A geometric error parameter identification method based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm

Abstract

The present invention discloses a method for identifying geometric error parameters based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm, which can identify the geometric error parameters of a parallel robot under the interference of external environmental errors. According to the degree of correlation of the end positions of the parallel mechanism, the method divides the robot into a side closed loop and a final closed loop, thereby simplifying the error model solution process. Then, the first-order perturbation theory is used to separate the geometric error, a linear model of the geometric error of the parallel robot is constructed, and the nonlinear optimization problem is converted into a linear optimization problem, thereby improving the identification accuracy of the identification algorithm. On the basis of the principal component regression algorithm, the robust estimation is used to correct the geometric error identification matrix, suppress gross error data, improve the robustness of the algorithm, and further improve the geometric error parameter identification accuracy of the model. The method can simplify the solution and construction of the error model, and use the weight function to reduce the interference of gross error data, so that the robustness of the principal component regression algorithm is increased, and the geometric error parameter identification accuracy is improved.

Description

Technical Field

[0001] The invention relates to a calibration method for improving the terminal accuracy of a parallel robot, and in particular to a geometric error parameter identification method based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm. Background Art

[0002] As my country's traditional industries upgrade and manufacturing intelligence enters a new stage, robots replacing natural people to perform intelligent factory operations has become the mainstream development trend. From the application level, parallel robots have the advantages of high rigidity, large load, high precision, fast speed, compact structure, etc. due to their closed-loop structure, which can make up for the shortcomings of serial robots. Therefore, they are widely used in important fields such as orthopedic surgery robots, sorting robots, large aircraft multi-degree-of-freedom simulation platforms, and parallel processing machines. Due to manufacturing errors, assembly errors, and structural wear errors during the working process, there is a deviation between the true value and the nominal value of the robot's structural parameters. However, the existing algorithm has low geometric error parameter identification accuracy due to the multicollinearity of the error model and is easily affected by gross error data, which further affects the comprehensive positioning accuracy of the parallel robot after parameter identification. Therefore, in order to ensure that the parallel robot can have a higher comprehensive positioning accuracy, it is necessary to improve the parallel robot's geometric error parameter identification accuracy.

[0003] Vector differential method is a general method for establishing the error model of parallel robots, but the error model established is generally a high-dimensional nonlinear equation. Although it can effectively avoid the singularity problem of the identification process, the nonlinear optimization has poor identification effect and requires more iterations when there are more identification parameters. In addition, due to the existence of multicollinearity in the identification matrix and the matrix is ​​ill-conditioned, it cannot be directly used for geometric error parameter identification. The principal component regression algorithm has good performance in the correction of ill-conditioned matrices, and the final identification principal component is selected according to the size of the principal component eigenvalue for parameter identification. However, in the identification process, since the number of identification principal components is less than the number of initial identification parameters, when there is an external measurement error, the error of the identification principal component will be further amplified, resulting in weak anti-error ability of the identified result and low identification accuracy of the geometric error parameters. The present invention utilizes closed-loop vector chain perturbation to construct a linear error model, and adopts the principal component regression algorithm based on anti-error estimation to perform parameter identification on the identification matrix, so as to improve the geometric error identification effect, so as to achieve the improvement of terminal positioning accuracy. Summary of the invention

[0004] The present invention mainly aims at the above-mentioned problems, performs linear error modeling on the parallel robot, reduces identification parameters, and combines robust estimation with principal component regression algorithm to identify the error parameter matrix, thereby improving the terminal positioning accuracy of the parallel robot.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A geometric error parameter identification method based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm includes the following:

[0007] Define the coordinate system used to describe all geometric errors;

[0008] After considering the geometric error sources, a closed-loop vector chain constraint equation is constructed, and the geometric error parameters are separated using the first-order perturbation, the nonlinear optimization problem is transformed into a linear optimization problem, and a linear model of the parallel robot geometric error is constructed.

[0009] The geometric error parameter identification matrix is ​​obtained based on the principal component regression algorithm, and is further corrected using robust estimation.

[0010] Random sampling is performed in the robot workspace to obtain the position error between the theoretical point and the actual point, and the geometric error parameters are identified based on the corrected geometric error parameter identification matrix.

[0011] In the above technical scheme, further, according to the degree of correlation of the end positions of the parallel mechanism, the robot is divided into a side closed loop and a final closed loop, the closed loop chain involving the end point posture is solved as the final closed loop vector chain, and the remaining closed loop chains are used as side closed loops for solving the parameters of the final closed loop parameter vector chain.

[0012] Furthermore, the constructed parallel robot geometric error linear model is as follows:

[0013] Δρ=HΔP err

[0014] Where: Δρ is the position error vector, H is the identification matrix, ΔP err is the geometric error parameter term.

[0015] Furthermore, the principal component regression algorithm is used to screen the principal components with greater influence to construct a new identification matrix and identification variables. The identification matrix after principal component regression is further corrected through robust estimation. The weight matrix is ​​used to suppress the gross error data points and control the proportion of different data points in the overall matrix.

[0016] Furthermore, the weight matrix is ​​constructed using an improved IGG3 weight function. According to the residual distribution of each iteration, the weights of the robust estimation weight matrix are updated through the weight function. When the identification accuracy meets the design requirements or the maximum number of iterations is reached, the iteration is exited.

[0017] The present invention is a method for geometric error parameter identification based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm. Its greatest feature and innovation is that it can construct a parallel robot geometric error linear model, suppress gross error data, and improve identification accuracy. According to an example of the present invention, the error identification method process can mainly include the following steps:

[0018] A. Define a coordinate system for describing all geometric errors. Separate the parallel structure vector closed-loop chain, and use the end point pose closed-loop chain as the final closed-loop vector chain for solution. The remaining closed-loop chains are used as side closed-loops for solving the parameters of the final closed-loop parameter vector chain, reducing the number of final closed-loop vector chains and the difficulty of solving. In the process, use the first-order perturbation to separate the geometric error parameters and implement the general method for solving the error model of the parallel robot. Define the following key points and coordinate systems:

[0019] {O} is the ideal fixed reference system of the frame and is the base coordinate system of the mechanism and closed-loop vector chain.

[0020] {O P} is the moving platform coordinate system, and its attitude matrix is ​​expressed as:

[0021] R O,P =Rot(z,θ+Δθ)Rot(x,Δα)Rot(y,Δβ) (1)

[0022] Formula (1) represents the moving platform coordinate system {O P} is the posture transformation relative to the base coordinate system {O}, where θ is the rotation angle of the moving platform around the Z axis; Δθ, Δα and Δβ represent the posture errors of the platform around the Z axis, X axis and Y axis respectively.

[0023] In addition, the branch chain moving platform center system, branch chain slider coordinate system, and branch chain base coordinate system need to be defined separately.

[0024] B. Use the first-order perturbation to separate the geometric error parameters and implement a general method to solve the error model of the parallel robot.

[0025] First, according to the coordinate system defined in step A, after considering the geometric error source, a closed-loop vector chain constraint equation can be constructed. In order to avoid too many equations affecting the accuracy of the error model solution, appropriate constraint equations are selected to separate the geometric error sources that affect the end position and posture. and attitude error The final expression is:

[0026]

[0027] Among them: G1, G2 are the converted error coefficient matrices, the position error of the center point at the end of the moving platform and the attitude error of the moving platform can be respectively expressed as Indicates; ΔP err , is the geometric error parameter term.

[0028] Based on the position error vector, the geometric error model of the parallel robot can be obtained as follows:

[0029] Δρ=HΔPerr (3)

[0030] Where: Δρ is the position error vector, and H is the identification matrix.

[0031] C. Identification of geometric error parameters based on robust estimation and principal component regression algorithm (RE-PCR).

[0032] The principal component regression algorithm is to construct a matrix H T H and solve its eigenvalues, select the principal components with greater influence, build a new identification matrix and identification variables, achieve dimension reduction of variables and correct the ill-conditioned matrix, and the principal component contribution is expressed as:

[0033]

[0034] Where: i is the principal component contribution of the i-th error parameter; i To construct the matrix H T H eigenvalue and λ1≥λ2≥…≥λ P , p is the number of geometric error parameters, and the characteristic matrix V = [v1,…,v i ,…v p ], where v i is the eigenvector, formula (3) can be rewritten as:

[0035] Δρ=Gβ (5)

[0036] Where: G = HV, β = V T ΔP err .

[0037] Define the cumulative pivot contribution, filter the pivots, and express the first P′ pivots as:

[0038]

[0039] Where: cpc is the cumulative contribution of the first P′ principal components, and G is defined PCA =[G1,…,G P′ ],V PCA =[v1,…,b P′ ] Therefore, formula (5) can be expressed through the first P′ pivots as:

[0040]

[0041] β PCA The identification matrix after cumulative iteration correction of principal components.

[0042] In order to improve the identification accuracy of the parallel robot, the identification matrix after principal component regression is further corrected by robust estimation, and the gross error data points are suppressed by the weight matrix to control the proportion of different data points in the overall matrix. The weight matrix can be expressed as follows:

[0043]

[0044] The weight matrix is ​​initially the unit matrix, w i (i=1,…,p) is the corresponding weight, which is constructed using the improved IGG3 weight function:

[0045]

[0046] Among them: k0 and k1 are the harmonic functions that control the segment length, is the standardized residual. In the weight function, the standardized residual is divided into four sections, namely the effective information section, the front section and back section of the sub-effective information, and the harmful information section. According to the residual distribution of each iteration, the weights of the robust estimation weight matrix are updated through the weight function. When the identification accuracy meets the design requirements or the maximum number of iterations is reached, the iteration is exited.

[0047] From this, the geometric error parameters after iteration k can be derived:

[0048]

[0049] D. Randomly sample in the robot workspace and record the joint angle value and the corresponding laser tracker coordinate measurement value of each sampling point for parameter identification. The position error Δρ between the theoretical point and the actual point is obtained based on the joint angle value and the corresponding laser tracker coordinate measurement value of each sampling point. Based on the geometric error parameter identification matrix of step C, the geometric error parameter is further identified.

[0050] The method of the present invention can simplify the solution and construction of the error model, and use the weight function to reduce the interference of gross error data, so as to increase the anti-error ability of the principal component regression algorithm and improve the identification accuracy of geometric error parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Attached Figure 1 It is a structural schematic diagram and a physical diagram of a parallel robot (4PPa-PaR type) implemented in the present invention.

[0052] Attached Figure 2 It is a schematic diagram of the coordinate system of the parallel robot vector chain implemented in the present invention.

[0053] Attached Figure 3 It is a schematic diagram of the effect of error compensation of the present invention. DETAILED DESCRIPTION

[0054] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific implementation steps.

[0055] Reference Figure 1 The physical picture and structural diagram of the 4PPa-PaR parallel robot are shown in the figure. Its motion platform has four degrees of freedom: movement along the X-axis, Y-axis, and Z-axis, and rotation around the Z-axis. The displacements of the four sliding joints along the slide rail are recorded as P1, P2, P3, and P4. In order to construct a full-parameter geometric error model, based on the above parallel robot, the whole is disassembled into the left, middle, and right closed-loop vector chains. Since the closed-loop vector links on the left and right sides are the same, only the left closed-loop vector chain and the middle closed-loop vector chain are analyzed.

[0056] Reference Figure 2 , define the following key points and coordinate systems:

[0057] {O}: The ideal fixed reference system of the frame is the base coordinate system of the left side of the mechanism and the closed-loop vector chain in the middle.

[0058] {O P}: Moving platform coordinate system, the coordinate system is established on O P Point, the moving platform theoretically performs three-dimensional translation and rotation around the axis, so {O P} relative to {O} posture matrix can be expressed as:

[0059] R O,P =Rot(z,θ+Δθ)Rot(x,Δα)Rot(y,Δβ) (1)

[0060] Wherein, θ is the rotation angle of the moving platform around the Z axis; Δθ, Δα, and Δβ represent the attitude errors of the platform around the Z axis, X axis, and Y axis, respectively.

[0061] {O1}: The left branch slider 1 coordinate system, the origin is located at O1, the coordinate system posture is the same as {O} posture, relative to the system {O} coordinate posture matrix R O,1 It can be represented as the identity matrix E.

[0062] {O2}: The left branch slider 2 coordinate system, the origin is located at O2, and can be rotated Δβ around the Y axis through {O} 2,1 , and then rotate Δγ around the Z axis 2,1 , the attitude matrix of the coordinates of system {O2} relative to system {O} can be expressed as:

[0063] R O,2 =Rot(y,Δβ 2,1 )Rot(z,Δγ 2,1 ) (2)

[0064] {O3}: The center system of the left branch chain moving platform, with the origin at O3. The attitude matrix of the system {O3} relative to the coordinates of the system {O} can be expressed as:

[0065] R O,3 =Rot(x,Δα1)Rot(y,Δβ1)Rot(z,Δγ1) (3)

[0066] Among them, Δα1, Δβ1, and Δγ1 represent the attitude errors of the left branch platform around the X, Y, and Z axes, respectively.

[0067] {O 11}、{O 12}: Left branch chain dynamic platform connection system, the origin is located at O 11 , O 12 , Department of {O 11 The attitude matrix of {O3} relative to the coordinate system can be expressed as:

[0068] R 3,11 =Rot(x,Δα 11 )Rot(y,Δβ 11 )Rot(z,Δγ 11 ) (4)

[0069] where Δα 11 , Δβ 11 , Δγ 11 They represent the attitude errors of the left branch platform around the X, Y, and Z axes respectively.

[0070] Department{O 12 The attitude matrix of {O3} relative to the coordinate system can be expressed as:

[0071] R 3,12 =Rot(x,Δα 12 )Rot(y,Δβ 12 )Rot(z,Δγ 12 ) (5)

[0072] where Δα 12 , Δβ 12 , Δγ 12 They represent the attitude errors of the left branch platform around the X, Y, and Z axes respectively.

[0073] After considering the geometric structure error sources, the closed-loop vector chain constraint equation can be constructed:

[0074]

[0075] in: is the position vector representation of point {O3} in {O}; x = [1 0 0] T ; is the position vector representation of the moving sliders 1 and 2 in {O}; Parallel Link The position vector in {O} is represented; Parallel Link The position vector in {O} represents; fl a 、fl b 、fl c 、fl d Represent the parallel link crossbar Length.

[0076] Rewrite the scalar and vector in the above formula into the form of adding the theoretical value and the error value, and rearrange the above formula. Use the first-order perturbation to offset the theoretical terms and remove the second-order infinitesimal terms. The center position and attitude error matrix of the left branch chain platform can be obtained as follows:

[0077]

[0078] in: represents the left branch platform posture error coefficient matrix, G L represents the corresponding geometric error parameter coefficient matrix, Represents the separated geometric error parameter vector.

[0079] Similarly, the closed-loop vector chain constraint equations of the middle branch chain and the right branch chain can be constructed to solve the center position and attitude error matrix of the middle branch chain platform and the right branch chain platform. The final moving platform end point position and attitude error matrix are obtained:

[0080]

[0081] In formula (8), G1 and G2 are the error coefficient matrices after transformation. They represent the position error of the center point at the end of the moving platform and the attitude error of the moving platform, ΔP err is the geometric error parameter term.

[0082] Based on the position error vector, the geometric error model of the parallel robot can be obtained as:

[0083] Δρ=HΔP err (9)

[0084] Where: Δρ is the position error vector, H is the identification matrix

[0085] The principal component regression algorithm is used to screen the principal components with greater influence, construct a new identification matrix and identification variables, achieve dimensionality reduction of the variable dimension and correct the ill-conditioned matrix. The principal component contribution is expressed as:

[0086]

[0087] Where: i is the principal component contribution λ of the i-th error parameter i To construct the matrix H T H eigenvalue and λ1≥λ2≥…≥λ P , p is the number of geometric error parameters, and the characteristic matrix V = [v1,…,v i ,…v p ], where v i is the eigenvector, formula (9) can be rewritten as:

[0088] Δρ=Gβ (11)

[0089] Where: G = HV, β = V T ΔP err .

[0090] Define the cumulative pivot contribution, filter the pivots, and express the first P′ pivots as:

[0091]

[0092] Where: cpc is the cumulative contribution of the first P′ principal components, and G is defined PCA =[G1,…,G P′ ],V PCA =[v1,…,v P′ ]; Therefore, formula (11) can be expressed through the first P′ pivot elements as:

[0093]

[0094] In order to improve the identification accuracy of the parallel robot, the identification matrix after principal component regression is further corrected by robust estimation. The gross error data points are suppressed by the weight matrix to control the proportion of different data points in the overall matrix. The weight matrix is ​​constructed using the improved IGG3 weight function:

[0095]

[0096] Among them: k0 and k1 are the harmonic functions that control the segment length, is the standardized residual. In the weight function, the standardized residual is divided into four sections, namely the effective information section, the front section and back section of the sub-effective information, and the harmful information section. According to the residual distribution of each iteration, the weights of the robust estimation weight matrix are updated through the weight function. When the identification accuracy meets the design requirements or the maximum number of iterations is reached, the iteration is exited.

[0097] From this, the geometric error parameters after iteration k can be derived:

[0098]

[0099] 120 points were randomly sampled in the robot workspace, and the joint angle value and the corresponding laser tracker coordinate measurement value of each sampling point were recorded for parameter identification. The position error Δρ between the theoretical point and the actual point was obtained based on the joint angle value and the corresponding laser tracker coordinate measurement value of each sampling point. The geometric error parameters were further identified based on the geometric error parameter identification matrix of step C. The difference between the theoretical position of the frozen product end and the measured point position of 60 sets of data calculated based on the nominal structural parameters of the parallel robot and the forward kinematics model was taken as the position error before identification. The structural parameters corrected by the RE-PCR identification algorithm were brought into the forward solution model to calculate the difference between the end position of the 60 sets of posture platform and the measured point position of the verification group as the position error after identification. The geometric error identification effect is shown as follows. Figure 3 shown.

Claims

1. A geometric error parameter identification method based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm, characterized in that: These include: Based on the parallel robot, the whole is split into left, middle and right closed-loop chains, and the closed-loop vector links on the left and right sides are the same; Define the coordinate system used to describe all geometric errors; After considering the geometric error sources, a closed-loop vector chain constraint equation is constructed, and the geometric error parameters are separated using the first-order perturbation, the nonlinear optimization problem is transformed into a linear optimization problem, and a linear model of the parallel robot geometric error is constructed. The geometric error parameter identification matrix is ​​obtained based on the principal component regression algorithm, and is further corrected using robust estimation. Random sampling is performed in the robot workspace to obtain the position error between the theoretical point and the actual point, and the geometric error parameters are identified based on the corrected geometric error parameter identification matrix; The coordinate system defined to describe all geometric errors is: separate the parallel structure vector closed-loop chain, and use the end point posture closed-loop chain as the final closed-loop vector chain for solution, and the remaining closed-loop chains are used as side closed loops for the final closed-loop parameter vector chain parameter solution; define the following key points and coordinate systems: {O} is the ideal fixed reference system of the frame, which is the base coordinate system of the mechanism and the closed-loop vector chain; {O P } is the moving platform coordinate system, and its attitude matrix is ​​expressed as: R O,P =Rot(z,θ+Δθ)Rot(x,Δα)Rot(y,Δβ) (1) Formula (1) represents the moving platform coordinate system {O P } is the attitude transformation relative to the base coordinate system {O}, where θ is the angle of rotation of the moving platform around the Z axis; Δθ, Δα and Δβ represent the attitude errors of the platform around the Z axis, X axis and Y axis respectively; In addition, the branch chain moving platform center system, branch chain slider coordinate system, and branch chain base coordinate system are defined separately; The closed-loop vector chain constraint equation is constructed, the first-order perturbation is used to separate the geometric error parameters, the nonlinear optimization problem is converted into a linear optimization problem, and the geometric error linear model of the parallel robot is constructed as follows: For the constructed closed-loop vector chain constraint equation, the first-order perturbation is used to offset the theoretical terms and remove the second-order infinitesimal terms to obtain the center position and attitude error matrix of the left branch chain platform. Similarly, the closed-loop vector chain constraint equation of the middle branch chain and the closed-loop vector chain constraint equation of the right branch chain are constructed to solve the center position and attitude error matrix of the middle branch chain platform and the right branch chain platform; finally, the end point position of the moving platform and attitude error It is expressed as: Among them: G1 and G2 are the error coefficient matrices after conversion, and the position error of the center point of the moving platform end and the attitude error of the moving platform are respectively given by Indicates; ΔP err is the geometric error parameter term; The constructed linear model of geometric error of parallel robot is as follows: Dr=HΔP err (3) Where: Δρ is the position error vector, H is the identification matrix, ΔP err is the geometric error parameter term; The geometric error parameter identification matrix obtained based on the principal component regression algorithm is specifically: The principal component regression algorithm is to construct a matrix H T H and solve its eigenvalues, select the principal components with greater influence, build a new identification matrix and identification variables, achieve dimension reduction of variables and correct the ill-conditioned matrix, and the principal component contribution is expressed as: Where: i is the principal component contribution of the i-th error parameter; i To construct the matrix H T H eigenvalue and λ1≥λ2≥…≥λ P , p is the number of geometric error parameters, and the characteristic matrix V = [v1,…,v i ,…v p ], where v i is the eigenvector, and formula (3) can be rewritten as: Δρ=Gβ (5) Where: G = HV, β = V T ΔP err ; Define the cumulative pivot contribution, filter the pivots, and express the first P′ pivots as: Where: cpc is the cumulative contribution of the first P′ principal components, and G is defined PCA =[G1,…,G P′ ],V PCA =[v1,…,v P′ ] Therefore, formula (5) is expressed through the first P′ pivots as: β PCA The identification matrix after cumulative iteration correction of principal components.

2. The method for geometric error parameter identification based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm according to claim 1 is characterized in that: The identification matrix after principal component regression is further corrected through robust estimation, and the gross error data points are suppressed using the weight matrix to control the proportion of different data points in the overall matrix.

3. The method for geometric error parameter identification based on closed-loop vector chain perturbation and robust estimation principal component regression algorithm according to claim 2 is characterized in that: The weight matrix is ​​constructed using an improved IGG3 weight function. According to the residual distribution of each iteration, the weights of the robust estimation weight matrix are updated through the weight function. When the identification accuracy meets the design requirements or the maximum number of iterations is reached, the iteration is exited.

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