mapping model to simultaneously apply kinematic constraints to the pose, ensuring both roundness accuracy and end effector pose accuracy, thus achieving high-precision calibration of the kinematic error parameters of the parallel robot.

[0020] First, the 2PRU-PSR parallel mechanism involved in this embodiment will be given an overall introduction. This parallel mechanism belongs to a three-axis parallel robot, and its structure mainly consists of a three-axis parallel module, a drive device, and an end effector. Figure 1 In the physical diagram of the parallel mechanism shown, label 1 represents the three-axis parallel module, label 2 represents the second circular grating angle measuring device, label 3 represents the first circular grating angle measuring device, and label 4 represents the ballbar length measuring device. This parallel mechanism has two rotational degrees of freedom and one translational degree of freedom, enabling complex movements in space. The motion accuracy and positioning accuracy of parallel robots are crucial performance indicators. Among the main factors affecting the accuracy of parallel robots, the geometric parameter error of the links has a much greater impact on the end effector accuracy than the flexible deformation error of the links and joints. The influence of geometric parameter errors accounts for approximately 80%. Almost 95% of parallel robots can reduce their position and orientation positioning errors through calibration techniques. Currently, the positioning accuracy of parallel robots on the market only reaches the millimeter level. It is necessary to improve the motion and positioning accuracy of the robotic arm end effector through kinematic calibration and error compensation techniques to expand its application areas.

[0021] The kinematic calibration method for the 2PRU-PSR parallel mechanism that integrates a ballbar and a circular grating, as described in this embodiment, includes the following core steps: The first step is to establish a kinematic error mapping model for the 2PRU-PSR parallel mechanism. This model includes at least a first mapping relationship from the structural parameter errors of the mechanism to the pose errors of the moving platform, and a second mapping relationship from the pose errors of the moving platform to the pose errors of the tool end effector. Error modeling is the foundation of the entire kinematic calibration. For parallel mechanisms, accurate kinematic error modeling and efficient calibration methods are particularly crucial. In this embodiment, the first mapping relationship is obtained by deriving the inverse kinematic equations of the parallel mechanism using a first-order perturbation. Specifically, based on an existing three-axis parallel robot model, the kinematics are derived using the closed-loop vector method to establish the kinematic model of the parallel mechanism. For the 2PRU-PSR parallel mechanism, its inverse kinematic expression can be obtained by solving the closed-loop vector equations of each branch of the mechanism. The mapping relationship between the pose errors and structural parameter errors of the parallel mechanism is derived based on the differential method. This mapping relationship can be obtained by taking the total differential of both sides of the inverse kinematic equations.

[0022] Specifically, let the inverse kinematic equation of the parallel mechanism be: Where X represents the pose vector of the moving platform. Let represent the structural parameter vector of the mechanism. Taking the total differential of both sides of this equation, we obtain: After sorting, we get: Rearranging the above formulas into matrix form, we obtain the mapping relationship between the origin position error of the moving platform and the kinematic error parameters: in, Let be the pose error vector of the moving platform. The Jacobian matrix represents the structural parameter error. This represents the structural parameter error vector, which includes the installation error of the fixed platform, the installation position error of the moving platform, and the link length error. This first mapping relationship establishes a linearized mapping between the structural parameter errors of the mechanism and the pose error of the moving platform, laying a theoretical foundation for subsequent error parameter identification.

[0023] Furthermore, based on the established moving platform error model, a tool end-effector error model, i.e., the second mapping relationship, also needs to be established. The relationship between the tool end-effector position and the moving platform pose is as follows: Where P represents the position vector of the tool end point in a fixed coordinate system. R represents the position vector of the origin of the moving platform, R represents the attitude matrix of the moving platform, r represents the vector of the tool in the moving coordinate system, and represents the theoretical size of the tool.

[0024] Combining the relationship between the end-effector pose and the tool, a first-order linear perturbation is applied to both sides to obtain the relationship between the tool end-effector position error and the end-effector pose error: in, For the tool tip position error, R represents the position error of the moving platform, and R represents the attitude matrix of the moving platform. For tool size error, Let r be the angular velocity vector of the moving platform, and r be the vector of the tool in the moving coordinate system. This second mapping relationship further transmits the pose error of the moving platform to the tool end effector, establishing a complete transmission chain from structural parameter error to tool end effector position error.

[0025] Thus, the mapping relationship between structural parameter errors and end-position errors is obtained, as shown below: in, This represents the Jacobian matrix, which maps positional errors to kinematic errors. By establishing the first and second mapping relationships described above, a complete error propagation model is achieved, from the errors in the mechanism's structural parameters to the tool end-effector's pose error.

[0026] The second step is to establish a ballbar error mapping model. A ballbar is a high-precision length measuring device with a resolution of 0.1 micrometers, capable of accurately measuring errors in the spatial motion of a robot. In this embodiment, the ballbar error mapping model establishes a third mapping relationship between the measured change in the ballbar length and the position error of the tool end effector. Specifically, the ballbar error mapping model is obtained by first-order perturbation derivation of the ballbar's geometric constraint equations.

[0027] The geometric constraint equations of the ballbar are: in, Let C represent the position vector of the tool tip, C represent the position vector of the fixed ball center of the ballbar, and L represent the length of the ballbar. The unit vector representing the direction of the lever in a ballbar instrument.

[0028] Applying a first-order perturbation to the above formula, we obtain: Since the clubbar measures the change in club length, and the change in club length direction is related to the end position error, after derivation and simplification, the final form is: in, The roundness error vector is composed of the measurements from the ballbar. The Jacobian matrix is ​​used to identify the error parameters of the ballbar. This third mapping establishes a direct link between the measured change in the ballbar length and the structural parameter errors of the mechanism, allowing the structural parameter errors of the mechanism to be identified using the ballbar's measurement data.

[0029] The process of establishing the ballbar error mapping model is as follows: For each measurement position, the ballbar provides a constraint equation. Multiple constraint equations can be obtained at multiple measurement positions, which can be simplified into matrix form. Assuming n measurements are performed, the ballbar total error parameter identification matrix is: in, Let be the ballbar error parameter identification matrix corresponding to the i-th circular trajectory. Thus, the ballbar error parameter mapping model of the three-axis parallel robot is obtained: This model utilizes the high-precision length measurement capability of a ballbar to effectively capture the positional error information of the end effector during spatial motion, and is particularly suitable for evaluating and ensuring the roundness accuracy of the end effector trajectory.

[0030] The third step is to establish a circular grating error mapping model. A circular grating is a high-precision angle measuring device capable of measuring the angle values ​​of a rotary joint in real time. In this embodiment, the circular grating error mapping model includes an installation error model and a measurement error model. The measurement error model establishes a fourth mapping relationship between the measured angle change of the circular grating and the attitude error of the moving platform.

[0031] In this embodiment, two circular gratings are used, respectively installed on the U-axis and S-axis of the 2PRU-PSR parallel mechanism, to measure the rotation angle of the corresponding joints. Figure 3 As shown, circular grating angle measuring device one is installed at the U-axis of the rotating shaft, and circular grating angle measuring device two is installed at the S-axis of the rotating shaft. Data is read using the Beckhoff system, and the encoded values ​​are converted into actual angle values.

[0032] First, a mapping model between joint rotation angles and generalized variable errors is established. Given the circular grating mounting position, the Cartesian coordinates of pair U in the parallel mechanism are established (see [reference needed]). Figure 3 As shown, the origin S of the moving coordinate system is at the rotation center of the S pair, the Z-axis is collinear with AS, the Y-axis is along the rotation axis of the U pair, and the X-axis satisfies the right-hand rule.

[0033] The relationship between joint angles and generalized coordinates can be expressed as: in, Let X represent the angle value of the i-th joint, and let X represent the pose vector of the moving platform. This represents the functional relationship between the angle and pose of the i-th joint.

[0034] Substituting the above relationships into the inverse kinematics solution of the parallel module, the specific expression is as follows: Or the corresponding trigonometric function relationship, Where x and y are the relevant coordinate components, representing the angle between specific planes.

[0035] Based on the differential method, the above formula is perturbated to the first order, and the specific expression is as follows: Thus, the mapping relationship between the circular grating angle error and the generalized variable error is obtained: in, This is the measurement error vector for the circular grating. The Jacobian matrix is ​​used to map the circular grating error. This fourth mapping establishes the relationship between the measured angle change of the circular grating and the attitude error of the moving platform, providing a mathematical basis for subsequent attitude error constraints.

[0036] Furthermore, the installation error model includes at least measurement error components caused by eccentricity error, tilt error, and zero-position error. The installation error of the circular grating is a significant factor affecting its measurement accuracy and must be considered and compensated for.

[0037] 1) Establishment of installation error mapping model The installation errors of circular gratings mainly include eccentricity error, tilt error, and zero-position error. For example... Figure 4 The schematic diagram of the eccentric model of the circular grating shown is as follows: Figure 5 The schematic diagram of the tilted circular grating model shown illustrates the types of errors that may occur during the installation of the circular grating.

[0038] Eccentricity error refers to the error caused by the misalignment of the rotation center and the geometric center of the circular grating. Let the eccentricity distance be e, and the eccentricity angle be θ. The measurement error caused by the eccentricity error is: Where R is the radius of the circular grating. This refers to the actual turning angle.

[0039] Tilt error refers to the error caused by the mounting plane of the circular grating not being perpendicular to the axis of rotation. Let the tilt angle be... The measurement error caused by the tilt error is: Zero-position error refers to the error caused by the zero-position mark of the circular grating not coinciding with the true zero position. in, This is the zero offset.

[0040] The installation error model is obtained by adding the three types of installation errors mentioned above: This scheme uses two circular gratings to measure the angles separately. By solving the simultaneous equations, the installation error mapping model can be obtained: in, This is a vector of installation error parameters. The installation error Jacobian matrix.

[0041] 2) Measurement error mapping model The measurement error mapping model establishes a mapping relationship between the measured angle change of the circular grating and the attitude error of the moving platform. Substituting the joint angle error into the above formula, we get: in, This is the Jacobian matrix for mapping the error of the circular grating.

[0042] 3) Circular grating error mapping model The circular grating error mapping model includes an installation error mapping model and a measurement error mapping model. Adding these models together yields the circular grating error mapping model: It should be noted that the error parameters of the installation error model are not directly related to the kinematic error parameters, so there is no need to perform repeated calibration.

[0043] The fourth step is to fuse the ballbar error mapping model with the circular grating error mapping model, and combine the third mapping relationship with the fourth mapping relationship to construct a fused error parameter mapping model.

[0044] Combining the circular grating error mapping model with the ballbar error mapping model yields: Thus, a fusion error parameter mapping model of the ballbar and circular grating for the 2PRU-PSR parallel robot was obtained. This fusion model utilizes both the length measurement information from the ballbar and the angle measurement information from the circular grating to impose dual constraints on the position and attitude of the end effector. This dual constraint mechanism successfully traces the end effector pose error precisely to the overall structural error of the parallel mechanism, achieving refined modeling of the kinematic mapping relationship.

[0045] The fifth step involves planning and controlling the end effector of the parallel mechanism to drive the ball bar instrument to move along a preset spatial circular trajectory, while simultaneously collecting the length measurement data of the ball bar instrument and the angle measurement data of the circular grating installed at the rotary joint of the parallel mechanism.

[0046] In this embodiment, the preset spatial circular trajectory is the circumference of the base of a cone with the fixed center of the ballbar as its apex and the ballbar shaft as its generatrix. By changing the angle between the ballbar shaft and the horizontal plane, the apex angle of the cone can be adjusted, thereby enabling the measurement of circular trajectories on different spatial planes. The angle between the ballbar shaft and the horizontal plane can be adjusted according to experimental needs. After verifying the feasibility of the trajectory through a robot simulation model, a calibration experiment is then conducted.

[0047] The specific experimental steps are as follows: First, a motion control program for the robot was written in the robot control software based on the given robot trajectory and operation method. The robot was then driven by the written program to verify that its trajectory matched the originally planned trajectory, preparing for subsequent testing of precision instruments. In addition, a MATLAB data processing program was written to process the experimental data.

[0048] Then, install circular gratings at two rotary joint positions of the parallel robot, such as... Figure 3 As shown. Data is read using Beckhoff, converting the encoded values ​​into actual angle values. The ballbar is connected to the designated workspace and the robot's end effector, and then connected to the PC via Bluetooth. The corresponding application for the instrument is started and debugged, and the instrument is zeroed before the experiment begins.

[0049] The robot's motion program is initiated, causing the end effector to drive the ballbar along a preset spatial circular trajectory. During the motion, the ballbar measures the change in bar length in real time and simultaneously records the data from the circular grating. The above experiment is repeated, as follows: Figure 1 As shown, multiple measurements are performed to improve the reliability of the data.

[0050] During data acquisition, the joint drive values ​​of the parallel mechanism are recorded synchronously. Using these joint drive values ​​and the forward kinematic model of the parallel mechanism, the theoretical position of the tool tip is calculated, which, together with the ballbar measurement data, is used to construct the roundness error vector ΔL.

[0051] The sixth step involves identifying parameters based on the measurement data collected in the fifth step and the fusion error parameter mapping model constructed in the fourth step, thereby obtaining the actual structural parameter errors of the parallel mechanism.

[0052] The measured actual values ​​of the circular grating are mapped to attitude angle values ​​through the circular grating error model, corresponding to the ballbar timestamp. By inputting the fused measurement data into the three-axis pose error mapping model, the actual structural parameters of the three-axis parallel robot can be identified.

[0053] The parameter identification process includes: based on the fusion error parameter mapping model, using the least squares method or iterative optimization algorithm to analyze the structural parameter error vector. Solve the problem.

[0054] Specifically, when using the least squares method for parameter identification, the objective function is: The solution yields: When the amount of measurement data is large or the model is complex, iterative optimization algorithms, such as the Levenberg-Marquardt algorithm and the Gauss-Newton method, can be used to iteratively optimize and solve the structural parameter error vector to obtain more accurate identification results.

[0055] The seventh step is to correct the theoretical kinematic model of the parallel mechanism using the identified actual structural parameter errors, and then control the parallel mechanism based on the corrected kinematic model.

[0056] By replacing the structural parameters in the theoretical model with the identified actual structural parameters, a new inverse kinematics of the parallel robot is established to describe the workspace of the three-axis parallel robot's end effector. This achieves compensation for the motion error of the parallel robot. The modified model is then substituted into experiments, and the above steps are repeated to verify the accuracy and effectiveness of the identified parameters.

[0057] This embodiment employs a calibration algorithm that combines ballbar and circular grating. The core advantage of this algorithm lies in using a traditional ballbar model to ensure the roundness accuracy of the parallel mechanism, while simultaneously leveraging a circular grating model to precisely constrain and calibrate the end effector's pose. This dual constraint mechanism successfully traces the end effector pose error precisely to the overall structural error of the parallel mechanism, achieving refined modeling of the kinematic mapping relationship.

[0058] Example 2 This embodiment provides a detailed method for establishing a ballbar error mapping model, as a further refinement and supplement to Embodiment 1.

[0059] This embodiment focuses on the detailed derivation of the ballbar error mapping model and its specific application in the 2PRU-PSR parallel mechanism.

[0060] A ballbar is a high-precision length measuring device based on a ball-and-socket joint. Its working principle is to evaluate the motion accuracy of a machine tool or robot by measuring the change in distance between the centers of two precision spheres. In the calibration of parallel mechanisms, one end of the ballbar is fixed to a base via a magnetic ball joint, and the other end is connected to the robot's end effector via a magnetic ball joint. When the robot's end effector moves along a preset trajectory, the ballbar measures the change in the length of the lever in real time; this change reflects the deviation between the actual and ideal positions of the end effector.

[0061] The process of establishing the ballbar error mapping model for the 2PRU-PSR parallel mechanism is as follows: First, establish the geometric constraint equations for the ballbar. Let C be the position vector of the fixed ball center of the ballbar, and P be the position vector of the cutter end. i The length of the ballbar is L, and the unit vector along the direction of the ballbar is u. i Then we have: This equation indicates that the tool tip position is located at a point originating from the fixed sphere center C and along the direction u. i On a straight line with a distance of L.

[0062] A first-order perturbation analysis is performed on the above geometric constraint equations. Let ΔP be the tool end position error caused by structural parameter errors. i The change in the length of the ballbar is ΔL, and the change in the direction vector is Δu. i Then we have: Expanding and ignoring higher-order minor quantities, we get: Since the ballbar measures the change in bar length, and the change in direction vector is related to the end-position error, the relationship between the change in bar length and the end-position error can be obtained through vector calculation and processing: The mapping relationship between the end position error and the structural parameter error established in Example 1 is applied. Substituting into the above equation, we get: For multiple measurement locations, suppose m measurements were performed, and each measurement yielded a change in the length of the ballbar. Then we can obtain m equations: Write it in matrix form: Right now: in, Identify the Jacobian matrix for the ballbar error parameters.

[0063] To improve the accuracy and reliability of parameter identification, this embodiment uses circular trajectories on multiple different spatial planes for measurement. Specifically, by changing the angle between the lever and the horizontal plane, the apex angle of the cone can be adjusted, thereby achieving circular trajectory measurement on different spatial planes. Assuming k circular trajectory measurements are performed on different planes, and each circular trajectory has n measurement points, the total number of measurement points is m = k × n.

[0064] For the i-th measurement point on the j-th circular trajectory, the ballbar error parameter identification matrix is: Then the total ballbar error parameter identification matrix is: By performing multiple measurements on different spatial planes, the redundancy of the measurement data can be increased, thereby improving the accuracy and robustness of parameter identification.

[0065] In this embodiment, the impact of environmental factors on measurement accuracy during the ballbar measurement process is also considered. Temperature changes cause thermal expansion and contraction of the ballbar shaft, thus affecting measurement accuracy. Therefore, it is necessary to control the ambient temperature during the experiment or perform temperature compensation on the measurement data. In addition, the installation posture of the ballbar also affects measurement accuracy; it is necessary to ensure that the ballbar maintains an appropriate posture during the measurement process to avoid bending deformation caused by gravity.

[0066] Example 3 This embodiment provides a detailed method for establishing a circular grating error mapping model, focusing on the establishment process of the circular grating installation error model and measurement error model.

[0067] In this embodiment, two circular gratings are respectively installed on the U-joint rotation axis and the S-joint rotation axis of the 2PRU-PSR parallel mechanism. The U-joint is a universal joint with two mutually perpendicular rotational degrees of freedom; the S-joint is a ball joint with three rotational degrees of freedom. The circular gratings are mounted on the rotation axes and are used to measure the rotation angle of the corresponding joints.

[0068] The installation error of a circular grating is a significant factor affecting its measurement accuracy. In this embodiment, the installation error model includes at least measurement error components caused by eccentricity error, tilt error, and null position error.

[0069] I. Eccentricity Error Model like Figure 4 As shown, the eccentricity error of a circular grating refers to the error caused by the rotation center O' of the circular grating not coinciding with its geometric center O. Let the eccentricity be e, and the angle between the eccentricity direction and the reference direction be... The radius of the circular grating is R, and the actual rotation angle is... .

[0070] When the circular grating is eccentric, the reading head actually measures the distance from the geometric center to the scale line, rather than the distance from the rotation center to the scale line. This results in a deviation between the measured angle value and the actual rotation angle.

[0071] Let A be the actual position of a certain graduation line on the circular grating, and A' be the position measured by the reading head due to eccentricity. Based on geometric relationships, the measurement error caused by eccentricity can be derived as: This formula shows that the measurement error caused by eccentricity varies sinusoidally, with an amplitude of e / R and a phase determined by the eccentricity angle. The decision is made when the eccentricity e is much smaller than the radius R of the circular grating. This approximation formula has high accuracy.

[0072] In practical applications, eccentricity error can be reduced by precisely adjusting the installation position of the circular grating, but it cannot be completely eliminated. Therefore, the influence of eccentricity error needs to be considered in the error model, and the eccentricity parameter needs to be identified and compensated during the parameter identification process.

[0073] II. Tilt Error Model like Figure 5 As shown, the tilt error of a circular grating refers to the error caused by the mounting plane of the circular grating not being perpendicular to the axis of rotation. Let the tilt angle be θ. , which is the angle between the normal to the circular grating plane and the axis of rotation.

[0074] When the circular grating is tilted, the reading head measures the angle on the tilted plane, not the angle on the plane perpendicular to the rotation axis. This results in a deviation between the measured angle value and the actual rotation angle.

[0075] Based on geometric optics and trigonometric relationships, the measurement error caused by tilt error can be derived as follows: This formula shows that the measurement error caused by tilt error also exhibits a sinusoidal variation, with its amplitude being the tilt angle β. The difference between tilt error and eccentricity error is that the phase of tilt error is fixed, while the phase of eccentricity error is determined by the installation position.

[0076] In practical applications, tilt error can be reduced by adjusting the mounting plane of the circular grating. A precision level or optical collimator is typically used to detect and adjust the mounting orientation of the circular grating, ensuring that its mounting plane is as perpendicular as possible to the axis of rotation.

[0077] III. Zero-position error model Zero-position error refers to the error caused by the zero-position mark of the circular grating not coinciding with the actual zero position. Let the zero-position offset be... Then the zero-position error is: Zero-position error is a constant error that does not change with the rotation angle. In practical applications, zero-position error can be determined by rotating the rotary joint to a known reference position (such as a mechanical limit position or an optical reference position), recording the reading of the circular grating, and the difference between this reading and the known reference angle is the zero-position error.

[0078] IV. Installation Error Mapping Model Adding the three types of installation errors together, we obtain the installation error model for the circular grating: For the two circular gratings, separate installation error models are established: By solving the simultaneous equations, we obtain the installation error mapping model: in, This is a vector of installation error parameters. The installation error Jacobian matrix.

[0079] V. Measurement Error Mapping Model The measurement error mapping model establishes a mapping relationship between the measured angle change of the circular grating and the attitude error of the moving platform. Based on the derivation in Example 1, the relationship between the joint angle error and the pose error of the moving platform is as follows: Mapping relationship between the pose error of the moving platform and the structural parameter error Substituting into the above equation, we get: in, This is the Jacobian matrix for mapping the error of the circular grating.

[0080] VI. Circular Grating Error Mapping Model The circular grating error mapping model includes an installation error mapping model and a measurement error mapping model. Since the error parameters of the installation error model are not directly related to the kinematic error parameters, repeated calibration is unnecessary. Adding the above models yields the circular grating error mapping model: In practical applications, if the installation error has been compensated for through precision adjustment or pre-calibration, the installation error term can be ignored, simplifying the process to: This embodiment establishes detailed installation error models and measurement error models for the circular grating, providing complete circular grating error information for the subsequent fusion error parameter mapping model, thus ensuring the accuracy and reliability of attitude error constraints.

[0081] Example 4 This embodiment provides a detailed method for constructing a fusion error parameter mapping model, as well as a method for parameter identification and error compensation based on the model.

[0082] In this embodiment, the ballbar error mapping model established in Embodiment 2 and the circular grating error mapping model established in Embodiment 3 are fused to construct a complete fused error parameter mapping model, and parameter identification and error compensation are performed based on this model.

[0083] I. Construction of the Fusion Error Parameter Mapping Model By combining the ballbar error mapping model and the circular grating error mapping model, we obtain the fused error parameter mapping model: Where ΔL is the roundness error vector composed of the ballbar measurements, ΔΘ is the circular grating measurement error vector, and J B To identify the Jacobian matrix for the ballbar error parameters, J R The Jacobian matrix is ​​used to map the error of the circular grating. This is the structural parameter error vector.

[0084] The core advantage of this fusion model lies in its simultaneous utilization of length measurement information from a ballbar and angle measurement information from a circular grating. The ballbar provides the position information of the end effector, primarily reflecting the roundness error of the end-effector trajectory; the circular grating provides joint angle information, which, through kinematic mapping, reflects the attitude information of the moving platform. By fusing the two, a dual constraint on the end effector's pose is achieved, ensuring both the roundness accuracy of the trajectory and the absolute accuracy of the pose.

[0085] When constructing the fusion error parameter mapping model, the time synchronization issue between the ballbar measurement data and the circular grating measurement data needs to be considered. Since the ballbar connects to the PC via Bluetooth, while the circular grating is read through the Beckhoff system, there may be a time delay in data acquisition. Therefore, during data acquisition, measurement timestamps need to be recorded synchronously, and time alignment needs to be performed during data processing.

[0086] The specific time synchronization method is as follows: Using the robot control system's clock as a reference, a timestamp is recorded each time ballbar and circular grating data are collected. During the data processing stage, ballbar and circular grating data at the same moment are paired based on the timestamp. If time discrepancies exist, interpolation methods can be used for data alignment.

[0087] II. Parameter Identification Method Based on the fusion error parameter mapping model, the least squares method or iterative optimization algorithm is used to analyze the structural parameter error vector. Solve the problem.

[0088] 1. Least Squares Method When there is sufficient measurement data and the model is linear, the least squares method can be used for parameter identification. The objective function is: Regarding the objective function Taking the derivative and setting it to zero, we obtain the normal equation: The solution yields: To ensure the stability of the solution, it is necessary to ensure that the matrix... It is a full-rank matrix. This requires that the measurement trajectory can sufficiently excite the parameters to be identified, that is, the measurement data should cover different areas of the mechanism's workspace, and the measurement trajectory should have sufficient diversity.

[0089] 2. Iterative optimization algorithm When the model exhibits nonlinearity or the measurement data contains noise, iterative optimization algorithms can be used for parameter identification. Commonly used iterative optimization algorithms include the Levenberg-Marquardt algorithm, the Gauss-Newton method, and the gradient descent method.

[0090] Taking the Levenberg-Marquardt algorithm as an example, its iterative formula is: Where J is the Jacobian matrix and Y is the measurement vector. λ is the model prediction value, I is the damping coefficient, and I is the identity matrix.

[0091] The Levenberg-Marquardt algorithm combines the advantages of the Gauss-Newton method and the gradient descent method. It uses a larger damping coefficient in the early stages of iteration, which behaves like the gradient descent method and ensures convergence; and it uses a smaller damping coefficient in the later stages of iteration, which behaves like the Gauss-Newton method and ensures convergence speed.

[0092] 3. Convergence Analysis of Parameter Identification The convergence of parameter identification depends on several factors, including the quantity and quality of measurement data, the number of parameters to be identified, and the excitation of the measurement trajectory. To ensure the convergence and accuracy of parameter identification, the following conditions must be met: (1) The amount of measurement data should be greater than the number of parameters to be identified. Usually, the amount of measurement data is required to be 3 to 5 times the number of parameters. (2) The measurement trajectory should fully cover the working space of the mechanism to avoid oversampling in some areas and undersampling in other areas; (3) The measurement data should have a high signal-to-noise ratio to avoid distortion of parameter identification results due to excessive measurement noise; (4) The parameters to be identified should have a certain degree of independence to avoid strong coupling between parameters leading to unstable identification results.

[0093] III. Error Compensation Methods The identified structural parameter errors are used to correct the theoretical kinematic model of the parallel mechanism, thereby achieving error compensation.

[0094] The specific steps are as follows: 1. Theoretical structural parameters Error with the identified structural parameters Add them together to obtain the actual structural parameters: 2. Substitute the actual structural parameters into the inverse kinematic model of the parallel mechanism to establish the corrected kinematic model: Where q is the joint variable and X is the pose of the moving platform.

[0095] 3. Based on the revised kinematic model, the robot's workspace and kinematic performance indicators are recalculated.

[0096] 4. Substitute the corrected model into the controller to control the parallel mechanism. During the control process, calculate the joint drive commands based on the corrected kinematic model, enabling the end effector to accurately reach the target pose.

[0097] 5. Verify the error compensation effect. By repeatedly performing calibration experiments, compare the end-effector pose error before and after compensation to evaluate the effectiveness of error compensation. If the accuracy after compensation still does not meet the requirements, the calibration and compensation process can be repeated until the expected accuracy index is achieved.

[0098] This embodiment achieves a complete process from measurement data to error compensation through detailed fusion model construction, parameter identification, and error compensation methods, ensuring the practicality and effectiveness of the calibration method.

[0099] Example 5 This embodiment provides a specific experimental verification method to verify the effectiveness and superiority of the kinematic calibration method for the 2PRU-PSR parallel mechanism that integrates a ballbar and a circular grating described in this invention.

[0100] In this embodiment, the following is adopted: Figure 1 The 2PRU-PSR parallel mechanism shown is used as the experimental object. The mechanism includes a three-axis parallel module, two circular grating angle measuring devices and a ball bar length measuring device.

[0101] I. Experimental Preparation 1. Equipment installation and commissioning (1) Install the circular grating at the two rotary joint positions of the parallel robot, namely the U-axis and S-axis. Ensure that the mounting plane of the circular grating is perpendicular to the axis of rotation to reduce tilting error. Adjust the eccentricity of the circular grating to make it as small as possible.

[0102] (2) Connect the ballbar to the designated workspace and the robot end effector. One end of the ballbar is fixed to the base via a magnetic ball joint, and the other end is connected to the robot end effector via a magnetic ball joint. Ensure the ballbar is securely installed to prevent loosening during the measurement process.

[0103] (3) Connect the ballbar to the PC via Bluetooth and read the circular grating data through the Beckhoff system. Start and debug the corresponding application of the instrument, and zero the instrument before starting the experiment.

[0104] 2. Motion trajectory planning The end effector of the parallel mechanism is planned and controlled to drive the ballbar to move along a preset spatial circular trajectory. In this embodiment, the preset spatial circular trajectory is the circumference of the base of a cone with the fixed center of the ballbar as the apex and the ballbar shaft as the generatrix.

[0105] Specifically, let the length of the lever be L, the center of the ball be fixed at C, and the apex angle of the cone be 2γ. Then, point P on the circular trajectory... i satisfy: Where n is the unit vector of the cone axis.

[0106] By changing the angle between the club shaft and the horizontal plane, the apex angle γ of the cone can be adjusted, thereby enabling the measurement of circular trajectories on different spatial planes. In this embodiment, three different apex angles, γ = 15°, 30°, and 45°, are selected to perform circular trajectory measurements on three different spatial planes. 36 measurement points are evenly collected on each circular trajectory, i.e., one data point is collected every 10°.

[0107] 3. Control program writing Write motion control programs for the robot in robot control software to drive the robot to move along a planned trajectory. Simultaneously, write MATLAB data processing programs to process and analyze the experimental data.

[0108] II. Data Collection 1. Start the robot motion program so that the end effector drives the ballbar to move along the preset spatial circular trajectory.

[0109] 2. During the movement, the clubbar instrument measures the change in club length in real time, with a sampling frequency of 1000Hz. Simultaneously, a circular grating measures the joint angle value in real time, with a sampling frequency of 1000Hz.

[0110] 3. Synchronously record the timestamps of the ball bar data and the circular grating data to ensure data time alignment.

[0111] 4. Synchronously record the joint drive values ​​of the parallel mechanism, which are used to calculate the theoretical position of the tool end through the positive kinematics model.

[0112] 5. Repeat the above experiment 5 times to improve the reliability and statistical significance of the data.

[0113] III. Data Processing and Parameter Identification 1. Data Preprocessing (1) The collected ballbar data and circular grating data were filtered to remove high-frequency noise. A low-pass filter with a cutoff frequency of 50Hz was used.

[0114] (2) Pair the ball bar data and circular grating data according to the timestamp to ensure that the data at the same time correspond.

[0115] (3) The theoretical position of the tool end is calculated by using the joint drive value through the positive kinematic model, and is used to construct the roundness error vector ΔL together with the ballbar measurement data.

[0116] 2. Construct a fusion error parameter mapping model Based on the methods of Examples 1 to 4, a ballbar error mapping model, a circular grating error mapping model, and a fusion error parameter mapping model are established.

[0117] 3. Parameter Identification The least squares method is used for parameter identification to solve for the structural parameter error vector Δξ. Simultaneously, the Levenberg-Marquardt algorithm is used for iterative optimization, and the identification results of the two methods are compared.

[0118] IV. Error Compensation and Verification 1. Substitute the identified structural parameter errors into the theoretical kinematic model to establish a corrected kinematic model.

[0119] 2. Based on the revised kinematic model, the motion trajectory is replanned to drive the robot to move.

[0120] 3. Collect measurement data from the ballbar and circular grating again, and calculate the compensated end-effector pose error.

[0121] 4. Compare the end-effector pose error before and after compensation, and evaluate the effect of error compensation.

[0122] V. Experimental Results and Analysis Through experimental verification, the kinematic calibration method of the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating described in this embodiment has the following beneficial technical effects: 1. The error parameter calibration model that integrates ballbar and circular grating proposed in this invention can effectively measure and map the multi-degree-of-freedom geometric errors of CNC machine tools or robots simultaneously. It not only solves the fundamental problem that traditional ballbar calibration methods cannot guarantee the absolute pose accuracy of the end effector, but also enhances the accuracy consistency of the equipment in various tasks such as positioning and contour machining.

[0123] 2. By fusing and solving multi-source sensor information, the coupling between error parameters and model overfitting are further reduced, making the calibrated error parameters more accurate and greatly improving the reliability and practicality of the kinematic model.

[0124] 3. The robot can maintain better high-precision standards during movement, and the end-effector pose accuracy is significantly improved.

[0125] Experimental results show that, after adopting the calibration method described in this invention, the end-effector position accuracy of the parallel mechanism is improved by approximately 60%, the attitude accuracy is improved by approximately 70%, and the roundness error is reduced by approximately 50%. Simultaneously, the calibrated robot exhibits significant improvements in repeatability and trajectory tracking accuracy, verifying the effectiveness and superiority of the method described in this invention.

[0126] Example 6 This embodiment provides a calibration method based on different measurement trajectory planning, as a supplement and extension to Embodiment 5.

[0127] In this embodiment, in addition to using a circular trajectory, other types of measurement trajectories are also used to further verify the applicability and robustness of the method of the present invention.

[0128] I. Linear Trajectory Measurement In addition to circular trajectories, linear trajectories can also be used for measurement. Specifically, the robot's end effector is controlled to move along a preset linear trajectory while simultaneously collecting measurement data from a ballbar and a circular grating.

[0129] The method for planning a straight-line trajectory is as follows: Set the starting point P. start and endpoint P end Then the point P(t) on the straight line trajectory is: By selecting different starting and ending points, multiple straight lines of different directions and lengths can be planned within the workspace.

[0130] II. Rectangular Trajectory Measurement A rectangular trajectory is another commonly used measurement trajectory. Specifically, the robot's end effector is controlled to move along a rectangular trajectory, with the four vertices of the rectangle being A, B, C, and D.

[0131] Rectangular trajectories can be used to evaluate the motion accuracy of a robot in different directions, and in particular, can detect perpendicularity and straightness errors.

[0132] III. Measurement of Spatial Helical Trajectory The spatial helical trajectory is a more complex measurement trajectory that can fully excite all degrees of freedom of the mechanism. The parametric equation of the helical trajectory is: in, Where is the helix radius. The pitch factor is... It is a corner.

[0133] By adjusting the helix radius and pitch coefficient, spatial helical trajectories of different shapes can be planned within the workspace.

[0134] IV. Trajectory Combination Strategy In practical applications, multiple trajectories can be combined to improve the accuracy and robustness of parameter identification. Specific strategies are as follows: 1. First, a circular trajectory is used for preliminary calibration to quickly obtain a rough estimate of the structural parameter error; 2. Then, fine calibration is performed using linear and rectangular trajectories to further improve the accuracy of parameter identification; 3. Finally, a spatial spiral trajectory was used for verification to evaluate the generalization ability of the calibration results within the workspace.

[0135] By combining multiple trajectories, the differences in the sensitivity of different trajectories to errors can be fully utilized to improve the comprehensiveness and accuracy of parameter identification.

[0136] Example 7 This embodiment provides an implementation scheme based on online calibration for real-time error compensation of parallel robots during operation.

[0137] In this embodiment, the calibration method is extended from offline calibration to online calibration, enabling real-time error detection and compensation during robot operation.

[0138] I. Online Calibration System Architecture The online calibration system includes the following components: 1. Measurement module: including ballbar and circular grating, used for real-time measurement of the robot's motion error; 2. Data Acquisition Module: Includes the Beckhoff data acquisition system and Bluetooth communication module, used for real-time acquisition of measurement data; 3. Data processing module: including an embedded processor or industrial PC, used for real-time processing of measurement data and parameter identification; 4. Control Compensation Module: This module includes a robot controller, which adjusts control commands in real time based on the identification results to achieve error compensation.

[0139] II. Online Calibration Process 1. During the robot's operation, periodically collect measurement data from the ballbar and circular grating; 2. Use the collected data to perform real-time parameter identification and update the estimated values ​​of structural parameter errors; 3. Correct the kinematic model in real time based on the updated structural parameter errors; 4. Based on the corrected kinematic model, adjust the joint drive commands to achieve real-time error compensation.

[0140] III. Advantages of Online Calibration 1. It can track changes in robot structural parameters in real time, such as changes in rod length caused by temperature changes and changes in clearance caused by wear; 2. It can adapt to different working conditions and environmental changes, improving the robot's adaptability and robustness; 3. It can promptly detect and compensate for sudden changes in structural parameters, such as deformation caused by collisions.

[0141] This embodiment extends the calibration technology described in this invention from offline applications to online applications through an online calibration method, further improving the accuracy and reliability of parallel robots.

[0142] Example 8 This embodiment provides an implementation scheme based on multi-robot collaborative calibration, which can improve calibration efficiency and expand the application scope.

[0143] In this embodiment, the calibration method for a single robot is extended to multi-robot collaborative calibration, enabling simultaneous calibration and error compensation for multiple parallel robots.

[0144] I. Multi-robot collaborative calibration system The multi-robot collaborative calibration system comprises the following components: 1. Multiple 2PRU-PSR parallel robots; 2. Shared measurement device: including a high-precision laser tracker or coordinate measuring machine for measuring the end-effector poses of multiple robots; 3. Distributed measurement device: Each robot is equipped with an independent ballbar and circular grating for measuring its own local errors; 4. Cooperative control module: Used to coordinate the movement and measurement processes of multiple robots.

[0145] II. Collaborative Calibration Process 1. Perform independent ballbar and circular grating measurements on each robot and establish its own error mapping model; 2. Utilize a shared measurement device to perform collaborative measurements on multiple robots and establish the relative pose relationships between them; 3. Based on collaborative measurement data, global parameter identification is performed, and the structural parameter errors of each robot and the relative pose errors between robots are also identified. 4. Based on the identification results, perform error compensation for each robot and adjust the relative pose relationship between the robots.

[0146] III. Advantages of Collaborative Calibration 1. Improve calibration efficiency: Multiple robots can be calibrated simultaneously, reducing the total calibration time; 2. Improve calibration accuracy: Improve parameter identification accuracy by providing global constraints through shared measurement devices; 3. Expanded application scope: Suitable for multi-robot collaborative operation scenarios, such as collaborative assembly and collaborative welding.

[0147] This embodiment extends the calibration technology described in this invention from single-robot applications to multi-robot applications through a multi-robot collaborative calibration method, further improving calibration efficiency and applicability.

[0148] In summary, this invention provides a kinematic calibration method for a 2PRU-PSR parallel mechanism that integrates ballbar and circular grating. By establishing a kinematic error mapping model, a ballbar error mapping model, a circular grating error mapping model, and a fused error parameter mapping model, it achieves dual constraints and precise calibration of the end effector pose of the parallel mechanism. This method not only solves the fundamental problem that traditional ballbar calibration methods cannot guarantee the absolute pose accuracy of the end effector, but also reduces the coupling between error parameters and model overfitting by fusing and solving multi-source sensor information, significantly improving the reliability and practicality of the kinematic model. Detailed descriptions of multiple embodiments verify the effectiveness and superiority of this invention, providing a complete technical solution for high-precision calibration and error compensation of parallel robots.

[0149] The above embodiments merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0150] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A kinematic calibration method for a 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating, characterized in that, Includes the following steps: S1. Establish a kinematic error mapping model for the 2PRU-PSR parallel mechanism. The model includes at least a first mapping relationship from the mechanism structure parameter error to the moving platform pose error, and a second mapping relationship from the moving platform pose error to the tool end pose error. S2. Establish a ballbar error mapping model, wherein the model establishes a third mapping relationship between the measured change in the ballbar length and the position error of the cutter end; S3. Establish a circular grating error mapping model, which includes an installation error model and a measurement error model; the measurement error model establishes a fourth mapping relationship between the measured angle change of the circular grating and the attitude error of the moving platform. S4. Merge the ballbar error mapping model with the circular grating error mapping model, and combine the third mapping relationship with the fourth mapping relationship to construct a fused error parameter mapping model; S5. Plan and control the end effector of the parallel mechanism to drive the ball bar to move along a preset spatial circular trajectory, while collecting the bar length measurement data of the ball bar and the angle measurement data of the circular grating installed at the rotary joint of the parallel mechanism; S6. Based on the measurement data collected in step S5 and the fusion error parameter mapping model constructed in step S4, parameter identification is performed to obtain the actual structural parameter error of the parallel mechanism. S7. The theoretical kinematic model of the parallel mechanism is corrected by using the identified actual structural parameter errors, and the parallel mechanism is controlled based on the corrected kinematic model.

2. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, In step S1, the first mapping relationship is obtained by performing a first-order perturbation derivation on the inverse kinematic equations of the parallel mechanism, specifically as follows: ,in Let be the pose error vector of the moving platform. The Jacobian matrix represents the structural parameter error. This is a structural parameter error vector that includes the installation error of the fixed platform, the installation position error of the moving platform, and the rod length error.

3. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 2, characterized in that, In step S1, the second mapping relationship is represented by the following formula: ,in For the tool tip position error, For the position error of the moving platform, For the attitude matrix of the moving platform, For tool size error, The angular velocity vector of the moving platform. The vector of the tool in the moving coordinate system.

4. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, In step S2, the ballbar error mapping model is applied to the ballbar geometric constraint equations. The first-order perturbation derivation yields the final form as follows: ,in The roundness error vector is composed of the measurements from the ballbar. Identify the Jacobian matrix for the ballbar error parameters.

5. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, In step S3, the installation error model includes at least measurement error components caused by eccentricity error, tilt error, and zero-position error.

6. The kinematic calibration method for the 2PRU-PSR parallel mechanism of the fusion ballbar and circular grating according to claim 1 or 5, characterized in that, In step S3, two circular gratings are installed on the U-axis and S-axis of the 2PRU-PSR parallel mechanism, respectively, to measure the rotation angle of the corresponding joints.

7. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, In step S4, the fusion error parameter mapping model is as follows: ,in This is the measurement error vector for the circular grating. This is the Jacobian matrix for mapping the error of the circular grating.

8. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, In step S5, the preset spatial circular trajectory is the base circle of a cone with the fixed center of the ball bar as the cone apex and the ball bar shaft as the generatrix. The apex angle of the cone is adjusted by changing the angle between the ball bar shaft and the horizontal plane, thereby realizing the measurement of the circular trajectory on different spatial planes.

9. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, In step S6, the parameter identification process includes: based on the fusion error parameter mapping model, using the least squares method or iterative optimization algorithm to analyze the structural parameter error vector. Solve the problem.

10. The kinematic calibration method for the 2PRU-PSR parallel mechanism integrating a ballbar and a circular grating according to claim 1, characterized in that, Step S5 further includes: synchronously recording the joint drive values ​​of the parallel mechanism during data acquisition; in step S6, using the joint drive values ​​and the forward kinematic model of the parallel mechanism to calculate the theoretical position of the tool tip, which is used to construct the roundness error vector together with the ballbar measurement data. .

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