Rope-driven parallel robot friction modeling method and system

Abstract

The invention discloses a friction modeling method and system for a rope-driven parallel robot, and relates to the technical field of robot high-precision control, and the method comprises the steps: generating a composite excitation track covering the whole working space of the rope-driven parallel robot, and collecting joint friction force data when the rope-driven parallel robot moves; based on joint friction force data when the rope-driven parallel robot moves, a multiple-input-multiple-output SVGP friction coupling model is constructed; a variational inference and lightweight training strategy is adopted to optimize parameters of the multiple-input-multiple-output SVGP friction coupling model, and a trained multiple-input-multiple-output SVGP friction coupling model is obtained; and the trained model is deployed to a real-time control system of the rope-driven parallel robot, dynamic friction feedforward compensation is conducted on the rope-driven parallel robot, and the control precision of the robot can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of high-precision robot control, and in particular to a friction modeling method and system for a rope-driven parallel robot. Background Art

[0002] Rope-driven parallel robots are widely used in the medical and precision operation fields due to their compact structure and large workspace. However, their multi-degree-of-freedom nonlinear friction seriously restricts high-precision control performance. Specifically, the large reduction ratio of the harmonic reducer, while enhancing the torque output, introduces the strong nonlinearity of the Stribeck effect and Coulomb friction. The elastic creep of the rope transmission and the contact friction of the pulley lead to rate-dependent hysteresis characteristics, forming a multi-valued mapping of position-torque. The kinematic coupling of the parallel mechanism causes the friction of each joint to interfere with each other through the parallel topology, further exacerbating the complexity of the system. Traditional physical models (such as the LuGre model) rely on precise parameter identification and are difficult to describe the synergistic effect of coupled friction. Although data-driven neural network methods can fit nonlinearity, they require massive training data and lack interpretability, making them difficult to deploy in real time. Although traditional Gaussian processes (GPs) have the advantage of probabilistic modeling, their O(N) 3 ) The computational complexity cannot meet the real-time requirements of the multi-joint system, and the existing technology independently models each joint as a single-input and single-output GP, ignoring the dynamic coupling between the joints of the parallel robot, resulting in cross-dimensional deviations in friction prediction. Summary of the Invention

[0003] The purpose of this application is to provide a friction modeling method and system for a rope-driven parallel robot, which can realize online compensation of the friction force of the rope-driven parallel robot and improve the control accuracy of the rope-driven parallel robot.

[0004] To achieve the above objectives, this application provides the following solutions:

[0005] In a first aspect, the present application provides a friction modeling method for a rope-driven parallel robot, comprising:

[0006] Generate a composite excitation trajectory covering the entire workspace of the rope-driven parallel robot, and collect joint friction force data during the movement of the rope-driven parallel robot; the composite excitation trajectory is composed of a layered spiral base trajectory superimposed with a broadband random sine perturbation;

[0007] Based on the joint friction force data of the rope-driven parallel robot during motion, a multi-input multi-output SVGP friction coupling model is constructed; the multi-input multi-output SVGP friction coupling model uses the multi-input multi-output SVGP model to jointly model the nonlinear coupling characteristics of the three joint positions and velocities;

[0008] The variational inference and lightweight training strategy are used to optimize the parameters of the multi-input multi-output SVGP friction coupling model, and the trained multi-input multi-output SVGP friction coupling model is obtained.

[0009] The trained multi-input and multi-output SVGP friction coupling model is deployed to the real-time control system of a rope-driven parallel robot to perform dynamic friction feedforward compensation on the rope-driven parallel robot.

[0010] Optionally, the joint friction force data includes joint position data, speed data and torque data of the rope-driven parallel robot.

[0011] Optionally, the formula expression of the layered spiral basis trajectory is:

[0012] rx(t) base =A×sin(ω1t)×cos(ω2t)+x0

[0013] ry(t) base =B×sin(ω1t)×sin(ω2t)+y0

[0014] Among them, ω1=0.01ω2, A and B are the axis lengths of the current layer, and x0, y0 are the coordinates of the center point of the rope-driven parallel robot workspace.

[0015] Optionally, the formula expression of broadband random sinusoidal perturbation is:

[0016]

[0017] Among them, N s is the number of random sinusoids, ω lx 、ω ly is a random frequency randomly selected from the fundamental frequency and fundamental phase, φ lx 、φ ly is a random phase randomly selected from the fundamental frequency and fundamental phase, A d is the disturbance amplitude.

[0018] Optionally, the formula expression of the composite excitation trajectory is:

[0019]

[0020]

[0021] Among them, rz(t) is the current layer height, rz0 is the initial layer height, ω1 and ω2 are phase frequencies, and the three radii of the ellipsoid are a, b, and c, respectively. C is the radius of the operating ellipsoid in the rz direction.

[0022] Optionally, based on the joint friction force data of the rope-driven parallel robot during motion, a multi-input and multi-output SVGP friction coupling model is constructed, specifically including:

[0023] The n-th order Butterworth low-pass filter is used to filter the joint position data, velocity data and torque data respectively;

[0024] In view of the strong coupling characteristics of the joint friction of the rope-driven parallel robot, a 6-dimensional input vector is defined as the joint position q1, q2, q3 and the velocity 3D output vector τ1, τ2, τ3, and construct a mixed product kernel function; the position dimension of the mixed product kernel function adopts the radial basis function kernel Modeling global nonlinear characteristics, the velocity dimension uses the Matern 3 / 2 kernel Capture local mutation behavior of velocity;

[0025] According to the position dimension and the speed dimension, a mixed product kernel function is constructed in the form of a product. in is a six-dimensional input vector, l v 、l q is a trainable length scale hyperparameter;

[0026] According to the mixed product kernel function, the multi-input and multi-output SVGP friction coupling model is determined.

[0027] Optionally, a variational inference and lightweight training strategy is used to optimize the parameters of the multi-input multi-output SVGP friction coupling model to obtain a trained multi-input multi-output SVGP friction coupling model, specifically including:

[0028] The filtered joint position data, velocity data, and torque data are divided into training sets and test sets in proportion;

[0029] The k-means clustering algorithm is used to select about 5% of the induction points in the workspace of the rope-driven parallel robot and construct the variational distribution q(u)=Ν(m,S); where m is the mean and S is the covariance;

[0030] The covariance matrix inversion operation is accelerated by Cholesky decomposition. A small batch stochastic gradient optimization strategy is adopted to divide the training set into multiple subsets of a set number of samples or batches. A subset is randomly selected in each iteration to calculate the gradient approximation, and the Adam optimizer is used to maximize the lower bound of the evidence.

[0031] Based on the trained variational parameters and induction points, sparse Gaussian process regression is used to predict the joint friction force of the test set, and the prediction error is calculated;

[0032] If the prediction error is less than the preset threshold, the trained multi-input and multi-output SVGP friction coupling model is output;

[0033] If the prediction error is greater than or equal to the preset threshold, the number of induction points, the initialization value of the variational parameter or the optimization strategy are adjusted, and the above training process is repeated until the prediction error is less than the preset threshold.

[0034] Optionally, the trained multi-input multi-output SVGP friction coupling model is deployed to a real-time control system of a rope-driven parallel robot to perform dynamic friction feedforward compensation on the rope-driven parallel robot, specifically including:

[0035] The trained multi-input and multi-output SVGP friction coupling model is compiled into a real-time module and embedded into the real-time control system of the rope-driven parallel robot.

[0036] Synchronously read the joint position data and velocity data of each joint at the set sampling frequency and predict the joint friction torque online;

[0037] Through current torque coefficient K t The feedforward current value is converted and injected into the q-axis current loop of the rope-driven parallel robot driver to form the feedforward compensation term where K p and K d is the current loop gain coefficient, e i is the current deviation, is the time derivative of the current deviation, is the predicted joint friction torque.

[0038] In a second aspect, the present application provides a friction modeling system for a rope-driven parallel robot, comprising:

[0039] An acquisition module is used to generate a composite excitation trajectory covering the entire workspace of the rope-driven parallel robot and to collect joint friction force data during the movement of the rope-driven parallel robot; the composite excitation trajectory is composed of a layered spiral base trajectory superimposed with a broadband random sinusoidal perturbation;

[0040] A model building module is used to build a multi-input multi-output SVGP friction coupling model based on the joint friction force data of the rope-driven parallel robot during movement; the multi-input multi-output SVGP friction coupling model uses the multi-input multi-output SVGP model to jointly model the nonlinear coupling characteristics of the three joint positions and velocities;

[0041] The model training module is used to optimize the parameters of the multi-input multi-output SVGP friction coupling model using variational inference and lightweight training strategies to obtain the trained multi-input multi-output SVGP friction coupling model;

[0042] The friction compensation module is used to deploy the trained multi-input and multi-output SVGP friction coupling model to the real-time control system of the rope-driven parallel robot and perform dynamic friction feedforward compensation on the rope-driven parallel robot.

[0043] Optionally, the joint friction force data includes joint position data, speed data and torque data of the rope-driven parallel robot.

[0044] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0045] This application provides a friction modeling method and system for a rope-driven parallel robot. This method uses a composite excitation trajectory to excite and collect joint position, velocity, and torque data. It constructs a multi-input, multi-output SVGP friction coupling model. It optimizes model parameters based on variational inference and lightweight training strategies, significantly reducing the computational complexity of traditional Gaussian processes. The training model is embedded in a real-time control system to dynamically offset friction interference using feedforward compensation. This application addresses the challenge of high-precision modeling of strongly coupled friction in multiple degrees of freedom. It can significantly reduce the position tracking error and phase lag of rope-driven parallel robots with large reduction ratios, thereby improving the control accuracy of rope-driven parallel robots. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 A schematic flow chart of a friction modeling method for a rope-driven parallel robot provided in one embodiment of the present application;

[0048] Figure 2 A schematic diagram of a cascade control architecture of a joint driver provided in one embodiment of the present application;

[0049] Figure 3 A schematic diagram of the functional modules of a friction modeling system for a rope-driven parallel robot provided in one embodiment of the present application. DETAILED DESCRIPTION

[0050] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0051] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0052] Example 1

[0053] like Figure 1 As shown, this embodiment provides a friction modeling method for a rope-driven parallel robot, including:

[0054] Step 101: Generate a composite excitation trajectory covering the entire workspace of the rope-driven parallel robot, and collect joint friction force data of the rope-driven parallel robot during motion; the composite excitation trajectory is composed of a layered spiral base trajectory superimposed with a broadband random sinusoidal perturbation;

[0055] Step 102: constructing a multi-input multi-output SVGP friction coupling model based on the joint friction force data of the rope-driven parallel robot during motion; the multi-input multi-output SVGP friction coupling model is a multi-input multi-output SVGP model that jointly models the nonlinear coupling characteristics of the positions and velocities of the three joints;

[0056] Step 103: Optimizing the parameters of the multi-input multi-output SVGP friction coupling model using a variational inference and lightweight training strategy to obtain a trained multi-input multi-output SVGP friction coupling model;

[0057] Step 104: Deploy the trained multi-input multi-output SVGP friction coupling model to the real-time control system of the rope-driven parallel robot, and perform dynamic friction feedforward compensation on the rope-driven parallel robot.

[0058] In some embodiments, when executing step 101, the specific steps may be as follows:

[0059] Through a composite excitation strategy of layered spiral scanning and broadband sinusoidal superposition disturbance, an excitation trajectory covering the entire workspace is planned in the workspace. The planned joint trajectories are obtained through the inverse kinematics algorithm. Each joint is driven to execute the trajectory and the joint friction force data is synchronously collected, including the joint position data, velocity data and torque data of the rope-driven parallel robot. The joint position data is determined by the joint encoder position signal, the velocity data is the differential velocity estimate, and the torque data is the raw data of the torque sensor.

[0060] Specifically, for a known ellipsoidal end workspace, in order to plan an excitation trajectory with full coverage of position information, a layered spiral basis trajectory is used to scan the multidimensional workspace. For an ellipsoidal workspace with diameters a, b, and c in each dimension and a center point at x0, y0, and z0, the layered spiral basis trajectory is:

[0061] rx(t)base =A×sin(ω1t)×cos(ω2t)+x0

[0062] ry(t) base =B×sin(ω1t)×sin(ω2t)+y0

[0063] ω1=0.01ω2

[0064] Where A and B are the axis lengths of the current layer. For a helix with a layer height of rz(t), A and B are:

[0065]

[0066] Among them, the three radii of the ellipsoid are a, b, and c, and c is the radius of the operating ellipsoid in the rz direction.

[0067] By adjusting the value of the rz direction, a spiral trajectory covering the entire end working space is formed to ensure uniform sampling of the end position. In order to ensure the completeness of the velocity information, a broadband random sine perturbation is superimposed on the end planning excitation trajectory as follows:

[0068]

[0069] Among them, N s is the number of random sinusoids, N randomly selected around the fundamental frequency and fundamental phase s A random frequency ω lx 、ω ly and random phase φ lx 、φ ly , for any layer of spiral, the equation is rx(t)=rx(t) base +rx(t) disturb ,ry(t)=ry(t) base +ry(t) disturb .

[0070] The robot is allowed to run according to the specified composite excitation trajectory and synchronously collect encoder position signals, differential velocity estimates, and torque sensor raw data.

[0071] Among them, the composite excitation trajectory is composed of a layered spiral base trajectory and a broadband random sinusoidal perturbation superposition, and the trajectory equation of the end effector is:

[0072]

[0073] Where ω1 and ω2 are used to control the extension speed of the spiral line, rz(t) is the current layer height, and N s is the number of random sinusoids, A dis the disturbance amplitude, rz0 is the initial layer height, ω1 and ω2 are the phase frequencies; the joint space reference trajectory is obtained by inverse kinematics solution, and the encoder position q is synchronously collected. i , differential speed and torque sensor data τ i , and based on the kinetic equation Separation friction torque.

[0074] In some embodiments, when executing step 102, the specific steps may be as follows:

[0075] The joint position data, velocity data and torque data are filtered respectively using an n-order Butterworth low-pass filter. In this embodiment, an n-order (n=6) Butterworth low-pass filter is used to perform the same filtering process on the joint position, velocity and torque signals:

[0076]

[0077] In view of the strong coupling characteristics of the joint friction of the rope-driven parallel robot, a 6-dimensional input vector is defined as the joint position q1, q2, q3 and the velocity The 3D output vectors τ1, τ2, τ3 are used to construct a multi-input and multi-output SVGP model. In the kernel function design, the radial basis function (RBF) kernel is used in the position dimension. Modeling global nonlinear characteristics, the velocity dimension uses the Matern 3 / 2 kernel Capture local mutation behavior of velocity;

[0078] According to the position dimension and the speed dimension, a mixed product kernel function is constructed in the form of a product. in is a six-dimensional input vector, l v 、l q is a trainable length scale hyperparameter;

[0079] According to the mixed product kernel function, the multi-input and multi-output SVGP friction coupling model is determined.

[0080] In some embodiments, when executing step 103, the specific steps may be as follows:

[0081] The filtered joint position data, velocity data, and torque data are divided into training sets and test sets in proportion;

[0082] The k-means clustering algorithm is used to select about 5% of the induction points in the workspace of the rope-driven parallel robot and construct the variational distribution q(u)=Ν(m,S); where m is the mean and S is the covariance;

[0083] The covariance matrix inversion operation is accelerated by Cholesky decomposition. A mini-batch stochastic gradient optimization strategy is adopted to divide the training set into multiple subsets of 128 samples / batch. A subset is randomly selected in each iteration to calculate the gradient approximation, and the Adam optimizer is used to maximize the lower bound of the evidence.

[0084] Based on the trained variational parameters and induction points, sparse Gaussian process regression is used to predict the joint friction force of the test set, and the prediction error is calculated;

[0085] If the prediction error is less than the preset threshold, the trained multi-input and multi-output SVGP friction coupling model is output;

[0086] If the prediction error is greater than or equal to the preset threshold, the number of induction points, the initialization value of the variational parameter or the optimization strategy are adjusted, and the above training process is repeated until the prediction error is less than the preset threshold.

[0087] Specifically, the preprocessed data is divided into training and test sets in a ratio of 7:3. The k-means clustering algorithm is used to select about 5% of the induction points in the 6-dimensional input space to construct the variational distribution q(u) = N(m, S); where m is the mean and S is the covariance. The Cholesky decomposition is used to accelerate the inversion of the covariance matrix, and the computational complexity is reduced from O(N 3 ) is reduced to O(M 2 N), where M is the number of induction points. A mini-batch stochastic gradient optimization strategy is used to divide the training set into multiple subsets of 128 samples / batch. In each iteration, a subset is randomly selected to calculate the gradient approximation, and the Adam optimizer is used to maximize the evidence lower bound (ELBO).

[0088] In some embodiments, when executing step 104, the specific steps may be as follows:

[0089] The trained multi-input and multi-output SVGP friction coupling model is compiled into a real-time module and embedded into the real-time control system of the rope-driven parallel robot.

[0090] Synchronously read the joint position data and velocity data of each joint at a sampling frequency of 200Hz, and predict the joint friction torque online;

[0091] Through current torque coefficient K t The feedforward current value is converted and injected into the q-axis current loop of the rope-driven parallel robot driver to form the feedforward compensation term where K p and K d is the current loop gain coefficient, e i is the current deviation, is the time derivative of the current deviation, is the predicted joint friction torque.

[0092] Specifically, it is sent to the following Figure 2 The cascade control architecture of the joint driver shown in the figure, in the cascade controller, the predicted joint friction force is converted into a feedforward current value through the current-torque constant k and injected into the current loop as a feedforward term. The current loop adjusts the joint motor. After adjustment, the speed loop and the position loop continue to collect speed and position data.

[0093] Example 2

[0094] like Figure 3 As shown, this embodiment provides a friction modeling system for a rope-driven parallel robot, comprising:

[0095] The acquisition module 301 is used to generate a composite excitation trajectory covering the entire workspace of the rope-driven parallel robot and collect joint friction force data during the movement of the rope-driven parallel robot; the composite excitation trajectory is composed of a layered spiral base trajectory superimposed with a broadband random sinusoidal perturbation;

[0096] A model building module 302 is configured to build a multi-input multi-output (SVGP) friction coupling model based on the joint friction force data during the motion of the rope-driven parallel robot; the multi-input multi-output (SVGP) friction coupling model is a multi-input multi-output (SVGP) friction coupling model that jointly models the nonlinear coupling characteristics of the positions and velocities of the three joints.

[0097] A model training module 303 is configured to optimize the parameters of the multi-input multi-output SVGP friction coupling model using a variational inference and lightweight training strategy to obtain a trained multi-input multi-output SVGP friction coupling model;

[0098] The friction compensation module 304 is used to deploy the trained multi-input multi-output SVGP friction coupling model to the real-time control system of the rope-driven parallel robot, and perform dynamic friction feedforward compensation on the rope-driven parallel robot.

[0099] The joint friction force data includes joint position data, speed data and torque data of the rope-driven parallel robot.

[0100] In summary, this application has the following technical effects:

[0101] This application uses sparse variational Gaussian processes (SVGP) to model the multi-source nonlinear friction coupling characteristics of a rope-driven robot in real time, and uses a composite excitation trajectory to stimulate and collect joint position, velocity, and torque data; constructs a multi-input and multi-output SVGP model to jointly predict the friction torque of three joints, explicitly capturing the interactive effects of hysteresis friction, harmonic reducer nonlinearity, and parallel mechanism dynamic coupling; optimizes model parameters based on variational inference and lightweight training strategies, significantly reducing the computational complexity of traditional Gaussian processes; embeds the training model into a real-time control system to dynamically offset friction interference in the form of feedforward compensation. The friction compensation method for rope-driven robots based on SVGP proposed in this application solves the problem of high-precision modeling of multi-degree-of-freedom strongly coupled friction, can significantly reduce the position tracking error and phase lag of rope-driven robots with large reduction ratios, improve the control bandwidth, and provide an efficient and robust nonlinear disturbance suppression solution for rope-driven robots in precision operation scenarios.

[0102] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0103] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A friction modeling method for a rope-driven parallel robot, characterized in that: include: Generate a composite excitation trajectory covering the entire workspace of the rope-driven parallel robot, and collect joint friction force data during the movement of the rope-driven parallel robot; the composite excitation trajectory is composed of a layered spiral base trajectory superimposed with a broadband random sine perturbation; Based on the joint friction force data of the rope-driven parallel robot during motion, a multi-input multi-output SVGP friction coupling model is constructed; the multi-input multi-output SVGP friction coupling model uses the multi-input multi-output SVGP model to jointly model the nonlinear coupling characteristics of the three joint positions and velocities; The variational inference and lightweight training strategy are used to optimize the parameters of the multi-input multi-output SVGP friction coupling model, and the trained multi-input multi-output SVGP friction coupling model is obtained. The trained multi-input and multi-output SVGP friction coupling model is deployed to the real-time control system of a rope-driven parallel robot to perform dynamic friction feedforward compensation on the rope-driven parallel robot.

2. The friction modeling method of a cable-driven parallel robot according to claim 1, characterized in that: The joint friction force data includes joint position data, velocity data, and torque data of the rope-driven parallel robot.

3. The friction modeling method of a cable-driven parallel robot according to claim 2, characterized in that: The formula expression of the layered spiral basis trajectory is: rx(t) base =A×sin(ω1t)×cos(ω2t)+x0 ry(t) base =B×sin(ω1t)×sin(ω2t)+y0 Among them, ω1=0.01ω2, A and B are the axis lengths of the current layer, and x0, y0 are the coordinates of the center point of the rope-driven parallel robot workspace.

4. The friction modeling method of a cable-driven parallel robot according to claim 3, characterized in that: The formula for broadband random sinusoidal disturbance is: Among them, N s is the number of random sinusoids, ω lx 、ω ly is a random frequency randomly selected from the fundamental frequency and fundamental phase, φ lx 、φ ly is a random phase randomly selected from the fundamental frequency and fundamental phase, A d is the disturbance amplitude.

5. The friction modeling method of a cable-driven parallel robot according to claim 4, characterized in that: The formula expression of the composite excitation trajectory is: Among them, rz(t) is the current layer height, rz0 is the initial layer height, ω1 and ω2 are phase frequencies, and the three radii of the ellipsoid are a, b, and c, respectively. C is the radius of the operating ellipsoid in the rz direction.

6. The friction modeling method of a cable-driven parallel robot according to claim 5, characterized in that: Based on the joint friction force data of the rope-driven parallel robot during motion, a multi-input and multi-output SVGP friction coupling model is constructed, which includes: The n-th order Butterworth low-pass filter is used to filter the joint position data, velocity data and torque data respectively; In view of the strong coupling characteristics of the joint friction of the rope-driven parallel robot, a 6-dimensional input vector is defined as the joint position q1, q2, q3 and the velocity 3D output vector τ1, τ2, τ3, and construct a mixed product kernel function; the position dimension of the mixed product kernel function adopts the radial basis function kernel Modeling global nonlinear characteristics, the velocity dimension uses the Matern 3 / 2 kernel Capture the local mutation behavior of speed; where i, j∈{1, 2, 3}; According to the position dimension and the speed dimension, a mixed product kernel function is constructed in the form of a product. in is a six-dimensional input vector, l v 、l q is a trainable length scale hyperparameter; According to the mixed product kernel function, the multi-input and multi-output SVGP friction coupling model is determined.

7. The friction modeling method of a cable-driven parallel robot according to claim 6, characterized in that: The variational inference and lightweight training strategy are used to optimize the parameters of the multi-input and multi-output SVGP friction coupling model, and the trained multi-input and multi-output SVGP friction coupling model is obtained, which specifically includes: The filtered joint position data, velocity data, and torque data are divided into training sets and test sets in proportion; The k-means clustering algorithm is used to select about 5% of the induction points in the workspace of the rope-driven parallel robot and construct the variational distribution q(u)=Ν(m,S); where m is the mean and S is the covariance; The covariance matrix inversion operation is accelerated by Cholesky decomposition. A small batch stochastic gradient optimization strategy is adopted to divide the training set into multiple subsets of a set number of samples or batches. A subset is randomly selected in each iteration to calculate the gradient approximation, and the Adam optimizer is used to maximize the lower bound of the evidence. Based on the trained variational parameters and induction points, sparse Gaussian process regression is used to predict the joint friction force of the test set, and the prediction error is calculated; If the prediction error is less than the preset threshold, the trained multi-input and multi-output SVGP friction coupling model is output; If the prediction error is greater than or equal to the preset threshold, the number of induction points, the initialization value of the variational parameter or the optimization strategy are adjusted, and the above training process is repeated until the prediction error is less than the preset threshold.

8. The friction modeling method of a cable-driven parallel robot according to claim 1, characterized in that: The trained multi-input multi-output SVGP friction coupling model is deployed to the real-time control system of the rope-driven parallel robot to perform dynamic friction feedforward compensation on the rope-driven parallel robot, specifically including: The trained multi-input and multi-output SVGP friction coupling model is compiled into a real-time module and embedded into the real-time control system of the rope-driven parallel robot. Synchronously read the joint position data and velocity data of each joint at the set sampling frequency and predict the joint friction torque online; Through current torque coefficient K t The feedforward current value is converted and injected into the q-axis current loop of the rope-driven parallel robot driver to form the feedforward compensation term where K p and K d is the current loop gain coefficient, e i is the current deviation, is the time derivative of the current deviation, is the predicted joint friction torque.

9. A friction modeling system for a rope-driven parallel robot, characterized in that: include: An acquisition module is used to generate a composite excitation trajectory covering the entire workspace of the rope-driven parallel robot and to collect joint friction force data during the movement of the rope-driven parallel robot; the composite excitation trajectory is composed of a layered spiral base trajectory superimposed with a broadband random sinusoidal perturbation; A model building module is used to build a multi-input multi-output SVGP friction coupling model based on the joint friction force data of the rope-driven parallel robot during movement; the multi-input multi-output SVGP friction coupling model uses the multi-input multi-output SVGP model to jointly model the nonlinear coupling characteristics of the three joint positions and velocities; The model training module is used to optimize the parameters of the multi-input multi-output SVGP friction coupling model using variational inference and lightweight training strategies to obtain the trained multi-input multi-output SVGP friction coupling model; The friction compensation module is used to deploy the trained multi-input and multi-output SVGP friction coupling model to the real-time control system of the rope-driven parallel robot and perform dynamic friction feedforward compensation on the rope-driven parallel robot.

10. The friction modeling system of a cable-driven parallel robot according to claim 9, characterized in that: The joint friction force data includes joint position data, velocity data, and torque data of the rope-driven parallel robot.

Images