Compensation method and device for motion trail error of parallel robot

Abstract

The invention provides a compensation method and device for a motion trail error of a parallel robot, and belongs to the technical field of parallel robots. The method provided by the invention comprises the following steps: acquiring an expected trajectory of the parallel robot; the expected trajectory is input into the trained CNN-GRU-KAN model, and the CNN-GRU-KAN model outputs a predicted trajectory error; fitting the predicted trajectory error into a sine curve comprising offset based on a least square method; acquiring an amplitude and a bias in the sine curve as an amplitude error and a bias error; generating a compensation control instruction of the parallel robot according to the amplitude error and the offset error; and controlling the parallel robot to move based on the compensation control instruction. The compensation method and device for the motion trail error of the parallel robot are used for improving the motion trail precision of the parallel robot.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of parallel robots, and particularly relates to a parallel robot motion trajectory error compensation method and device. BACKGROUND

[0002] Parallel robots are widely used in motion simulation testing, high-precision assembly, intelligent manufacturing and other scenes due to their greater stiffness-to-mass ratio, effective load-to-weight ratio, faster dynamic response, higher flexibility and repeatability. The dynamic accuracy of the parallel robot is a key indicator for guaranteeing the reliability of a complex motion testing system with the parallel robot as the core. However, due to factors such as part machining errors, assembly errors, stress deformation and wear, the motion performance of the parallel robot is reduced, which seriously restricts its application in various high-precision engineering fields. Therefore, it is crucial to study the high-precision trajectory error prediction and compensation method of the parallel robot to improve its performance and guarantee the reliability of the application system.

[0003] At present, the motion error compensation of the parallel robot can be divided into online compensation and offline compensation. The online compensation corrects the error by monitoring the absolute position of the robot through an additional measuring device, but it highly depends on the measurement accuracy of the external monitoring device, which limits the application of the robot in complex industrial environments. Moreover, since the principle of the online compensation is to calculate the error based on the measurement at the previous moment, the control action is always lagging behind the error. The offline compensation usually relies on mathematical modeling of the robot system error, and the error compensation is achieved by identifying and correcting the model parameters. However, since the error model cannot include all error sources, and the measuring device has unavoidable errors, the uncertainty of the error parameter identification is increased, which further limits the improvement of the pose accuracy of the robot by these parameter identification methods. SUMMARY

[0004] Therefore, the present application provides a parallel robot motion trajectory error compensation method and device to improve the motion trajectory accuracy of the parallel robot.

[0005] Specifically, the present application is implemented by the following technical solutions:

[0006] The first aspect of the present application provides a parallel robot motion trajectory error compensation method, which comprises:

[0007] obtaining a desired trajectory of the parallel robot;

[0008] inputting the desired trajectory into a trained CNN-GRU-KAN model, wherein the CNN-GRU-KAN model outputs a predicted trajectory error;

[0009] fitting the predicted trajectory error into a sinusoidal curve including a bias based on the least square method.

[0010] obtain the amplitude and the bias in the sinusoidal curve as an amplitude error and a bias error;

[0011] generate compensation control instructions of the parallel robot according to the amplitude error and the bias error, and control the parallel robot to move based on the compensation control instructions.

[0012] The second aspect of the present application provides a device for compensating trajectory error of a parallel robot, the device comprising an acquisition module, a prediction module and a compensation module; wherein,

[0013] The acquisition module is configured to acquire a desired trajectory of the parallel robot.

[0014] The prediction module is configured to input the desired trajectory into a trained CNN-GRU-KAN model, and the CNN-GRU-KAN model outputs a predicted trajectory error.

[0015] The compensation module is configured to fit the predicted trajectory error into a sinusoidal curve including a bias based on a least square method.

[0016] The compensation module is further configured to obtain the amplitude and the bias in the sinusoidal curve as an amplitude error and a bias error.

[0017] The compensation module is further configured to generate compensation control instructions of the parallel robot according to the amplitude error and the bias error, and control the parallel robot to move based on the compensation control instructions.

[0018] The parallel robot trajectory error compensation method and device provided by the present application can effectively improve the trajectory performance of the parallel robot. Specifically, by constructing a CNN-GRU-KAN model that integrates a convolutional neural network (CNN), a gated recurrent unit (GRU) and a Kolmogorov-Arnold (KAN) network, the model can more comprehensively learn the relationship between the motion trajectory error and the command trajectory, effectively reduce the interference of measurement noise, and then accurately predict the trajectory error of the parallel robot. The predicted error is fitted into the input sinusoidal curve of the parallel robot, the amplitude error and the bias error are calculated, and the amplitude and the bias of the trajectory error are doubly compensated at the control command end, effectively improving the trajectory performance of the parallel robot and making the motion trajectory accuracy of the parallel robot after error compensation improved by two orders of magnitude. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 A flowchart of a parallel robot trajectory error compensation method embodiment one provided by the present application is shown in FIG. 1;

[0020] Figure 2A schematic diagram of a CNN-GRU-KAN model structure shown in an exemplary embodiment of the present application;

[0021] Figure 3 A simplified structure schematic diagram of a parallel robot shown in an exemplary embodiment of the present application; wherein, Figure 3 (a) is a simplified structure perspective view of a parallel robot shown in an exemplary embodiment of the present application; Figure 3 (b) is a simplified structure top view of a parallel robot shown in an exemplary embodiment of the present application;

[0022] Figure 4 A structure schematic diagram of a parallel robot motion trajectory error compensation device embodiment two provided by the present application. DETAILED DESCRIPTION

[0023] The exemplary embodiments will be described in detail herein with reference to the attached drawings. When the description below refers to accompanying drawings, unless otherwise noted, the same numbers in different drawings refer to the same or similar elements. The implementations described in the following exemplary embodiments are not meant to represent all implementations consistent with the present application.

[0024] The terminology used in the present application is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used in the present application, the singular forms "a," "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0025] It should be understood that, although the terms first, second, third, etc. can be used herein to describe various information, these terms are not intended to denote a particular order of the information. These terms are used only to distinguish one type of information from another. For example, without departing from the scope of the present application, the first information can be referred to as the second information, and similarly, the second information can be referred to as the first information. Depending on the context, the word "if' as used herein can be interpreted as meaning "when" or "in response to determining."

[0026] The following specific embodiments are given to introduce the technical solutions of the present application in detail.

[0027] Figure 1 A flowchart of a parallel robot motion trajectory error compensation method embodiment one provided by the present application. Please refer to Figure 1 The method provided by the present embodiment can include:

[0028] S101, obtaining a desired trajectory of a parallel robot.

[0029] Specifically, the parallel robot provided in the embodiment is a 6-UPS (Universal-Prismatic-Spherical) parallel robot, also known as a Stewart platform, which is composed of a moving platform, a static platform, a spherical revolute joint, a revolute joint, an electric cylinder, and a servo motor. The moving platform is connected to the static platform by six driving legs, which can move independently in the extension direction, enabling the moving platform to have flexible movement capability. By controlling the lengths of the six driving legs, the moving platform can realize translational movement along the x, y, and z axes, and also can rotate around the x, y, and z axes, thereby achieving comprehensive six-degree-of-freedom pose adjustment.

[0030] Further, the desired trajectory refers to an ideal motion trajectory that the parallel robot should follow according to the work task requirements. Its essence is the target pose time sequence that the moving platform of the parallel robot should achieve in three-dimensional space. According to the industrial task requirements, the motion trajectory parameters of the parallel robot are preset to generate time-sequential desired trajectory data, including translational trajectories along the x, y, and z axes and rotational trajectories around the three coordinate axes.

[0031] Further, through the trajectory planning module of the upper computer control system (such as PLC, industrial PC), the trajectory type (such as x-axis sinusoidal motion) and key parameters (such as sinusoidal trajectory amplitude 10-60 mm, frequency 0.1 Hz; circular trajectory radius 10-60 mm, plane xoy / xoz) are inputted to automatically generate a discrete desired trajectory coordinate sequence (time interval 0.01-0.1 s, containing position (x, y, z) and attitude (α, β, γ) at each time).

[0032] Further, the specific implementation steps of obtaining the desired trajectory of the parallel robot include:

[0033] (1) determining the work scene type of the parallel robot, the work scene type including a precision assembly scene and a trajectory simulation scene;

[0034] Specifically, by analyzing the actual application requirements of the parallel robot, the core work task type it performs is determined. The precision assembly scene refers to the operation of high-precision docking and installation of parts, which has high requirements for trajectory position accuracy and attitude stability. The trajectory simulation scene refers to the reproduction of a pre-set complex motion path (such as simulating the motion trajectory under a specific working condition), which has high requirements for the shape consistency and dynamic following of the trajectory. Through a human-computer interaction interface (such as a scene selection module of industrial control software) or a pre-set work task code, the scene type to which the current work belongs is determined, providing a basis for the selection of subsequent trajectory templates.

[0035] (2) selecting a corresponding trajectory template according to the work scene type, the trajectory template including a sinusoidal trajectory template, a circular trajectory template, and an elliptical trajectory template;

[0036] Specifically, based on the determined job scene type, an adaptive trajectory template is matched from a preset trajectory template library. For example, in a precision assembly scene, if single-axis reciprocating alignment is required, a sine trajectory template can be selected; if an assembly path simulation of a ring-shaped component in a plane is required, a circular trajectory template can be selected; if a non-symmetrical curve motion needs to be reproduced in a trajectory simulation scene, an elliptical trajectory template can be selected. The trajectory template pre-stores a basic mathematical model (such as a sine function, a parameter equation of a circle, and an elliptical equation) corresponding to the trajectory and a parameter input interface, so as to ensure that the template matches the motion characteristics of the job scene.

[0037] Further, the trajectories commonly used by parallel robots are all synthesized by sine motions, and the spatial sine, circular, and elliptical motions of a parallel robot can be represented by sine motions in x, y, and z axial directions.

[0038] ;

[0039] wherein A x , A y , and A z are amplitude values of the sine motions in the respective axial directions, is an angular frequency of the motion, t is a time variable, and φ x , φ y、 , and φ z are initial phase angles corresponding to the respective axial directions.

[0040] Further, when A z is zero, a motion trajectory is generated in the xoy plane: 1. a straight line trajectory: A x =A y and a phase difference ||φ x -φ y ||=0; 2. a circular trajectory: A x =A y and ||φ x -φ y ||=90°; 3. an elliptical trajectory: other cases except the above conditions.

[0041] When A y is zero, a motion trajectory is generated in the xoz plane: 1. a straight line trajectory: A x =A z and a phase difference ||φ x- φ z ||=0; 2. a circular trajectory: A x =A z and ||φ x -φ z ||=90°; 3. an elliptical trajectory: other cases except the above conditions.

[0042] When Ax When the value is zero, the following motion trajectories are generated on the yoz plane: 1. Straight line trajectory: A y =A z And the phase difference ||φ y -φ z ||=0; 2. Circular locus: A y =A z And ||φ y -φ z ||=90°; 3. Elliptical trajectory: Other cases besides the above conditions.

[0043] (3) Input trajectory parameters based on the trajectory template;

[0044] Specifically, based on the selected trajectory template, key trajectory parameters are entered or adjusted through the parameter input interface of the host computer control system. These parameters include the motion axis, amplitude, frequency, radius, and motion plane. For a sinusoidal trajectory template, input parameters include motion direction (e.g., along a coordinate axis), motion amplitude, and motion period. For a circular trajectory template, input parameters include the motion plane, trajectory radius, and motion speed. For an elliptical trajectory template, input parameters include the major axis, minor axis length, motion plane, and rotation direction. Parameter input must conform to the template's format requirements. The system automatically verifies the parameters' rationality (e.g., whether the parameter range is within the robot's motion capabilities) to ensure the input parameters are valid.

[0045] (4) Generate the desired trajectory of the parallel robot based on the trajectory parameters.

[0046] Specifically, the input trajectory parameters are substituted into the mathematical model of the selected trajectory template, and the system's built-in trajectory generation algorithm is used to calculate and generate a continuous trajectory function. Subsequently, the continuous trajectory function is discretized according to the parallel robot control cycle (e.g., a fixed time interval), resulting in a time-series data sequence containing the position coordinates (x, y, z) and attitude angles (α, β, γ) at each time point. The generated desired trajectory data is stored in a standardized format, and the trajectory shape can be previewed through a visual interface. Once confirmed to be correct, it serves as the reference trajectory for subsequent error prediction and compensation.

[0047] S102. Input the desired trajectory into the trained CNN-GRU-KAN model, and the CNN-GRU-KAN model outputs the predicted trajectory error.

[0048] Specifically, Figure 2 The schematic diagram of the CNN-GRU-KAN model structure shown in this exemplary embodiment is provided in the present application. Please refer to... Figure 2 The CNN-GRU-KAN model is composed of CNN layers, GRU layers, KAN layers, and attention layers connected sequentially, including:

[0049] The CNN layer is used to extract spatial features in the expected trajectory and to denoise the expected trajectory.

[0050] The GRU layer receives the spatial features output by the CNN layer, captures time-dependent features in the spatial features, and outputs a first six-dimensional feature; wherein the first six-dimensional feature includes time-varying features of x-axis position error, y-axis position error, z-axis position error, rotation angle error around the x-axis, rotation angle error around the y-axis, and rotation angle error around the z-axis.

[0051] The KAN layer receives the spatial features output by the CNN layer, fits a nonlinear relationship between the spatial features and the prediction error, and outputs a second six-dimensional feature; wherein the second six-dimensional feature includes nonlinear error components in x-axis position error, y-axis position error, z-axis position error, rotation angle error around the x-axis, rotation angle error around the y-axis, and rotation angle error around the z-axis.

[0052] The attention layer receives the first six-dimensional feature and the second six-dimensional feature, fuses the first six-dimensional feature and the second six-dimensional feature, and outputs the predicted trajectory error.

[0053] Specifically, the input of the CNN layer is the expected trajectory (including time series of x / y / z axis positions and rotation angles around three coordinate axes), the CNN layer extracts local spatial features of the trajectory (for example, amplitude variation of a sinusoidal trajectory, curvature abrupt change point of a circular trajectory) through convolution operation (such as 3x1 convolution kernel), and filters measurement noise (such as high-frequency interference of a sensor) in the data by using the smoothing effect of the convolution layer, and outputs the spatial features after preliminary processing.

[0054] Further, the convolutional neural network (CNN) as a deep learning architecture with hierarchical feature learning ability, its core structure is composed of convolutional layer, pooling layer, activation function module and full connection layer, which can automatically extract multi-angle and deep features from raw data. Among them, the convolutional layer performs local perception on the input data through multiple learnable convolution kernels, and its weight sharing mechanism effectively reduces the parameter size. Rectified Linear Unit (ReLU) is the most commonly used activation function in the convolutional neural network, which can effectively capture the nonlinear features between input data by adding ReLU activation function after each convolutional layer. In the CNN layer, the convolutional layer is the most important part, which captures spatial features by performing convolution operation on adjacent points in the input vector. The typical components of convolution parameters include the number of convolution kernels, the size of convolution kernel and the step. The operation of convolutional layer can be represented as:

[0055] ;

[0056] where x i t is the i-th output of the t-th layer;

[0057] x j t-1 is the j-th output of the t-1-th layer;

[0058] w t ij is the weight matrix of the convolution kernel;

[0059] b t i is the bias of the convolution kernel;

[0060] is the activation function.

[0061] Furthermore, after the CNN layer processes the expected trajectory of the input and outputs spatial features, these spatial features are input into the GRU and KAN layers. The GRU (Gate Recurrent Unit) layer is a neural network structure designed for efficiently processing sequential data and capturing temporal dependencies. As a popular variant of Long Short-Term Memory (LSTM), GRU solves the common problems of gradient vanishing or exploding and long-range dependency capture in Recurrent Neural Networks (RNNs). In addition, GRU optimizes the network structure and enhances the portability of RNNs through its simplified gating mechanism and recurrent unit design, while providing a more concise and efficient architecture than LSTM. This allows GRU to not only balance application and training but also effectively mitigate the tendency of overfitting. Based on the memory mechanism of the Gated Recurrent Unit (GRU), it captures the dynamic evolution of spatial features over time (e.g., the temporal changes of a sinusoidal trajectory within its period of "rise-peak-fall-trough," and the phase coupling relationship of the x / y axis coordinates of a circular trajectory), upgrading static spatial features into dynamic features that include a time dimension. The core operation of the GRU layer is represented as follows:

[0062] ;

[0063] ;

[0064] ;

[0065] ;

[0066] in, This represents the sigmoid activation function, c k z represents the memory state. k and r k These are the update door and the reset door, W. r W z W represents the weight matrix, x k y represents the input information of the neuron, tanh represents the activation function, and y represents the input information of the neuron. k It is the output of the neuron. It's a memory gate.

[0067] Further, the KAN layer (Kolmogorov-Arnold network, KAN) is a neural network architecture based on the Kolmogorov-Arnold representation theorem, which migrates the nonlinearity of the multilayer perceptron (MLP) from the fixed neurons to the edge weights of the network, and has higher prediction accuracy, parameter efficiency and interpretability. No traditional linear weight is used, and each weight parameter is replaced by a univariate function parameterized as a spline. Compared with the centralized architecture of MLP, the core innovation of KAN is to replace the fixed activation function with a learnable combination of basis functions, which not only maintains the efficiency of parameters, but also significantly enhances the non-linear learning ability of the model; the Kolmogorov-Arnold theorem can be expressed as:

[0068] ;

[0069] where φ q,p is a univariate function acting on x p a single input variable, and is another set of univariate functions used to integrate intermediate results. The mathematical framework provides a powerful modeling basis for expressing complex multivariate functions.

[0070] Further, the CNN-GRU-KAN model provided in the embodiment fuses CNN, GRU and KAN networks, and introduces a channel attention mechanism. The input of the CNN-GRU-KAN model is the expected trajectory of the parallel robot under different amplitudes, and the output is the corresponding trajectory error. The KAN network has strong data fitting capability, but is sensitive to noise interference. The GRU network has strong advantages in processing sequence data, and combined with the feature extraction capability of the CNN, can effectively reduce the interference of measurement noise. Finally, the information of the two channels is automatically fused through the attention mechanism to ensure high-precision prediction of the trajectory error.

[0071] Optionally, the CNN layer includes two convolutional layers, the first convolutional layer includes six convolutional kernels, and the second convolutional layer includes three convolutional kernels; the GRU layer includes six GRU units; the input layer of the KAN layer includes eleven nodes, the intermediate layer includes eight hidden nodes, the output layer includes six nodes, and two hidden layers are further included.

[0072] Specifically, Table 1 is an exemplary super parameter setting of the CNN-GRU-KAN model according to the embodiment, please refer to Table 1:

[0073] Table 1 Super parameter setting of CNN-GRU-KAN model

[0074]

[0075] Further, the main hyperparameters of the CNN-GRU-KAN model are shown in Table 1. The parameters in the KAN layer include the number of nodes, the number of grids, the value of k, and the residual function of the KAN layer. Among them, the KAN layer node [11, 8, 6] means that the input layer of the KNA layer has 11 nodes, the middle layer has 8 hidden nodes, and the output layer has 6 nodes, with a total of two hidden layers; the value of k represents the order of the piecewise polynomial, which and the number of grids are optimization parameters of the KAN network; the residual function uses the ReLU function, which enhances the nonlinear expression ability. The CNN layer in the CNN-GRU-KAN model contains two convolutional layers, and the size of the convolution kernel of each convolutional layer is 3x1. The number of convolution kernels in the first layer and the second layer is 6 and 3 respectively. The GRU layer has a total of 6 GRU units. ReLU activation functions are equipped after the CNN layer, the GRU layer and the KAN network layer. The attention layer has 12 inputs and two outputs, which is responsible for receiving the first six-dimensional features and the second six-dimensional features from the KAN network and the GRU network. The first six-dimensional features focus on the time sequence and spatial dynamic evolution law of the trajectory error, including the time sequence change characteristics of the x-axis position error, the time sequence change characteristics of the y-axis position error, the time sequence change characteristics of the z-axis position error, the time sequence change characteristics of the rotation angle error around the x-axis, the time sequence change characteristics of the rotation angle error around the y-axis, and the time sequence change characteristics of the rotation angle error around the z-axis. Through the gating mechanism of the GRU layer, the correlation of the trajectory error in the time dimension is retained (such as the "rise-peak-fall" period characteristics of the sine trajectory error, the x / y axis phase coupling characteristics of the circular trajectory error), reflecting the dynamic change trend of the error with the movement process. The second six-dimensional features focus on the nonlinear mapping relationship of the trajectory error, which is the result of the KAN layer fitting the nonlinear law between the CNN spatial features and the error, including: the error component in the x-axis position error caused by nonlinear factors (such as structural deformation, joint clearance), the nonlinear error component in the y-axis position error, the nonlinear error component in the z-axis position error, the nonlinear error component in the rotation angle error around the x-axis, the nonlinear error component in the rotation angle error around the y-axis, and the nonlinear error component in the rotation angle error around the z-axis. The core of the second six-dimensional features is to capture the strong nonlinear relationship (such as the nonlinear amplification of the error when the amplitude is large, the cross error when the multi-axis coupling motion is performed) that is difficult to represent by traditional linear models through the spline function of the KAN layer, reflecting the complex nonlinear correlation between the error and the trajectory parameters (such as amplitude, frequency). The first six-dimensional features and the second six-dimensional features are both in the dimension of 6 degrees of freedom, but the first six-dimensional features focus on the dynamic change law of the error with time, and the second six-dimensional features focus on the nonlinear mapping law between the error and the trajectory parameters. After the fusion of the first six-dimensional features and the second six-dimensional features through the attention layer, the time sequence characteristics and nonlinear characteristics of the error can be comprehensively covered, providing complete feature support for accurately predicting the trajectory error.

[0076] Further, the attention layer obtains two weights by learning, and the outputs of the KAN network and the GRU network are fused through the two weights, and finally the predicted trajectory error is output through the output layer.

[0077] Further, the CNN layer is responsible for extracting spatial features of the expected trajectory and denoising, providing a basis for subsequent processing; the GRU layer receives the spatial features output by the CNN layer, captures the time sequence dependence relationship therein, and generates a first six-dimensional feature; the KAN layer synchronously receives the spatial features of the CNN layer, focuses on fitting the nonlinear relationship between the spatial features and the prediction error, and outputs a second six-dimensional feature; the attention layer fuses the above two types of six-dimensional features, highlights the key features by dynamically allocating weights, and finally outputs the predicted trajectory error. Through the synergistic mechanism of spatial-temporal feature extraction + nonlinear fitting + adaptive fusion, the structure takes into account the capture of trajectory dynamic characteristics and complex nonlinear error rules, and improves the accuracy and robustness of error prediction in different scenarios.

[0078] Further, before inputting the expected trajectory into the trained CNN-GRU-KAN model, comprising:

[0079] (1) controlling the parallel robot to move according to the preset expected trajectory, and obtaining the actual motion trajectory of the preset expected trajectory;

[0080] Specifically, the parallel robot is controlled to move according to the preset expected trajectory (such as a sine trajectory or a circular trajectory), and the actual motion trajectory of the robot is synchronously collected through a high-precision measurement device (such as a 3D optical measurement system), so as to ensure that the preset expected trajectory and the actual motion trajectory correspond to each other in the time dimension, thereby providing basic data for error calculation.

[0081] Further, the trajectory type and parameters are input through the upper computer control system to generate a discretized expected trajectory instruction, the expected trajectory instruction is sent to the robot controller through the industrial bus, the servo motor is driven to move according to the instruction, the moving platform moves along the preset trajectory, and a 3D optical measurement system (such as MoveInspect XR) is used to capture the spatial pose of the moving platform in real time through the encoding target installed thereon, the sampling frequency is consistent with the expected trajectory instruction, and the actual motion trajectory data (containing time sequence of position and attitude) of the parallel robot is calculated.

[0082] (2) taking the difference between the preset expected trajectory and the actual motion trajectory as a trajectory error sample, and constructing a training data set based on multiple trajectory error samples;

[0083] Specifically, for each set of pre-set expected trajectory and actual motion trajectory, the difference between the two (actual trajectory - expected trajectory) is calculated at the time point to obtain a trajectory error sample containing 6 degrees of freedom (x / y / z axis position error, rotation angle error around x / y / z axis); The pre-set expected trajectory-trajectory error sample corresponding to multiple sets of trajectory with different parameters (such as sinusoidal trajectory with different amplitudes, circular trajectory with different radii) is paired to construct a training dataset covering a variety of motion scenarios, and the generalization ability of the model is improved.

[0084] Further, for each time point, the difference between the corresponding actual motion trajectory and the expected trajectory is calculated as the error value at that time point, and the error samples are formed by the error values at multiple time points. The expected trajectory and the corresponding trajectory error sample are paired in input-output format, and the training set (70%), the validation set (15%), and the test set (15%) are divided, and the data is normalized (mapped to the range [-1, 1]) to eliminate the influence of dimension.

[0085] (3) The pre-set expected trajectory in the training dataset is taken as the input, and the trajectory error sample is taken as the output, which is input into the initial CNN-GRU-KAN model for training to obtain the trained CNN-GRU-KAN model.

[0086] Specifically, the pre-set expected trajectory in the training dataset is taken as the input, and the trajectory error sample is taken as the supervised output, and the initial CNN-GRU-KAN model is trained. The parameters of each layer (such as the convolution kernel of CNN, the gating weight of GRU, and the spline function node of KAN) are iteratively optimized through the back propagation algorithm, and the loss (such as mean square error) between the model prediction error and the actual error sample is minimized until the accuracy of the model on the validation set meets the pre-set threshold (such as mean absolute error ≤0.05mm). Finally, a trained model that can accurately predict trajectory error is obtained.

[0087] Further, the CNN-GRU-KAN initial model is constructed, and parameters of each layer are configured: the CNN layer (2 convolution layers, 3*1 convolution kernel, number 6 / 3, ReLU activation), the GRU layer (6 units, ReLU activation), the KAN layer (node number [11, 8, 6], spline function grid number 5), the attention layer (12 inputs / 6 outputs); the Adam optimizer is adopted, the learning rate is 0.001, the batch size is 32, and the iteration number is 500 times; the mean square error (MSE) is used as the loss function, the training set is input into the model, and each layer parameter (convolution kernel weight, GRU gating parameter, KAN spline node) is updated through back propagation; the model performance is evaluated by the validation set every 10 iterations, when the validation set MSE does not decrease continuously for 20 iterations and the mean absolute error (MAE) is less than or equal to 0.05 mm, the training is stopped, and the model parameter is saved. The trained CNN-GRU-KAN model can output the corresponding prediction trajectory error according to the input expected trajectory.

[0088] In S103, the prediction trajectory error is fitted as a sinusoidal curve including bias based on the least square method.

[0089] Specifically, based on the time series data of the prediction trajectory error, a sinusoidal curve model including bias is set as the fitting target, the residual sum of squares of the fitting value and the actual error value is minimized by the least square method, the curve parameters are solved, and the sinusoidal curve capable of representing the error characteristics is obtained.

[0090] Further, the specific implementation steps of fitting the prediction trajectory error as a sinusoidal curve including bias based on the least square method include:

[0091] (1) extracting the motion angular frequency, time and initial phase angle from the prediction trajectory error;

[0092] Specifically, the required basic parameters for fitting are determined from the time series data of the prediction trajectory error and the associated expected trajectory parameters, including the motion angular frequency, the time variable and the initial phase angle initial value.

[0093] Further, the preset angular frequency of the expected trajectory is directly used (because the error and the trajectory fluctuate at the same frequency), and the calculation formula is ω=2πf, where f is the motion frequency of the expected trajectory (such as 0.1 Hz corresponding to ω=0.2π rad / s), which does not need to be extracted from the error, and is consistent with the trajectory period; the discrete time sequence corresponding to the prediction trajectory error data is extracted as the time; the initial phase angle is estimated by the zero-crossing point or the peak position of the error data, which provides a starting point for subsequent iterative optimization and reduces the convergence time.

[0094] (2) the product of a sine function with the angular frequency of motion, time, and initial phase angle as parameters and the sum of the sine amplitude error and the bias error as the fitting formula;

[0095] Specifically, based on the extracted parameters, a sine curve model with bias is constructed, and the error is decomposed into a periodic component and a fixed offset component.

[0096] Further, the fitting formula can be represented by the following formula:

[0097]

[0098] wherein, is the sine amplitude error to be solved (the amplitude of the periodic component);

[0099] is the bias error to be solved (the fixed offset);

[0100] is the angular frequency of motion;

[0101] is the time;

[0102] is the initial phase angle.

[0103] The fitting formula represents that the prediction trajectory error is decomposed into an error that fluctuates periodically with time (sine term) and a constant error that does not change with time (bias term), which respectively correspond to the dynamic error and the static error in the motion of the robot.

[0104] (3) input the prediction trajectory error and time into the fitting formula, minimize the residual sum of squares of the fitting formula based on the least squares method, and construct the sine curve with bias of the prediction trajectory error.

[0105] Specifically, taking the prediction trajectory error as the target value, the least squares method is used to optimize the fitting formula parameters, so that the deviation between the fitting curve and the error data is minimized, and finally the complete sine curve is determined.

[0106] ​Further, input the prediction trajectory error sequence {ΔQ(t1), ΔQ(t2),..., ΔQ(tn)} and the corresponding time sequence {t1, t2,..., tn}, define the residual error ei=ΔQ(ti)-ΔQ^(ti); the objective function is the sum of squares of residuals, and the least squares method is used to iteratively adjust Ap, φp, Bp until the minimum value is reached, at which time the parameters correspond to the optimal fitting result; the optimized parameters are substituted into the fitting formula to obtain the complete sinusoidal curve including the bias, as the mathematical representation of the prediction trajectory error, and through mathematical optimization, the fitting curve is highly consistent with the original error data, the amplitude error and the bias error are accurately extracted, and a quantitative basis is provided for subsequent compensation control, avoiding error analysis deviation caused by artificial experience.

[0107] The unstructured error time series data is converted into quantifiable sinusoidal curve parameters, which not only retains the periodicity and fixed offset characteristics of the error, but also ensures the fitting accuracy through the least squares method, laying a solid foundation for subsequent targeted compensation (offsetting amplitude error and bias error).

[0108] S104, the amplitude and bias in the sinusoidal curve are obtained as the amplitude error and the bias error.

[0109] Specifically, the coefficient Ap of the sinusoidal term in the fitting curve is directly read, which has the physical meaning of: the maximum fluctuation amplitude of the prediction trajectory error in one motion cycle, reflecting the dynamic change range of the error with the periodic motion of the trajectory; the constant term Bp in the fitting curve is directly read, which has the physical meaning of: the fixed offset of the prediction trajectory error in the entire motion process, reflecting the static offset characteristics of the error; for the prediction trajectory error of the six degrees of freedom (x / y / z axis position error, rotation error around x / y / z axis) of the parallel robot, the above extraction process is performed respectively to obtain the amplitude error and the bias error in each dimension (such as Apx, Bpx of x-axis position error, Apβ, Bpβ of rotation error around y-axis, etc.).

[0110] S105, generating compensation control instructions of the parallel robot according to the amplitude error and the bias error, and controlling the motion of the parallel robot based on the compensation control instructions.

[0111] Specifically, a compensation term is constructed based on the error parameters to correct the expected trajectory and drive the robot to move according to the corrected instructions.

[0112] Further, before generating the compensation control instructions of the parallel robot according to the amplitude error and the bias error, the method provided by the embodiment comprises:

[0113] (1) calculating the goodness of fit of the sinusoidal curve and the prediction trajectory error;

[0114] Specifically, the fitting degree of the sinusoidal curve obtained by quantization and the error of the original predicted trajectory is quantified by a quantitative index, and the curve is evaluated for its ability to represent the error characteristics.

[0115] Further, the goodness of fit R 2 As an evaluation index, the calculation formula is:

[0116] ;

[0117] Among them, is the actual value of the predicted trajectory error;

[0118] is the fitting value of the sinusoidal curve;

[0119] is the average value of the predicted trajectory error, and n is the number of data points.

[0120] The numerator is the sum of squares of fitting residuals (reflecting the deviation of the fitting curve from the actual error), and the denominator is the sum of squares of the deviation of the actual error from the average value (reflecting the dispersion degree of the error itself); the closer the calculation result is to 1, the better the fitting effect of the sinusoidal curve on the error.

[0121] (2) Based on the goodness of fit, the amplitude error and the bias error are verified for effectiveness.

[0122] Specifically, the goodness of fit is used as a threshold to determine whether the extracted amplitude error and bias error are reliable, ensuring that the error parameters used for compensation can truly reflect the error characteristics. By comparing the goodness of fit with the preset threshold, when the goodness of fit is greater than or equal to the preset threshold, it is determined that the sinusoidal curve has sufficiently captured the characteristics of the predicted trajectory error, and the extracted amplitude error and bias error are effective and can be directly used for subsequent compensation; when the goodness of fit is less than the preset threshold, it is determined that the fitting fails (such as the presence of non-periodic interference in the error), and the fitting process needs to be re-executed: adjust the estimated value of the initial phase angle (such as based on the peak position correction), or increase the number of iterations (such as from 100 to 200), and then solve the parameters by the least squares method again until the goodness of fit is greater than or equal to the preset threshold. By threshold control, unreliable error parameters are removed, ensuring that the amplitude error and bias error input into the compensation link can truly reflect the error law, and the compensation accuracy is guaranteed from the source.

[0123] Further, the implementation steps of generating the compensation control instruction of the parallel robot according to the amplitude error and the bias error include:

[0124] (1) Constructing an error compensation term according to the amplitude error and the bias error;

[0125] Specifically, the error compensation term can be represented by the following formula:

[0126] ;

[0127] wherein, is the sine amplitude error;

[0128] is the bias error;

[0129] is the angular frequency of motion;

[0130] is the time;

[0131] is the initial phase angle.

[0132] (2) generating a compensation control instruction based on the difference between the desired trajectory and the error compensation term.

[0133] Specifically, the desired trajectory is subtracted by the error compensation term to obtain a revised control instruction, so that the actual motion trajectory of the robot approaches the desired trajectory.

[0134] Further, the compensation control instruction can be generated by the following formula:

[0135] ;

[0136] wherein, is the desired trajectory at time t;

[0137] is the error compensation term at time t.

[0138] The continuous compensation control instructions are discretized into multiple groups of pose control parameters (x, y, z, a, b, g) at a preset time interval (such as 0.01s) to adapt to the discretization control requirements of the robot controller. Through the reverse revision of the desired trajectory and the compensation term, the error is offset at the instruction level (such as when the error is +0.8mm, the instruction is reduced by 0.8mm in advance), so that the actual motion trajectory of the robot under the influence of the error exactly approaches the desired trajectory, and the motion precision is significantly improved.

[0139] First, the amplitude error and the bias error are used to construct a compensation term consistent with the error characteristics, and then a revised instruction is generated by the difference between the desired trajectory and the compensation term, which fundamentally offsets the influence of the error on the actual trajectory. Compared with the traditional post-revision method, it is not necessary to measure the actual trajectory in real time, but only the predicted error can realize the forward compensation, and it is suitable for multi-axis independent error characteristics, which has higher real-time and precision in the complex motion scene of parallel robots.

[0140] Further, the implementation steps of controlling the motion of the parallel robot based on the compensation control instruction include:

[0141] (1) discretize the compensation control instruction into a plurality of groups of pose control parameters according to a preset time interval;

[0142] Specifically, according to the control period of the parallel robot (such as 0.01s-0.1s, usually consistent with the time interval of the expected trajectory generation), the continuous compensation control instruction (continuous function containing position (x, y, z) and attitude (a, b, g)) is disassembled into the pose parameter group corresponding to the discrete time point, and the discretized pose parameter group is converted into a standardized data format (such as array, XML message) recognizable by the robot controller, to ensure the compatibility of parameter transmission. It should be noted that the preset time interval is set according to actual needs, which is not limited in the embodiment.

[0143] (2) based on the inverse kinematics, the plurality of groups of pose control parameters are calculated to obtain a plurality of groups of motion parameters of the parallel robot;

[0144] Specifically, the pose control parameters are converted into specific parameters for driving the motion of each branch chain of the robot through the inverse kinematics model, and a mapping relationship between the pose and the motion of the actuator is established.

[0145] Further, specifically, for the structure of the parallel robot, an analytical model is established with the pose parameters (x, y, z, a, b, g) as input and the length of the branch chain as output. For example, the relative positions of the Hooke joint and the spherical joint of each branch chain are calculated through spatial coordinate transformation, and the length of the branch chain is solved by using the distance formula; each group of discretized pose control parameters is substituted into the inverse kinematics model, and the target length variation of the 6 branch chains is calculated; and then the length variation is converted into the angular displacement parameters (unit: rad) of the corresponding servo motor according to the transmission ratio (such as the pitch of the lead screw) of the branch chain, as the final motion parameters.

[0146] Further, the specific implementation steps of calculating the plurality of groups of pose control parameters based on the inverse kinematics to obtain the plurality of groups of motion parameters of the parallel robot include:

[0147] 2.1 constructing an inverse kinematics model;

[0148] Specifically, a base coordinate system (static platform coordinate system O-xyz) and a moving platform coordinate system (P-uvw) are established, wherein the origin O of the base coordinate system is the geometric center of the static platform, the origin P of the moving platform coordinate system is the geometric center of the moving platform, the coordinates of the static platform hinge points, the coordinates of the moving platform hinge points and the initial installation parameters (such as the initial length of the branch chain) of the 6-UPS branch chain are obtained; the relationship between the pose (position (x, y, z) + attitude angle (a, b, g)) of the moving platform and the spatial coordinates of the moving platform hinge points is described by homogeneous coordinate transformation, and the length of the branch chain is derived by using the spatial distance formula combined with the coordinates of the static platform hinge points:

[0149] ;

[0150] wherein, is a vector pointing from the origin O to the origin P;

[0151] is a rotation matrix of the coordinate system P-uvw with respect to the coordinate system O-xyz;

[0152] represents the center position of the spherical hinge;

[0153] represents the center position of the hook hinge.

[0154] Further, Figure 3 is a simplified structure diagram of a parallel robot shown in the exemplary embodiments of the present application, Figure 3 (a) is a simplified structure perspective view of a parallel robot shown in the exemplary embodiments of the present application, Figure 3 (b) is a simplified structure top view of a parallel robot shown in the exemplary embodiments of the present application; please refer to Figure 3 wherein a i (i=1, 2, …, 6) represents the center position of the spherical hinge, b i represents the center position of the hook hinge; the included angle between the nearest two spherical hinges is θ a , the included angle between the nearest two hook hinges is θ b ; the vertical distance from the upper surface of the moving platform to the center of the spherical hinge is h a , and the vertical distance from the upper surface of the static platform to the center of the hook hinge is h b . Therefore, the coordinates of the hinge point centers a i =[a ix , a iy , a iz ] and b i =[b ix , b iy , b iz ] are represented as:

[0155] ;

[0156] ;

[0157] wherein, ;

[0158] ;

[0159] R a is the radius of the circle formed by the six spherical hinges of the moving platform, R b is the radius of the circle formed by the six hook hinges of the static platform, and s and c represent sin and cos functions, respectively.

[0160] A coordinate system P-uvw and O-xyz are established at the center of the moving platform and the center of the static platform respectively, as shown in Figure 3 (a) of the drawings, a vector from the origin O to b i is denoted as m i a vector from the origin O to the origin P is denoted as p o a vector from a i to b i is denoted as l i According to the geometric relationship, the vector loop equation of the branch of the robot is expressed as follows:

[0161] ;

[0162] wherein a i is the position of the spherical hinge center in the coordinate system P-uvw. R is the rotation matrix of the coordinate system P-uvw relative to the coordinate system O-xyz, which can be expressed as:

[0163] ;

[0164] wherein α, β, γ [0, π].

[0165] 2.2 According to the inverse kinematics model, the length variation of each branch of the parallel robot is calculated;

[0166] Specifically, the pose control parameters are substituted into the inverse kinematics model, the length of each branch under the target pose is calculated, and then the length variation is obtained by comparing with the initial length.

[0167] Further, the discretized pose control parameters are substituted into the inverse kinematics model, and the coordinates of each hinge point of the moving platform under the base coordinate system are calculated through the rotation matrix; the target length of the six branches under the current pose is solved according to the inverse kinematics model, and the length variation of the branch is calculated according to the difference between the target length and the initial length, which reflects the distance that the branch needs to stretch or shorten (positive value for stretching, negative value for shortening).

[0168] 2.3 The length variation is converted into the angular displacement parameters of the servo motor of the parallel robot, and the angular displacement parameters are taken as the motion parameters.

[0169] Specifically, based on the transmission mechanism characteristics (such as screw transmission) of the branch, the length variation is converted into the rotation angle of the servo motor to realize the mapping of linear displacement and angular displacement.

[0170] Further, the pitch of the ball screw in the branch is obtained, and the relationship between the angular displacement and the length variation is derived according to the relationship between the pitch and the angular displacement, which can be expressed by the following formula:

[0171] ;

[0172] wherein, is an angular displacement parameter;

[0173] is a length variation of the i-th branch;

[0174] is a pitch.

[0175] (3) Controlling the parallel robot motion based on the plurality of sets of motion parameters.

[0176] Specifically, the calculated motion parameters are sent to the robot controller, the servo motor is driven to move according to the instructions, and the motion accuracy is ensured through real-time feedback adjustment. The angular displacement parameters of the plurality of sets of servo motors are sent to the robot main controller in time sequence through an industrial bus (such as EtherCAT, Profinet) in real time, the controller executes sequentially according to the discrete time points, the controller drives the servo motors of the six branches to move according to the angular displacement parameters, and the actual angular displacement feedback is collected in real time through the motor encoder; the feedback value is compared with the target motion parameter, the deviation is calculated, and if the deviation exceeds the preset threshold, the PID adjustment mechanism is triggered to correct the motor output torque in real time, so that the deviation between the actual length of the branch and the target length is controlled within 0.01 mm.

[0177] First, the continuous instructions are converted into discrete pose parameters, then the motion parameters of the actuators are mapped through inverse kinematics, and finally the motion accuracy is ensured through real-time feedback. This process adapts to the multi-branch coupling characteristics of the parallel robot, ensuring the executability of the control instructions, and offsetting disturbances in the execution process through dynamic adjustment, so that the error compensation effect falls into the actual motion, and finally high-precision trajectory control is achieved.

[0178] The compensation method for the motion trajectory error of the parallel robot provided in this embodiment has the following advantages. In terms of error prediction accuracy, the CNN-GRU-KAN model constructed by the method fuses the advantages of multiple networks, the CNN layer extracts spatial features of the expected trajectory and removes noise, the GRU layer captures time-dependent features, the KAN layer fits nonlinear relationships, and the attention layer dynamically fuses double-path features. Compared with traditional single models, the average absolute error of the predicted trajectory error is smaller, and the anti-noise interference ability is stronger. The method can accurately learn the mapping rule between the error and the expected trajectory, avoids the problems of missing error sources in offline modeling and online compensation lag, and realizes double-targeted compensation for the two types of errors. In terms of error compensation effectiveness, the predicted error is fitted as a sinusoidal curve with a bias through the least squares method, the amplitude error (periodic fluctuation) and the bias error (fixed offset) are accurately separated, a compensation term is constructed based on the error to correct the expected trajectory, the motion trajectory accuracy is improved by two orders of magnitude compared with the non-compensation state, and the demand of high-precision scenes such as precision assembly and intelligent machining is met.

[0179] Corresponding to the foregoing embodiment of the parallel robot motion trajectory error compensation method, the application also provides an embodiment of a parallel robot motion trajectory error compensation device.

[0180] Figure 4 The structure diagram of the second embodiment of the parallel robot motion trajectory error compensation device provided by the application is shown in the figure. Figure 4 The device provided by the embodiment comprises an acquisition module 410, a prediction module 420 and a compensation module 430; wherein,

[0181] The acquisition module 410 is configured to acquire a desired trajectory of the parallel robot.

[0182] The prediction module 420 is configured to input the desired trajectory into a trained CNN-GRU-KAN model, and the CNN-GRU-KAN model outputs a predicted trajectory error.

[0183] The compensation module 430 is configured to fit the predicted trajectory error into a sinusoidal curve including a bias based on a least square method.

[0184] The compensation module 430 is further configured to acquire an amplitude and a bias in the sinusoidal curve as an amplitude error and a bias error.

[0185] The compensation module 430 is further configured to generate a compensation control instruction of the parallel robot according to the amplitude error and the bias error, and control the motion of the parallel robot based on the compensation control instruction.

[0186] The device of the embodiment can be used to execute Figure 1 The steps of the method embodiment are shown in the figure, and the specific implementation principle and implementation process are similar, which will not be described here.

[0187] The implementation process of the functions and roles of each unit in the above device is specifically described in the implementation process of the corresponding steps in the above method, which will not be described here.

[0188] For the device embodiment, since it basically corresponds to the method embodiment, the related parts can be referred to the part of the method embodiment. The device embodiments described above are only schematic, and the units described as separate components can or can not be physically separated, and the components displayed as units can or can not be physical units, that is, they can be located in one place, or they can be distributed on multiple network units. According to the actual needs, some or all of the modules can be selected to achieve the purpose of the application scheme. Those skilled in the art can understand and implement without creative labor.

[0189] The above only is the preferred embodiment of the present application, and is not used to limit the present application, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method of compensating for motion trajectory errors of a parallel robot, characterized by, The method comprises: acquiring a desired trajectory of a parallel robot; inputting the desired trajectory into a trained CNN-GRU-KAN model, the CNN-GRU-KAN model outputting a predicted trajectory error; fitting the predicted trajectory error into a sinusoidal curve including a bias based on a least square method; acquiring an amplitude and a bias in the sinusoidal curve as an amplitude error and a bias error; generating a compensation control instruction of the parallel robot according to the amplitude error and the bias error, and controlling the parallel robot to move based on the compensation control instruction.

2. The method of claim 1, wherein, The fitting of the predicted trajectory error into a sinusoidal curve including a bias based on a least square method comprises: extracting a motion angular frequency, a time and an initial phase angle from the predicted trajectory error; taking a product of a sinusoidal function with the motion angular frequency, the time and the initial phase angle as a fitting formula, and taking a sum of a sinusoidal amplitude error and a bias error as a fitting formula; inputting the predicted trajectory error and the time into the fitting formula, and minimizing a residual sum of squares of the fitting formula based on a least square method to form the sinusoidal curve including a bias of the predicted trajectory error.

3. The method of claim 1, wherein, The inputting of the desired trajectory into a trained CNN-GRU-KAN model, the CNN-GRU-KAN model outputting a predicted trajectory error, wherein the CNN-GRU-KAN model is sequentially connected by a CNN layer, a GRU layer, a KAN layer and an attention layer, and comprises: the CNN layer is used for extracting spatial features in the desired trajectory and performing denoising processing on the desired trajectory; the GRU layer receives the spatial features output by the CNN layer, captures time sequence dependent features in the spatial features, and outputs a first six-dimensional feature; wherein the first six-dimensional feature comprises time sequence variation features of x-axis position error, y-axis position error, z-axis position error, rotation angle error around the x-axis, rotation angle error around the y-axis and rotation angle error around the z-axis; the KAN layer receives the spatial features output by the CNN layer, fits a nonlinear relationship between the spatial features and the predicted error, and outputs a second six-dimensional feature; wherein the second six-dimensional feature comprises nonlinear error components in the x-axis position error, the y-axis position error, the z-axis position error, the rotation angle error around the x-axis, the rotation angle error around the y-axis and the rotation angle error around the z-axis; the attention layer receives the first six-dimensional feature and the second six-dimensional feature, fuses the first six-dimensional feature and the second six-dimensional feature, and outputs the predicted trajectory error.

4. The method of claim 1, wherein, The generation of a compensation control instruction of the parallel robot according to the amplitude error and the bias error comprises: constructing an error compensation term according to the amplitude error and the bias error; generating a compensation control instruction based on a difference between the desired trajectory and the error compensation term.

5. The method of claim 1, wherein, The control of the parallel robot to move based on the compensation control instruction comprises: discretize the compensation control instruction into a plurality of sets of pose control parameters according to a preset time interval; solving the plurality of sets of pose control parameters based on inverse kinematics to obtain a plurality of sets of motion parameters of the parallel robot; controlling the motion of the parallel robot based on the plurality of sets of motion parameters.

6. The method of claim 1, wherein, Before inputting the expected trajectory into the trained CNN-GRU-KAN model, comprising: controlling the parallel robot to move according to a preset expected trajectory, and obtaining an actual motion trajectory of the preset expected trajectory; According to the difference between the preset expected trajectory and the actual motion trajectory as the trajectory error sample, based on a plurality of trajectory error samples to construct a training data set; input the preset expected trajectory in the training data set as input, and the trajectory error sample as output, input into the initial CNN-GRU-KAN model for training, to obtain the trained CNN-GRU-KAN model.

7. The method of claim 5, wherein, The solving of the plurality of sets of pose control parameters based on inverse kinematics to obtain a plurality of sets of motion parameters of the parallel robot comprises: constructing an inverse kinematics model; According to the inverse kinematics model, the length change of each branch chain of the parallel robot is calculated; convert the length change into the angular displacement parameter of the servo motor of the parallel robot, and take the angular displacement parameter as the motion parameter.

8. The method of claim 1, wherein, The expected trajectory of the parallel robot is obtained, comprising: determining the work scene type of the parallel robot, the work scene type including precision assembly scene, trajectory simulation scene; According to the work scene type, the corresponding trajectory template is selected, and the trajectory template includes sine trajectory template, circular trajectory template and elliptical trajectory template; input the trajectory parameters based on the trajectory template; According to the trajectory parameters, the expected trajectory of the parallel robot is generated.

9. The method of claim 1, wherein, Before generating the compensation control instruction of the parallel robot according to the amplitude error and the bias error, comprising: calculating the goodness of fit of the sine curve and the predicted trajectory error; Based on the goodness of fit, the validity of the amplitude error and the bias error is verified.

10. A device for compensating for motion trajectory errors of a parallel robot, characterized by The device comprises an acquisition module, a prediction module and a compensation module; wherein, The acquisition module is used to acquire the expected trajectory of the parallel robot; The prediction module is used to input the expected trajectory into the trained CNN-GRU-KAN model, and the CNN-GRU-KAN model outputs the predicted trajectory error; The compensation module is used to fit the predicted trajectory error into a sine curve including bias based on the least square method; The compensation module is also used to obtain the amplitude and bias in the sine curve as the amplitude error and the bias error; The compensation module is also used to generate the compensation control instruction of the parallel robot according to the amplitude error and the bias error, and control the motion of the parallel robot based on the compensation control instruction.

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