A probe calibration method for an articulated arm coordinate measuring machine based on a sphere fitting model

Abstract

The present invention provides a probe calibration method for an articulated coordinate measuring machine based on a sphere fitting model, which relates to the technical field of precision measurement methods. The method specifically includes the following steps: According to the nominal structural parameters of the articulated coordinate measuring machine, establish the D-H model of the articulated coordinate measuring machine, and use the D-H model to calculate the coordinates of the center of the probe ball. According to the articulated coordinate measuring machine, by measuring the surface coordinates of the standard ball, calculate the measured radius of the standard ball. Establish a parameter vector to be calibrated, and the parameter vector to be calibrated includes: the length of the probe rod, the radius of the probe ball, and the center of the standard ball. Take the parameter vector to be calibrated as the initial value, and use the central particle swarm optimization algorithm to optimize and iteratively search for the optimal parameter to be calibrated. The technical solution of the present invention overcomes the problems of low calibration accuracy, large amount of measurement data, and complex measurement steps in the prior art for the probe calibration of the articulated coordinate measuring machine.

Description

Technical Field

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

[0002] Compared with traditional orthogonal coordinate measuring machines, articulated arm coordinate measuring machines have the advantages of small volume, simple operation, large measurement range, etc., and are often used for measuring large parts. Due to the influence of factors such as the structure of the workpiece to be measured and the on-site measurement environment, the articulated arm coordinate measuring machine needs to replace the probe to adapt to different measurement scenarios, so as to obtain more accurate measurement results.

[0003] The measurement model of the articulated arm coordinate measuring machine is established through the D-H model. The spatial transformation relationship between two adjacent joints of the articulated arm coordinate measuring machine is described by 4 D-H model parameters, so as to obtain the spatial coordinates of the probe end relative to the base. Since the probe is replaced, the D-H parameter (i.e., the stylus length) is 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 actual coordinates where the probe is located, resulting in measurement errors. In addition, the parameters used when the articulated arm coordinate measuring machine actually performs measurements also include other unmodeled parameters. Taking the probe radius as an example, although this parameter does not belong to the D-H model parameters, the relationship between the measurement result and this parameter often needs to be considered when actually measuring the size of the workpiece to obtain the true size of the workpiece. Therefore, accurate parameters need to be obtained through calibration technology to correct the model and improve the measurement accuracy.

[0004] The calibration of the articulated arm coordinate measuring machine is to measure a certain standard quantity by using the articulated arm coordinate measuring machine, compare it with the standard quantity to obtain the measurement error, and the parameters of the articulated arm coordinate measuring machine can be deduced inversely through the measurement error by using a suitable optimization method. The current mainstream method is to measure a single-point cone socket, take the average value of the measurement values as the standard quantity, and calibrate the probe parameters by combining 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 D-H 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 sphere fitting model with high measurement accuracy, less measurement data volume, and simple measurement steps. Summary of the Invention

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

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

[0008] S1. According to the nominal structural parameters of the articulated arm coordinate measuring machine, establish the D-H model of the articulated arm coordinate measuring machine, and calculate the coordinates of the probe ball center using the D-H model.

[0009] S2. According to the articulated arm coordinate measuring machine, calculate the measured standard ball radius by measuring the surface coordinates of the standard ball.

[0010] S3. Establish the parameter vector to be calibrated , the parameter vector to be calibrated includes: stylus length, probe ball radius, and standard ball center.

[0011] S4. Use the parameter vector to be calibrated as the initial value, and use the central particle swarm optimization algorithm to optimize and iteratively search for the optimal parameter to be calibrated .

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

[0013] S1.1. Describe the spatial pose transformation relationship between two adjacent coordinate systems in space through the rod length , joint twist angle , offset and joint rotation angle . The spatial pose transformation relationship between two adjacent coordinate systems is represented by a homogeneous matrix as:

[0014] (1).

[0015] S1.2. The established position relationship between the probe of the articulated arm coordinate measuring machine and the base is:

[0016] (2);

[0017] wherein, is the coordinate of the probe ball center, represents the stylus length.

[0018] Further, step S2 specifically includes the following steps:

[0019] S2.1. Fix the articulated arm coordinate measuring machine and the standard ball on the optical platform.

[0020] S2.2. Touch the probe of the articulated arm coordinate measuring machine against the surface of the standard sphere, and record the vector formed by the 6 joint angle values of the current articulated arm coordinate measuring machine :

[0021] (3);

[0022] Among them, represents the serial number of the measurement times.

[0023] S2.3. Repeat step S2.2 at least times, where , and the positions where the probe touches the standard sphere are evenly distributed on the standard sphere, and record the joint angle values corresponding to all positions , including groups of joint angle data , expressed as:

[0024] (4);

[0025] Among them, .

[0026] S2.4. According to calculate the coordinates of the surface of the standard sphere measured by the articulated arm coordinate measuring machine, fit to obtain the center of the standard sphere , and calculate the radius of the measured standard sphere.

[0027] Furthermore, step S2.4 specifically includes the following steps:

[0028] S2.4.1. According to the groups of joint angle data measured by the articulated arm coordinate measuring machine and the D-H model constructed in step S1, calculate and obtain groups of probe center coordinates, and the th probe center coordinate is expressed as:

[0029] (5);

[0030] Among them, .

[0031] S2.4.2. The expression for the distance between the center of the standard sphere and the center of the probe is:

[0032] (6);

[0033] Among them, represents the distance between the center of the standard sphere and the center of the probe , .

[0034] S2.4.3. Assuming that all are equal under ideal measurement conditions, we have:

[0035] (7);

[0036] Rewrite formula (7) as:

[0037] (8).

[0038] Then the center of the fitted standard sphere is:

[0039] (9).

[0040] S2.4.4. The distance from the center of the measuring sphere to the center of the standard sphere minus the radius of the measuring sphere gives the measured radius of the standard sphere :

[0041] (10).

[0042] Furthermore, the positions where the probe touches the standard sphere in step S2.3 are evenly distributed on the standard sphere, specifically including at least 1 pole of the standard sphere and 4 positions on the equator corresponding to the pole.

[0043] Furthermore, step S3 is specifically as follows:

[0044] Establish the vector of parameters to be calibrated , denoted as:

[0045] (11);

[0046] where is the transpose of the center of the standard sphere .

[0047] Furthermore, step S4 specifically includes the following steps:

[0048] S4.1. Set the relevant parameters of the central particle swarm optimization algorithm, including: the maximum number of iterations , the population size , the maximum velocity weight , the minimum velocity weight , the individual learning constant , the social learning constant , and the search range .

[0049] S4.2, Initialize the population of the central particle swarm algorithm and velocity , the population includes vectors randomly generated within the search range , , the velocity includes vectors of the same dimension as , , , where .

[0050] S4.3, Execute the central particle swarm algorithm to iteratively search for the optimal parameters to be calibrated .

[0051] Furthermore, step S4.3 specifically includes the following steps:

[0052] S4.3.1, Calculate the fitness of each particle in the population , update the individual historical optimal solutions of the first particles in the population and the historical optimal solution of all particles .

[0053] S4.3.2, Determine whether the current iteration number has reached the maximum value , if it has reached the maximum value, then output , otherwise transfer to step S4.3.3

[0054] S4.3.3, According to the individual historical optimal solutions of the first particles and the historical optimal solution of all particles , update the velocities of the first particles in the population:

[0055] (12);

[0056] where, is the updated particle velocity, is the particle velocity before update, represents a random number within the range , represents the velocity weight, which is continuously updated according to the set and with the iteration number, and the update formula is:

[0057] (13);

[0058] where, is the current iteration number.

[0059] S4.3.4. Update the position of the particle according to the velocities of the previous particles:

[0060] (14);

[0061] where is the position of the particle before update, is the position of the particle after update.

[0062] S4.3.5. Update the position of the -th particle according to the positions of the previous particles :

[0063] (15).

[0064] S4.3.6. Return to step S3.4.1 and output the individual historical optimal solutions of the population particles and the historical optimal solutions of all particles .

[0065] Furthermore, in step S4.3.1, calculate the fitness of each particle in the population specifically as follows:

[0066] Use the particle to calculate the objective function :

[0067] (16);

[0068] In the formula, represents the radius of the standard sphere, is expressed as:

[0069] (17).

[0070] The present invention has the following beneficial effects:

[0071] The method provided by the present invention can calibrate the parameters related to the probe. Using the method provided by the present invention for calibration can effectively improve the measurement accuracy of the articulated arm coordinate measuring machine. Moreover, only one fixed installation standard sphere is required as the standard part in the present invention, with less measurement data and simple measurement steps, which is suitable for rapid calibration at the measurement site. The algorithm used in the present invention does not require error modeling of the articulated arm coordinate measuring machine, greatly reducing the labor cost and being easy to be programmed and implemented, having practical value. Description of the Drawings

[0072] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings. In the drawings:

[0073] Figure 1 Shows the probe calibration method of the articulated arm coordinate measuring machine based on the sphere fitting model, which is applied to the calibration system of the articulated arm coordinate measuring machine.

[0074] Figure 2 Shows the schematic diagram of the standard sphere radius measurement model.

[0075] Figure 3 Shows the joint twist angle Position schematic diagram.

[0076] Figure 4 Shows the rod length , offset and joint rotation angle Position schematic diagram.

[0077] The reference numerals in the above drawings are:

[0078] 1, rod; 10, probe rod; 20, probe ball, 30, standard ball; 40, joint. Specific embodiments

[0079] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the drawings. Obviously, the described embodiments are some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0080] A probe calibration method for an articulated arm coordinate measuring machine based on a sphere fitting model, which is applied to Figure 1 The articulated arm coordinate measuring machine calibration system shown, specifically including the following steps:

[0081] S1. According to the nominal structural parameters of the articulated arm coordinate measuring machine, establish the D-H model of the articulated arm coordinate measuring machine, and calculate the coordinates of the probe ball center using the D-H model.

[0082] S2. According to the articulated arm coordinate measuring machine, calculate the measured standard sphere radius by measuring the surface coordinates of the standard sphere.

[0083] S3. Establish the parameter vector to be calibrated , the parameter vector to be calibrated including: the length of the probe rod, the radius of the probe ball, and the center of the standard ball.

[0084] S4. Use the parameter vector to be calibrated as the initial value, and use the central particle swarm optimization algorithm to optimize and iteratively search for the optimal parameter to be calibrated .

[0085] Specifically, step S1 specifically includes the following steps:

[0086] S1.1. Describe the spatial pose transformation relationship between two adjacent coordinate systems in space through the rod length , joint twist angle , offset , and joint rotation angle . The spatial pose transformation relationship between two adjacent coordinate systems is represented by a homogeneous matrix as:

[0087] (1).

[0088] As Figure 3 and Figure 4 shown, the rod length is the shortest distance between the axes of two adjacent rotary joints 40, that is, the length of the common perpendicular between the two axes; the joint twist angle is to move any axis of the same rod to the other axis so that they intersect, then the plane determined by these two straight lines is perpendicular to the rod length , and the plane angle between these two straight lines is the joint twist angle of this rod; the offset is the distance intercepted by the rod length line and on the joint axis; the joint rotation angle refers to the change in the relative position between two adjacent rods. When two rods are connected by a rotary joint, the joint variable is the rotation angle .

[0089] Among them, rod 1 includes probe rod 10 and all other rods of the articulated coordinate measuring machine.

[0090] S1.2. The established position relationship between the probe of the articulated coordinate measuring machine and the base is:

[0091] (2);

[0092] where is the coordinate of the center of the probe ball, represents the length of the probe rod.

[0093] Specifically, step S2 specifically includes the following steps:

[0094] S2.1, Fix the articulated arm coordinate measuring machine and the standard ball on the optical platform. The radius of the standard ball is known and precise and will not change during the calibration process.

[0095] S2.2, As shown in Figure 2 , contact the probe of the articulated arm coordinate measuring machine with the surface of the standard ball 30, and record the vector formed by the 6 joint angle values of the current articulated arm coordinate measuring machine :

[0096] (3);

[0097] Among them, represents the serial number of the measurement times.

[0098] The probe includes: a probe ball 20 and a probe rod 10.

[0099] S2.3, Repeat step S2.2 at least times, where , and the positions where the probe contacts the standard ball are evenly distributed on the standard ball, and record the joint angle values corresponding to all positions , including groups of joint angle data , expressed as:

[0100] (4);

[0101] Among them, .

[0102] S2.4, According to calculate the coordinates of the surface of the standard ball measured by the articulated arm coordinate measuring machine, fit to obtain the center of the standard ball , and calculate the radius of the measured standard ball.

[0103] Specifically, step S2.4 specifically includes the following steps:

[0104] S2.4.1, According to the groups of joint angle data measured by the articulated arm coordinate measuring machine and the D-H model constructed in step S1, calculate to obtain groups of probe ball center coordinates, and the th probe ball center coordinate is expressed as:

[0105] (5);

[0106] Among them, .

[0107] S2.4.2, The center of the standard ball The expression for the distance between the center of the measuring sphere and [it] is:

[0108] (6);

[0109] Wherein, represents the distance between the center of the standard sphere and the center of the measuring sphere ; .

[0110] S2.4.3. Assuming that all measured under ideal conditions are equal, then there is:

[0111] (7).

[0112] Write formula (7) as:

[0113] (8);

[0114] Then the fitted center of the standard sphere is:

[0115] (9).

[0116] S2.4.4. The distance from the center of the measuring sphere to the center of the standard sphere minus the radius of the measuring sphere gives the measured radius of the standard sphere :

[0117] (10).

[0118] Specifically, in step S2.3, the positions where the probe touches the standard sphere are evenly distributed on the standard sphere, specifically: at least including 1 pole of the standard sphere and 4 positions on the equator corresponding to the pole.

[0119] Specifically, step S3 is specifically:

[0120] Establish the vector of parameters to be calibrated , expressed as:

[0121] (11);

[0122] Wherein, is the transpose of the center of the standard sphere .

[0123] Specifically, step S4 specifically includes the following steps:

[0124] S4.1, Set the relevant parameters of the central particle swarm algorithm, including: the maximum number of iterations , the population size , the maximum value of the velocity weight , the minimum value of the velocity weight , the individual learning constant , the social learning constant , the search range . The search range , which can be set according to the design parameters of the probe and the machining accuracy, generally not exceeding 10 mm.

[0125] S4.2, Initialize the population and velocity of the central particle swarm algorithm. The population includes vectors randomly generated within the search range , and the velocity includes vectors with the same dimension as . , where . is the number of particles. Among them, .

[0126] S4.3, Execute the central particle swarm algorithm to iteratively search for the optimal parameters to be calibrated .

[0127] Specifically, step S4.3 specifically includes the following steps:

[0128] S4.3.1, Calculate the fitness of each particle in the population , and update the individual historical optimal solutions of the first particles in the population and the historical optimal solution of all particles.

[0129] S4.3.2, Determine whether the current iteration number has reached the maximum value . If it has reached the maximum value, output , otherwise go to step S4.3.3.

[0130] S4.3.3, Update the velocities of the first particles in the population according to the individual historical optimal solutions of the first particles and the historical optimal solution of all particles:

[0131] (12);

[0132] where, is the updated particle velocity, is the particle velocity before update, represents a random number in the range of and represents the velocity weight, which is continuously updated according to the set and with the iteration number. The update formula is:

[0133] (13);

[0134] where is the current iteration number.

[0135] S4.3.4. Update the particle positions according to the velocities of the previous particles:

[0136] (14);

[0137] where is the particle position before update, is the updated particle position.

[0138] S4.3.5. Update the position of the -th particle according to the positions of the previous particles :

[0139] (15).

[0140] S4.3.6. Return to step S3.4.1 and output the individual historical optimal solutions of the population particles and the historical optimal solutions of all particles .

[0141] Specifically, in step S4.3.1, calculate the fitness of each particle in the population as follows:

[0142] Use the particle to calculate the objective function :

[0143] (16);

[0144] In the formula, represents the radius of the standard sphere, is expressed as:

[0145] (17).

[0146] Certainly, 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 those skilled in the art within the scope of the essence 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. ; 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 ; 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 ; 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）。 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 .

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