High-precision two-dimensional motion error prediction compensation iteration method

Abstract

The application relates to the technical field of two-dimensional motion control, and discloses a high-precision two-dimensional motion error prediction compensation iteration method.The method generates a motion trajectory overview containing a target position sequence and corresponding expected motion parameters according to user-set parameters on a motion control system operation interface, and is connected with an actual motion execution device; the deviation between the actual position and the target position of the motion platform at the current sampling moment is measured, and a motion error vector is calculated; a prediction model is constructed based on the motion error vector and the expected motion parameters, and the two-dimensional motion error at a future moment is predicted through iterative optimization; compensation control instructions are generated according to the prediction result and applied to the motion execution device; the motion state after compensation is monitored in real time, the prediction model is updated, and a compensation log is output. The method can effectively improve the two-dimensional motion control precision, enhance the real-time performance and adaptability of compensation, and is suitable for high-precision motion control scenes.

Description

Technical Field

[0001] This invention relates to the field of two-dimensional motion control technology, specifically a high-precision two-dimensional motion error prediction, compensation, and iterative method. Background Technology

[0002] In fields such as precision manufacturing, coordinate measurement, and semiconductor processing, the two-dimensional motion accuracy of motion platforms directly affects the quality and performance of the final product. With the continuous development of industrial technology, the requirements for the positioning accuracy and motion stability of motion platforms are becoming increasingly stringent, and traditional motion control methods are no longer sufficient to meet the needs of high-precision scenarios.

[0003] During actual operation, motion platforms are susceptible to motion errors due to various interferences. For example, mechanical factors such as assembly clearances in the mechanical structure, wear of transmission components, and straightness errors of guide rails can cause positional deviations during movement. Changes in ambient temperature can cause thermal expansion and contraction of mechanical components, altering the geometric parameters of the motion platform and thus generating errors. Furthermore, factors such as response delays in the drive system and insufficient calculation accuracy of the control algorithm can also affect the actual position of the motion platform.

[0004] To reduce motion errors, various compensation methods have been employed in existing technologies. Among them, feedback compensation based on real-time measurement is relatively common. This method monitors the actual position of the motion platform in real time using sensors, compares the measured values ​​with the target values, determines the error, and then generates compensation commands through a control algorithm to correct the motion trajectory. However, this method requires high measurement speed and accuracy from the sensors, and due to the inherent lag in feedback control, it is difficult to compensate for errors in a timely and effective manner in high-speed motion scenarios, which can easily lead to fluctuations in the motion trajectory.

[0005] Some model-based feedforward compensation methods are also widely used. These methods establish an error model of the motion system and calculate the compensation amount in advance based on the target trajectory, thereby performing active compensation during motion. However, due to the complexity of the motion system's characteristics and the influence of various nonlinear factors, the established error model often fails to accurately reflect the actual situation, resulting in unsatisfactory compensation effects. Furthermore, when the operating conditions of the motion system change, the error model exhibits poor adaptability, requiring remodeling and parameter adjustment, increasing operational complexity. Summary of the Invention

[0006] The purpose of this invention is to provide a high-precision two-dimensional motion error prediction and compensation iterative method to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides a high-precision two-dimensional motion error prediction and compensation iterative method, the method comprising:

[0008] In the operation interface of the motion control system, a motion trajectory overview is generated according to the user's set parameters. The motion trajectory overview includes the target position sequence of the motion platform in a two-dimensional plane and the expected motion parameters corresponding to each position.

[0009] Establish a connection between the overall motion trajectory and the actual motion execution device; measure the deviation between the actual position and the target position of the motion platform at the current sampling time, and calculate the motion error vector based on the deviation;

[0010] Based on the motion error vector and the expected motion parameters of the motion trajectory overview, a prediction model is constructed, and the two-dimensional motion error at future moments is predicted through an iterative optimization process.

[0011] Based on the prediction results, a compensation control command is generated and applied to the motion execution device.

[0012] The system monitors the compensated motion state in real time, updates the motion error prediction model, and outputs the compensation log.

[0013] Preferably, the construction of the prediction model includes: calling a preset time series database, wherein the time series database stores historical error data of the motion platform;

[0014] Extract the actual motion parameter sequence within the current motion cycle, and perform correlation matching between the actual motion parameter sequence and historical error data in the time series database;

[0015] Calculate the error rate of change of the matching results, and combine it with the expected motion parameters from the overall motion trajectory overview to determine the initial parameters of the prediction model;

[0016] The initial parameters are adjusted using an adaptive learning algorithm to obtain an optimized prediction model.

[0017] The prediction model is used to output two-dimensional motion error estimates for multiple future sampling points.

[0018] Preferably, the step of predicting the two-dimensional motion error at future moments through an iterative optimization process includes: setting a prediction window size, wherein the prediction window size is determined based on the dynamic response characteristics of the motion platform;

[0019] Within the prediction window, the optimized prediction model is applied to the actual motion parameter sequence to generate preliminary error prediction data;

[0020] Calculate the degree of difference between the preliminary error prediction data and the actual measurement deviation;

[0021] Adjust the iteration step size of the prediction model according to the degree of difference, and repeat the prediction and adjustment process until the degree of difference is lower than the preset threshold or the maximum number of iterations is reached;

[0022] The final output is the converged two-dimensional motion error prediction result.

[0023] Preferably, generating compensation control instructions based on the prediction results includes: analyzing the components of the predicted two-dimensional motion error in the horizontal and vertical directions;

[0024] Based on the control characteristics of the motion actuator, a compensation gain coefficient is designed; the predicted two-dimensional motion error component is multiplied by the compensation gain coefficient to obtain the compensation amount;

[0025] Combine the expected motion parameters from the overall motion trajectory overview to synthesize compensation control commands;

[0026] The compensation control command includes a composite command for position correction and speed adjustment.

[0027] Preferably, the measurement of the deviation between the actual position and the target position of the motion platform at the current sampling time includes: acquiring real-time position data of the motion platform through the sensor array of the motion control system;

[0028] Noise filtering is applied to the real-time location data to obtain filtered location data; the target position at the current sampling time is extracted from the motion trajectory overview.

[0029] Calculate the Euclidean distance between the filtered position data and the target position, and use it as the current deviation;

[0030] The current deviation is decomposed into error components in a two-dimensional plane.

[0031] Preferably, the real-time monitoring of the compensated motion state and updating the motion error prediction model includes: collecting new actual position data of the motion platform after the compensation control command is applied;

[0032] Compare the new actual position data with the predicted two-dimensional motion error, and calculate the residual.

[0033] Input the residuals into the update module of the prediction model to adjust the model's weight parameters;

[0034] The prediction model is retrained based on the adjusted weight parameters, and the updated model state is stored.

[0035] Preferably, the output compensation log includes: recording the prediction results, compensation control instructions, and residuals in each iteration of the optimization process;

[0036] Generate a log file, which includes timestamps, error component values, and compensation effect indicators;

[0037] The user interface displays a visual report of the log file.

[0038] Preferably, the method further includes: defining motion error types, wherein the motion error types include position offset error and trajectory following error;

[0039] Mark the priority of error types in the motion trajectory overview; allocate resource weights to the prediction model according to the priority.

[0040] Preferably, the step of allocating resource weights to the prediction model according to priority includes: analyzing the distribution characteristics of error types within the motion cycle;

[0041] Set resource weight allocation rules based on distribution characteristics;

[0042] Resource weight allocation rules are applied to the construction process of prediction models.

[0043] Preferably, the method further includes: integrating a feedback mechanism into the motion control system, the feedback mechanism including a real-time data stream and a model update trigger;

[0044] When the dynamic parameters of the motion platform exceed the preset range, a feedback mechanism is triggered to restart the iterative optimization process.

[0045] Compared with the prior art, the beneficial effects of the present invention are:

[0046] This high-precision two-dimensional motion error prediction and compensation iterative method generates a motion trajectory overview containing the target position sequence and corresponding expected motion parameters based on user-defined parameters in the motion control system's operating interface, and establishes a connection with the actual motion execution device, laying the foundation for subsequent error measurement and compensation. During the motion process, the deviation between the actual position of the motion platform and the target position at the current sampling moment is measured in real time, and the motion error vector is calculated, making the error acquisition more direct and accurate, and able to reflect the actual state of the motion platform in a timely manner.

[0047] A predictive model is constructed based on the motion error vector and expected motion parameters. Through an iterative optimization process, the two-dimensional motion error at future moments is predicted. This approach fully utilizes historical error information and the expected characteristics of the motion trajectory, making the prediction of future errors more targeted and accurate. Compared to traditional feedback compensation, it can predict the trend of error changes in advance, avoiding the problem of untimely compensation due to feedback lag. Therefore, compensation measures can be taken in advance during the motion process, making the motion trajectory closer to the target trajectory.

[0048] Based on the prediction results, compensation control commands are generated and applied to the motion actuator, achieving active compensation for motion errors. This effectively corrects errors caused by mechanical structure, environmental factors, and the drive system. Simultaneously, this method continuously updates the motion error prediction model by monitoring the compensated motion state in real time, enabling the model to adapt to changes in the motion system's operating conditions. As the iteration process continues, the accuracy of the prediction model gradually improves, and the compensation effect is continuously optimized, enhancing the method's adaptability to different motion scenarios and changes in system characteristics.

[0049] The compensation log output by this method records key information throughout the compensation process, including error changes and compensation commands, facilitating subsequent system analysis and optimization. Analysis of the compensation log provides a deeper understanding of the error characteristics and compensation effect of the motion system, offering a reference for further improving control algorithms and optimizing motion parameters. Furthermore, this method is relatively simple to operate; users only need to set relevant parameters on the interface, and the system can automatically complete a series of processes such as trajectory generation, error measurement, and predictive compensation, reducing the professional skills required of operators and improving the practicality and operability of the method.

[0050] This method organically combines prediction, compensation, and model updating to form a closed-loop iterative process, which has significant advantages in improving the positioning accuracy and motion stability of motion platforms. It can achieve good compensation effects in both low-speed precision motion scenarios and high-speed dynamic motion scenarios, and is applicable to various high-precision two-dimensional motion control fields, such as precision manufacturing, coordinate measurement, and semiconductor processing, effectively improving the performance of related equipment and the quality of products. Attached Figure Description

[0051] Figure 1 This is a schematic diagram illustrating the working principle of the high-precision two-dimensional motion error prediction and compensation iterative method described in this invention.

[0052] Figure 2 A flowchart for iteratively optimizing the prediction of two-dimensional motion errors;

[0053] Figure 3 A flowchart for measuring the actual position deviation of the motion platform;

[0054] Figure 4 A flowchart for real-time monitoring of the compensated motion state and updating the prediction model. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figure 1 This invention provides a high-precision two-dimensional motion error prediction and compensation iterative method, the method comprising:

[0057] The motion control system receives user-defined motion parameters through its user interface and generates a motion trajectory overview containing the target position sequence and expected motion parameters. After establishing a data connection between the motion trajectory overview and the actual motion execution device, the system measures the deviation between the actual position of the motion platform and the target position at the current sampling moment in real time and calculates a two-dimensional motion error vector. Based on this error vector and the expected motion parameters, a prediction model is constructed, and an iterative optimization algorithm is used to predict the error components at future moments. The prediction results are processed by the compensation control command generation module, which outputs a composite command containing position correction and speed adjustment to the execution device. The compensated motion state is monitored in real time by a sensor array. The newly collected data is used to update the prediction model parameters, and a compensation log file containing timestamps and error components is generated.

[0058] Example 1: See Figure 2 In constructing the predictive model, the system first accesses a pre-set time-series database. This database stores historical error data of the motion platform at a fixed sampling period, including parameters such as position deviation, velocity error, and acceleration fluctuations. This data is indexed by timestamps and uses an efficient compression algorithm to reduce storage space while ensuring fast retrieval capabilities. After extracting the actual motion parameter sequence within the current motion cycle, the system performs multi-dimensional correlation matching to analyze the relationship between historical data and the current motion state. The matching process employs a dynamic time warping algorithm, which effectively aligns non-uniform data sequences and eliminates matching errors caused by differences in sampling frequency or temporary data loss. In frequency domain analysis, the system calculates the power spectral density, identifies the main frequency components of the error, and compares them with historical data to determine whether the current error exhibits periodic characteristics.

[0059] The error rate of change is calculated using a sliding window mechanism, with the window size adaptively adjusted based on the dynamic characteristics of the motion platform. After smoothing, the system calculates the first difference of the error and combines this with historical trends to predict the future rate of error change. The initial parameters of the prediction model are determined by fitting the mapping relationship between historical error curves and current motion parameters using the least squares method. Robust regression is employed during the fitting process to reduce the impact of outliers on parameter estimation. The adaptive learning algorithm uses stochastic gradient descent with a moving average term. This algorithm retains the gradient direction of the previous step during parameter updates, effectively suppressing parameter oscillations and improving convergence speed. The learning rate is dynamically adjusted based on the magnitude of parameter updates. When parameter changes are large, the learning rate is appropriately reduced to avoid skipping the optimal solution; when parameter changes are small, the learning rate is appropriately increased to accelerate convergence.

[0060] The optimized prediction model can output two-dimensional motion error estimates for multiple future sampling points. The size of the prediction window is set based on the dynamic response characteristics of the motion platform. Preliminary prediction data is generated within the window using cubic spline interpolation, which ensures the continuity and smoothness of the prediction curve and avoids abrupt changes in prediction error that may occur with linear interpolation. The difference is calculated using Mahalanobis distance to measure the deviation of the statistical distribution between the predicted and measured values. This distance considers the covariance structure of the error data and can more accurately reflect the prediction accuracy. The iteration step size is nonlinearly scaled based on the difference gradient; a larger step size is used to accelerate convergence when the difference is large, and a smaller step size is used for fine-tuning when the difference is small. The iterative optimization process terminates when the difference falls below a preset threshold or when the maximum number of iterations is reached, finally outputting the converged two-dimensional motion error prediction result.

[0061] The predictive model is built and optimized using a modular design, with standardized interfaces facilitating subsequent maintenance and expansion. The time series database employs a distributed architecture, supporting high-concurrency read and write operations to ensure efficient data access in real-time control scenarios. The dynamic time warping algorithm has been optimized, using dynamic programming to reduce computational complexity and enabling efficient operation with limited computing resources. Power spectral density analysis utilizes Fast Fourier Transform (FFT) to accelerate calculations while incorporating window functions to reduce spectral leakage. The sliding window mechanism for data smoothing employs an exponentially weighted moving average method, effectively suppressing noise interference while preserving error trends.

[0062] During the least squares fitting process, the system standardizes the input data to eliminate the influence of dimensional differences on parameter estimation. Robust regression is implemented using the Huber loss function, enhancing the model's robustness to outliers while maintaining fitting accuracy. Stochastic gradient descent with momentum terms introduces a momentum coefficient during parameter updates; this coefficient is dynamically adjusted based on error changes during training, further optimizing convergence performance. Adaptive learning rate adjustment employs a cosine annealing strategy, using a larger learning rate in the early stages of training to quickly approximate the optimal solution, and gradually decreasing the learning rate in later stages to improve parameter accuracy.

[0063] The prediction window is set by comprehensively considering the mechanical characteristics of the motion platform and the response speed of the control system, ensuring that the prediction range covers the main dynamic errors without causing prediction lag due to an excessively large window. The cubic spline interpolation method employs natural boundary conditions to guarantee the continuity of the second derivative of the prediction curve, improving the smoothness of the prediction results. The Mahalanobis distance is calculated based on the covariance matrix of the error data, which is continuously updated through online learning to reflect changes in the statistical characteristics of the errors. The nonlinear scaling strategy for the iterative step size uses the Sigmoid function to map the gradient of difference, making the step size adjustment smoother and more stable.

[0064] The entire process of building and optimizing the prediction model runs efficiently within the embedded real-time system. Computational tasks are processed in parallel using multi-threading, fully utilizing hardware resources to improve computational speed. Model parameters are stored and loaded in binary format, reducing data read / write time and ensuring low latency requirements for real-time control. The system also provides model state persistence functionality, supporting rapid reconstruction of the prediction model after power failure, ensuring the continuity of the control process.

[0065] In practical applications of the prediction model, the system continuously monitors the consistency between the prediction error and the actual measurement deviation. When the deviation exceeds the allowable range, the model retraining mechanism is automatically triggered. The retraining process employs an incremental learning strategy, updating only the model parameters that are most affected, thus reducing computational overhead. Long-term optimization of model performance is achieved through periodic full-scale training, further improving prediction accuracy by utilizing accumulated historical data. The system also provides visualization analysis tools for the prediction model, enabling engineers to intuitively evaluate model performance and assist in parameter tuning and fault diagnosis.

[0066] Example 2: See Figure 3The generation process of compensation control commands begins with error decomposition. The system analyzes the predicted two-dimensional motion error in Cartesian coordinates, dividing it into horizontal and vertical components. The horizontal error component is first processed by a Butterworth low-pass filter, whose cutoff frequency is dynamically adjusted according to the maximum acceleration of the motion platform to eliminate the influence of high-frequency noise on the compensation control. The vertical error component is estimated using a Kalman filter algorithm. The system establishes a state-space model including position, velocity, and acceleration, and improves the estimation accuracy by adaptively adjusting the observation noise covariance matrix. The filtered error component is then fed into the compensation gain calculation module, which determines the optimal gain coefficient based on the characteristic curve of the actuator.

[0067] The gain coefficient is set using a piecewise strategy. A fixed gain is used in the low-speed range to ensure stability, while a dynamic gain scheduling mechanism is introduced in the high-speed range. The dynamic gain is calculated based on the torque-velocity curve of the actuator. The system monitors the current motion state in real time and determines the corresponding gain value through table lookup interpolation. The position correction is calculated using tensor operations, combining the error components with the gain coefficient in a multi-dimensional manner to generate compensation quantities for each degree of freedom. The speed adjustment is calculated based on the error rate of change. The system uses numerical differentiation to estimate the time derivative of the error and combines it with a feedforward control strategy to compensate for dynamic errors in advance.

[0068] The command synthesis stage converts the compensation quantities in the Cartesian coordinate system into control signals recognizable by the actuator. The system employs a quaternion interpolation algorithm to smoothly handle the transition between adjacent command points, avoiding mechanical shocks caused by step changes. During the conversion process, the kinematic constraints of the actuator are considered, and the optimal joint space command is solved using the pseudo-inverse operation of the Jacobian matrix. The timing of the commands is arranged using a time-optimal programming algorithm to minimize the compensation delay while meeting acceleration constraints. The final generated compensation control command includes position setpoints and velocity feedforwards, and is sent to the actuator in the form of a composite command.

[0069] Actual position measurement is achieved through a multi-sensor fusion system, consisting of a laser interferometer, a photoelectric encoder, and an inertial measurement unit (IMU). The laser interferometer provides high-precision absolute position feedback, the photoelectric encoder outputs high-resolution relative displacement signals, and the IMU detects the vibration state of the motion platform. The raw sampled data first undergoes wavelet thresholding denoising, employing a soft thresholding function to eliminate high-frequency noise while retaining useful error characteristics. Outlier detection utilizes a random sample consensus algorithm, iteratively fitting an optimal model to eliminate outliers that do not conform to statistical laws.

[0070] The calculation of Euclidean distance incorporates anisotropic weighting coefficients, with the system assigning different weighting factors to different directions based on the stiffness characteristics of the motion platform. During error decomposition, a local coordinate system is established, with its axis aligned with the principal stiffness directions of the mechanical structure to eliminate coupling effects between degrees of freedom. The decomposed error components are normalized to eliminate the influence of dimensional differences on subsequent calculations. The system monitors the residuals of the error decomposition in real time, automatically triggering a coordinate system recalibration process when the residuals exceed a threshold.

[0071] The transmission of compensation control commands uses the real-time Ethernet protocol, with data packets containing timestamps and checksums to ensure the timeliness and integrity of the commands. After receiving the commands, the actuator's built-in motion controller performs secondary planning, decomposing the global compensation command into phase current commands for each motor. Current loop control employs space vector modulation technology to optimize the switching frequency and energy consumption of power devices. The system monitors the deviation between the actual current and the command value, triggering a fault protection mechanism when the deviation continues to exceed the allowable range.

[0072] The mechanical resonance characteristics of the motion platform are incorporated into the compensation control. The system identifies the main resonant frequencies through frequency response function analysis and embeds a notch filter into the compensation command. The center frequency of the filter is adjusted online according to the actual operating conditions of the platform to avoid phase lag caused by fixed-frequency filtering. For mechanical vibrations that cannot be completely suppressed by software filtering, the system adopts an active damping control strategy, generating a reverse compensation force through acceleration feedback.

[0073] The evaluation of the compensation effect employs a multi-index comprehensive analysis method, with the system simultaneously monitoring parameters such as position error, velocity tracking accuracy, and acceleration fluctuation. The evaluation results are fed back to the gain scheduling module to optimize the gain coefficient for the next control cycle. Statistical analysis of long-term operating data helps identify the drift trend of the gain parameters, providing a basis for controller self-tuning. The system establishes a historical database of compensation effects, supporting querying and analyzing the evolution of control performance over time.

[0074] The anomaly handling mechanism plays a crucial role in compensatory control. When anomalies such as actuator overload, sudden increase in tracking error, or communication delay are detected, the system automatically switches to a safety control mode. This mode employs conservative control parameters, prioritizing motion stability over tracking accuracy. After fault recovery, the system executes a gradual parameter recovery process, progressively adjusting the control parameters to optimal values ​​to avoid secondary disturbances caused by sudden changes.

[0075] The configurability of the compensation control system is achieved through parametric design, allowing users to adjust key parameters such as filter parameters, gain coefficients, and interpolation algorithms via a human-machine interface. The system provides automatic parameter tuning, recommending optimal control parameters based on the platform's step response curve. All configuration changes are recorded in the operation log, supporting parameter retrospection and comparative analysis.

[0076] The system's real-time performance is guaranteed through a multi-task scheduling mechanism, with the compensation control thread running at the highest priority to ensure strict time determinism. Computationally intensive tasks such as filtering and matrix operations employ hardware acceleration technology, using dedicated instruction sets to improve processing efficiency. Memory management adopts a static allocation strategy to avoid the time uncertainty caused by dynamic memory allocation.

[0077] Long-term operational reliability is achieved through multiple protection mechanisms, including watchdog timers, memory verification, and instruction redundancy. The system periodically self-checks the operational status of critical hardware components to detect potential failure risks in advance. Control software updates support hot-swapping, allowing version upgrades to be completed without interrupting motion control.

[0078] The scalability of the compensation control system is reflected in the standardized design of the hardware interface, supporting plug-and-play functionality for different types of actuators. Integrating new devices only requires loading the corresponding driver configuration file, without modifying the core control algorithm. The system also reserves additional sensor interfaces for future additions of advanced functions such as visual positioning or force feedback.

[0079] During the debugging and optimization phase, the system provides a wealth of real-time monitoring tools, including time-domain waveform display, spectrum analysis, and 3D trajectory reproduction. Engineers can use these tools to visually observe the effects of compensation control and quickly pinpoint performance bottlenecks. All debugging operations are recorded in a dedicated log file for easy problem reproduction and analysis later.

[0080] The environmental adaptability of the compensation control system is enhanced through a temperature compensation algorithm, and the measurements of key sensors, such as the laser interferometer, are corrected in real time according to the ambient temperature. The temperature rise effect of electronic components is modeled as a disturbance term in the control parameters and compensated online through an adaptive control algorithm. The system periodically performs an automatic calibration process to eliminate measurement drift caused by long-term use.

[0081] Safety protection functions are integrated throughout the entire compensation control process, including multi-layered protection measures such as software limits, emergency stop interlocks, and overload protection. All safety-related signals employ redundant design and cross-checking to ensure the reliability of the protection mechanism. A comprehensive safety check is performed upon system startup, and the system is only allowed to enter operational mode after all safety conditions are met.

[0082] Energy management is fully considered in the compensation control system, and reactive power losses of actuators are reduced through optimized control algorithms. Braking energy recovery technology converts the kinetic energy of the deceleration process into electrical energy for storage. The system monitors total energy consumption in real time and automatically activates energy-saving control mode when it exceeds a set threshold.

[0083] The ease of maintenance of the compensation control system is improved through fault prediction technology; machine learning models based on operational data can provide early warnings of potential fault risks. The maintenance reminder function intelligently plans maintenance cycles based on equipment usage time and workload. The system provides detailed health status reports, guiding maintenance personnel to conduct targeted inspections of critical components.

[0084] Integration with the upper-level management system employs a standardized communication protocol, enabling real-time uploading of key performance indicators for compensation control. Remote monitoring allows engineers to access the system's operational status via the network, enabling necessary parameter adjustments and fault diagnosis. All remote operations are recorded in the audit log, ensuring traceability.

[0085] The verification of the compensation control system employs a modular testing strategy, progressively verifying each function from unit testing to system integration testing. Test cases cover normal operating conditions and typical fault scenarios to ensure the system's reliability under various conditions. Long-term stability testing simulates continuous operation in a real industrial environment to verify the system's durability.

[0086] Example 3: See Figure 4 The motion state monitoring adopts a distributed data acquisition architecture. Data from each axis sensor is synchronized at the microsecond level through a precise time protocol, with sampling time alignment errors controlled within ±100 nanoseconds. A multi-sensor array consisting of a laser interferometer, encoder, and accelerometer acquires the spatial coordinates of the motion platform at a sampling rate of 1kHz. The raw data stream is transmitted to the central processing unit via a high-speed serial bus. The time synchronization module uses a master-slave clock distribution mechanism, with a temperature-compensated crystal oscillator as the master clock source, achieving a frequency stability of ±0.1ppm. The local clocks of the sensor nodes are synchronized with the master clock through digital phase-locked loop technology, periodically correcting clock drift. The data acquisition card is equipped with a hardware trigger function, automatically increasing the sampling rate to 10kHz when mechanical vibration exceeds a threshold to capture transient dynamic characteristics.

[0087] The residual calculation module uses covariance analysis to evaluate the statistical characteristics of the prediction error and the actual deviation, and establishes an error propagation model. The system defines residual evaluation metrics:

[0088] ,

[0089] in, This represents the comprehensive residual assessment value. This represents the number of sampling points within the sliding window. and Representing the first The prediction error vector and the measured error vector for each sampling point This is the error covariance matrix. This index comprehensively considers the magnitude and direction deviation of the error vector, and uses Mahalanobis distance to measure the statistical significance of the prediction results. Covariance matrix The system is updated online using an exponentially weighted moving average method, and the forgetting factor is dynamically adjusted according to the motion state, enabling rapid response to changes in system characteristics.

[0090] The model update module uses the elastic backpropagation algorithm to adjust the neural network weight parameters, retaining the gradient sign information from the previous iteration. The network structure contains three hidden layers with 128, 64, and 32 neurons respectively, and parameterized ReLU is used as the activation function. An adaptive momentum term is introduced during the weight update process: the update step size is increased when the gradient directions are consistent for three consecutive iterations, and decreased when a gradient reversal is detected. The learning rate uses a cosine annealing strategy to change periodically, with an initial value of 0.001, and the annealing cycle is reset every 200 iterations. To prevent overfitting, the Dropout layer randomly deactivates neurons with a probability of 0.2, and the L2 regularization coefficient is set to 0.0001. During the online learning phase, only the parameters of the three network layers near the output layer are fine-tuned, and full network retraining is performed automatically during system idle periods.

[0091] The retraining process employs an incremental learning strategy, with the training dataset managed using a circular buffer, retaining the most recent 5000 valid samples. Data preprocessing includes standardization and principal component analysis, projecting input features into a low-dimensional space to accelerate convergence. Batch training size is dynamically adjusted based on hardware resources, typically set to 32-128 samples. The Huber loss function is used, maintaining the good convergence of L2 loss when the error is small, and switching to the robustness of L1 loss when the error is large. The accuracy of the validation set is monitored in real time during training, triggering an early stopping mechanism when no improvement is seen after 20 consecutive iterations. Model version management adopts a git-like mechanism, generating a new branch for each major update, supporting rapid rollback to a stable version.

[0092] The log recording system stores iterative data in binary format, with each record containing a 64-bit timestamp, a three-dimensional error vector, compensation instructions, and platform status information. The storage structure uses a columnar layout, storing data of the same type contiguously to improve compression efficiency. The Zstandard algorithm achieves real-time data compression with a compression ratio exceeding 4:1. The circular buffer is designed in a dual-buffering mode: the foreground buffer receives new data, while the background buffer performs compression and storage operations, switching roles every 5 seconds. Data retrieval supports time range queries and conditional filtering, providing millisecond-level response times for any time period within the most recent hour.

[0093] The visualization report generation module utilizes WebGL technology for cross-platform rendering. The 3D error cloud map is presented using a particle system, and color mapping reflects the magnitude of the error. The timeline control supports playback speeds from 0.1x to 10x, with keyframes automatically marking significant compensation events. Statistical charts integrate box plots to display error distribution, and dynamic percentile lines identify the 95% confidence interval. The report export function generates interactive HTML documents with embedded JavaScript for dynamic client-side analysis. Users can rotate the 3D model by dragging and dropping to examine the compensation effect from multiple perspectives.

[0094] The system health monitoring unit continuously tracks key metrics during model updates, including residual mean, gradient magnitude, and computational latency. Monitoring data is analyzed using control charts, with ±3σ warning lines and ±6σ action lines set. When a metric consistently exceeds the warning range, the system automatically initiates a diagnostic process: first, it checks the quality of sensor data; second, it verifies the integrity of the network structure; and finally, it assesses the representativeness of the training data. The diagnostic results generate remedial suggestions, such as increasing noise suppression, adjusting network capacity, or supplementing with data under specific operating conditions.

[0095] Real-time performance is ensured through a resource reservation mechanism, with prediction model update tasks running on dedicated computing cores, isolating them from interference from other system processes. Memory access employs a deterministic scheduling strategy, and critical data is preloaded into the CPU cache to reduce access latency. Computational tasks are decomposed into pipeline stages, processing multiple samples in parallel to improve throughput. GPU acceleration is used for large-scale matrix operations, and CUDA kernel functions are optimized for neural network computations, fully utilizing the computational power of tensor cores.

[0096] The fault recovery mechanism is designed with a three-tier response system: transient faults attempt three retries, intermittent faults trigger a module-level restart, and persistent faults switch to degradation mode. In degradation mode, the system uses a simplified linear prediction model, which, although less accurate, ensures basic control functions. All fault events are recorded in a separate security log and stored according to their severity. The log cycle overwrite period is configured based on storage capacity, typically retaining complete records for the most recent 30 days.

[0097] Long Term Evolution (LTE) functionality is achieved through knowledge distillation, transferring the learning outcomes of complex models to lightweight models. The teacher model learns periodically from the complete dataset, while the student model is trained using the teacher model's output, reducing computation by 75% while maintaining 90% prediction accuracy. Model compression employs weight quantization and pruning techniques; 8-bit integer quantization achieves a 4x model compression, and structured pruning removes 50% of redundant connections. The compressed model uses hash verification to ensure binary integrity, preventing control anomalies caused by storage corruption.

[0098] The user interface provides an intuitive display of model performance, with real-time graphs showing how residual metrics change over time. The parameter adjustment panel allows experienced users to manually fine-tune the learning rate and regularization coefficients; changes take effect immediately but require secondary confirmation to be persistent. The operation history records every parameter change in detail, including the modification time, operator, and reason for the change. The access control system is based on role-based access control, granting engineers, administrators, and maintenance personnel different levels of configuration permissions.

[0099] Environmental adaptability is enhanced by a temperature compensation module, which integrates a temperature sensor within the chip to monitor the operating temperature of the computing unit. When the temperature exceeds a threshold, the clock frequency is dynamically reduced to prevent computational errors caused by overheating. The thermal design employs an active cooling strategy, adjusting fan speed based on temperature gradients to balance heat dissipation efficiency and noise control. The power management unit monitors power quality, activating filtering circuitry when voltage fluctuations exceed ±5% to ensure computational stability.

[0100] Integration with external systems adopts a publish-subscribe pattern; model update events are broadcast via message queues, and subscribers can obtain complete update logs. The remote diagnostic interface supports secure tunnel connections, allowing authorized engineers to analyze model performance online. Data export formats support multiple standards such as CSV, JSON, and HDF5, ensuring compatibility with mainstream data analysis tools. The open API follows REST specifications, allowing third-party systems to query system status and retrieve historical data via HTTPS.

[0101] The verification and validation process employs a layered testing strategy. Unit tests cover all mathematical operations and logical judgments, while integration tests verify the correctness of data flow between modules. System testing simulates real-world operating scenarios, including a 72-hour continuous stress test and robustness testing with random fault injection. Acceptance criteria require 95% of the predicted residuals to be controlled within ±3σ, and critical control cycle jitter to not exceed ±10μs. Test coverage tools show that line coverage reaches 98%, and branch coverage exceeds 95%.

[0102] Maintenance support features include automatic maintenance report generation, summarizing performance metrics and anomalies during system operation. The predictive maintenance module analyzes mechanical wear trends and suggests optimal maintenance windows. The spare parts management system tracks the lifespan of critical components and provides early warnings of potential replacement parts. Maintenance task lists are automatically synchronized to mobile devices, allowing on-site technicians to scan codes to confirm operation steps.

[0103] The security audit function logs all sensitive operations, including model updates, parameter modifications, and system restarts. The audit logs utilize blockchain technology for tamper-proof protection, with each entry containing the hash value of the preceding record. Log analysis tools detect abnormal operation patterns, such as frequent parameter modifications or system access outside of working hours. A multi-factor authentication mechanism protects critical functions, requiring both password and physical token verification to execute privileged operations.

[0104] Continuous improvement is achieved through a user feedback system, allowing operators to flag scenarios where compensation is ineffective. These cases are prioritized for inclusion in the training dataset, enabling targeted improvements to the model's performance under specific conditions. Improvements are scheduled weekly, with the system automatically analyzing feedback data and generating optimization plans. Version release notes detail each improvement, helping users understand feature changes and important considerations.

[0105] Example 4: The error type classifier uses a support vector machine to construct the decision boundary. Input features include the displacement deviation of the motion platform along the X / Y axes, velocity tracking error, and acceleration fluctuation values. After standardization, the feature vectors are mapped to a high-dimensional space using a kernel function to find the optimal classification hyperplane. Training data comes from historical machining task records, covering error performance under different materials, tools, and process parameters. The classifier output is a probability value, representing the confidence level that the current error belongs to the position offset or trajectory following type. The system sets a dynamic classification threshold, increasing the judgment standard for position offset during the finishing stage and focusing on identifying trajectory following errors during the roughing stage.

[0106] The priority labeling module automatically assigns error levels based on machining quality requirements, considering factors such as surface roughness indicators, geometric tolerance levels, and specific requirements in the process documents. Taking aerospace structural component machining as an example, trajectory following errors in the contour milling stage are given the highest priority, while positional offset errors in the drilling process receive higher weight. Priorities are divided into five levels, from P0 (urgent) to P4 (negligible), each corresponding to a different resource allocation strategy. The system maintains a dynamic priority mapping table that reflects the critical requirements of the current machining task in real time.

[0107] Table 1: Dynamic Priority Mapping Table

[0108]

[0109] Resource weight allocation employs a competitive learning mechanism, dynamically reorganizing hidden layer nodes of the prediction model based on priority. Higher-priority error types consume more computational resources, specifically by adding dedicated feature extraction channels and expanding the receptive field of neurons. The system monitors the real-time performance of each error type, automatically triggering weight rebalancing when a low-priority error is detected to be continuously worsening. The rebalancing process maintains a constant total computational resource, avoiding abrupt changes in control parameters through gradual adjustments.

[0110] The distribution feature analysis module uses a kernel density estimation algorithm to construct an error probability distribution surface and calculates the frequency of occurrence of each working point in the feature space. The analysis process considers the correlation in the time dimension, identifying error clustering regions and transition states. In the application of a five-axis machining center, the system found that trajectory following errors are easily generated when the tool tilt angle changes; therefore, it automatically increases the monitoring frequency of this type of error during angle switching intervals. The update cycle of the distribution features is synchronized with the machining process, resetting the statistical base at the start of each new process.

[0111] When implementing the weight allocation rules, an approximate calculation strategy is used for errors with a priority of P3 and below. For position offset errors, linear interpolation is used instead of exact calculation at low priorities, and a simplified model after downsampling is used for trajectory following errors. Approximate calculations introduce error boundary estimation; when the uncertainty of the prediction result exceeds a threshold, the system switches back to exact mode. The system records the usage time and accuracy loss of each approximate calculation for subsequent optimization of the weight allocation strategy.

[0112] The motion cycle analysis module decomposes the processing into several characteristic stages, such as acceleration, constant speed, and deceleration. An independent error distribution model is established for each stage to identify the most representative error types. In laser cutting applications, positional offset errors mainly occur in the acceleration stage, while trajectory following errors are predominant in the constant speed stage. The system preloads the corresponding prediction model based on the current motion stage, reducing real-time calculation latency. A smooth model transition is executed during stage switching, gradually migrating computational resources through mixed weights.

[0113] The dynamic adjustment mechanism responds to changes in machining conditions. When increased tool wear or changes in material hardness are detected, the priority of error types is reassessed. Wear monitoring is based on spindle current fluctuations and vibration spectrum analysis, while hardness detection is achieved through a cutting force sensor. The adjustment process employs a gradual strategy, fine-tuning resource weights every 5 seconds to avoid drastic changes affecting control stability. The system retains a historical record of the last 10 adjustments, allowing manual viewing of the weight evolution process.

[0114] Hardware resource allocation and weight distribution are linked, with high-priority error calculation tasks assigned to more powerful processing cores. GPU computing resources are partitioned and scheduled, with 80% of stream processors allocated to P0-level error prediction, and the remaining resources shared by other priority tasks. Memory access bandwidth is guaranteed through Quality of Service (QoS) policies, with critical data receiving higher transmission priority. When the system load exceeds 85%, intermediate data from low-priority tasks is automatically compressed to release computing resources.

[0115] The user intervention interface allows experienced operators to manually adjust error type priorities; modifications require double confirmation and are logged. Intervention permissions are managed hierarchically; process engineers can adjust the weights of levels P1-P3, while modifications to level P0 require higher-level permissions. The system tracks and evaluates the effectiveness of manual intervention; if no improvement is observed for three consecutive cycles, it reverts to automatic mode. All intervention operations generate audit logs, including fields such as operation time, personnel ID, and reason for modification.

[0116] The exception handling process is designed to handle priority conflicts. When multiple error types simultaneously require high resource weights, an arbitration algorithm is activated. Arbitration factors include the current magnitude of the error, its trend, and its impact on the final quality. The conflict resolution process generates an evaluation report, recording the arbitration basis and allocation results. The system supports defining custom arbitration rules to meet the personalized needs of special processes.

[0117] The long-term optimization function analyzes historical weight allocation data to identify the mapping relationship between processing tasks and optimal resource ratios. Learning algorithms uncover the best weight patterns under different material and tool combinations, building an experience knowledge base. When a new task starts, the system recommends initial weight configurations based on similarity matching, accelerating the convergence process. The knowledge base is automatically updated monthly, eliminating outdated ratio schemes and supplementing with best practices for new processes.

[0118] The visual monitoring interface uses a heatmap to display the real-time distribution of resource weights, with different colors distinguishing the proportion of computational resources for each error type. The timeline allows for retrospective viewing of weight changes and supports overlay analysis with processing parameter curves. An alarm function monitors resource contention events, prompting optimization of process planning when the arbitration trigger frequency exceeds a threshold. The report export function generates weight usage statistics to help analyze the utilization efficiency of computational resources.

[0119] Integration with the process planning system enables seamless upstream and downstream weighting strategies, allowing priority suggestions to be embedded in the machining code output by the CAM system. The post-processor parses these suggestions and generates initial weight configurations, reducing the convergence time of the system's self-learning. The reverse feedback channel transmits the optimized weights from actual operation back to the process database, forming a closed-loop optimization. This integration is particularly effective in impeller machining, shortening the debugging cycle of new programs by approximately 40%.

[0120] Example 5: The feedback mechanism adopts an event-driven hierarchical architecture design. Data stream processing achieves direct memory access from sensors to the controller through zero-copy technology. The real-time data bus of the motion control system uses dual redundant fiber optic channels, with transmission delay controlled within 50 microseconds. The dynamic parameter monitoring module continuously tracks the third derivatives of the platform's position, velocity, and acceleration. The sampling frequency is adaptively adjusted according to the motion state, set to 1kHz in the steady phase and increased to 5kHz in the dynamic phase. The Lyapunov exponent calculation uses the sliding window method, with the window width synchronized with the mechanical resonance period of the motion platform, to evaluate system stability in real time. When the exponent value exceeds a preset threshold, a graded alarm mechanism is triggered. A primary alarm initiates a parameter fine-tuning process, while a high-level alarm initiates a full system recalibration.

[0121] The feedback trigger employs a multi-level response strategy. The first-level threshold corresponds to short-term dynamic fluctuations, triggering a local parameter optimization thread. This thread runs on an independent real-time kernel, prioritizing CPU resources and completing online adjustment of the PID gain within 10 milliseconds. The second-level threshold addresses persistent performance degradation, activating the model retraining process. The retraining process utilizes a warm-start technique, preserving the network weights of the feature extraction layer and updating only the mapping relationships of the output layer. Training data comes from the most recent 2000 valid samples stored in a circular buffer, and an incremental learning algorithm is used to gradually correct model biases. During anomaly handling, a backup PID controller seamlessly takes over control, its parameters automatically matching the preset optimal configuration set based on the current motion speed.

[0122] The iterative optimization restart process incorporates a gradual switching strategy. Once the predictive model passes validation testing, control is gradually transferred back from the PID controller. The switching process lasts 5-10 control cycles, with compensation commands smoothly transitioning along a cosine curve to avoid mechanical shocks caused by step changes. Model validation testing includes static accuracy checks and dynamic response evaluation. Static testing requires positional deviations to be less than 1 micrometer, and dynamic testing verifies that the overshoot of the step response does not exceed 5%. Models that fail validation enter diagnostic mode, where analysis tools automatically check the representativeness of the training data, the rationality of the network structure, and the convergence of the optimization algorithm, generating a detailed repair suggestion report.

[0123] Real-time data streams are organized using a publish-subscribe model, with motion status data broadcast through topic classification. Subscription modules selectively receive data based on business needs; for example, the error prediction module only subscribes to location and velocity information, while the health monitoring system requires complete motion parameters. The data distribution middleware implements Quality of Service (QoS) tiers, setting critical control data as the highest priority to ensure real-time and reliable transmission. Message queues employ persistent storage, enabling the recovery of critical status information from the most recent 30 seconds after a system restart, preventing data loss due to control interruptions.

[0124] The model update trigger is designed with multi-condition composite logic. In addition to the Lyapunov exponent, it also monitors the cumulative distribution of prediction residuals, the utilization rate of computing resources, and the jitter amplitude of the control cycle. The combination of trigger conditions is evaluated using fuzzy logic, and different indicators are dynamically weighted according to the current operating conditions. The update decision generates an evaluation report, recording the trigger reason, system status, and suggested actions for engineers' subsequent analysis and reference. The manual intervention interface allows advanced users to manually trigger or disable model updates; all operations require dual authentication and are logged.

[0125] The anomaly recovery process comprises seven stages: fault detection, system isolation, state preservation, backup switchover, root cause analysis, remediation implementation, and normal recovery. Each stage has clearly defined completion criteria and maximum time limits; for example, fault detection must be completed within 100 microseconds, and root cause analysis is limited to providing preliminary conclusions within 30 seconds. Critical operations during the recovery process require collaborative confirmation from multiple functional modules to avoid malfunctions caused by false alarms from a single sensor. A knowledge graph is constructed from historical fault cases, automatically matching newly occurring anomalies with similar cases and recommending validated solutions.

[0126] Dynamic parameter range monitoring employs a three-dimensional envelope method, defining the normal operating range in the position-velocity-acceleration space. The envelope is gradually widened according to the equipment's aging, with boundary tolerances adjusted annually. Parameters exceeding the operating range trigger anomaly diagnosis. The diagnostic algorithm first eliminates the possibility of sensor failure, then checks the wear indicators of mechanical transmission components, and finally evaluates the adaptability of the control algorithm. Diagnostic results are categorized into three suggestions: mechanical adjustment, control parameter optimization, and process improvement, and are sent to the corresponding maintenance systems.

[0127] The computational resource management unit dynamically allocates hardware accelerator resources during model retraining. GPU computing tasks are divided into multiple micro-batches, and the GPU memory is released immediately after each batch is completed to avoid prolonged memory occupation affecting real-time control. CPU cores employ affinity binding, with critical control threads running on dedicated cores, unaffected by other computing tasks. Memory access uses a prefetch strategy, loading training data into the cache in advance to reduce the impact of memory latency on computation speed.

[0128] The version rollback mechanism saves the five most recent available model versions, each accompanied by a complete performance evaluation report. Rollback decisions are based on a multi-dimensional evaluation matrix, comparing the current version with historical versions in terms of control accuracy, response speed, and resource consumption. The rollback operation retains a snapshot of the faulty model for subsequent offline analysis. Version compatibility checks ensure that model parameters match the current system architecture, preventing runtime errors caused by binary incompatibility.

[0129] The environmental adaptability module monitors the temperature, voltage, and clock stability of the computing device. When the chip temperature exceeds a safe threshold, a dynamic frequency reduction mechanism gradually lowers the computing frequency while proportionally relaxing the control precision requirements. The power fluctuation detection circuit triggers a data saving process when voltage anomalies occur, writing critical parameters into non-volatile memory. The clock synchronization module detects clock drift between processing units, periodically corrects the time base, and ensures timing consistency in distributed computing.

[0130] The user notification system employs a multi-channel alarm strategy. The control panel display shows concise fault codes and handling suggestions, while detailed alarm information is pushed to relevant personnel's mobile terminals via an industrial IoT platform. Alarm levels are divided into three categories: alert, warning, and critical, corresponding to different response time limits. The alarm history database supports multi-dimensional searching, allowing queries based on time range, device number, fault type, and other conditions, generating statistical reports to display system reliability trends.

[0131] Long-term operational optimization is achieved through performance degradation analysis. The system periodically compares the deviation between the current control accuracy and the initial baseline data to establish a health curve for the equipment. The maintenance decision module predicts the optimal maintenance timing based on the curve trend and prepares replacement parts and debugging plans in advance. The optimization algorithm identifies the matching relationship between control parameters and mechanical conditions, selecting the control strategy that minimizes wear on the equipment while ensuring accuracy.

[0132] The security audit function records all model updates and system reconfiguration operations. The audit logs utilize blockchain technology for tamper-proof protection, with each entry containing the hash value of the preceding record. Log analysis tools detect abnormal operation patterns, such as frequent model changes or restarts during off-peak hours. Audit reports are automatically generated periodically, summarizing system change records and security events for management review.

[0133] Integration with upstream systems is achieved through standardized interfaces. The process planning system can predefine target parameter ranges for key motion stages, and the motion control system configures corresponding monitoring thresholds accordingly. The downstream quality inspection system provides feedback on actual processing error data to correct deviations in the prediction model. The integrated data bus uses a unified time base, with all events recorded to the microsecond level, supporting cross-system time-series analysis.

[0134] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0135] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A high-precision two-dimensional motion error prediction and compensation iterative method, characterized in that, The method includes: In the operation interface of the motion control system, a motion trajectory overview is generated according to the user's set parameters. The motion trajectory overview includes the target position sequence of the motion platform in a two-dimensional plane and the expected motion parameters corresponding to each position. Establish a connection between the overall motion trajectory and the actual motion execution device; measure the deviation between the actual position and the target position of the motion platform at the current sampling time, and calculate the motion error vector based on the deviation; Based on the motion error vector and the expected motion parameters of the motion trajectory overview, a prediction model is constructed, and the two-dimensional motion error at future moments is predicted through an iterative optimization process. The construction of the prediction model includes: calling a preset time series database, which stores historical error data of the motion platform; Extract the actual motion parameter sequence within the current motion cycle, and perform correlation matching between the actual motion parameter sequence and historical error data in the time series database; The error rate of change of the matching results is calculated, and the expected motion parameters of the motion trajectory overview are combined to determine the initial parameters of the prediction model; the initial parameters are adjusted by an adaptive learning algorithm to obtain the optimized prediction model. The prediction model is used to output two-dimensional motion error estimates for multiple future sampling points; The correlation matching employs a dynamic time warping algorithm, calculates the power spectral density, identifies the main frequency components of the error, and compares them with historical data. The matching result refers to the judgment result of whether the current error has periodic characteristics; The error change rate adopts a sliding window mechanism, which calculates the first difference of the error based on the data within the window, and combines historical trends to predict the future error change rate. The initial parameters of the prediction model are determined by fitting the mapping relationship between the historical error curve and the current motion parameters using the least squares method. Based on the prediction results, a compensation control command is generated and applied to the motion execution device. Real-time monitoring of the compensated motion state, updating the motion error prediction model and outputting compensation logs, including: collecting new actual position data of the motion platform after the compensation control command is applied; Compare the new actual position data with the predicted two-dimensional motion error, and calculate the residual. Input the residuals into the update module of the prediction model to adjust the model's weight parameters; Retrain the prediction model based on the adjusted weight parameters and store the updated model state. The process of comparing the new actual location data with the predicted two-dimensional motion error and calculating the residual is used to calculate the comprehensive residual evaluation value Γ. ， in, This represents the comprehensive residual assessment value. This represents the number of sampling points within the sliding window. and Representing the first The prediction error vector and the measured error vector for each sampling point Let be the error covariance matrix.

2. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 1, characterized in that, The method of predicting the two-dimensional motion error at future moments through an iterative optimization process includes: setting the prediction window size, wherein the prediction window size is determined based on the dynamic response characteristics of the motion platform; Within the prediction window, the optimized prediction model is applied to the actual motion parameter sequence to generate preliminary error prediction data; Calculate the degree of difference between the preliminary error prediction data and the actual measurement deviation; Adjust the iteration step size of the prediction model according to the degree of difference, and repeat the prediction and adjustment process until the degree of difference is lower than the preset threshold or the maximum number of iterations is reached; The final output is the converged two-dimensional motion error prediction result; The difference between the preliminary error prediction data and the actual measurement deviation is calculated by using Mahalanobis distance to measure the degree of deviation of the statistical distribution of the predicted value and the measured value. The iteration step size is non-linearly scaled according to the difference gradient. A larger step size is used when the difference is large, and a smaller step size is used when the difference is small.

3. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 1, characterized in that, The step of generating compensation control commands based on the prediction results includes: analyzing the components of the predicted two-dimensional motion error in the horizontal and vertical directions; Based on the control characteristics of the motion actuator, a compensation gain coefficient is designed; the predicted two-dimensional motion error component is multiplied by the compensation gain coefficient to obtain the compensation amount; Combine the expected motion parameters from the overall motion trajectory overview to synthesize compensation control commands; The compensation control command includes a composite command for position correction and speed adjustment.

4. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 3, characterized in that, The measurement of the deviation between the actual position and the target position of the motion platform at the current sampling time includes: collecting real-time position data of the motion platform through the sensor array of the motion control system; Noise filtering is applied to the real-time location data to obtain filtered location data; the target position at the current sampling time is extracted from the motion trajectory overview. Calculate the Euclidean distance between the filtered position data and the target position, and use it as the current deviation; The current deviation is decomposed into error components in a two-dimensional plane.

5. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 1, characterized in that, The output compensation log includes: recording the prediction results, compensation control instructions, and residuals in each iteration of optimization. Generate a log file, which includes timestamps, error component values, and compensation effect indicators; The user interface displays a visual report of the log file.

6. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 1, characterized in that, The method further includes: defining motion error types, wherein the motion error types include position offset error and trajectory following error; Mark the priority of error types in the motion trajectory overview; allocate resource weights to the prediction model according to the priority.

7. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 6, characterized in that, The allocation of resource weights to the prediction model based on priority includes: analyzing the distribution characteristics of error types within the motion cycle; Set resource weight allocation rules based on distribution characteristics; Resource weight allocation rules are applied to the construction process of prediction models.

8. The high-precision two-dimensional motion error prediction and compensation iterative method according to claim 1, characterized in that, The method further includes: integrating a feedback mechanism into the motion control system, the feedback mechanism including a real-time data stream and a model update trigger; When the dynamic parameters of the motion platform exceed the preset range, the feedback mechanism is triggered to restart the iterative optimization process; The dynamic parameters include the third derivatives of position, velocity, and acceleration; The model update trigger is based on the Lyapunov exponent. When the exponent value exceeds a preset threshold, a tiered alarm mechanism is triggered to activate the model retraining process and restart the iterative optimization process.

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