Customized redundant degree-of-freedom robot calibration method and system based on function approximation

Abstract

The invention provides a customized redundant degree-of-freedom robot calibration method and system based on function approximation. The method comprises the following steps: acquiring planned pose data of a robot; obtaining an estimated value of a position error according to the obtained planning pose data and a preset estimator; position revision is carried out according to the estimated value of the position error, and a robot planning instruction is obtained to calibrate the robot; wherein the learning process of the preset estimator is as follows: regarding the position error as a nonlinear function of the planning pose data to obtain an error function; performing approximation on the error function by using a tensor ring network, and obtaining an estimator through sampling and learning; according to the method, a tensor ring network machine learning tool is applied to a precision calibration task of the robot, robot positioning error estimation is realized by learning a complex function relationship between a planned pose and position deviation, explicit derivation of a kinematics model and an error model of the robot is not needed, and geometric and non-geometric error sources can be considered at the same time.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot calibration, and in particular relates to a customized redundant degree of freedom robot calibration method and system based on function approximation. Background Art

[0002] Industrial robots are an important cornerstone of intelligent manufacturing. In the construction of intelligent factories in large-scale high-precision manufacturing fields such as pipeline prefabrication, pressure vessels and building structures, there are a series of unconventional manufacturing tasks that traditional industrial robots are unable to handle due to many negative factors such as large pipeline size, complex workpiece shape, precise processing granularity, harsh molding process and harsh working environment. For this reason, it is often necessary to carry out secondary transformation of traditional industrial robots (such as series connection, parallel connection, etc.) to obtain customized redundant degree of freedom robots to meet the high standards of robot accessibility, efficiency, accuracy and robustness for unconventional tasks. First and foremost, positioning accuracy has become a key technical bottleneck that restricts the actual performance improvement of customized robots.

[0003] In principle, the robot motion control system explicitly calculates the position and posture of the tool center point through a kinematic model with connecting rod size and joint angle as main parameters. However, due to factors such as part manufacturing errors, assembly errors, transmission errors and joint wear, there is a deviation between the default kinematic parameters and their actual values. This deviation will be transmitted to the position and posture calculation results of the tool center, resulting in (absolute) positioning errors. In order to improve the absolute positioning accuracy of customized robots, we can start from both hardware and software perspectives. The former requires higher-precision processing instruments and assembly technologies, which are often expensive and cannot solve the problem of reduced accuracy due to wear and deformation. The latter uses high-precision measurement tools and carefully designed algorithms to calibrate (identify and correct) positioning errors. It has lower hardware costs than the first method and can more effectively compensate for the accuracy degradation caused by wear or structural deformation.

[0004] In response to the problem of precision calibration, Knasinski et al. found in 1990 that the absolute positioning error is mainly caused by the error of the robot kinematic model parameters; therefore, the research and development of robot calibration technology mainly focuses on the error identification and compensation of kinematic parameters. In most cases, there are four basic steps for parameter calibration: first, establish a kinematic model with connecting rod size and joint angle as the main parameters to describe the relationship from joint space to actuator space; second, measure the actual position of the robot by high-precision measuring equipment; then, derive the error model based on the kinematic model, and use the deviation between the measured and theoretical positions for parameter identification; finally, compensate the identified parameter deviation to the robot motion control system to correct the positioning error.

[0005] However, the inventors have found that for common customized redundant DOF robots, the above-mentioned error identification and compensation based on kinematic parameters has the following disadvantages: since most redundant robots are customized and modified from standard six-axis robots, in the absence of full cooperation from robot manufacturers, the openness of their motion control systems is relatively low, and it is often necessary to guess the complex configuration parameters of each motion structure in the configuration file (such as the position of the coordinate system origin, the direction of the coordinate axis, the direction of the angle, etc.). This process is extremely error-prone and has a high trial and error cost; since redundant robots need to identify a large number of kinematic parameters, their error models are often very complex, and the design and implementation of parameter deviation identification algorithms are difficult and computationally complex; in the absence of authorization from the robot manufacturer, the identified parameter deviations are difficult to accurately correct to the configuration file, and the trial and error cost is high, and safety accidents are prone to occur; positioning errors caused by non-geometric error sources (such as joint flexibility errors caused by their own weight and load, clearances and thermal effects of gear transmissions, etc.) are not considered. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a customized redundant degree of freedom robot calibration method and system based on function approximation. The present invention applies the tensor ring network machine learning tool to the accuracy calibration task of the robot (especially the customized redundant degree of freedom robot), and realizes the robot positioning error estimation by learning the complex functional relationship between the planned posture and position deviation. There is no need to explicitly derive the robot's kinematic model and error model, and both geometric and non-geometric error sources can be taken into account at the same time.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions:

[0008] In a first aspect, the present invention provides a customized redundant degree of freedom robot calibration method based on function approximation, comprising:

[0009] Obtain the robot's planned posture data;

[0010] According to the acquired planning posture data and the preset estimator, an estimated value of the position error is obtained;

[0011] The position is revised according to the estimated value of the position error, and the robot planning instruction is obtained to calibrate the robot;

[0012] Among them, the learning process of the preset estimator is: regard the position error as a nonlinear function of the planning posture data to obtain the error function; use the tensor ring network to approximate the error function, and obtain the estimator through sampling and learning.

[0013] Furthermore, the planning posture data includes posture angle information and position information.

[0014] Furthermore, when the error function is approximated using a tensor ring network, a low-rank approximation is performed on the coefficient tensor, including: providing a core tensor according to the number of elements in the coefficient tensor, wherein the core tensor is a third-order core tensor; introducing a tensor tube nuclear norm as a low-rank regularization term for each third-order core tensor, and minimizing the tensor tube nuclear norm to induce a low-rank structure of the third-order core tensor.

[0015] Furthermore, the estimation model of the core tensor is:

[0016]

[0017] in, and represents the core tensor; ∑ cyc (·) represents the rotation sum with x, y, and z as the summation index; λ represents the regularization parameter; ‖·‖ ＊ As a low-rank regularization term; Δ x =(Δx1, Δx2, ..., Δx N ) T The actual error component in the x direction in N measurements is recorded, vector; h x =(h x，1 ,h x，2 ,…,h x，N ) T represents the approximation error component based on the tensor ring representation; where for any k = 1, 2, …, N.

[0018] Furthermore, the estimation model of the core tensor is solved using an alternating direction multiplier method.

[0019] Furthermore, the components of the nonlinear function are approximated respectively according to the three directions in the coordinate system.

[0020] Furthermore, spline curves are selected as basis functions in the tensor ring network.

[0021] In a second aspect, the present invention further provides a customized redundant degree of freedom robot calibration system based on function approximation, comprising:

[0022] The data acquisition module is configured to: obtain the planning posture data of the robot;

[0023] The estimation module is configured to: obtain an estimated value of the position error based on the acquired planning posture data and a preset estimator;

[0024] The calibration module is configured to: revise the position according to the estimated value of the position error, obtain the robot planning instruction and calibrate the robot;

[0025] Among them, the learning process of the preset estimator is: regard the position error as a nonlinear function of the planning posture data to obtain the error function; use the tensor ring network to approximate the error function, and obtain the estimator through sampling and learning.

[0026] In a third aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the customized redundant degree of freedom robot calibration method based on function approximation described in the first aspect.

[0027] In a fourth aspect, the present invention further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the customized redundant degree of freedom robot calibration method based on function approximation described in the first aspect are implemented.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. The present invention regards the position error as a nonlinear function of the planning posture data to obtain the error function; uses a tensor ring network to approximate the error function, and obtains an estimator for position error estimation through sampling and learning; applies the tensor ring network machine learning tool to the precision calibration task of the robot (especially the customized redundant degree of freedom robot), and realizes the robot positioning error estimation by learning the complex functional relationship between the planning posture and the position deviation, which does not require the explicit derivation of the robot's kinematic model and error model, and can take into account both geometric and non-geometric error sources.

[0030] 2. In the present invention, the attitude angle information is used as auxiliary information for error estimation, thereby improving the accuracy of the estimated error vector;

[0031] 3. In order to solve the problem of heavy parameter adjustment workload caused by manually selecting the tensor TR rank parameter, the present invention introduces the tensor tube nuclear norm as a low-rank regularization term for each third-order core tensor. Minimizing the tube nuclear norm will lead to a low-tube rank structure, that is, most of the diagonal tubes in the tensor singular value decomposition are 0, thereby effectively limiting the complexity of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings in the specification that constitute a part of this embodiment are used to provide a further understanding of this embodiment. The schematic embodiments of this embodiment and their descriptions are used to explain this embodiment and do not constitute improper limitations on this embodiment.

[0033] Figure 1 This is a schematic diagram of Embodiment 1 of the present invention;

[0034] Figure 2 Schematic diagram of a tensor ring network according to Embodiment 1 of the present invention;

[0035] Figure 3 Schematic diagram of the low-tube-rank structure of the core tensor of Example 1 of the present invention. DETAILED DESCRIPTION

[0036] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0037] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0038] Embodiment 1:

[0039] This embodiment provides a customized redundant degree of freedom robot calibration method based on function approximation, including: obtaining the robot's planned posture data; obtaining an estimated value of the position error based on the obtained planned posture data and a preset estimator; revising the position according to the estimated value of the position error, obtaining the robot planning instruction to calibrate the robot; wherein, the learning process of the preset estimator is: treating the position error as a nonlinear function of the planned posture data to obtain the error function; using a tensor ring network to approximate the error function, and obtaining the estimator through sampling and learning. The principle of the method of the present invention is to use a tensor ring network to approximate the complex functional relationship between the robot's theoretical posture and the actual positioning error, thereby predicting the positioning error and compensating it; it is of great significance in improving the absolute positioning accuracy of the robot and expanding the application scope of the redundant degree of freedom robot; the specific implementation process is:

[0040] Assume that you want the robot end to move to a known "planned position" P = (x, y, z) T However, due to the complex errors in the application scenario, the robot end will actually move to the "execution position" P * =(x * ,y * , z * ) T (Here, we ignore the influence of the error on the attitude angles (a, b, c). In most application scenarios, it is not possible to use real-time online measurement tools, and thus it is impossible to accurately measure the execution position P. * However, in many high-precision robot tasks, it is hoped that the final execution position of the robot end is as close to the planned position P as possible. To this end, one solution is to first estimate the position error PP * Estimation is performed to obtain the estimated positioning error ΔP≈PP * , and then use the estimated value as the position offset to revise the robot planning command, so as to achieve the robot precision calibration; at this time, the problem emerges: due to the actual execution position P *is unknown, how to establish an estimate of the position error ΔP?

[0041] In order to estimate the error vector ΔP more accurately, this implementation considers the attitude angle information as auxiliary information for error estimation. Assuming the preset attitude angle is (a, b, c), then consider using the planned posture data P * =(x, y, z, a, b, c) T Instead of the planned position P = (x, y, z) T Make an error estimate.

[0042] According to the idea of ​​machine learning, the position error ΔP is regarded as the planning posture P * The nonlinear function ΔP=F * (P * ), and select the function approximator F(·) to approximate the error function F * (·) approximate F(P * )≈F * (P * ), and then through sampling, learn the estimator of the function F(·) Compared with classical function approximators such as polynomial functions, wavelet functions and neural networks, the newly proposed tensor network exhibits nearly optimal nonlinear approximation capabilities. Therefore, this embodiment uses a new type of tensor network, a tensor ring network, as a function approximator to learn the estimated error ΔP.

[0043] In this embodiment, the position error ΔP=(Δx, Δy, Δz) T Considered as the planning pose P * = unknown nonlinear function F of (x, y, z, a, b, c) * :

[0044]

[0045] In this embodiment, the function F(p * ) for the nonlinear function F * (P * ) to approximate:

[0046]

[0047] Among them, the function F is used x (P * ), F y (P * ) and F z (P * ) respectively approach F * (P * ) and Component Approximator and The definition is shown in the following formula (3):

[0048]

[0049] The main mathematical objects in formula (3) are defined as follows:

[0050] For j = 1, 2, ..., 6, and A (scalar) basis function selected as a nonlinear approximation tool, which may be a polynomial function, a radial basis function, a wavelet basis function, a spline function and / or a neural network, etc.;

[0051] For k = 1, 2, ..., 6, the positive integer I k The complexity of the approximator is controlled, thereby further controlling the accuracy of the function approximation. If I k →+∞, then the approximation error ∈→0 under the appropriate basis function;

[0052] For k = 1, 2, ..., 6, is the vectorized basis function; similarly, we can define and

[0053] For k = 1, 2, ..., 6, the vectorized basis functions Perform tensor outer product operations It can be expanded into a 6-order tensor basis function:

[0054] Similarly, we can define and

[0055] Tensor The weight coefficients corresponding to each basis function are recorded; is the tensor inner product operation, that is, the tensor and The sum of the products of all corresponding elements.

[0056] According to the component approximation function F in formula (3) x (P * ), F y (P * ) and F z (P * ), given the tensor basis function and Afterwards, the function F x (P * ), F y (P * ) and F z (P *) is transformed into a coefficient tensor and estimation problem.

[0057] Assume that N pairs of data are measured:

[0058] Then the tensor is realized by solving the following minimization problem and Estimates:

[0059]

[0060] From the perspective of optimization and statistics, we can find that problem (4) requires high computational complexity and sample complexity: unknown quantity, we need to Matrix inversion, the computational complexity is And in order to ensure the existence of the matrix inverse, the sample complexity is also required For example, when I1=I2=…=I6=10, the required time complexity is O(10 18 ), sample complexity N ≥ 10 6 , which means at least one million measurements are required, which is unacceptable in practical application scenarios.

[0061] To overcome the "curse of dimensionality" in problem (4), this embodiment uses the recently proposed TensorRing network (TR) to transform the coefficient tensor and Perform a low-rank approximation:

[0062]

[0063] Among them, for k = 1, 2, ..., 6, the third-order tensor For tensors TR core tensor, vector For tensors TR rank, and r0 = r6. According to the definition of tensor ring network, The (i1, i2, ..., i6)th element of can be represented by the core tensor gives:

[0064]

[0065] Among them, tr(·) is the trace operator of the matrix, because is a third-order matrix, is of size r k-1 × k The matrix of .

[0066] Substituting the TR expression of formula (5) into formula (4) yields:

[0067]

[0068] In formula (7): vector Δ x =(Δx1, Δx2, ..., Δx N ) T , Δ y =(Δy1, Δy2, ..., Δy N ) T , Δ z =(Δz1, Δz2, ..., Δz N ) T The actual error components in the x, y, and z directions in N measurements are recorded respectively, and the vector h x =(h x，1 ,h x，2 ,…,h x，N ) T ,,h y =(h y，1 ,h y，2 ,…,h y，N ) T ,h z =(h z，1 ,h z，2 ,…,h z，N ) T They represent the approximate error components based on the tensor ring representation, where for any k = 1, 2, ..., N:

[0069]

[0070] The above model (7) requires manual selection of the tensor TR rank parameter r, which brings a heavy workload of parameter adjustment. Introducing the tensor tube nuclear norm ★ As a low-rank regularization term, minimizing the nuclear norm leads to The low-rank structure of The tensor singular value decomposition (t-SVD) of the formula is 0, where most of the diagonal channels of the "f-diagonal tensor" are 0, which effectively limits the model complexity (such as Figure 3 Then we get the following model:

[0071]

[0072] Among them, ∑ cyc (·) represents the rotation sum with x, y, z as the sum index, for example, ∑ cyc f x =f x+f y +f z ; λ represents the regularization parameter.

[0073] There are many algorithms for solving problem (9), such as Accelerated Proximal Gradient Method, Composite Gradient Descent Method, Alternating Direction Method of Multipliers (ADMM), etc. In the specific implementation, a solution algorithm based on ADMM will be given.

[0074] Assume that the algorithm output solution of problem (9) is:

[0075] Then the coefficient tensor is reconstructed according to formula (5):

[0076]

[0077] According to equations (2) and (3), for the new posture to be planned P′(x ′ ,y′,z ′ , a′, b′, c′), and get the estimated

[0078] The error vector is:

[0079]

[0080] Thus, the planned pose is adjusted to And send it to the robot for execution.

[0081] First, add auxiliary variables to problem (9) and We can get:

[0082]

[0083] The following is a solution to problem (10) based on the alternating direction multiplier method (ADMM).

[0084] First, the augmented Lagrangian function of problem (10) is:

[0085]

[0086] in, is the Lagrange multiplier, ρ>0 is the penalty coefficient, ‖·‖ F is the Frobenius norm of the tensor.

[0087] Next, each variable is updated alternately according to the variable update rule under the ADMM algorithm framework.

[0088] renew and because and It has symmetry, so we only need The closed-form solution of and The closed form solution of .

[0089] Specifically, fixing other variables, by minimizing the augmented Lagrangian function L in equation (11) ρ To update

[0090]

[0091] In order to unify the notation, we write vector Right now Similarly, define the vector and Remember the matrix The ×2 operation represents the modulo-2 product of tensors; similarly, we define the matrix and Remember again Note that the subscript j of the matrix product operation is arranged in circular order (k+1, ..., 6, 1, ..., k-1); similarly, the matrix is ​​defined and

[0092] First, simplify equation (12):

[0093]

[0094] where unfold2(·) is the modulo-2 matrix expansion operation of the tensor, and vec(·) is the vectorization operation of the matrix / tensor. According to the properties of the matrix trace function, we get:

[0095]

[0096] The matrix vector and They are defined as:

[0097]

[0098] Then use To express h x :

[0099]

[0100] The matrix

[0101] Therefore, there is Therefore, problem (12) becomes:

[0102]

[0103] in, and According to the first-order optimality condition, in formula (13) Taking the derivative and setting it to zero, we get:

[0104]

[0105] Solving equation (14) yields The closed-form solution of is:

[0106]

[0107] where fold(·) represents a tensorization operation on a vector or matrix, k = 1, 2, …, 6,

[0108]

[0109] According to the symmetry, it is easy to get The closed-form solutions are and The closed-form solution of is given by equation (16) and equation (17):

[0110]

[0111] Where k = 1, 2, ..., 6,

[0112] Where k = 1, 2, ..., 6,

[0113] renew and because and With symmetry, we can also only ask The closed-form solution of and The closed form solution of .

[0114] Specifically, fixing other variables, by minimizing the augmented Lagrangian function L in equation (11) ρ To update

[0115]

[0116] The closed-form solution to problem (18) is as follows:

[0117]

[0118] The tensor singular tube thresholding operator STT is used in formula (19): τ (·). For any third-order tensor Assume that its t-SVD decomposition is where * is the tensor t-product, is an orthogonal tensor, f is a diagonal tensor, then the tensor The singular tube thresholding operator is defined as:

[0119]

[0120] Where τ is a non-negative parameter, dft3(·) and idft3(·) represent the one-dimensional discrete Fourier transform and one-dimensional inverse discrete Fourier transform of each tube fiber of the third-order tensor along the third mode, respectively.

[0121] According to the symmetry, we can get The closed-form solutions are and The closed-form solution of is shown in equations (20) and (21):

[0122]

[0123] renew and According to the dual variable update rule of the ADMM framework, the dual variable is updated using the dual ascent method and

[0124]

[0125] In this embodiment, the above steps are summarized as an algorithm, see Table 1:

[0126] Table 1:

[0127]

[0128] In this embodiment, data sampling: According to the actual operation tasks of the industrial robot under field conditions, the Cartesian space of the robot's operating range is limited to a size S x ×S y ×S z , the target point attitude angle (a, b, c) are all within (±θ a , ±θx, ±θ c) within the range. According to the following Latin hypercube sampling method variant, N sampling points are planned in this space to obtain the theoretical poses of N groups of sampling points. For the sample set.

[0129] For a single random variable X, select n nodes x=(x1, x2, ..., x n ) T , the goal is to select N ≤ n values ​​(for experiment). First, arrange the n nodes from small to large to get x′ = (x′1, x′2, …, x′ n ) T , then for i=1, 2, ..., N, use l=Round(im / n) to calculate the coordinate l and construct a new vector x″=(x″1, x″2, ..., x″ N ) T , so that x″ i = x′ l , and then randomly sort the new vector x″ to get N single variable sampling values. For the 6-dimensional random variable (X, Y, Z, A, B, C), the above steps are used to obtain 6 N-dimensional new vectors x″, y″, z″, a″, b″, c″, and N data points can be selected.

[0130] Get N pairs of data After the points are clicked, the laser tracker is used to measure and record the actual positioning coordinates of the corresponding points, and the actual positioning error ΔP of the corresponding sampling points is obtained through calculation. i =(Δx i , Δy i , Δz i ). The sample data is randomly divided into training set and test set according to the set ratio. For example, the number of samples in the training set and the test set are 1900 and 100 respectively.

[0131] Basis function selection problem: In practical applications, this embodiment recommends selecting a spline curve as the basis function and Specifically, a univariate spline curve S(·) is a piecewise polynomial function on the interval [α, β]. Any ρ-order spline can be expressed as a unique linear combination of I B-splines of the same degree:

[0132]

[0133] Among them, the B-spline basis function B i , ρ (t) is composed of the node sequence {s0, s1, ..., s m} and spline degree ρ. The node sequence {s0, s1, …, s m} is a non-decreasing sequence defined on the interval [α, β] α=s0≤s1≤…≤s I =β, so that the spline curve S(t) is in any interval [s i ,s i+1 ] are all polynomials. Given the number of nodes m+1 and the spline degree ρ, the number of B-spline basis functions can be determined as I=m-ρ. B-spline basis functions of any degree can be given by the Cox-de Boor formula:

[0134]

[0135]

[0136] This embodiment considers nodes {s0, s1, ..., s m}. For the planned position P * (x, y, z, a, b, c), in this embodiment, ρ = 3, m = 13, then I1 = I2 = ... = I6 = 10. Therefore, the coefficient tensor in formula (3) is and The dimensions are all 10×10×10×10×10×10.

[0137] Hyperparameter settings of model (9): This implementation is in the interval {10 -5 , 10 -4 , …, 10 5}The optimal regularization parameter λ is selected through a grid search cross-validation scheme; the initial tensor TR rank Set to (10, 10, 10, 10, 10, 10, 10).

[0138] Parameter setting in Algorithm 1: The penalty parameter ρ is initialized to 10 -6 , multiplicative factor γ = 1.1, maximum penalty parameter ρ max =10 6 , the resolution of convergence accuracy is δ = 10 -6 , the maximum number of iterations is set to T max =500.

[0139] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

[0140] Embodiment 2:

[0141] This embodiment provides a customized redundant degree of freedom robot calibration system based on function approximation, including:

[0142] The data acquisition module is configured to: obtain the planning posture data of the robot;

[0143] The estimation module is configured to: obtain an estimated value of the position error based on the acquired planning posture data and a preset estimator;

[0144] The calibration module is configured to: revise the position according to the estimated value of the position error, obtain the robot planning instruction and calibrate the robot;

[0145] Among them, the learning process of the preset estimator is: regard the position error as a nonlinear function of the planning posture data to obtain the error function; use the tensor ring network to approximate the error function, and obtain the estimator through sampling and learning.

[0146] The working method of the system is the same as the customized redundant degree of freedom robot calibration method based on function approximation in Example 1, and will not be repeated here.

[0147] Embodiment 3:

[0148] This embodiment provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the steps of the customized redundant degree of freedom robot calibration method based on function approximation described in Embodiment 1 are implemented.

[0149] Embodiment 4:

[0150] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the customized redundant degree of freedom robot calibration method based on function approximation described in Example 1 are implemented.

[0151] The above description is only a preferred embodiment of the present embodiment and is not intended to limit the present embodiment. For those skilled in the art, the present embodiment may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present embodiment shall be included in the protection scope of the present embodiment.

Claims

1. A customized redundant degree of freedom robot calibration method based on function approximation, characterized in that: include: Obtain the robot's planned posture data; According to the acquired planning posture data and the preset estimator, an estimated value of the position error is obtained; The position is revised according to the estimated value of the position error, and the robot planning instruction is obtained to calibrate the robot; The learning process of the preset estimator is as follows: the position error is regarded as a nonlinear function of the planning posture data to obtain an error function; The error function is approximated by a tensor ring network, and the estimator is obtained through sampling and learning.

2. The customized redundant degree of freedom robot calibration method based on function approximation according to claim 1, characterized in that: The planned posture data includes posture angle information and position information.

3. The customized redundant degree of freedom robot calibration method based on function approximation according to claim 1, characterized in that: When the error function is approximated by a tensor ring network, a low-rank approximation is performed on the coefficient tensor, including: providing a core tensor according to the number of elements in the coefficient tensor, wherein the core tensor is a third-order core tensor; introducing a tensor tube nuclear norm as a low-rank regularization term for each third-order core tensor, and minimizing the tensor tube nuclear norm leads to a low-rank structure of the third-order core tensor.

4. The customized redundant degree of freedom robot calibration method based on function approximation as claimed in claim 3, characterized in that: The estimation model of the core tensor is: in, and represents the core tensor; ∑ cyc (·) represents the rotation sum with x, y, and z as the summation index; λ represents the regularization parameter; ‖·‖ ＊ As a low-rank regularization term; Δ x =(Δx1, Δx2, ..., Δx N ) T The actual error component in the x direction in N measurements is recorded, vector; h x =(h x，1 ,h x，2 ,…,h x，N ) T Represents the approximation error component based on the tensor ring representation; where for any k = 1, 2, …, N.

5. The customized redundant degree of freedom robot calibration method based on function approximation as claimed in claim 4, characterized in that: The estimation model of the core tensor is solved using the alternating direction multiplier method.

6. The customized redundant degree of freedom robot calibration method based on function approximation according to claim 1, characterized in that: According to the three directions in the coordinate system, the components of the nonlinear function are approximated respectively.

7. The customized redundant degree of freedom robot calibration method based on function approximation according to claim 1, characterized in that: Spline curves are chosen as basis functions in the tensor ring network.

8. Customized redundant degree of freedom robot calibration system based on function approximation, characterized in that: include: The data acquisition module is configured to: obtain the planning posture data of the robot; The estimation module is configured to: obtain an estimated value of the position error based on the acquired planning posture data and a preset estimator; The calibration module is configured to: revise the position according to the estimated value of the position error, obtain the robot planning instruction and calibrate the robot; The learning process of the preset estimator is as follows: the position error is regarded as a nonlinear function of the planning posture data to obtain an error function; The error function is approximated by a tensor ring network, and the estimator is obtained through sampling and learning.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the customized redundant degree of freedom robot calibration method based on function approximation as described in any one of claims 1 to 7 are implemented.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the customized redundant degree of freedom robot calibration method based on function approximation as described in any one of claims 1 to 7 are implemented.

Images