Precision measurement configuration optimization index of numerical control equipment and kinematics calibration method of precision measurement configuration optimization index

Abstract

The invention discloses a numerical control equipment precision measurement configuration optimization index and a kinematics calibration method thereof, and belongs to the technical field of industrial robot kinematics calibration, and the method comprises the steps: S1, building a geometric error transmission model of a target robot, and screening parameters to be identified; s2, establishing a new index based on the morbid theory and the spatial analysis theory of the matrix; s3, taking the new index as a fitness function of a genetic algorithm to obtain an optimal configuration for parameter identification; s4, obtaining an identification result of the geometric error parameter by using a regularization method; s5, selecting a verification configuration in the whole working area for error compensation; according to the method, firstly, a POE method is used for establishing a geometric error transfer model of the robot and screening identification parameters, then, a working space of the robot is discretized and serves as an optimization range of a genetic algorithm, a new index serves as a fitness function to find an optimal configuration, and finally, a regularization method is used for parameter identification. And the superiority of the new index is revealed by comparing and analyzing the observability index with the previous observability index.

Description

Technical Field

[0001] The invention relates to the technical field of kinematic calibration of industrial robots, and in particular to a numerical control equipment precision measurement configuration optimization index and a kinematic calibration method thereof. Background Art

[0002] The absolute accuracy and repeatability of the end effector of an industrial robot are important precision indicators for industrial manufacturing. In addition to thermal deformation errors and control system errors, precision robots still have certain geometric errors and structural errors, which can be compensated for by kinematic calibration. The kinematic calibration process mainly includes the following four steps: geometric error modeling, end error measurement, error parameter identification, and error compensation. In the step of error parameter identification, the parameter identification results obtained with a well-behaved identification matrix can often improve the accuracy of parameter identification.

[0003] In order for the identification matrix to calculate the estimation of the geometric error parameters through the identification algorithm, it is necessary to construct at least a matrix with the same number of rows as the number of error source parameters, and the matrix needs to be as conducive to parameter identification as possible, which requires the matrix to have characteristics such as low morbidity, strong robustness, and full rank.

[0004] Previous studies have explored multiple observability indicators as the basis for screening the optimal configuration. The most commonly used one is the condition number. The significance of the condition number is to find the maximum difference in the degree of stretching of the matrix as a whole in different dimensions, and to exchange the accuracy of judging the properties of the matrix for the maximum fault tolerance range. Its disadvantage is that it cannot reflect the distribution state of the remaining singular values, and a large amount of information from the remaining singular values ​​is lost.

[0005] Among the five observability indicators O1 to O5, O2, O3, and O4 are all deformations of the condition number calculation method. In essence, they are no different from the geometric meaning symbolized by the condition number, and a lot of information is also lost; O1 and O5 retain all the singular value information. O1 represents the square root mean of the product of each singular value. Its geometric meaning is a quantity related to the volume of the ellipsoid, emphasizing the overall characteristics. The larger the value, the more it can be explained that the selected configuration is conducive to parameter identification; and O5 represents the harmonic mean of all singular values. The geometric meaning is similar to O1. The disadvantage of the latter is that it cannot eliminate redundant information, which increases the calculation burden. Points with large difference values ​​may affect the overall identification results.

[0006] Therefore, although the existing observability indicators can screen out posture combinations that are conducive to parameter identification from a large number of postures through evolutionary algorithms, they cannot further improve the parameter identification effect due to the omission of matrix information. This difficulty needs to be solved. Summary of the invention

[0007] The purpose of the present invention is to provide a numerical control equipment precision measurement configuration optimization index and a kinematic calibration method thereof, so as to solve the problems existing in the above-mentioned background technology.

[0008] To achieve the above object, the present invention provides a numerical control equipment precision measurement configuration optimization index and a kinematic calibration method thereof, comprising the following steps:

[0009] S1. Establish a geometric error transfer model of the target robot and select parameters to be identified;

[0010] S2. Establish a new index based on the pathological theory of matrix and spatial analysis theory;

[0011] S3, using the new index as the fitness function of the genetic algorithm to obtain the optimal configuration for parameter identification;

[0012] S4. Using the regularization method to obtain the identification result of the geometric error parameters;

[0013] S5. Select the verification configuration in the entire working area for error compensation.

[0014] Preferably, step S1 specifically includes:

[0015] S11. A robot geometric error transfer model based on the POE method is established. The POE method avoids the singularity problem in the modeling process. The general formula of the model can be expressed as:

[0016]

[0017] Where S represents the geometric posture error of the moving platform of this motion platform, Q = J -1 , J is a 6×6 matrix, which is the driving Jacobian matrix of the robot, G represents a diagonal matrix with the product of the unit driving force spinor of a branch and all the adjoint transformation matrices of the branch as diagonal elements, δζ represents the structural error of the robot joint, δξ represents the motion error of the joint; H represents the error transfer Jacobian matrix, η represents the geometric error source vector;

[0018] S12. Eliminate redundant parameters from all error parameters of the robot.

[0019] Preferably, step S2 specifically includes:

[0020] S21. Perform matrix ill-conditioning analysis on the robot's error transfer Jacobian matrix. Assume that the identification Jacobian matrix A obtained from the robot's geometric error model has m rows and n columns. The row vectors of the matrix represent different geometric error parameters of the robot in the same configuration, and the column vectors represent the same geometric error parameters of the robot in different configurations. In order for the identification matrix to calculate the estimated geometric error parameters through the identification algorithm, it is necessary to construct at least a matrix with the same number of rows as the number of error source parameters, and the matrix needs to be as conducive to parameter identification as possible. This requires the matrix to have characteristics such as low ill-conditioning, strong robustness, and full rank. By designing indicators for the properties of the matrix itself, it is helpful to quickly construct an identification matrix with excellent performance. In order to construct an indicator that can reflect the relationship between matrix rows (or columns), it is necessary to establish a theoretical foundation for the new indicator based on the row and column vectors of the matrix;

[0021] S22. Expand the robot's error transfer Jacobian matrix in high-dimensional space and give it a geometric meaning using the volume of a hyperparallel polyhedron as an index value.

[0022] Preferably, in step S12, redundant parameters are eliminated from the error transfer Jacobian matrix of the established whole-machine geometric error transfer model through column correlation analysis to ensure that the error transfer Jacobian matrix of the robot can normally perform various index operations.

[0023] Preferably, the construction process of the new indicator in step S2 includes:

[0024] Assume that the m*n identification matrix A is obtained by robot modeling and point selection. Assume that m≥n. When the column of A is full rank, perform elementary transformation on A and transform it into a trapezoidal matrix M. Then take the first n rows of M to obtain an n-dimensional square matrix N, which is called the information matrix.

[0025] The information matrix N is Gram-Schmidt orthogonalized (hereinafter referred to as GS orthogonalization) by column vectors and normalized to obtain an n*n matrix G: GS orthogonalization is specifically as follows: Let G = [g1, g2, g3, ...] be a finite or listable number of linearly independent vectors in the inner product space H, then there must be an orthogonal system in H that is So that for every natural number x, g x It is h1,h2,…h x The linear combination of x is g1, g2, … g x A linear combination of h x Except for a constant factor with an absolute value of 1, g1, g2, …g x Completely sure;

[0026] The column vectors in B represent a set of bases e1, e2, …, e n, the volume formed by the basis vectors is V = 1, and the space is an n-dimensional standard space:

[0027] V=||e1||·||e2||·…·||e n ||=1;

[0028] Normalize the row vectors of the information matrix N to get the matrix N0, and perform Gram-Schmidt orthogonalization on N0 to get the matrix N a , N a The row vector is represented by n1,n2,…n n , in order to calculate the volume U of the hyperparallel polyhedron that can be expanded by the information matrix G n , then the metric of the identification matrix is ​​expressed as O7:

[0029] O7=U / V=||n1||·||n2||·…·||n n || / V=||n1||·||n2||·…·||n n ||.

[0030] Preferably, in step S3, the calculation method of the new indicator is used as the fitness function, and a genetic algorithm is used as an evolutionary algorithm for configuration optimization. The genetic algorithm has a dynamically updated crossover probability and inheritance probability for faster convergence.

[0031] Preferably, in step S4, the generalized cross-validation criterion is used to optimize the regularization parameter, and the Tikhonov regularization method is used to estimate the parameters of the identification equation group A=Jε. The essence of generalized cross validation (GCV) can be summarized as follows: the detection data set is arbitrarily divided into two subsets, and the error parameters are identified using the data of one subset and used to predict the other subset. The optimal regularization parameter should make the above-mentioned prediction accuracy optimal in a statistical sense. The valuation criterion of the regularization method applied to the present invention can be expressed as:

[0032]

[0033] Among them, α>0 is the regularization parameter; L is a symmetric positive definite matrix, and the unit matrix I is usually taken in engineering; ε0 is the true value of the geometric error source; ε is the estimation of the geometric error source parameter, specifically the variable that needs to be optimized and solved. When the parameter estimation criteria are met, the solution of the error identification model is:

[0034]

[0035] Compared with the least squares solution, the Tikhonov regularized solution is solved by using the normal matrix J T The damping term αI is added to the diagonal elements of J to improve the stability of the parameter identification results.

[0036] Preferably, in step S5, the new index configuration is preferably combined as a parameter identification matrix, and the regularization method is used as the identification method of the robot geometric error parameters, which are respectively introduced into the optimal configuration and the verification configuration to calculate the estimated terminal posture error ε e , the end posture error is used to obtain the equivalent motion error ρ of the driving joint through the mapping matrix. The equivalent motion error is the rod length error of each driving joint, and its inverse is the error compensation Δq:

[0037] Δq=-JTζ;

[0038] Among them, J is the driving Jacobian matrix of the 6-UPS six-degree-of-freedom parallel robot, T is the identification matrix, and ζ is the combination of geometric error sources.

[0039] Preferably, the specific process of the genetic algorithm is:

[0040] Individual coding: After discretizing the workspace according to the specified spatial coordinate interval and posture angle interval, use binary coding to encode the robot's posture combination as a biological individual, and select a points in the workspace as internal genes in each posture combination;

[0041] Set the relevant parameters of the genetic algorithm;

[0042] Set the fitness function: The fitness function of the genetic algorithm selects the new evaluation index O7;

[0043] Generate an initial population, calculate the identification matrix corresponding to each organism in the population to calculate the fitness function;

[0044] In the population, the corresponding probability is generated according to the fitness function to select the parent generation for crossover, generate offspring, and then perform gene mutation in the offspring according to the mutation function to form a new generation of population as a whole;

[0045] The number of iterations increases by 1 until the upper limit of the number of iterations is exceeded;

[0046] The population or individual with the best fitness is obtained, and the posture combination corresponding to the individual is used as the basis for parameter identification.

[0047] The driving joint variable q combined with the compensation amount Δq is added to the control system, and then the end posture information of the compensated posture is measured using a laser tracker. Finally, the six-degree-of-freedom errors before and after compensation and the overall error of the optimal posture obtained based on the new index and the optimal posture obtained based on the condition number are analyzed and compared.

[0048] Therefore, the present invention adopts the above numerical control equipment precision measurement configuration optimization index and its kinematic calibration method, which has the following beneficial effects:

[0049] (1) Compared with the original index, the proposed new index increases the effective information carrying capacity of the error propagation Jacobian matrix in the configuration optimization step, so that the parameter identification of the geometric error source can obtain more accurate results;

[0050] (2) Genetic algorithms that dynamically update parameters can converge faster than traditional methods, allowing the algorithm to traverse more configuration combinations in the robot's workspace to find the optimal configuration;

[0051] (3) The Tikhonov regularization method based on the generalized cross-validation criterion will obtain more stable parameter identification results compared with the least squares method.

[0052] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the numerical control equipment precision measurement configuration optimization index and its kinematic calibration method of the present invention;

[0054] Figure 2 Schematic diagram of the geometric meaning of the new index proposed in the embodiment of the present invention; wherein (a) represents no pathological state, (b) represents mild pathological state, and (c) represents severe pathological state;

[0055] Figure 3 is a flow chart of a genetic algorithm according to an embodiment of the present invention;

[0056] Figure 4 It is an iteration graph of a genetic algorithm using condition number as fitness in an embodiment of the present invention;

[0057] Figure 5 It is an iteration diagram of a genetic algorithm using a new indicator as fitness in an embodiment of the present invention;

[0058] Figure 6 : is a comparison diagram of the root mean square error of multiple parameter identification results in the embodiment of the present invention; wherein (a) is the root mean square error of the parameter identification result based on the condition number, and (b) is the root mean square error of the parameter identification result based on the new index;

[0059] Figure 7 The figure is a comparison diagram of the spatial position before and after compensation for verifying the configuration in the embodiment of the present invention; wherein (a) is before compensation, (b) is after compensation based on the condition number, and (c) is after compensation based on the new index;

[0060] Figure 8 The figures are comparison diagrams before and after the posture angle compensation for verifying the configuration in the embodiment of the present invention; wherein, (a) is before compensation, (b) is after compensation based on the condition number, and (c) is after compensation based on the new indicator. DETAILED DESCRIPTION

[0061] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. 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.

[0062] See also Figure 1 , the numerical control equipment precision measurement configuration optimization index and its kinematic calibration method include the following steps:

[0063] S1. The geometric error transfer model of the six-DOF parallel robot is established by the exponential product method. The specific process is as follows:

[0064] From the geometric error model of the series kinematic chain, we can get:

[0065]

[0066] in, 0 'S represents the terminal posture error of the platform, δξ j represents the motion error of joint j, δζ j represents the joint structure error, represents the permissible small displacement rotation of joint j, Representation system {R j}The adjoint transformation matrix of the relative system {R'0}.

[0067] The six-degree-of-freedom platform is connected by six series kinematic chains, so "i" is added to the lower right corner of all variables on the right side of the equal sign in equation (1) to describe the number of the branch chain, and we can get:

[0068]

[0069] Formula (2) is further described by the following formula:

[0070]

[0071] δζ 0,i =( 0 δx 1,i 0 δy 1,i (1-m) 0 δz 1,i 0 δα 1,i 0 δβ 1,i m 0 δγ 1,i ) T ;

[0072] δζ j,i =( j δx j+1,i j δy j+1,i (1-m) j δz j+1,i j δα j+1,i j δβ j+1,i m j δγ j+1,i ) T ;

[0073] (j=1,2,…,n i ,i=1,2,…,6);

[0074] Among them, S represents the geometric posture error of the moving platform of this motion platform, n i Represents the degree of freedom of branch chain i. Construct the unit allowable small displacement rotation of each joint of each branch chain:

[0075]

[0076] Among them, w 1,i -w 6,i represents the angular velocity of each joint of each branch chain, a i represents the coordinate vector from the origin of the system {R6} to the center of each hinge point of the moving platform in the system {R6}, b i represents the coordinate vector from the origin of the system {R0} to the center of each hinge point of the moving platform in the system {R0}, q i represents the direction vector of the driving rod i in the system {R0}, r is the vector from the origin of the system {R0} to the origin of the system {R0}, and the closed-loop equation of the i-th branch of the robot satisfies r = b i +q i -Ra i , R represents the posture matrix.

[0077] Using the property that the driving (constraining) joint force screw only does work on the unit allowable small displacement screw caused by it, the unit driving force screws at both ends of equation (2) about branch i are Taking the inner product, we get:

[0078]

[0079] Write the above formula in matrix form:

[0080] JS=δξ+Gδζ (6)

[0081] J is a 6×6 matrix, which is called the driving Jacobian matrix of the 6-UPS six-degree-of-freedom parallel robot. Each column of the transpose of J represents a unit driving force spinor acting on the moving platform. Note that in a non-singular configuration, J is reversible, so let Q = J -1 , so the formula can be further written as:

[0082]

[0083] Where S represents the geometric posture error of the moving platform of this motion platform, Q = J -1 , J is a 6×6 matrix, which is the driving Jacobian matrix of the robot. G represents a diagonal matrix with the product of the unit driving force spinor of a branch and all the adjoint transformation matrices of the branch as diagonal elements. δζ represents the structural error of the robot joint, and δξ ​​represents the motion error of the joint. H represents the error transfer Jacobian matrix, and η represents the geometric error source vector. So far, the whole machine geometric error model of the 6-UPS six-degree-of-freedom parallel robot has been established. The error transfer Jacobian matrix H has 6 rows and 216 columns. The 6 rows represent the six-dimensional posture of the robot, and the 216 columns represent the 216 error sources of the robot.

[0084] Selecting n configurations, we can obtain n geometric error relations S i =H i η(i=1,2,…,n), written in matrix format, is the identification equation set for error parameter identification:

[0085]

[0086] in, This is the identification matrix.

[0087] S2. Construct a new index based on the matrix pathological theory and spatial analysis theory. The construction method is as follows:

[0088] (1) Assume that the m*n identification matrix A is obtained by robot modeling and point selection. Assuming m ≥ n, when A is full column rank, A can be transformed into a trapezoidal matrix M by elementary transformation. Then, the first n rows of M are taken to obtain an n-dimensional square matrix N, which is called the information matrix.

[0089] (2) The information matrix N is subjected to Gram-Schmidt orthogonalization (hereinafter referred to as GS orthogonalization) according to column vectors and normalized to obtain an n*n matrix G.

[0090] Gram-Schmidt: Let G = [g1, g2, g3, ...] be a finite or enumerable number of linearly independent vectors in the inner product space H, then there must be an orthogonal system in H So that for every natural number x, g x It is h1,h2,…h x The linear combination of x is g1, g2, … g x This h x Except for a constant factor with an absolute value of 1, g1, g2, …g x Absolutely sure.

[0091] The column vectors in B represent a set of bases e1, e2, …, e n , the volume formed by the basis vectors is V = 1, and the space is a standard n-dimensional space;

[0092] V=||e1||·||e2||·…·||e n ||=1 (9)

[0093] (3) Normalize the row vectors of the information matrix N to obtain the matrix N0. Perform GS orthogonalization on N0 to obtain the matrix N a , N a The row vector is represented by n1,n2,…n n , in order to calculate the volume U of the hyperparallel polyhedron that can be expanded by the information matrix G n , then the metric of the identification matrix can be expressed as:

[0094] O7=U / V=||n1||·||n2||·…·||n n || / V=||n1||·||n2||·…·||n n || (10)

[0095] O7 is the new indicator value.

[0096] Combination Figure 2 , taking an information matrix as an example, assume that the length of its three edges is 0.6. In the diagram on the left, the edges of the green polyhedron are perpendicular to each other, so its volume reaches the maximum value, which is 0.216. In the diagram in the middle, the angle between the two edges of the bottom surface of the blue polyhedron is an acute angle, resulting in a slight decrease in volume compared to the green polyhedron, which is 0.187. Finally, in the diagram on the right, the angles between all the edges of the red polyhedron are acute angles, which makes the volume reach the minimum value, which is 0.162.

[0097] S3, such as Figure 3 As shown, the process of using the new index as the fitness function for the genetic algorithm for configuration optimization is as follows:

[0098] (1) Individual coding: After discretizing the workspace according to the specified spatial coordinate interval and posture angle interval, the robot's posture combination is encoded in binary and regarded as a biological individual. In each posture combination, n points in the workspace are selected as internal genes.

[0099] (2) Set the relevant parameters of the genetic algorithm: such as initial population size, dynamic crossover probability, dynamic mutation probability, crossover point, elimination method, number of iterations or algorithm termination conditions, etc.

[0100] (3) Setting the fitness function: The fitness function of the genetic algorithm selects the new evaluation index O7 and the condition number κ respectively. It is believed that the robot posture combination with a larger new evaluation index or a smaller condition number is more conducive to the parameter identification of kinematic calibration.

[0101] (4) Generate an initial population and calculate the identification matrix corresponding to each organism in the population to calculate the fitness function.

[0102] (5) The fitness function is used to generate corresponding probabilities in the population to select the parent generation for crossover, generate offspring, and then perform gene mutation in the offspring according to the mutation function to form the new generation of the population as a whole.

[0103] (6) The number of iterations increases by 1 until the upper limit of the number of iterations is exceeded.

[0104] (7) Obtain the population or individual with the best fitness, and use the posture combination corresponding to the individual as the basis for parameter identification.

[0105] Combination Figure 4 and Figure 5 , respectively, are the genetic algorithm iteration graphs obtained by using the condition number and the new index as the fitness function. The biological individuals in the genetic algorithm are a set of configuration combinations containing 40 different points, the number of biological populations is 200, the initial crossover probability of the genetic algorithm is 0.75, the number of iterations is 100, and when the algorithm continues for 80 times, the degree of change of the fitness function is less than 1.0×10 -6 After reaching the maximum number of iterations, the optimal configuration is considered to be found, and the iterations are stopped after reaching 200. The optimal condition number obtained by the genetic algorithm is 2.3914×10 7 ; The optimal new index value obtained by the genetic algorithm is 0.7276.

[0106] As the number of iterations increases, the mean of the condition number of the population changes dramatically, indicating that using the condition number as the fitness function of the genetic algorithm cannot effectively ensure the stable evolution of the population. Since the mutation function in the genetic algorithm maintains the diversity of species, the mean of the last generation is not necessarily the minimum mean in the iterative process.

[0107] Combination Figure 6The root mean square error between the robot terminal error estimate and the true value obtained by the genetic algorithm with the new index as the fitness function after verification with the randomly generated verification configuration is smaller than the result obtained by the genetic algorithm with the condition number as the fitness function.

[0108] S4. The error compensation method of the robot's verification configuration is as follows: the optimal combination of the new index configuration is used as the parameter identification matrix, and the least square method is used as the identification method of the robot's geometric error parameters. They are respectively introduced into the optimal configuration and the verification configuration to calculate the estimated terminal posture error ε e , the end posture error is used to obtain the equivalent motion error ρ of the driving joint through the mapping matrix. The equivalent motion error is actually the rod length error of each driving joint, and its inverse is the error compensation Δq:

[0109] Δq=-JTζ (11)

[0110] Among them, J is the driving Jacobian matrix of the 6-UPS six-degree-of-freedom parallel robot, T is the identification matrix, and ζ is the combination of geometric error sources.

[0111] The driving joint variable q combined with the compensation amount Δq is added to the control system, and then the end posture information of the compensated posture is measured using a laser tracker. Finally, the six-degree-of-freedom errors before and after compensation and the overall error of the optimal posture obtained based on the new index and the optimal posture obtained based on the condition number are analyzed and compared.

[0112] Combination Figure 7 and Figure 8 ,Through comparison, the compensation result of the spatial coordinate based on the new ,indicator is obviously better than that of the spatial coordinate based on the ,condition number, and a large number of points can get good optimization effect; ,while the compensation result of the attitude angle based on the new ,indicator does not have obvious advantages over that of the attitude angle based on the ,condition number, and there is a gap in the optimization effect between different ,points.

[0113] Therefore, the present invention adopts the above-mentioned CNC equipment precision measurement configuration optimization index and its kinematic calibration method. First, based on the POE method, the geometric error transfer model of the target robot is established and redundant parameters are eliminated. Then, the proposed new index is used as the fitness function of the genetic algorithm to find the optimal configuration. Finally, the regularization method is used for parameter estimation. The valuation results are compared and analyzed with the observability index represented by the condition number to reveal and verify the regularity and superiority of the new index.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. Optimal index for precision measurement of numerical control equipment and its kinematic calibration method, characterized in that: The following steps are involved: S1. Establish a geometric error transfer model of the target robot and select parameters to be identified; S2. Establish a new index based on the pathological theory of matrix and spatial analysis theory; S3, using the new index as the fitness function of the genetic algorithm to obtain the optimal configuration for parameter identification; S4. Using the regularization method to obtain the identification result of the geometric error parameters; S5. Select the verification configuration in the entire working area for error compensation.

2. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method according to claim 1 is characterized in that: Step S1 specifically includes: S11. Establish a robot geometric error transfer model based on the POE method; S12. Eliminate redundant parameters from all error parameters of the robot.

3. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method thereof according to claim 2 is characterized in that: Step S2 specifically includes: S21. Perform matrix ill-conditioning analysis on the robot's error propagation Jacobian matrix; S22. Expand the robot's error transfer Jacobian matrix in high-dimensional space and give it a geometric meaning using the volume of a hyperparallel polyhedron as an index value.

4. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method thereof according to claim 3 is characterized by: In step S12, redundant parameters are eliminated from the error transfer Jacobian matrix of the established whole-machine geometric error transfer model through column correlation analysis.

5. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method thereof according to claim 1 is characterized in that: The construction process of the new indicator in step S2 includes: Assume that the m*n identification matrix A is obtained by robot modeling and point selection. Assume that m≥n. When the column of A is full rank, perform elementary transformation on A and transform it into a trapezoidal matrix M. Then take the first n rows of M to obtain an n-dimensional square matrix N, which is called the information matrix. The information matrix N is Gram-Schmidt orthogonalized by column vectors and normalized to obtain an n*n matrix G: Gram-Schmidt orthogonalization is as follows: Let G = [g1, g2, g3, ...] be a finite or listable number of linearly independent vectors in the inner product space H, then there must be an orthogonal system in H So that for every natural number x, g x It is h1,h2,…h x The linear combination of x is g1, g2, … g x Linear combinations of The column vectors in B represent a set of bases e1, e2, …, e n , the volume formed by the basis vectors is V = 1, and the space is an n-dimensional standard space: V=||e1||·||e2||·…·||e n ||=1; Normalize the row vectors of the information matrix N to get the matrix N0, and perform Gram-Schmidt orthogonalization on N0 to get the matrix N a , N a The row vector is represented by n1,n2,…n n , in order to calculate the volume U of the hyperparallel polyhedron that can be expanded by the information matrix G n , then the metric of the identification matrix is ​​expressed as O7: O7=U / V=||n1||·||n2||·…·||n n || / V=||n1||·||n2||·…·||n n ||。 6. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method according to claim 1, characterized in that: In step S3, the calculation method of the new index is used as the fitness function, and a genetic algorithm is used as an evolutionary algorithm for configuration optimization. The genetic algorithm has a dynamically updated crossover probability and inheritance probability.

7. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method according to claim 1, characterized in that: In step S4, the generalized cross-validation criterion is used to optimize the regularization parameter, and the Tikhonov regularization method is used to identify the geometric error parameter.

8. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method according to claim 1, characterized in that: Step S5 uses the optimal combination of the new index configuration as the parameter identification matrix, and uses the regularization method as the identification method of the robot geometric error parameters, which are respectively introduced into the optimal configuration and the verification configuration to calculate the estimated terminal posture error ε e The end posture error is used to obtain the equivalent motion error ρ of the driving joint through the mapping matrix. The equivalent motion error is the rod length error of each driving joint, and its inverse is the error compensation Δq.

9. The numerical control equipment precision measurement configuration optimization index and kinematic calibration method thereof according to claim 6, characterized in that: The specific process of genetic algorithm is as follows: Individual coding: After discretizing the workspace according to the specified spatial coordinate interval and posture angle interval, use binary coding to encode the robot's posture combination as a biological individual, and select a points in the workspace as internal genes in each posture combination; Set the relevant parameters of the genetic algorithm; Set the fitness function: The fitness function of the genetic algorithm selects the new evaluation index O7; Generate an initial population, calculate the identification matrix corresponding to each organism in the population to calculate the fitness function; In the population, the corresponding probability is generated according to the fitness function to select the parent generation for crossover, generate offspring, and then perform gene mutation in the offspring according to the mutation function to form a new generation of population as a whole; The number of iterations increases by 1 until the upper limit of the number of iterations is exceeded; The population or individual with the best fitness is obtained, and the posture combination corresponding to the individual is used as the basis for parameter identification.

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