A GPR-based method for predicting weak dynamic stiffness pose of milling robot

Abstract

The present invention relates to a method for predicting the weak dynamic stiffness posture of a milling robot based on GPR, and belongs to the technical field of robot milling processing. A terminal frequency response function matrix is ​​constructed, a hammer excitation test is carried out to obtain the frequency response data of the milling robot, a rational fraction polynomial of the theoretical frequency response of the N-order modal viscous damping system is constructed, and a GPR prediction model with anisotropic rational quadratic kernels is established to predict the weak dynamic stiffness posture of the milling robot at a specified milling spindle speed, and find the X, Y coordinate values ​​and redundancy A corresponding to the blade passing frequency being close to the 8 main modal natural frequencies. The advantage of the present invention is that it can accurately obtain the weak dynamic stiffness posture of the milling robot at different spindle speeds, and the weak dynamic stiffness posture can be avoided in milling processing through the association mechanism between redundancy and dynamic stiffness, thereby ensuring the processing quality of the workpiece.

Description

Technical Field

[0001] The present invention belongs to the technical field of robot milling processing, and more specifically, relates to a method for predicting the weak dynamic stiffness posture of a milling robot based on GPR (Gaussian process regression). Background Art

[0002] Articulated industrial robots have been widely used in aerospace, automotive, and other manufacturing fields in recent years, offering advantages such as low cost and flexible processing modes. However, during high-load milling tasks, the robot's weak stiffness can easily lead to chatter instability during milling, significantly reducing the surface quality of the workpiece and even causing the scrapping of high-value-added parts, resulting in huge economic losses. Therefore, avoiding milling robot postures with weak end-end stiffness is an important research topic in the field of robotic milling. Stiffness can be divided into static stiffness and dynamic stiffness. Dynamic stiffness reflects the stiffness performance of the milling robot under dynamic excitation during machining and is a key factor directly affecting milling stability.

[0003] Currently, robot dynamic stiffness is primarily derived based on multibody dynamics analysis. For example, Pan et al. (USA) abstracted a robotic milling system into a spring-mass-damper system to model the chatter process, thereby studying the mechanisms of stability and chatter suppression during machining. Baglioni et al. (Italy) established a dynamic model of a milling robot with rigid links and flexible joints based on the standard DH parameter method. They determined the mass matrix by calculating the moment of inertia and the joint elastic parameters based on the harmonic drive specifications. Mousavi et al. (France) used Euler-Bernoulli elements to consider the influence of each joint's stiffness and damping, establishing a dynamic model of the robot. However, all of these studies considered mechanistic models. Due to the complex structure of the robot and assembly area, the mechanistic models cannot fully account for their geometry, material parameters, and internal assembly methods, resulting in significant deviations between the calculated and actual values. Furthermore, these mechanistic models primarily focus on single-order models of the robot body or end-of-line tool, often ignoring the impact of the actual assembly conditions of the milling system on end-of-line vibration. Simplified analyses make it difficult to balance the impact of each subsystem, while incorporating all subsystems would significantly increase the model complexity.

[0004] Therefore, the field of robotic milling processing urgently needs an efficient and accurate method for predicting the weak dynamic stiffness posture of milling robots. Summary of the Invention

[0005] The present invention provides a GPR-based method for predicting the weak dynamic stiffness and posture of a milling robot. According to the changing characteristics of the dynamic stiffness frequency response curve, multi-order modal natural frequencies are used as judgment factors for the weak dynamic stiffness of the milling robot. By conducting a hammer excitation test, three-directional terminal frequency response data under 100 groups of robot postures are obtained. Based on the Levy method, a rational polynomial fitting frequency response function is constructed. The influence of each subsystem on the processing vibration is weighed, and eight main modes in the X / Y / Z directions are selected to form a multi-modal natural frequency training set. Based on the test data, a GPR prediction model with anisotropic rational quadratic kernel is established. This model can quickly obtain the main modal natural frequencies under different postures of the milling robot, and accurately predict the weak dynamic stiffness and posture of the milling robot under a specified milling spindle speed.

[0006] The technical solution adopted by the present invention comprises the following steps:

[0007] (a) For a six-degree-of-freedom milling robot, constructing the terminal frequency response function matrix can describe the system dynamic stiffness;

[0008] (b) Conduct hammer excitation tests to obtain frequency response data of the milling robot;

[0009] (c) The Levy method, a multimodal identification method, is used to fit the experimental frequency response data and construct a rational fraction polynomial for the theoretical frequency response of the N-order modal viscous damping system;

[0010] (d) A GPR prediction model with anisotropic rational quadratic kernels was established to predict the weak dynamic stiffness pose of the milling robot at a specified milling spindle speed. The GPR prediction model contained eight sub-models. Each sub-model input consisted of three dimensions: the X and Y coordinates of the machining TCP point and the redundancy A. The output was the main modal natural frequency Fn.

[0011] (e) The GPR prediction model composed of eight sub-models can obtain the natural frequency of the milling robot under any posture. For specified milling processing conditions, the blade pass frequency of the milling force is calculated. At this time, the X, Y coordinate values ​​and redundancy A corresponding to the blade pass frequency close to the eight main modal natural frequencies are found, which is the weak dynamic stiffness posture of the milling robot at the specified speed.

[0012] In step (a) of the present invention, the tool coordinate system i-1 The frequency response functions in the XYZ directions in P represent the dynamic stiffness of the milling robot. The terminal frequency response H in the tool coordinate system tool(ω) can be composed of direct frequency response and cross-coupled frequency response. In fact, for the frequency response of the articulated milling robot in each direction, compared with the contribution of the excitation in this direction to its vibration, the influence of the excitation in the orthogonal direction on the vibration is small. Therefore, only the direct frequency response in each direction is considered, and the cross-coupled frequency response is ignored. The terminal frequency response function can be composed of the direct frequency response function H in each direction. x (ω), H y (ω), H z (ω) is expressed as:

[0013] H tool (ω)=diag[H x (ω),H y (ω),H z (ω)]

[0014] The natural angular frequency ω of each mode in the X, Y, and Z directions of the articulated milling robot n It is the core judgment factor for whether the system is in a weak dynamic stiffness posture.

[0015] In step (b) of the present invention, a hammer method is used to obtain frequency response data of 100 sets of milling robot postures. The milling robot posture of the test is selected with reference to the TCP relative base coordinate system in the robot end tool coordinate system. In the specified processing plane, points are equally spaced in the X and Y directions within the processing range, and a total of 20 points are selected. At each point, 5 postures are equally spaced within the range of redundancy A. In each set of postures, frequency response data are measured in the X, Y, and Z directions respectively. A total of 300 sets of milling robot end frequency response data are obtained. The selected postures basically cover the changes of the robot in the end milling processing plane.

[0016] In step (c) of the present invention, the rational fraction polynomial for constructing the theoretical frequency response of the N-order modal viscous damping system is:

[0017]

[0018] Let the theoretical frequency response function H L (ω) and the variance of the test frequency response data are minimized, thereby identifying the numerator and denominator coefficient vectors of the rational fraction and obtaining the natural angular frequency ω of the v-th order mode of the milling robot in one direction nv ,ω nv =2πf nv , for subsequent calculations, to form the natural frequency f nv A training set of data corresponding to the poses of the milling robot.

[0019] In step (d) of the present invention, the GPR model kernel function directly determines the model regression effect. A rational quadratic kernel is used to describe the complex characteristics of the data. At the same time, combined with the automatic correlation determination technology in machine learning, a rational quadratic kernel with various anisotropic properties is constructed in the model to adapt to the multi-scale and multi-dimensional complex data feature peaks between the natural frequency and posture of the milling robot, which can be expressed as:

[0020]

[0021] Where, σ 2 is the output scale parameter, i.e., the output spatial variance, M h It is a diagonal matrix of the kernel function length scale, and each element on the diagonal is the length scale l of each input dimension X, Y, and A respectively. x 、l y 、l A The square inverse of , which is used to control the overall smoothness of the kernel function. α is the mixed scale parameter, which determines the sensitivity of the kernel function to multiple scales.

[0022] After setting the kernel function, it is necessary to train the prior Gaussian process with the model data set, search for the optimal function hyperparameters, and optimize by minimizing the negative logarithmic function of the likelihood. Assuming that the data has normal noise, the Gaussian likelihood function is used for prediction, and its negative logarithmic function can be written as:

[0023]

[0024] Where, σ n 2 is the noise variance, which indicates the deviation between the measured data output value and the true value of the data. By taking the partial derivative of this equation and solving it by the quasi-Newton method, we can obtain the optimized function hyperparameters to match the data characteristics between the natural frequency and the robot posture.

[0025] The function settings in a single sub-model are clarified, and the rational quadratic kernel function, constant mean function and Gaussian likelihood function of various anisotropies are selected for construction. The hyperparameter group composed of the function parameters in the v-th order modal sub-model is

[0026]

[0027] In step (d) of the present invention, the redundant angle is adjusted by maintaining the position unchanged at the weak dynamic stiffness position so that the natural frequency of the milling robot is away from the natural frequency of the main mode, thereby avoiding the weak dynamic stiffness position, effectively reducing machining vibration, and improving the surface quality of the machined workpiece. The present invention has the following beneficial effects:

[0028] 1. The data-driven GPR prediction model is closer to the actual structure of the system, and can take into account the complex geometric models, material parameters and internal assembly methods of the robot and assembly area, avoiding the deviation of the mechanism model.

[0029] 2. The model weighs the impact of each subsystem based on test results and incorporates all major modes into the analysis. Compared to the current simplified analysis of a single mode of the robot body or end-of-line tool, this more comprehensively considers the impact of the structure on the vibration of the machining end. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The drawings described herein are used to provide further understanding of the present invention and constitute a part of this application. The illustrative examples of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0031] Figure 1 is a flow chart of the method of the present invention;

[0032] Figure 2 These are the eight main modal diagrams of the end frequency response of the milling robot of the present invention;

[0033] Figure 3 Schematic diagram of the GPR weak dynamic stiffness prediction model of the present invention;

[0034] Figure 4 This is a diagram showing the prediction of the weak dynamic stiffness model under redundancy control of the present invention;

[0035] Figure 5 Schematic diagram of redundancy of the present invention. DETAILED DESCRIPTION

[0036] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0037] The present invention provides a GPR-based method for predicting the weak dynamic stiffness and posture of a milling robot. The method is based on the changing characteristics of the dynamic stiffness frequency response curve, takes multi-modal natural frequencies as weak dynamic stiffness prediction factors, constructs a terminal three-way frequency response function through a hammering method, identifies the main modal natural frequencies that play a dominant role in the terminal vibration to form a training set, and establishes a GPR prediction model with an anisotropic rational quadratic kernel to achieve accurate prediction of the weak dynamic stiffness and posture of the milling robot at a specified speed.

[0038] The present invention is described in detail below with reference to the accompanying drawings.

[0039] (a) To obtain the dynamic stiffness model of the milling robot, it is necessary to perform a dynamic modeling and perform a Laplace transform on the dynamic equations. The frequency response function of the single degree of freedom system is obtained as follows:

[0040]

[0041] Where k is the stiffness, ω n is the natural angular frequency of the system (distinguished from the natural frequency f n ,ω n =2πf n ), ζ is the damping ratio. For a six-degree-of-freedom milling robot, constructing the terminal frequency response function matrix can describe the system dynamic stiffness. In the tool coordinate system i-1 The frequency response functions in the XYZ directions in P represent the dynamic stiffness of the milling robot. The terminal frequency response H in the tool coordinate system tool (ω) can be composed of direct frequency response and cross-coupled frequency response. In fact, for the frequency response of the articulated milling robot in each direction, compared with the contribution of the excitation in this direction to its vibration, the influence of the excitation in the orthogonal direction on the vibration is small. Therefore, assuming that only the direct frequency response in each direction is considered and the cross-coupled frequency response is ignored, the terminal frequency response function can be obtained by the direct frequency response function H in each direction. x (ω), H y (ω), H z (ω) is expressed as:

[0042]

[0043] The single direction frequency response function reflects the modes of different subsystems of the milling robot. According to the modal superposition theory, the natural angular frequency, damping ratio and stiffness of the v-th order independent mode in a single direction are set as ω respectively. nv ,ξ v 、k v , combined with formula (1), the frequency response function of a single direction under a fixed posture of the robot can be expressed as the superposition of multiple modes:

[0044]

[0045] Where r v is the natural frequency ratio r v =ω / ω nv , v=1,2,3,…,M;

[0046] In summary, the changes in the modal parameters of each order independent mode of the system under different postures can be obtained through the experimental modal, and the direct frequency response functions H of the robot milling system dependent on the posture can be derived and calculated. x (ω), H y (ω), H z(ω), the end dynamic stiffness frequency response model of the articulated milling robot can be obtained, which is used to measure the dynamic stiffness performance of the robot at different postures during the milling process.

[0047] Analysis of the dynamic stiffness frequency response curve shows that at the natural frequency, the dynamic stiffness is determined by damping. At this time, the system is in a weak dynamic stiffness region, meaning that the structure's ability to resist deformation is minimal and it is easily excited by similar vibration frequencies. Therefore, the natural frequency of each mode in the articulated milling robot is the core factor in determining whether the system is in a weak dynamic stiffness position.

[0048] (b) The hammer method is used to obtain the frequency response data of 100 sets of milling robot postures in the processing space. The milling robot posture selection described in the test is based on the tool center point TCP relative to the base coordinate system in the robot end tool coordinate system. In the specified processing plane, points are taken at equal intervals in the X and Y directions within the processing range, and a total of 20 points are selected. At each point, 5 postures are selected at equal intervals within the range with redundancy A. In each set of postures, the frequency response data of the X, Y, and Z directions are measured respectively. A total of 300 sets of milling robot end frequency response data are obtained. The selected postures basically cover the changes of the robot in the vertical milling processing plane.

[0049] (c) The Levy method, a multimodal identification method, was used to fit 300 sets of experimental frequency response data. The rational fraction polynomial of the theoretical frequency response of the M-order modal viscous damping system was constructed as follows:

[0050]

[0051] In the formula, the frequency response of the M-order modal system corresponds to the 2M-order rational fraction polynomial, a k and b k are the numerator coefficient vector and denominator coefficient vector of the transfer function sorted by ascending power, k = 0, 1, 2, …, 2M;

[0052] Let the theoretical frequency response function H L The sum of the variances of (ω) and the test frequency response data is minimized, thereby identifying the numerator and denominator coefficient vectors of the rational polynomial;

[0053] Convert (4) to a transfer function using the Laplace operator, set the denominator of the power polynomial to 0, and obtain M pairs of complex roots, where the expression of one pair of complex roots is:

[0054]

[0055] Furthermore, the natural angular frequency of the v-th order mode in one direction of the milling robot can be obtained as

[0056]

[0057] Where, v = 1, 2, 3, ..., M; k = 0, 1, 2, ..., 2M;

[0058] Obtain the natural angular frequency ω of the vth order mode in one direction of the milling robot nv (ω nv =2πf nv ), for subsequent calculations, to form the natural frequency f nv A training set of data corresponding to the milling robot's poses;

[0059] (d) Establish the GPR prediction model of anisotropic rational quadratic kernels such as Figure 3 , to predict the weak dynamic stiffness posture of the milling robot at a specified milling spindle speed. It has been verified that there are 8 main modes in the terminal frequency response function of the robot that have a greater influence on the terminal, such as Figure 2 The model uses the natural frequencies of 8 main modes as the model training set and uses Gaussian process regression to predict the weakest dynamic stiffness area of ​​each main mode of the robot body and milling processing system in the milling robot under different postures, that is, the natural frequency damping control area;

[0060] The natural frequencies of the eight main modes in the experimental modal analysis (referred to as modes XL, XH, YL1, YL2, YH, ZL1, ZL2, and ZH according to their natural frequencies in the X / Y / Z directions from low to high) were used as the training set to establish a GPR prediction model. The model contains a total of eight sub-models. Each sub-model input contains three dimensions, namely the X and Y coordinate values ​​of the milling robot TCP point and the redundancy A, and the output is the natural frequency of the main mode.

[0061] Fn in (in=XL,XH,YL1,YL2,YH,ZL1,ZL2,ZH), the sub-model can be expressed as:

[0062] f(x)~N(μ(x),κ(x,x))(7)

[0063] Where μ(x) is the mean function and κ(x,x) is the covariance function, also known as the kernel function, which together can determine a Gaussian process.

[0064] The GPR prediction model function is set based on the characteristics of the training set data. By analyzing the data results, that is, analyzing the change pattern of the milling robot's natural frequency with posture, it can be found that the natural frequency has both local characteristics of subtle changes and global characteristics of trend changes in a single input dimension. At the same time, the change characteristics of the natural frequency in the three input dimensions are quite different.

[0065] The variation of the natural frequency of the milling robot with its posture is analyzed, and the rational quadratic kernel (RQ) is introduced to describe the complex characteristics of the data. At the same time, combined with the automatic correlation determination technology in machine learning, the rational quadratic kernel of various anisotropies in the model is constructed to adapt to complex data of multiple scales and dimensions. It can be expressed as:

[0066]

[0067] Where, σ 2 Is the output scale parameter, that is, the output spatial variance, which determines the overall variation of the function. h It is a diagonal matrix of the kernel function length scale, and each element on the diagonal is the length scale l of each input dimension X, Y, and A respectively. x 、l y 、l A The square inverse of , which is used to control the overall smoothness of the kernel function. α is the mixed scale parameter, which determines the sensitivity of the kernel function to multiple scales.

[0068] Compared to the widely used radial basis function kernel, the anisotropic rational quadratic kernel offers greater flexibility, being equivalent to the weighted sum of an infinite number of radial basis function kernels of varying length scales. By adjusting the mixed scale parameter, the kernel can adapt to varying characteristics at different scales, allowing the model to strike a balance between data overfitting and generalization, while also taking into account both the local and global characteristics of the natural frequency as it varies with a single pose parameter. At the same time, ensuring that each input dimension has an independent length scale to adjust allows for more refined capture of the varying characteristics of different input dimensions. In summary, the anisotropic rational quadratic kernel is superior for capturing the complex relationship between the natural frequency of a robot and its pose.

[0069] After setting the kernel function, the prior Gaussian process needs to be trained with the model data set to search for the optimal function hyperparameters. Optimization is performed by minimizing the negative logarithmic function of the likelihood. Assuming that the data has normal noise, the Gaussian likelihood function is used for prediction. Its negative logarithmic function can be written as:

[0070]

[0071] Where, is the noise variance, representing the deviation between the measured data output and the true value of the data. Taking the partial derivative of this equation and solving it using the quasi-Newton method yields optimized function hyperparameters that match the data characteristics between the natural frequency and the robot's pose.

[0072] At this point, the function settings in a single sub-model have been clarified. The model is constructed using various anisotropic rational quadratic kernel functions, constant mean functions, and Gaussian likelihood functions. The hyperparameter group composed of the function parameters in the v-th order modal sub-model is expressed as:

[0073]

[0074] The initial value is set to β0 = {(0; 0; 0); 0; 0; 0; 1}, and the negative log-marginal likelihood optimization is performed to obtain the optimized model hyperparameter set. The submodels have significant differences at different length scales, and the natural frequencies vary with different dimensions. The varying mixing scales indicate the presence of multi-scale variations within a single input dimension, confirming the necessity of using anisotropic rational quadratic kernel functions.

[0075] Furthermore, it is necessary to eliminate the overfitting of the GPR prediction model, test the prediction effect and generalization ability of the model, and conduct internal verification of the GPR multimodal weak stiffness prediction model based on the holdout method. The optimized hyperparameter group is set as the initial value, and the experimental data set is randomly shuffled and divided into 80% training set and 20% test set. The mean relative error (MRE) and determination coefficient (R) are used to calculate the mean relative error (MRE) and determination coefficient (R) of the GPR multimodal weak stiffness prediction model. 2 As an evaluation indicator of the regression model, it can evaluate the accuracy and fitting precision of the regression model;

[0076] (e) During the end milling process, the spindle speed is selected to obtain the theoretical cutting force edge pass frequency. The model predicts how the main modal natural frequency changes with position. When the main modal natural frequency approaches the excitation frequency, the TCP coordinates and redundancy A are output, allowing the milling robot's weak dynamic stiffness position to be accurately determined.

[0077] At this time, the redundancy angle can be adjusted to make the multi-modal natural frequency away from the excitation frequency, such as Figure 4 , so that the redundant angle of the milling robot avoids the weak dynamic stiffness posture, effectively reducing the end processing vibration and improving the surface quality of the processed workpiece.

[0078] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A GPR-based method for predicting the weak dynamic stiffness and pose of a milling robot, characterized in that: The following steps are involved: (a) For a six-degree-of-freedom milling robot, the terminal frequency response function matrix can be constructed to describe the system dynamic stiffness, where the tool coordinate system The frequency response functions in the XYZ directions represent the dynamic stiffness of the milling robot, and the terminal frequency response function in the tool coordinate system is It can be composed of direct frequency response and cross-coupled frequency response. Since the influence of orthogonal direction excitation on vibration is small, only the direct frequency response in each direction is considered, and the cross-coupled frequency response is ignored. The terminal frequency response function can be composed of the direct frequency response function in each direction. , , Expressed as: ； (b) Conducting a force hammer excitation test to obtain frequency response data of the milling robot. The force hammer excitation test was used to obtain frequency response data of the milling robot in 100 positions. The milling robot position selection in the test was based on the TCP relative base coordinate system in the robot end tool coordinate system. Within the specified processing plane, points were equally spaced in the X and Y directions within the processing range, for a total of 20 points. At each point, five postures were equally spaced within the range with redundancy A. Frequency response data were measured in the X, Y, and Z directions for each position. A total of 300 sets of frequency response data of the milling robot end were obtained. (c) The experimental frequency response data are fitted using the Levy method, a multimodal identification method, to construct a rational fraction polynomial for the theoretical frequency response of the N-order modal viscous damping system. The rational fraction polynomial for constructing the theoretical frequency response of the N-order modal viscous damping system is: ； Theoretical frequency response function The sum of the variances of the test frequency response data is minimized, thereby identifying the numerator and denominator coefficient vectors of the rational fraction and obtaining the natural angular frequency of the V-th order mode in a single direction of the milling robot. , , forming the natural frequency A training set of data corresponding to the milling robot's poses; (d) A GPR prediction model with anisotropic rational quadratic kernels was established to predict the weak dynamic stiffness and posture of the milling robot at a specified milling spindle speed. The GPR prediction model contains eight sub-models. Each sub-model input contains three dimensions, namely the X and Y coordinates of the machining TCP point and the redundancy A, and the output is the main modal natural frequency Fn. A rational quadratic kernel is used to describe the complex characteristics of the data. At the same time, combined with the automatic correlation determination technology in machine learning, anisotropic rational quadratic kernels are constructed in the model to adapt to the multi-scale and multi-dimensional complex data feature peaks between the natural frequency and posture of the milling robot, which can be expressed as: ； ； Where, is the output scale parameter, i.e. the output spatial variance, It is a diagonal matrix of the kernel function length scale, and each element on the diagonal is the length scale of each input dimension X, Y, and A respectively. 、 、 The square inverse of , this matrix is ​​used to control the overall smoothness of the kernel function, is the mixing scale parameter, which determines the sensitivity of the kernel function to multiple scales; After setting the kernel function, it is necessary to train the prior Gaussian process with the model data set, search for the optimal function hyperparameters, and optimize by minimizing the negative logarithmic function of the likelihood. Assuming that the data has normal noise, the Gaussian likelihood function is used for prediction, and its negative logarithmic function can be written as: ； Where, is the noise variance, which indicates the deviation between the measured data output value and the true value of the data. By taking the partial derivative of this equation and solving it by the quasi-Newton method, we can obtain the optimized function hyperparameters to match the data characteristics between the natural frequency and the robot posture. The function settings in a single sub-model are clarified, and the rational quadratic kernel function, constant mean function and Gaussian likelihood function of various anisotropies are selected for construction. The hyperparameter group composed of the function parameters in the v-th order modal sub-model is ; (e) The GPR prediction model, composed of eight sub-models, can obtain the natural frequency of the milling robot under any posture. For specified milling processing conditions, the blade pass frequency of the milling force is calculated. At this time, the X, Y coordinate values ​​and redundancy A corresponding to the blade pass frequency close to the eight main modal natural frequencies are found, which is the weak dynamic stiffness posture of the milling robot at the specified speed.

2. A GPR-based milling robot weak dynamic stiffness pose prediction method according to claim 1, characterized in that: In the step (d), the redundant angle is adjusted by keeping the point position unchanged at the weak dynamic stiffness posture so that the natural frequency of the milling robot is far away from the natural frequency of the main mode, thereby avoiding the weak dynamic stiffness posture, effectively reducing the processing vibration, and improving the surface quality of the processed workpiece.

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