High-dimensional spherical harmonic calibration method and system for improving robot absolute positioning accuracy

Abstract

The application discloses a high-dimensional spherical harmonic calibration method and system for improving robot absolute positioning accuracy, and belongs to the technical field of robots. The method is suitable for calibration of a robot of a rotary joint type or a robot with periodic errors, can greatly reduce periodic errors of a mechanical arm caused by deformation, axial center deviation and the like, and can complete calibration through simple linear equation solving, and is high in calculation efficiency. Specific steps include the following steps that S1, end pose residual errors and joint angles of the mechanical arm are acquired through calibration; S2, a residual error function is constructed; S3, the residual error function is fitted according to data quantity and actual requirements; and S4, error compensation is carried out based on a fitting result of the residual error function. The method calibrates the robot of the rotary joint type or the robot with the periodic errors through the high-dimensional spherical harmonic model, converts the periodic errors into simple linear equation solving, is easier to calculate, and thus greatly improves calibration accuracy and calibration efficiency.

Description

Technical Field

[0001] This disclosure relates to the field of robotics technology, and in particular to a high-dimensional spherical harmonic calibration method and system for improving the absolute positioning accuracy of robots. Background Technology

[0002] The positioning accuracy of a robot is a crucial parameter for evaluating its performance. Robot positioning accuracy generally includes absolute accuracy and repeatability (also known as theoretical positioning accuracy). Currently, rotary joint robots have high repeatability, but due to manufacturing errors, assembly errors, and component wear, they exhibit periodic errors, resulting in lower absolute positioning accuracy. To improve the absolute positioning accuracy of rotary joint robots or those with periodic errors, high-precision calibration is needed to obtain the actual and theoretical values ​​of the robot arm's end-effector pose, calculate the residuals, and then optimize and compensate for them. Existing calibration methods typically involve directly compensating for errors using the measured residuals, which involves complex equation solving and low computational efficiency. Summary of the Invention

[0003] In view of this, the present disclosure provides a high-dimensional spherical harmonic calibration method and system for improving the absolute positioning accuracy of robots, so as to at least partially solve the problems existing in the prior art.

[0004] In a first aspect, embodiments of this disclosure provide a high-dimensional spherical harmonic calibration method for improving the absolute positioning accuracy of a robot, including:

[0005] S1: Obtain the actual and theoretical values ​​of the end-effector posture of a robotic arm with a rotary joint or periodic error through calibration, and calculate the residuals and joint angles;

[0006] S2: Construct a residual function based on the end-effector posture residual and joint angles;

[0007] S3: Fit the residual function according to the amount of data and actual needs;

[0008] S4: Based on the fitted residual function, perform error compensation for the positioning of the robot's robotic arm.

[0009] According to a specific implementation of this disclosure, the step of constructing a residual function based on the end-effector posture residual and joint angles includes:

[0010] Define the residual of the robotic arm's end-effector pose as Where T represents the theoretical value of the robotic arm's end-effector pose. Represents the actual value, and log(·) represents the Lie algebra that maps the se3 Lie group to a 6-dimensional vector;

[0011] The residual of the robotic arm's end-effector pose is calculated as follows: Where ξ is a random perturbation, g is a periodic function related to the joint angle q of the robotic arm, and the period of g is 2π.

[0012] According to a specific implementation of this disclosure, fitting the residual function based on the data volume and actual requirements includes:

[0013] Assuming residual function It is a multivariate function with a period of 2π. It is the corresponding scalar field, which satisfies Where g′ m It is an m-order spherical harmonic fitting function, i.e.

[0014]

[0015] in They are pairwise orthogonal (1) The m-th order p-dimensional spherical harmonic function, α mi It is Y (m,i) The corresponding coefficients are calculated from the calibration data;

[0016] Applying an m-th order spherical harmonic fit to g, we obtain:

[0017]

[0018] The remaining residual function is:

[0019] According to a specific implementation of this disclosure, the step of fitting the residual function based on the data volume and actual requirements further includes:

[0020] For n joint angles, obtain n sets of residuals. and corresponding joint angles satisfy

[0021] Let the order m and the function be defined. satisfy

[0022]

[0023] Parameter λ (I,k) yes The corresponding coefficients are calculated from the calibration data.

[0024] According to a specific implementation of this disclosure, the step of fitting the residual function based on the data volume and actual requirements further includes:

[0025] Within a local range, when the amount of prior data n is not too large, discarding the higher-order terms of g yields a locally simple linear fitting equation.

[0026]

[0027] coefficient Calculated from calibration data:

[0028] matrix get Then the fitting function is obtained.

[0029] This method yields It requires only 2n+1 parameters, but its accuracy is relatively lower compared to spherical harmonic fitting and Fourier fitting.

[0030] According to a specific implementation of this disclosure, the error compensation for the positioning of the robot's robotic arm based on the fitted residual function includes:

[0031] The obtained residual function or For any set of theoretical values ​​T for the joint angle q and end-effector pose of the robotic arm, a new theoretical value with small error is obtained. or

[0032] According to a specific implementation of an embodiment of this disclosure, the method further includes:

[0033] For multivariate functions with a period of 2π It is an arbitrary scalar field, and its spherical harmonic series decomposition is g′ m It is an m-order spherical harmonic fitting function;

[0034] For any order m, the function g′ m satisfy:

[0035]

[0036] Where N(p,0)=1, Y0≡1, when m≥1 They are pairwise orthogonal (1) m-order p-dimensional spherical harmonics, orthogonalized using Gram-Schmidt. (2) Generate; α mi It is Y (m,i) Corresponding coefficients;

[0037]

[0038]

[0039] According to a specific implementation of an embodiment of this disclosure, the method further includes:

[0040] Will Represented as:

[0041]

[0042] Let the parameter matrix [λ] be... (I,k) Let ] = Λ, and let the matrix be Λ. have

[0043]

[0044] In order to make To reach the minimum, we obtain

[0045] Finally, the fitting function is obtained.

[0046] According to a specific implementation of an embodiment of this disclosure, the method further includes:

[0047] For a 7-axis robotic arm, the domain of its residual function is isomorphic to a unit sphere S7 embedded in 8-dimensional space, and the spherical harmonic fitting functions of order 1 to m are: The parameters, the order of fit, and the amount of data (m, n) satisfy the following conditions:

[0048] Represented as:

[0049] g′ m (q)=[Y (m,i) ] T [α mi ]

[0050] get:

[0051]

[0052] Secondly, embodiments of this disclosure provide a high-dimensional spherical harmonic calibration system for improving the absolute positioning accuracy of a robot, comprising:

[0053] A multi-axis robotic arm, wherein the multi-axis robotic arm is a rotary joint type or a robotic arm with periodic errors, has multiple robotic arm joint angles q, and a theoretical value T for the end-effector pose;

[0054] A camera, fixed in space outside the robotic arm, maintains its pose relative to the world coordinate system and is used for high-precision calibration to detect the actual pose of the robotic arm's end effector.

[0055] Computer: Connected to a multi-axis robotic arm and a camera, it calculates the residual of the robotic arm end-effector pose based on the joint angles of the robotic arm measured by the robotic arm, the theoretical value of the robotic arm end-effector pose, and the actual value of the robotic arm end-effector pose measured by the camera. It then compensates for the residual using a high-dimensional spherical harmonic calibration method, thereby improving the absolute positioning accuracy of the robot using the high-dimensional spherical harmonic calibration method in any of the aforementioned aspects or the first aspect.

[0056] Thirdly, embodiments of this disclosure also provide a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the high-dimensional spherical harmonic calibration method for improving the absolute positioning accuracy of a robot in the first aspect or any implementation thereof.

[0057] Fourthly, embodiments of this disclosure also provide a computer program product, which includes a computing program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, cause the computer to perform the high-dimensional spherical harmonic calibration method for improving the absolute positioning accuracy of a robot as described in the first aspect or any implementation thereof.

[0058] The high-dimensional spherical harmonic calibration scheme for improving the absolute positioning accuracy of a robot, as disclosed in this embodiment, includes: S1: obtaining the actual and theoretical values ​​of the end-effector posture of a robotic arm with a rotational joint or periodic error through calibration, and calculating the residuals and joint angles; S2: constructing a residual function based on the residuals of the end-effector posture and joint angles; S3: fitting the residual function according to the amount of data and actual requirements; S4: performing error compensation for the positioning of the robot's robotic arm based on the fitted residual function. This invention calibrates the absolute positioning accuracy of a robot through spherical harmonic / Fourier series fitting, which can significantly reduce repeatable periodic errors and achieve high calibration accuracy. The calculation method used in this invention compresses all calculations into a single large matrix operation, thus fully utilizing computer computing resources through parallel computing and significantly improving computational efficiency. Attached Figure Description

[0059] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 A schematic diagram of the system composition provided in the embodiments of this disclosure;

[0061] Figure 2This is a schematic diagram of system calibration provided for an embodiment of the present disclosure;

[0062] Figure 3 A flowchart of a high-dimensional spherical harmonic calibration method for robot absolute positioning accuracy provided in this embodiment of the disclosure;

[0063] Figure 4 This is a schematic diagram of the residual primitive function provided in an embodiment of the present disclosure;

[0064] Figure 5 A schematic diagram of a 1D 0th-order spherical harmonic function provided in an embodiment of this disclosure;

[0065] Figure 6 A schematic diagram of a 1D first-order spherical harmonic function provided in an embodiment of this disclosure;

[0066] Figure 7 A schematic diagram of a 1D second-order spherical harmonic function provided in an embodiment of this disclosure. Detailed Implementation

[0067] See Figure 1 , Figure 2 and Figure 3 The present invention discloses a high-dimensional spherical harmonic calibration method for improving the absolute positioning accuracy of a robot, comprising the following steps:

[0068] S1: Obtain the actual and theoretical values ​​of the end-effector posture of a robotic arm with a rotary joint or periodic error through calibration, and calculate the residuals and joint angles;

[0069] S2: Construct a residual function based on the end-effector posture residual and joint angles;

[0070] S3: Fit the residual function according to the amount of data and actual needs;

[0071] S4: Based on the fitted residual function, perform error compensation for the positioning of the robot's robotic arm.

[0072] Specifically, the systems used in high-dimensional spherical harmonic calibration methods to improve the absolute positioning accuracy of robots include:

[0073] 1. Multi-axis robotic arm: High-performance multi-axis robotic arm, wherein the multi-axis robotic arm is a rotary joint type or a robotic arm with periodic errors, used for calculation and control processing, where q represents the joint angle of the robotic arm and T represents the theoretical value of the end-effector pose of the robotic arm;

[0074] 2. Camera: Fixed in space outside the robotic arm body, the camera's pose remains unchanged relative to the world coordinate system. It is used for high-precision calibration to detect the actual value of the robotic arm's end effector pose.

[0075] 3. Computer: Connected to the robotic arm and camera, it can calculate the residual of the robotic arm's end-effector pose based on the joint angles of the robotic arm measured by the robotic arm, the theoretical value of the robotic arm's end-effector pose, and the actual value of the robotic arm's end-effector pose measured by the camera, and compensate for the residual through a high-dimensional spherical harmonic calibration method.

[0076] System calibration

[0077] Due to manufacturing errors, assembly errors, and component wear, rotary joint robots generally exhibit periodic errors, resulting in low absolute positioning accuracy. To improve the absolute positioning accuracy of rotary joint robots or robots with periodic errors, this invention divides the residual of the robot arm's end-effector pose into a periodic function and a random perturbation. The periodic error is then fitted as a multidimensional, multi-order spherical harmonic function, and compensation is applied to address the periodic error. After fitting and compensation, only the random perturbation component remains in the robot arm's end-effector pose error, thus significantly improving absolute positioning accuracy. Compared to existing technologies, the advantages of this invention are:

[0078] 1) Its decomposed basis functions are more in line with the actual motion of robots with rotary joints or periodic errors. It can periodically compensate for the residual of the end pose of the robotic arm, thus greatly reducing repeatable periodic errors. It is especially suitable for robots with rotary joints or robots with periodic errors, eccentricity, and gear backlash errors.

[0079] 2) The fitting method can be adaptively adjusted according to the amount of data and the application environment to achieve better calculation accuracy and efficiency, making data solving more convenient and calculation more efficient.

[0080] 3) It can be used for online and offline calibration. This invention compresses all calculations into a single large matrix operation and completes the calibration by solving a simple linear equation, which is easier to calculate. Therefore, it can make full use of the computer's computing resources through parallel computing, resulting in higher computational efficiency and significant application value.

[0081] Taking a 1D spherical harmonic function as an example, the relationship between the residuals before and after system calibration and the spherical harmonic function is as follows:

[0082] (1) When decomposing the residual function based on the 1D 0th order spherical harmonic function:

[0083] r=α0Y0+r0

[0084] (2) r0 can be further decomposed into a first-order signal, resulting in a smaller error. The expression for the residual function after decomposition is as follows:

[0085] r=α0Y0+α 1,1 Y 1,1 +α 1,2 Y 1,2+r1

[0086] (3) Similarly, the first-order signal can be further decomposed. After second-order decomposition, the residual function expression is as follows:

[0087] r=α0Y0+α 1,1 Y 1,1 +α 1,2 Y 1,2 +α 2,1 Y 2,1 +α 2,2 Y 2,2 +r2

[0088] (4) The higher the decomposition order, the smaller the residual after calibration:

[0089] r>r0>r1>r2

[0090] In the formula: r represents the residual primitive function ( Figure 2 Left 1); r k Represents the residual function after fitting compensation ( Figure 2 Right 1); Y represents the spherical harmonic functions of each order; α represents the coefficients of the spherical harmonic functions of each order, which are calculated from the calibration data.

[0091] See Figure 3 The solution provided by this invention is: (1) Detecting the residual of the end-effector pose using a camera to obtain the original residual function. Figure 2 Left 1 represents the residual function of the end-effector pose before calibration; (2) The residual function is fitted by a spherical harmonic function, the order of which can be selected according to the amount of data and accuracy requirements. Figure 2 Left 2 represents a simple example of a 1D 0-2 order spherical harmonic function; (3) Compensate the original residual function according to the fitting result, that is, subtract the multi-order spherical harmonic function from the pose error function at the end of the robotic arm to obtain a more accurate residual function. Figure 2 The rightmost curve represents the residual of the robotic arm's end-effector pose after calibration. The three curves represent the residuals after 1st, 2nd, and 3rd order 1D spherical harmonic fitting compensation, respectively. The higher the order, the smaller the residual after calibration.

[0092] High-dimensional high-order spherical harmonic calibration method

[0093] The purpose of this invention is to provide a high-dimensional spherical harmonic calibration method for improving the absolute positioning accuracy of robots, aiming to solve the problems of low accuracy and low computational efficiency in existing robot calibration methods. To achieve the above objective, this invention provides a high-dimensional spherical harmonic calibration method, comprising the following steps:

[0094] S1: Obtain the residual of the end-effector pose and the corresponding joint angle of the robotic arm through high-precision calibration.

[0095] S2: Based on the residuals of the robot arm's end-effector pose and joint angles, establish a residual function. Taking a 7-axis robot arm as an example, after high-precision calibration, the residuals of the robot arm's end-effector pose are... Where T represents the theoretical value of the robotic arm's end-effector pose. represents the actual value, and log(·) represents the Lie algebra that maps the se3 Lie group to a 6-dimensional vector.

[0096] Assuming the residual of the robotic arm's end effector pose Where ξ is a random perturbation, and g is a periodic function related to the joint angle q of the robotic arm. Therefore, the period of g is 2π and...

[0097] S3: Select spherical harmonic fitting or local simple linear fitting for the residual function based on the amount of data and actual needs; S3 specifically includes:

[0098] S3-1: Based on the residuals and joint angles obtained in S1, perform spherical harmonic fitting on the residual function established in S2, assuming the residual function... It is a multivariate function with a period of 2π. It is the corresponding scalar field. It satisfies... Where g′ m It is an m-order spherical harmonic fitting function, i.e.

[0099]

[0100] in They are pairwise orthogonal (1) The m-th order p-dimensional spherical harmonic function, α mi It is Y (m,i) The corresponding coefficients are calculated from the calibration data.

[0101] Therefore, by performing an m-order spherical harmonic fit on g, we can obtain...

[0102]

[0103] The remaining residual function is

[0104]

[0105] S3-2: If there is a large amount of residual data or high accuracy is required, perform Fourier fitting on the residual function established in S2 based on the residuals and joint angles obtained in S1.

[0106] Assume there are n joint angles, and n sets of residuals are obtained. and corresponding joint angles satisfy

[0107] To obtain an approximation of g, we define an order m and a function... satisfy

[0108]

[0109] When (n,m)=(2,2),

[0110]

[0111] There are 25 parameters in total.

[0112] Parameter λ (I,k) yes The corresponding coefficients are calculated from the calibration data.

[0113] Since the above equation has (2m+1) n There are several parameters, (n, m, n), which need to satisfy (2m+1). n < <n。

[0114] S3-3: If the residual data is small and the accuracy requirement is not high, perform a simple linear fit on the residual function established by S2 within a local range based on the residuals and joint angles obtained by S1.

[0115] When the amount of residual data is limited, higher-order terms of the residual function can be discarded locally, allowing the residual function to be established with a smaller amount of data. This residual compensation can then improve the robot's positioning accuracy. Locally, when the amount of prior data n is not large, higher-order terms of g need to be discarded to obtain a locally simple linear fitting equation.

[0116]

[0117] coefficient Calculated from calibration data:

[0118] Let matrix Then we can get Then the fitting function is obtained.

[0119] This method yields It only requires 2n+1 parameters, but its accuracy is relatively lower than that of spherical harmonic fitting and Fourier fitting.

[0120] S4: Perform error compensation based on the residual function fitting results.

[0121] Furthermore, S4 specifically includes:

[0122] S4: Apply the residual function fitted by S3 to the newly acquired theoretical value to perform residual compensation.

[0123] The residual function obtained from step S3 or For any set of theoretical values ​​T for the joint angle q and end-effector pose of the robotic arm, a new theoretical value with smaller error can be obtained. or

[0124] Multivariable spherical harmonic series Suppose there is a multivariate function with a period of 2π. It is an arbitrary scalar field. Its spherical harmonic series decomposition is:

[0125] g, has Where g′ m It is an m-order spherical harmonic fitting function

[0126] For any order m, the function g′ m satisfy

[0127]

[0128] Where N(p,0)=1, Y0≡1. When m≥1... They are pairwise orthogonal (1) The m-th order p-dimensional spherical harmonics can be orthogonalized using Gram-Schmidt. (2) Generate; α mi It is Y (m,i) Corresponding coefficients;

[0129]

[0130]

[0131] Multivariate Fourier series

[0132] Suppose there is a multivariate function with a period of 2π. It is an arbitrary scalar field. Its Fourier series decomposition is:

[0133]

[0134] in It is a parameter related to g.

[0135] In particular, when When, the Fourier decomposition of this function can be written as

[0136]

[0137] ,in

[0138]

[0139] robotic arm residual function

[0140] See Figure 4 , Figure 5 , Figure 6 and Figure 7 Taking a 7-axis robotic arm as an example, after high-precision calibration, the residual position of the robotic arm's end effector... Where T represents the theoretical value of the robotic arm's end-effector pose. Represents the actual value, and log(·) is the Lie algebra that maps the se3 Lie group to a 6-dimensional vector.

[0141] Assumption

[0142] r=g(q)+ξ

[0143] Where ξ is a random perturbation, and g is a periodic function related to the joint angle q of the robotic arm. Therefore, the period of g is 2π and...

[0144] Spherical harmonic (Fourier series) fitting of residual functions

[0145] Assume that n sets of residuals are obtained and corresponding joint angles satisfy For any function g, we have Where g′ m The m-th order spherical harmonic fitting function is the function g′ for any order m. m satisfy By performing an m-th order spherical harmonic fitting on g, we can obtain...

[0146]

[0147] The residual function is

[0148]

[0149] Generally speaking, second- to third-order spherical harmonic fitting is sufficient to make the residual function very small.

[0150] Obtaining the parameter α

[0151] For a 7-axis robotic arm, the domain of its residual function is isomorphic to a unit sphere S7 embedded in 8-dimensional space, and the spherical harmonic fitting functions of order 1 to m are: There are several parameters, so the order of fit and the amount of data (m,n) need to satisfy... on the other hand, It can also be written as

[0152] g′ m (q)=[Y (m,i) ] T [α mi]

[0153] It can be obtained

[0154] Fourier fitting

[0155] Approximate function of g satisfy

[0156]

[0157] Since the above equation has (2m+1) 7 There are several parameters, (m, n), which need to satisfy (2m+1). 7 < <n。

[0158] on the other hand, It can also be written as

[0159]

[0160] Let the parameter matrix [λ] be... (I,k) Let ] = Λ, and let the matrix be Λ. have

[0161]

[0162] In order to make To reach the minimum, one can obtain

[0163] In summary, the fitting function was obtained.

[0164] Comparison of spherical harmonic fitting and Fourier fitting

[0165] Spherical harmonic fitting requires fewer parameters and less data than Fourier fitting, resulting in lower demands on storage and computation. However, high-dimensional spherical harmonic functions are inherently more complex. First-order Fourier fitting encompasses all linear operations on cos(q) and sin(q), and the fitted function can perfectly cover the computational errors of forward kinematics (and may even replace it), but it has a large number of parameters and requires a significant amount of data.

[0166] Residual compensation

[0167] Based on the preceding text, the residual function has already been obtained. For any set of theoretical values ​​T for the joint angle q and end-effector pose of the robotic arm, a new theoretical value with smaller error can be obtained.

[0168] Local area Simple Linear fitting

[0169] Within a local range, when the amount of prior data n is insufficient, the higher-order terms of g need to be discarded to obtain a locally simple linear fitting equation.

[0170]

[0171] remember Let matrix

[0172] Then we can get Then the fitting function is obtained.

[0173] This method yields It only requires 15 parameters, but its accuracy is relatively lower than that of spherical harmonic fitting and Fourier fitting.

[0174] (1) Orthogonal:

[0175] If unit vector set obey

[0176] in

[0177]

[0178] Then it is called Orthogonal pairs

[0179] For example, when m = 1

[0180]

[0181] The above conditions are met.

[0182] (2) Gram-Schmidt orthogonalization:

[0183] First in S p-1 Take any set of linearly independent m-th harmonic monomials

[0184] make

[0185]

[0186]

[0187]

[0188]

[0189]

[0190] but Two orthogonal pairs.

[0191] According to a specific implementation of this disclosure, the step of constructing a residual function based on the end-effector posture residual and joint angles includes:

[0192] Define the residual of the robotic arm's end-effector pose as Where T represents the theoretical value of the robotic arm's end-effector pose. Represents the actual value, and log(·) represents the Lie algebra that maps the se3 Lie group to a 6-dimensional vector;

[0193] The residual of the robotic arm's end-effector pose is calculated as follows: Where ξ is a random perturbation, g is a periodic function related to the joint angle q of the robotic arm, and the period of g is 2π.

[0194] According to a specific implementation of this disclosure, fitting the residual function based on the data volume and actual requirements includes:

[0195] Assuming residual function It is a multivariate function with a period of 2π. It is the corresponding scalar field, which satisfies Where g′ m It is an m-order spherical harmonic fitting function, i.e.

[0196]

[0197] in They are pairwise orthogonal (1) The m-th order p-dimensional spherical harmonic function, α mi It is Y (m,i) The corresponding coefficients are calculated from the calibration data;

[0198] Performing an m-th order spherical harmonic fit on g, we obtain:

[0199]

[0200] The remaining residual function is:

[0201] According to a specific implementation of this disclosure, the step of fitting the residual function based on the data volume and actual requirements further includes:

[0202] For n joint angles, obtain n sets of residuals. and corresponding joint angles satisfy

[0203] Let the order m and the function be defined. satisfy

[0204]

[0205] Parameter λ (I,k) yes The corresponding coefficients are calculated from the calibration data.

[0206] According to a specific implementation of this disclosure, the step of fitting the residual function based on the data volume and actual requirements further includes:

[0207] Within a local range, when the amount of prior data n is not too large, discarding the higher-order terms of g yields a locally linear fitting equation.

[0208]

[0209] coefficient Calculated from calibration data:

[0210] matrix get Then the fitting function is obtained.

[0211] This method yields It requires only 2n+1 parameters, but its accuracy is relatively lower compared to spherical harmonic fitting and Fourier fitting.

[0212] According to a specific implementation of this disclosure, the error compensation for the positioning of the robot's robotic arm based on the fitted residual function includes:

[0213] The obtained residual function or For any set of theoretical values ​​T for the joint angle q and end-effector pose of the robotic arm, a new theoretical value with small error is obtained. or

[0214] According to a specific implementation of an embodiment of this disclosure, the method further includes:

[0215] For multivariate functions with a period of 2π It is an arbitrary scalar field, and its spherical harmonic series decomposition is g′ m It is an m-order spherical harmonic fitting function;

[0216] For any order m, the function g′ m satisfy:

[0217]

[0218] Where N(p,0)=1, Y0≡1, when m≥1 They are pairwise orthogonal (1)m-order p-dimensional spherical harmonics, orthogonalized using Gram-Schmidt. (2) Generate; α mi It is Y (m,i) Corresponding coefficients;

[0219]

[0220]

[0221] According to a specific implementation of an embodiment of this disclosure, the method further includes:

[0222] Will Represented as:

[0223]

[0224] Let the parameter matrix [λ] be... (I,k) Let ] = Λ, and let the matrix be Λ. have

[0225]

[0226] In order to make To reach the minimum, we obtain

[0227] Finally, the fitting function is obtained.

[0228] According to a specific implementation of an embodiment of this disclosure, the method further includes:

[0229] For a 7-axis robotic arm, the domain of its residual function is isomorphic to a unit sphere S7 embedded in 8-dimensional space, and the spherical harmonic fitting functions of order 1 to m are: The parameters, the order of fit, and the amount of data (m, n) satisfy the following conditions:

[0230] Represented as:

[0231] g′ m (q)=[Y (m,i) ] T [α mi ]

[0232] get:

[0233]

[0234] Corresponding to the above method embodiments, the present invention also provides a high-dimensional spherical harmonic calibration system for improving the absolute positioning accuracy of a robot, comprising:

[0235] A multi-axis robotic arm, wherein the multi-axis robotic arm is a rotary joint type or a robotic arm with periodic errors, has multiple robotic arm joint angles q, and a theoretical value T for the end-effector pose;

[0236] A camera, fixed in space outside the robotic arm, maintains its pose relative to the world coordinate system and is used for high-precision calibration to detect the actual pose of the robotic arm's end effector.

[0237] Computer: Connected to a multi-axis robotic arm and a camera, it calculates the residual of the robotic arm's end-effector pose based on the joint angles of the robotic arm measured by the robotic arm, the theoretical value of the end-effector pose, and the actual value of the end-effector pose measured by the camera. The residual is then compensated using a high-dimensional spherical harmonic calibration method, thereby implementing the method described in the aforementioned embodiments.

[0238] The above description is merely a specific embodiment of this disclosure, but the scope of protection of this disclosure is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this disclosure should be included within the scope of protection of this disclosure. Therefore, the scope of protection of this disclosure should be determined by the scope of the claims.

Claims

1. A high-dimensional spherical harmonic calibration method for improving the absolute positioning accuracy of robots, characterized in that, include: S1: Obtain the actual and theoretical values ​​of the end-effector posture of a robotic arm with a rotary joint or periodic error through calibration, and calculate the residuals and joint angles; S2: Construct a residual function based on the end-effector posture residual and joint angles; S3: Fit the residual function according to the amount of data and actual needs; S4: Based on the fitted residual function, perform error compensation for the positioning of the robot's robotic arm; in The process of constructing a residual function based on the end-effector posture residual and joint angles includes: Define the residual of the robotic arm's end-effector pose as Where T represents the theoretical value of the robotic arm's end-effector pose. Indicates the actual value. Indicates to Lie algebra of Lie groups mapped to 6-dimensional vectors; The residual of the robotic arm's end-effector pose is calculated as follows: Where ξ is a random perturbation, and g is a periodic function related to the joint angle q of the robotic arm, with a period of . ,and ; The fitting of the residual function based on the amount of data and actual needs includes: Assuming residual function It is in a cycle multivariate functions, It is the corresponding scalar field, which satisfies ,in It is an m-order spherical harmonic fitting function, i.e. in They are pairwise orthogonal (1) The m-th order p-dimensional spherical harmonic function, yes The corresponding coefficients are calculated from the calibration data; Applying an m-th order spherical harmonic fit to g, we obtain: The remaining residual function is: ; For n joint angles, obtain n sets of residuals. and corresponding joint angles ,satisfy Let the order m and the function be defined. satisfy parameter yes The corresponding coefficients are calculated from the calibration data.

2. The method according to claim 1, characterized in that, The fitting of the residual function based on the data volume and actual needs further includes: Within a local range, when the amount of prior data n is not too large, discarding the higher-order terms of g yields a locally simple linear fitting equation. coefficient Calculated from calibration data: matrix get Thus, the fitting function is obtained. ; This method yields It only requires 2n+1 parameters, but its accuracy is relatively lower than that of spherical harmonic fitting and Fourier fitting.

3. The method according to claim 2, characterized in that, The error compensation for the positioning of the robot's robotic arm based on the fitted residual function includes: The obtained residual function or For any set of theoretical values ​​T for the joint angle q and end-effector pose of the robotic arm, a new theoretical value with small error is obtained. .

4. The method according to claim 3, characterized in that, The method further includes: For the period is multivariate functions , It is an arbitrary scalar field, and its spherical harmonic series decomposition is , It is an m-order spherical harmonic fitting function; For any order m, the function satisfy: in ,when hour, They are pairwise orthogonal (1) m-order p-dimensional spherical harmonics, orthogonalized using Gram-Schmidt. (2) generate; yes Corresponding coefficients; 。 5. The method according to claim 3, characterized in that, The method further includes: Will Represented as: Let the parameter matrix be... Let matrix ,have In order to make To reach the minimum, we obtain ; Finally, the fitting function is obtained. .

6. The method according to claim 3, characterized in that, The method further includes: For a 7-axis robotic arm, the domain of its residual function is isomorphic to a unit sphere embedded in 8-dimensional space. , The spherical harmonic fitting function of order 1 has The parameters, the order of fit, and the amount of data (m, n) satisfy the following conditions: ; Represented as: get: 。 7. A high-dimensional spherical harmonic calibration system for improving the absolute positioning accuracy of a robot, characterized in that, include: A multi-axis robotic arm, wherein the multi-axis robotic arm is a rotary joint type or a robotic arm with periodic errors, has multiple robotic arm joint angles q, and a theoretical value T for the end-effector pose; A camera, fixed in space outside the robotic arm, maintains its pose relative to the world coordinate system and is used for high-precision calibration to detect the actual pose of the robotic arm's end effector. ; Computer: Connected to a multi-axis robotic arm and a camera, the computer calculates the residual of the robotic arm end-effector pose based on the joint angles of the robotic arm measured by the robotic arm, the theoretical value of the robotic arm end-effector pose, and the actual value of the robotic arm end-effector pose measured by the camera, and compensates for the residual using a high-dimensional spherical harmonic calibration method, thereby realizing the method described in any one of claims 1-6.

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