Method for calibrating measuring head of articulated arm type coordinate measuring machine based on ball fitting model

Abstract

The invention provides an articulated arm type coordinate measuring machine measuring head calibration method based on a ball fitting model, and relates to the technical field of precision measurement methods, and the method specifically comprises the following steps: building a D-H model of an articulated arm type coordinate measuring machine according to the nominal structure parameters of the articulated arm type coordinate measuring machine, and calculating the center coordinates of a measuring ball through the D-H model. The radius of the measured standard ball is calculated by measuring the surface coordinates of the standard ball according to the articulated arm type coordinate measuring machine. Establishing a to-be-calibrated parameter vector, wherein the to-be-calibrated parameter vector comprises the length of the measuring rod, the radius of the measuring ball and the center of the standard ball; and the to-be-calibrated parameter vector is used as an initial value, and the optimal to-be-calibrated parameter is searched through optimization iteration by using the central particle swarm optimization. According to the technical scheme, the problems that in the prior art, an articulated arm type coordinate measuring machine is low in measuring head calibration precision, large in measuring data size and complex in measuring step are solved.

Description

Technical Field

[0001] The invention relates to the field of precision measurement methods, and in particular to a probe calibration method for an articulated arm type coordinate measuring machine based on a ball fitting model. Background Art

[0002] Compared with traditional orthogonal coordinate measuring machines, articulated arm coordinate measuring machines have the advantages of small size, simple operation, and large measurement range, and are often used to measure large parts. Due to the influence of factors such as the structure of the workpiece being measured and the on-site measurement environment, articulated arm coordinate measuring machines need to replace the probe to adapt to different measurement scenarios in order to obtain more accurate measurement results.

[0003] The measurement model of the articulated arm coordinate measuring machine is established through the DH model. The four DH model parameters are used to describe the spatial transformation relationship between two adjacent joints of the articulated arm coordinate measuring machine, so as to obtain the spatial coordinates of the probe end relative to the base. Due to the replacement of the probe, the DH parameters (i.e., the probe rod length) are changed, and the actual structure of the articulated arm coordinate measuring machine does not match the measurement model. At this time, the measurement coordinates calculated by the measurement model are inconsistent with the coordinates of the actual probe, resulting in measurement errors. In addition, the parameters used by the articulated arm coordinate measuring machine in actual measurement also include other unmodeled parameters. For example, the radius of the probe ball, although this parameter does not belong to the DH model parameters, it is often necessary to consider the relationship between the measurement result and the parameter when actually measuring the workpiece size to obtain the true workpiece size. Therefore, it is necessary to obtain accurate parameters through calibration technology to correct the model and improve measurement accuracy.

[0004] The calibration of an articulated arm coordinate measuring machine is to use the articulated arm coordinate measuring machine to measure a certain standard quantity and compare it with the standard quantity to obtain the measurement error. The parameters of the articulated arm coordinate measuring machine can be inferred by using a suitable optimization method through the measurement error. The current mainstream method is to measure the single-point cone socket, take the average value of the measured value as the standard quantity, and calibrate the probe parameters in combination with numerical optimization methods or intelligent search algorithms. However, this method is greatly affected by the initial parameters of the articulated arm coordinate measuring machine, and the calibrated parameters only calibrate the DH parameters of the probe. Although the calibration method is simple, the measurement accuracy after calibration cannot be guaranteed.

[0005] Therefore, there is a need for a probe calibration method for an articulated arm coordinate measuring machine based on a ball fitting model with high measurement accuracy, less measurement data volume and simple measurement steps. Summary of the invention

[0006] The main purpose of the present invention is to provide a method for calibrating the probe of an articulated arm coordinate measuring machine based on a ball fitting model, so as to solve the problems of low calibration accuracy, large amount of measurement data and complex measurement steps in the prior art of the articulated arm coordinate measuring machine probe.

[0007] To achieve the above object, the present invention provides a method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model, which specifically comprises the following steps:

[0008] S1, according to the nominal structural parameters of the articulated arm coordinate measuring machine, the DH model of the articulated arm coordinate measuring machine is established, and the coordinates of the center of the measuring ball are calculated using the DH model.

[0009] S2, the radius of the standard sphere is calculated by measuring the surface coordinates of the standard sphere using an articulated arm coordinate measuring machine.

[0010] S3, establish the parameter vector to be calibrated , parameter vector to be calibrated Includes: measuring rod length, measuring ball radius and standard ball center.

[0011] S4, the parameter vector to be calibrated As the initial value, the center particle swarm algorithm is used to optimize the iterative search for the optimal parameters to be calibrated. .

[0012] Furthermore, step S1 specifically includes the following steps:

[0013] S1.1, through the length of the member 、Joint torsion angle , offset and joint rotation Describes the spatial pose transformation relationship between two adjacent coordinate systems in space, and the spatial pose transformation relationship between two adjacent coordinate systems It can be expressed as a homogeneous matrix: (1).

[0014] S1.2, the established positional relationship between the probe of the articulated arm coordinate measuring machine and the base is: (2); in, is the coordinate of the center of the measuring ball, Indicates the length of the measuring rod.

[0015] Furthermore, step S2 specifically includes the following steps: S2.1, fix the articulated arm coordinate measuring machine and the calibration ball on the optical table.

[0016] S2.2, contact the probe of the articulated arm coordinate measuring machine with the surface of the standard ball, and record the vector formed by the current 6 joint angle values ​​of the articulated arm coordinate measuring machine : (3); in, A serial number indicating the number of measurements.

[0017] S2.3, repeat step S2.2 at least times, among which , and the positions where the probe contacts the standard ball are evenly distributed on the standard ball, and the joint angle values ​​corresponding to all positions are recorded , include Group joint angle data , expressed as: (4); in, .

[0018] S2.4, according to Calculate the surface coordinates of the standard sphere measured by the articulated arm coordinate measuring machine and fit the center of the standard sphere , and calculate the measured standard sphere radius.

[0019] Furthermore, step S2.4 specifically includes the following steps: S2.4.1, measured by an articulated arm coordinate measuring machine Combine the joint angle data and the DH model constructed in step S1 to calculate The coordinates of the center of the ball, The coordinates of the center of the measuring ball are expressed as: (5); in, .

[0020] S2.4.2, Standard ball center With the center of the ball The expression of the distance between is: (6); in, Indicates the center of the standard ball With the center of the ball The distance between .

[0021] S2.4.3, assuming that all measurements are ideally If they are equal, then: (7); Formula (7) can be written as: (8).

[0022] The center of the standard sphere is for: (9).

[0023] S2.4.4, Center of the ball To the center of the standard ball Distance minus the radius of the probe ball Get the measured standard sphere radius : (10).

[0024] Furthermore, in step S2.3, the positions where the probe contacts the standard sphere are evenly distributed on the standard sphere, specifically including at least one pole of the standard sphere and four positions on the equator corresponding to the pole.

[0025] Furthermore, step S3 is specifically as follows: Establish the parameter vector to be calibrated , It is expressed as: (11); in, Standard ball center The transpose of .

[0026] Furthermore, step S4 specifically includes the following steps: S4.1, set the relevant parameters of the central particle swarm algorithm, including: maximum number of iterations , population size , maximum speed weight , minimum speed weight , individual learning constant , social learning constant , search range .

[0027] S4.2, Initialize the population of the central particle swarm algorithm and speed , population include In search range A randomly generated vector ,speed include Individual and Vectors of the same dimension , is the number of particles, where .

[0028] S4.3, execute the central particle swarm algorithm to iteratively search for the optimal parameters to be calibrated .

[0029] Furthermore, step S4.3 specifically includes the following steps: S4.3.1. Calculate the population The fitness of each particle in the population is updated before The individual historical optimal solution of each particle and the historical optimal solution of all particles .

[0030] S4.3.2, determine whether the current number of iterations has reached the maximum value If it reaches the maximum value, the output , otherwise go to step S4.3.3.

[0031] S4.3.3, according to the previous The individual historical optimal solution of each particle and the historical optimal solution of all particles , update the population The speed of a particle: (12); in, is the updated particle velocity, is the particle velocity before updating, Indicates the range A random number between Indicates the speed weight, according to the set and It is continuously updated with the number of iterations, and the update formula is: (13); in, is the current iteration number.

[0032] S4.3.4, according to the previous The velocity of each particle updates the position of the particle: (14); in, is the particle position before updating, is the updated particle position.

[0033] S4.3.5, according to the previous The position of the particle is updated The position of the particle : (15).

[0034] S4.3.6, return to step S3.4.1, output the individual historical optimal solution of the population particle and the historical optimal solution of all particles .

[0035] Furthermore, in step S4.3.1, the population is calculated The fitness of each particle in is:

[0036] Using Particle Computation Objective Function : (16); In the formula, represents the radius of the standard sphere, It is expressed as: (17).

[0037] The present invention has the following beneficial effects: The method provided by the present invention can calibrate parameters related to the probe. Calibration using the method provided by the present invention can effectively improve the measurement accuracy of the articulated arm coordinate measuring machine, and the standard part required in the present invention is only a fixedly installed standard ball, the measurement data is less, the measurement steps are simple, and it is suitable for rapid calibration on the measurement site. The algorithm used in the present invention does not require error modeling of the articulated arm coordinate measuring machine, which greatly reduces the labor cost, is easy to program and implement, and has practical value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the specific implementation of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the specific implementation or the prior art description. Obviously, the drawings described below are some implementations of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings: Figure 1 The invention shows the probe calibration method of an articulated arm type coordinate measuring machine based on a ball fitting model, which is applied to the calibration system of an articulated arm type coordinate measuring machine.

[0039] Figure 2 A schematic diagram of the standard sphere radius measurement model is shown.

[0040] Figure 3 The joint torsion angle is shown Location diagram.

[0041] Figure 4 Shows the rod length , offset and joint rotation Location diagram.

[0042] The reference numerals in the above drawings are: 1. Rod; 10. Measuring rod; 20. Measuring ball; 30. Standard ball; 40. Joint. DETAILED DESCRIPTION

[0043] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. 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.

[0044] A probe calibration method for articulated arm coordinate measuring machine based on ball fitting model is applied to Figure 1 The articulated arm coordinate measuring machine calibration system shown in the figure specifically includes the following steps: S1, according to the nominal structural parameters of the articulated arm coordinate measuring machine, the DH model of the articulated arm coordinate measuring machine is established, and the coordinates of the center of the measuring ball are calculated using the DH model.

[0045] S2, the radius of the standard sphere is calculated by measuring the surface coordinates of the standard sphere using an articulated arm coordinate measuring machine.

[0046] S3, establish the parameter vector to be calibrated , parameter vector to be calibrated Includes: measuring rod length, measuring ball radius and standard ball center.

[0047] S4, the parameter vector to be calibrated As the initial value, the center particle swarm algorithm is used to optimize the iterative search for the optimal parameters to be calibrated. .

[0048] Specifically, step S1 includes the following steps: S1.1, through the length of the member 、Joint torsion angle , offset and joint rotation Describes the spatial pose transformation relationship between two adjacent coordinate systems in space, and the spatial pose transformation relationship between two adjacent coordinate systems It can be expressed as a homogeneous matrix: (1).

[0049] like Figure 3 and Figure 4 As shown, the rod length is the shortest distance between the axes of adjacent revolute joints 40, that is, the length of the common perpendicular line between the two axes; If any axis of the same rod is moved to another axis so that they intersect, then these two straight lines determine a line that is equal to the length of the rod. The vertical plane, the angle between these two straight lines is the joint torsion angle of the rod ; Bias is the length line of the member and The distance intercepted on the joint axis; joint rotation Refers to the change in the relative position between adjacent rods. When two rods are connected by a revolute joint, the joint variable is the rotation angle. .

[0050] The rod component 1 includes the measuring rod 10 and all other rod components of the articulated arm coordinate measuring machine.

[0051] S1.2, the established positional relationship between the probe of the articulated arm coordinate measuring machine and the base is: (2); in, is the coordinate of the center of the measuring ball, Indicates the length of the measuring rod.

[0052] Specifically, step S2 includes the following steps: S2.1, fix the articulated arm coordinate measuring machine and the calibration sphere on the optical table. The radius of the calibration sphere is known and accurate and will not change during the calibration process.

[0053] S2.2, such as Figure 2 As shown, the probe of the articulated arm coordinate measuring machine is brought into contact with the surface of the standard ball 30, and the vector formed by the current 6 joint angle values ​​of the articulated arm coordinate measuring machine is recorded. : (3); in, A serial number indicating the number of measurements.

[0054] The probe comprises a probe ball 20 and a probe rod 10 .

[0055] S2.3, repeat step S2.2 at least times, among which , and the positions where the probe contacts the standard ball are evenly distributed on the standard ball, and the joint angle values ​​corresponding to all positions are recorded , include Group joint angle data , expressed as: (4); in, .

[0056] S2.4, according to Calculate the surface coordinates of the standard sphere measured by the articulated arm coordinate measuring machine and fit the center of the standard sphere , and calculate the measured standard sphere radius.

[0057] Specifically, step S2.4 includes the following steps: S2.4.1, measured by an articulated arm coordinate measuring machine Combine the joint angle data and the DH model constructed in step S1 to calculate The coordinates of the center of the ball, The coordinates of the center of the measuring ball are expressed as: (5); in, .

[0058] S2.4.2, Standard ball center With the center of the ball The expression of the distance between is: (6); in, Indicates the center of the standard ball With the center of the ball The distance between .

[0059] S2.4.3, assuming that all measurements are ideally If they are equal, then: (7).

[0060] Formula (7) can be written as: (8); The center of the standard sphere is for: (9).

[0061] S2.4.4, Center of the ball To the center of the standard ball Distance minus the radius of the probe ball Get the measured standard sphere radius : (10).

[0062] Specifically, the positions where the probe contacts the standard sphere in step S2.3 are evenly distributed on the standard sphere, specifically including at least one pole of the standard sphere and four positions on the equator corresponding to the pole.

[0063] Specifically, step S3 is as follows: Establish the parameter vector to be calibrated , It is expressed as: (11); in, Standard ball center The transpose of .

[0064] Specifically, step S4 includes the following steps: S4.1, set the relevant parameters of the central particle swarm algorithm, including: maximum number of iterations , population size , maximum speed weight , minimum speed weight , individual learning constant , social learning constant , search range . Search scope , which can be set according to the design parameters of the probe and the processing accuracy, generally not exceeding 10mm.

[0065] S4.2, Initialize the population of the central particle swarm algorithm and speed , population include In search range A randomly generated vector ,speed include Individual and Vectors of the same dimension , is the number of particles, where .

[0066] S4.3, execute the central particle swarm algorithm to iteratively search for the optimal parameters to be calibrated .

[0067] Specifically, step S4.3 includes the following steps: S4.3.1. Calculate the population The fitness of each particle in the population is updated before The individual historical optimal solution of each particle and the historical optimal solution of all particles .

[0068] S4.3.2, determine whether the current number of iterations has reached the maximum value If it reaches the maximum value, the output , otherwise go to step S4.3.3.

[0069] S4.3.3, according to the previous The individual historical optimal solution of each particle and the historical optimal solution of all particles , update the population The speed of a particle: (12); in, is the updated particle velocity, is the particle velocity before updating, Indicates the range A random number between Indicates the speed weight, according to the set and It is continuously updated with the number of iterations, and the update formula is: (13); in, is the current iteration number.

[0070] S4.3.4, according to the previous The velocity of each particle updates the position of the particle: (14); in, is the particle position before updating, is the updated particle position.

[0071] S4.3.5, according to the previous The position of the particle is updated The position of the particle : (15).

[0072] S4.3.6, return to step S3.4.1, output the individual historical optimal solution of the population particle and the historical optimal solution of all particles .

[0073] Specifically, in step S4.3.1, the population is calculated The fitness of each particle in is: Using Particle Computation Objective Function : (16); In the formula, represents the radius of the standard sphere, It is expressed as: (17).

[0074] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model, characterized in that: The specific steps include: S1, establishing a DH model of the articulated arm coordinate measuring machine according to the nominal structural parameters of the articulated arm coordinate measuring machine, and calculating the coordinates of the center of the measuring ball using the DH model; S2, the radius of the standard sphere is calculated by measuring the surface coordinates of the standard sphere using an articulated arm coordinate measuring machine; S3, establish the parameter vector to be calibrated , parameter vector to be calibrated Including: measuring rod length, measuring ball radius and standard ball center; S4, the parameter vector to be calibrated As the initial value, the center particle swarm algorithm is used to optimize the iterative search for the optimal parameters to be calibrated. .

2. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 1, characterized in that: Step S1 specifically includes the following steps: S1.1, through the length of the member 、Joint torsion angle , offset and joint rotation Describes the spatial pose transformation relationship between two adjacent coordinate systems in space, and the spatial pose transformation relationship between two adjacent coordinate systems It can be expressed as a homogeneous matrix: （1）； S1.2, the established positional relationship between the probe of the articulated arm coordinate measuring machine and the base is: （2）； in, is the coordinate of the center of the measuring ball, Indicates the length of the measuring rod.

3. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 1, characterized in that: Step S2 specifically includes the following steps: S2.1, fix the articulated arm coordinate measuring machine and the calibration ball on the optical table; S2.2, contact the probe of the articulated arm coordinate measuring machine with the surface of the standard ball, and record the vector formed by the current 6 joint angle values ​​of the articulated arm coordinate measuring machine : （3）； in, A serial number indicating the number of measurements; S2.3, repeat step S2.2 at least times, among which , and the positions where the probe contacts the standard ball are evenly distributed on the standard ball, and the joint angle values ​​corresponding to all positions are recorded , include Group joint angle data , expressed as: （4）； in, ; S2.4, according to Calculate the surface coordinates of the standard sphere measured by the articulated arm coordinate measuring machine and fit the center of the standard sphere , and calculate the measured standard sphere radius.

4. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 3, characterized in that: Step S2.4 specifically includes the following steps: S2.4.1, measured by an articulated arm coordinate measuring machine Combine the joint angle data and the DH model constructed in step S1 to calculate The coordinates of the center of the ball, The coordinates of the center of the measuring ball are expressed as: （5）； in, ; S2.4.2, Standard ball center With the center of the ball The expression of the distance between is: （6）； in, Indicates the center of the standard ball With the center of the ball The distance between ; S2.4.3, assuming that all measurements are ideally If they are equal, then: （7）； Formula (7) can be written as: （8）； The center of the standard sphere is for: （9）； S2.4.4, Center of the ball To the center of the standard ball Distance minus the radius of the probe ball Get the measured standard sphere radius : （10）。 5. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 3, characterized in that: In step S2.3, the positions where the probe contacts the standard sphere are evenly distributed on the standard sphere, specifically including at least one pole of the standard sphere and four positions on the equator corresponding to the pole.

6. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 1, characterized in that: Step S3 is specifically as follows: Establish the parameter vector to be calibrated , It is expressed as: （11）； in, Standard ball center The transpose of .

7. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 1, characterized in that: Step S4 specifically includes the following steps: S4.1, set the relevant parameters of the central particle swarm algorithm, including: maximum number of iterations , population size , maximum speed weight , minimum speed weight , individual learning constant , social learning constant , search range ; S4.2, Initialize the population of the central particle swarm algorithm and speed , population include In search range A randomly generated vector ,speed include Individual and Vectors of the same dimension , is the number of particles, where ; S4.3, execute the central particle swarm algorithm to iteratively search for the optimal parameters to be calibrated .

8. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 7, characterized in that: Step S4.3 specifically includes the following steps: S4.3.

1. Calculate the population The fitness of each particle in the population is updated before The individual historical optimal solution of each particle and the historical optimal solution of all particles ; S4.3.2, determine whether the current number of iterations has reached the maximum value If it reaches the maximum value, the output , otherwise go to step S4.3.3; S4.3.3, according to the previous The individual historical optimal solution of each particle and the historical optimal solution of all particles , update the population The speed of a particle: （12）； in, is the updated particle velocity, is the particle velocity before updating, Indicates the range A random number between Indicates the speed weight, according to the set and It is continuously updated with the number of iterations, and the update formula is: （13）； in, is the current iteration number; S4.3.4, according to the previous The velocity of each particle updates the position of the particle: （14）； in, is the particle position before updating, is the updated particle position; S4.3.5, according to the previous The position of the particle is updated The position of the particle : （15）； S4.3.6, return to step S3.4.1, output the individual historical optimal solution of the population particle and the historical optimal solution of all particles .

9. The method for calibrating a probe of an articulated arm coordinate measuring machine based on a ball fitting model according to claim 8, characterized in that: Calculate the population in step S4.3.1 The fitness of each particle in is: Using Particle Computation Objective Function : （16）； In the formula, represents the radius of the standard sphere, It is expressed as: （17）。

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