Mechanical arm control method based on multi-scale dynamic state estimation and error compensation

Abstract

According to the mechanical arm control method based on multi-scale dynamic state estimation and error compensation, high-frequency and high-precision estimation of the state of a mechanical arm system is achieved through multi-sensor data fusion and an extended Kalman filtering algorithm, and the accuracy and reliability of state estimation are remarkably improved; on the basis, a multi-scale error analysis method combining a time domain and a frequency domain is provided, and an autoregressive moving average model is utilized to dynamically predict system errors, so that the sensing and pre-judging capability of the system on the errors is enhanced; a comprehensive control strategy including multiple links of feedforward, self-adaption and feedback is designed, a dynamic compensation and adjustment mechanism of errors is introduced, meanwhile, a real-time execution framework based on three-layer task scheduling is constructed, cooperative operation of all functional modules is coordinated, and the real-time performance and high efficiency of a control system are ensured. The method is suitable for multiple fields of industrial manufacturing, intelligent robots and the like, and provides technical support for precise control of mechanical arms in complex scenes.

Description

Technical Field

[0001] The present invention belongs to the technical field of robotic arm control, and particularly relates to a robotic arm control method based on multi-scale dynamic state estimation and error compensation. Background Art

[0002] State estimation and error compensation of a robotic arm control system are key technologies for achieving high-precision control. In modern robotic arm control systems, advanced algorithms such as the Extended Kalman Filter (EKF) or Particle Filter (PF) are often used for state estimation. These methods can handle the state dynamic changes of nonlinear systems and provide high estimation accuracy when fusing multi-sensor data. However, the existing control schemes for robotic arm systems have the following deficiencies:

[0003] (1) Traditional state estimation often relies on single-sensor data, and it is difficult to ensure estimation accuracy in complex dynamic environments;

[0004] (2) Existing error analysis methods are mostly limited to a single dimension in the time domain or frequency domain, and cannot comprehensively characterize the multi-scale characteristics of system errors;

[0005] (3) The control strategy for the robotic arm system is mainly feedback control, lacking the ability to predict and feedforward compensate for system errors, and the execution architecture of the control system generally adopts a simple hierarchical or centralized structure, making it difficult to achieve efficient cooperation among functional modules.

[0006] Therefore, we need to develop a robotic arm control method based on multi-scale dynamic state estimation and error compensation, which can cooperate through a three-layer architecture to perform high-precision estimation of multi-sensor fusion, predict multi-scale prediction errors, and perform high-precision compensation control. Summary of the Invention

[0007] The purpose of the present invention is to provide a robotic arm control method based on multi-scale dynamic state estimation and error compensation to solve the problems of single data, limited error analysis dimension, lack of feedforward compensation control, and lack of an efficient cooperation architecture in the existing robotic arm control system mentioned in the above background art. [[ID=?]]

[0008] To achieve the above purpose, the present invention provides a robotic arm control method based on multi-scale dynamic state estimation and error compensation, and the method is as follows:

[0009] Step S1: Real-time fuse multi-sensor data, dynamically estimate the state of the robotic arm system by constructing an Extended Kalman Filter, and output a state estimate;

[0010] Step S2: Based on the state estimate, perform multi-scale error analysis in the time domain and frequency domain, construct an autoregressive moving average model based on the error analysis results for error prediction in the future period, and output an error prediction result;

[0011] The multi-scale error analysis includes taking the state estimator as the center, determining the confidence interval of the true state of the robotic arm system with the covariance matrix of the posterior state estimation error to define the ellipsoid interface, discretizing the interface of the ellipsoid into a series of points to obtain a high-confidence sampling set of the true state; calculating the energy distribution of the state estimation error of the robotic arm system on different frequency components based on the high-confidence sampling set;

[0012] Step S3: Based on the state estimator and the error prediction result, formulate a multi-link compensation control strategy including feedforward compensation, adaptive correction, and feedback control to perform precise compensation control on the robotic arm system;

[0013] The output of the feedforward compensation controller consists of the times of the current state estimator, the predicted value of the output of the future feedback control, and the cumulative influence of the error prediction value at the future moment; the adaptive correction updates the feedforward compensation gain matrix through the error prediction residual to obtain the feedforward compensation control quantity ; the feedback control adopts proportional-integral-derivative control or linear quadratic control to obtain the closed-loop control quantity based on the closed-loop control of the state estimator ;

[0014] Superimpose the outputs of the feedforward compensation and the feedback control to obtain the total output of the compensation control strategy : ;

[0015] Step S4: Take the total output as a unified execution instruction, and after dynamic amplitude limiting processing, drive the actuator to perform stable control on the robotic arm system, and at the same time collect the state information of the robotic arm system as a new round of the multi-sensor data to form a closed-loop control.

[0016] Based on the foregoing solution, the error prediction is to construct an error prediction model on the basis of the multi-scale error analysis to predict the state estimation error of the robotic arm system at future moments. An autoregressive moving average model is used as the error prediction model to predict the state estimation error. Assume that the state estimation error at a future moment is represented by a linear combination of the state estimation errors at several past moments and random noise. The calculation formula is as follows: , where is the state estimation error at the moment, and are the orders of the autoregressive term and the moving average term respectively, and is the model coefficient, and is the random noise at time

[0017] Based on the foregoing solution, based on the autoregressive moving average model, the state estimation error of the robotic arm system at the next times is recursively predicted, and N error prediction values are obtained as the error prediction result, as follows:

[0018]

[0019] where represents the predicted value of the state estimation error at time for time the predicted value of the state estimation error.

[0020] Based on the foregoing solution, based on the state estimation quantity and the error prediction result, the feedforward compensation controller is set as: , where is the output of the feedforward compensation controller at time is the feedforward compensation gain matrix, is for the next times the predicted value of the state estimation quantity, denoted as the state prediction value.

[0021] Based on the foregoing solution, the state prediction value is expressed as the sum of the current state estimation quantity and the error prediction value, and the expression is:

[0022]

[0023]

[0024] where and are respectively the state transition matrix and the control input matrix of the robotic arm system, is the output of the feedback controller at time

[0025] .

[0026] Based on the foregoing solution, the adaptive correction updates the feedforward compensation gain matrix based on the error prediction residual, and defines the error prediction residual vector at time

[0027]

[0028] where represents at time for time The predicted value of the time error; correspondingly, the gradient direction of the feedforward compensation gain matrix is defined as:

[0029]

[0030] According to the gradient descent method, the update law of the feedforward compensation gain matrix is:

[0031]

[0032] where, is the learning rate.

[0033] Based on the foregoing scheme, the feedback control is a closed-loop control based on the state estimator. The feedback controller calculates the state feedback control law according to the deviation between the state estimator and the given state command value, and drives the actuator in real time to make the state of the robotic arm system approach the desired value;

[0034] The state feedback control law includes proportional-integral-differential control or optimal linear quadratic control. When using proportional-integral-differential control, its mathematical model is:

[0035]

[0036] where, is the output of the feedback controller at time is the state command value at time , , are the proportional, integral, and differential coefficients respectively.

[0037] Based on the foregoing scheme, calculating the energy distribution of the state estimation error of the robotic arm system on different frequency components through the spectral analysis method of discrete Fourier transform based on the high-confidence sampling set includes:

[0038] Calculating the deviation between each state sample in the high-confidence sampling set and the state estimator to obtain a high-confidence error sample set of the state estimation error at time

[0039] Performing statistical analysis on the error sample set to obtain the mean, covariance matrix, and other higher-order statistical quantities of the state estimation error of the robotic arm system at time k.

[0040] Based on the foregoing scheme, calculating the energy distribution of the state estimation error of the robotic arm system on different frequency components further includes:

[0041] Arrange the error samples within a time window in chronological order to form an error time series, perform a DFT transformation on the error time series to obtain its spectral function, calculate the energy distribution of the state estimation error of the robotic arm system on different frequency components according to the spectral function to obtain the power spectral density, and perform normalization processing on the power spectral density to obtain the probability density function of the frequency domain distribution of the state estimation error;

[0042] By analyzing the shape characteristics of the probability density function curve in the frequency domain, including peak value, peak width, mean value, and variance, to judge the main components and distribution rules of the state estimation error of the robotic arm system in the frequency domain.

[0043] Based on the foregoing solution, construct a real-time execution architecture based on dynamic state estimation, the multi-scale error analysis, the error prediction, and the compensation control strategy. The real-time execution architecture is a three-layer task scheduling model, which is the decision-making layer, the management layer, and the execution layer from top to bottom in sequence.

[0044] The present invention has the following advantages and effects compared with the prior art:

[0045] (1) Adopt the multi-sensor data fusion technology and the extended Kalman filter algorithm to achieve high-frequency and high-precision estimation of the state of the robotic arm system, effectively improving the accuracy and reliability of state estimation;

[0046] (2) Through the multi-scale error analysis in the time domain and frequency domain, combined with the autoregressive moving average model to dynamically predict the system error, enhancing the system's ability to perceive and predict errors;

[0047] (3) Design a multi-link control strategy of "feedforward + adaptive + feedback" to achieve active compensation for the errors of the robotic arm system, better improving the dynamic response performance of the system, and constructing a real-time execution architecture based on three-layer task scheduling to ensure the efficient collaborative operation of the control algorithm. Brief Description of the Drawings

[0048] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for use in the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts do not necessarily draw according to the actual ratio.

[0049] Figure 1 It is a flowchart of a robotic arm control method based on multi-scale dynamic state estimation and error compensation provided by an embodiment of the present invention. Detailed Embodiments

[0050] To more clearly illustrate the objectives, technical solutions, and advantages of the present invention, the following will describe the technical solutions in the embodiments of the present invention clearly and completely in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. The example embodiments can be implemented in multiple forms and should not be construed as limited to the examples set forth herein; on the contrary, providing these embodiments makes the present invention more comprehensive and complete, and fully conveys the concept of the example embodiments to those skilled in the art.

[0051] In addition, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to give a thorough understanding of the embodiments of the present invention. However, those skilled in the art will realize that the technical solutions of the present invention can be practiced without one or more of the specific details, or other methods, components, devices, steps, etc. can be used. In other cases, well-known methods, devices, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the present invention.

[0052] The block diagrams shown in the accompanying drawings are only functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0053] The flowcharts shown in the accompanying drawings are only illustrative and do not necessarily include all the content and operations / steps, nor do they necessarily need to be executed in the described order. For example, some operations / steps can be decomposed, while some operations / steps can be combined or partially combined. Therefore, the actual execution order may change according to the actual situation.

[0054] The following will describe the present invention in detail with specific embodiments:

[0055] As shown in the Figure 1 accompanying drawings, the embodiment of the present invention provides a manipulator control method based on multi-scale dynamic state estimation and error compensation. The specific steps of this method are as follows:

[0056] Step S1: Perform real-time fusion of multi-sensor data. By constructing an extended Kalman filter, dynamically estimate the state of the manipulator system with high frequency and high precision, and output the state estimation quantity;

[0057] Preferably, the multi-sensor data is complete information on the state of the robotic arm system obtained through various types of sensors, including position, velocity, and acceleration sensors; the data sampling frequency of each sensor can be set according to actual requirements. In this embodiment, the minimum frequency that satisfies the Nyquist sampling theorem is selected to balance information integrity and computational efficiency.

[0058] Preferably, during the real-time fusion, a time synchronization method (PTP) based on the IEEE 1588 Precision Time Protocol is adopted to ensure the temporal consistency of data fusion. All sensors and processing nodes are connected through an Ethernet network, and PTP is used to achieve global clock synchronization. After the multi-sensor data is marked with a unified timestamp, it is sent to the data fusion center for the real-time fusion.

[0059] Specifically, after the multi-sensor data undergoes the real-time fusion, unified preprocessing is performed to provide a standardized input for the state estimation algorithm; the data preprocessing may include: detecting outliers using the 3σ criterion, identifying and removing random pulse noise and continuous abnormal offsets through a Hampel filter; smoothing the data using a second-order Savitzky-Golay filtering algorithm; converting the data of different sensors to the system centroid coordinate system according to the installation position and attitude of the sensors to complete coordinate transformation; performing time alignment and interpolation processing on the data of different sensors to achieve data synchronization.

[0060] Furthermore, taking the multi-sensor data after data preprocessing as input, based on the Extended Kalman Filter algorithm (EKF), combined with the state transition equation and observation equation of the robotic arm system, the current observation value and prior estimate, the dynamic estimation of the state of the robotic arm system is achieved through recursive estimation, and the optimal state estimate is obtained as the state estimator.

[0061] Specifically, position, velocity, and acceleration are selected as state variables, and the state vector is defined as: , where respectively represent the position, velocity, and acceleration at time , and represents the transpose operation; assuming the sampling period of the robotic arm system is

[0062]

[0063] where, is the control input at time , that is, the jerk of the robotic arm system , and the state transition equation is abbreviated as: is the state transition matrix of the robotic arm system, is the control input matrix of the robotic arm system.

[0064] Specifically, the observation equation describes the relationship between the sensor measurement values and the state variables of the robotic arm system. Let the measurement values of the position, velocity, and acceleration sensors be , respectively. Then the observation equation is expressed as:

[0065] , where , , are the measurement noises of the position, velocity, and acceleration sensors, respectively. The observation equation is abbreviated as:

[0066]

[0067] where is the observation matrix, is the observation noise vector.

[0068] Furthermore, based on the state estimate and control input of the robotic arm system at the previous moment, the state of the robotic arm system at the current moment is predicted through the state transition equation. The formula is:

[0069]

[0070]

[0071] where is the prior estimate of the state of the robotic arm system at time is the posterior estimate of the state of the robotic arm system at time is the control input at time is the covariance matrix of the state estimation error at time k, is the covariance matrix of the state estimation error at time is the state transition matrix of the state transition equation, is the control input matrix of the robotic arm system. Here is the transpose operation, is the covariance matrix of the state estimation error, is the process noise covariance matrix.

[0072] Furthermore, based on the sensor measurement values at the current moment, the prediction result of the state of the robotic arm system at the current moment is corrected to obtain the posterior optimal estimate. The formula is:

[0073]

[0074]

[0075]

[0076] wherein, is the Kalman gain matrix, is the sensor measurement value vector, which is the same as the observation equation, is the identity matrix, is the observation noise covariance matrix, and the posterior optimal estimate of the manipulator system state is represented by indicated, indicates at time, according to all the observations from 1 to time to estimate the state vector of the manipulator system to obtain the optimal result. Similarly, indicates at time, according to the observations from 1 to time to predict the prior estimate of the state vector of the manipulator system; through prediction and update, recursively calculate the posterior optimal estimate of the manipulator system state as the state estimator, is the covariance matrix of the posterior state estimation error.

[0077] Step S2, receive the state estimator, perform multi-scale error analysis in the time domain and frequency domain, construct an autoregressive moving average model to predict the error of the error analysis result, and output the error prediction result.

[0078] Preferably, the multi-scale error analysis is to statistically analyze the deviation between the state estimator of the manipulator system and the true state, and characterize the time-domain and frequency-domain characteristics of the manipulator system error; the error prediction is to construct a mathematical model based on historical error data on the basis of error analysis as the autoregressive moving average model to forward-estimate the state estimation error of the manipulator system at a future time; it should be noted that the error analysis and prediction of the manipulator system in this embodiment are mainly divided into two steps: multi-scale error analysis and autoregressive moving average error prediction;

[0079] Specifically, in the multi-scale error analysis, the analysis of the time-domain characteristics of the manipulator system error includes:

[0080] Define the state estimation error of the manipulator system as: where is The true value of the state of the robotic arm system at a moment, is the state estimator of the robotic arm system obtained by the EKF algorithm at that moment;

[0081] It should be noted that for an actual robotic arm system, the true state is often difficult to obtain directly. This embodiment proposes an error analysis method based on a high confidence interval, including:

[0082] For the state estimator at each moment , the EKF algorithm simultaneously gives the covariance matrix of the corresponding posterior estimation error ;

[0083] The diagonal elements of reflect the uncertainty of the state estimation error, that is: where is the standard deviation of the estimation error of the th robotic arm state component at moment; According to the properties of the multivariate Gaussian distribution, the true state falls within an ellipsoid centered on the state estimator with a constant probability. The interface of the ellipsoid is used as the confidence interval of the true state. This embodiment selects a confidence level of , and the corresponding ellipsoid equation is:

[0084]

[0085] where the superscript represents matrix transpose, the superscript represents matrix inversion, is the quantile of the chi-square distribution; Further, the interface of the ellipsoid is discretized into a series of points to obtain a high-confidence sampling set of the true state , where is the number of sampling points; Calculate the deviation between each state sample in the high-confidence sampling set and the state estimator to obtain a high-confidence error sample set of the state estimation error at moment, and ;

[0086] Perform statistical analysis on the error sample set to obtain the mean , covariance matrix and other higher-order statistics of the robotic arm system error at time k.

[0087] Furthermore, to analyze the frequency-domain characteristics of the state estimation error of the robotic arm system, in this embodiment, a spectrum analysis method based on the discrete Fourier transform (DFT) is introduced as follows:

[0088] Arrange the error samples within a time window in chronological order to form an error time series , where is the time window length, and perform a DFT transformation on the error time series to obtain its spectrum function as:

[0089]

[0090] where is the normalized frequency, is the imaginary unit;

[0091] According to the spectrum function , calculate the energy distribution of the state estimation error of the robotic arm system on different frequency components to obtain the power spectral density as: , perform a normalization process on the power spectral density PSD to obtain the frequency-domain distribution probability density function PDF of the state estimation error as: ; By analyzing the shape characteristics of the PDF curve, including peak value, peak width, mean value, and variance, to judge the main components and distribution rules of the state estimation error of the robotic arm system in the frequency domain.

[0092] Preferably, for the error prediction, on the basis of the multi-scale error analysis, an error prediction model is constructed to estimate the state estimation error of the robotic arm system at future moments. Considering that the state estimation error of the robotic arm system has a certain temporal correlation, an autoregressive moving average model (ARMA) is used as the error prediction model to predict the state estimation error, that is, assume that the state estimation error at a future moment is represented by a linear combination of the state estimation errors at past moments and random noise, and the calculation formula is as follows:

[0093]

[0094] where is the state estimation error at moment, are the historical state estimation errors, and are the orders of the autoregressive term and the moving average term respectively, and are the model coefficients, is moment random noise; Based on the identified autoregressive moving average model (ARMA), for the future Recursively predict the state estimation error of the robotic arm system at each moment to obtain N error prediction values as the error prediction result, as follows:

[0095]

[0096]

[0097]

[0098]

[0099] Among them, represents the predicted value of the state estimation error at the moment of for the moment of . Then the error prediction values for the next moments are .

[0100] It should be noted that in step S2 of this embodiment, an error estimation method based on multi-scale analysis and autoregressive prediction is used, which can effectively characterize the dynamic evolution law of the state estimation error of the robotic arm system, and perform forward prediction on the state estimation error at future moments, providing reliable prior information for compensation control; compared with the traditional error estimation method based on a fixed model, this embodiment adopts an adaptive error modeling strategy, which can track the changes in the statistical characteristics of system errors, has better robustness, and avoids direct observation of the true state through high-confidence interval sampling, reducing the hardware complexity of state estimation error analysis. At the same time, the combination of frequency-domain analysis and time-domain prediction reveals the multi-scale characteristics of the state estimation error of the robotic arm system, which helps to design a compensation control rate targeted.

[0101] Step S3, based on the state estimation quantity and the error prediction result, formulate a multi-link compensation control strategy including feedforward compensation, adaptive correction, and feedback control to perform precise compensation control on the robotic arm system;

[0102] It should be noted that on the basis of feedback control, according to the error prediction result of the state estimation error of the robotic arm system, pre-correct the output of the controller to suppress system errors and improve control quality; by combining error compensation and feedback control, the dynamic response performance and steady-state control accuracy of the system can be significantly improved. The compensation control strategy proposed in this embodiment is based on the state estimation quantity and the error prediction result, and combines the feedforward compensation, the feedback control, and the adaptive correction and other methods to achieve precise control of the output of the robotic arm system.

[0103] It should be noted that in step S1, the state of the robotic arm system is estimated at a high speed. Through the EKF algorithm, the measurement data of multiple sensors are fused to achieve real-time dynamic estimation of the state of the robotic arm system, and the state estimators at each moment are obtained. and the covariance matrix of its posterior estimation error ; in step S2, error analysis and prediction are performed on the state estimator . Multiscale statistical modeling and dynamic prediction are carried out on the state estimation error to obtain the error prediction values at the next moments.

[0104] Preferably, based on the state estimator and the error prediction result, the feedforward compensation controller is expressed as: , where is the output of the feedforward compensation controller at moment, is the feedforward compensation gain matrix, is the predicted value of the state estimator at the next moments, denoted as the state prediction value. The state prediction value is expressed as the sum of the current state estimator and the error prediction value, and the expression is:

[0105] ,

[0106] where and are the state transition matrix and the control input matrix of the robotic arm system respectively, is the output of the feedback controller at moment. Substituting it into the feedforward compensation controller model and arranging, we get:

[0107]

[0108] The above formula shows that the output of the feedforward compensation controller consists of three parts: times of the current state estimator, the predicted value of the future feedback control output, and the cumulative influence of the error prediction values at future moments; by reasonably designing the feedforward compensation gain matrix , the dynamic lag effect of the system can be offset to a certain extent and the tracking error can be reduced.

[0109] Preferably, through an adaptive correction mechanism, the feedforward compensation gain matrix is adjusted online;

[0110] Specifically, the core of the adaptive correction mechanism is to update the feedforward compensation gain matrix based on the error prediction residual. Define the error prediction residual vector at moment as:

[0111]

[0112] wherein, represents the predicted value of the time error at moment with respect to the time error;

[0113] Correspondingly, the gradient direction of the feedforward compensation gain matrix is defined as:

[0114] ; in each control cycle, the system dynamically adjusts the update step size of the feedforward compensation gain matrix according to the norm of the error prediction residual vector E(k). The error prediction residual vector E(k) reflects the error prediction ability of the system. When its norm value is large, it indicates that there is a large deviation in the current error prediction, and the system will increase the update step size of the feedforward compensation gain matrix to make the compensation strategy more aggressive; on the contrary, when its norm value is small, it indicates that the error prediction is relatively accurate. At this time, the update step size is reduced to make the control strategy more stable and avoid system oscillation caused by overcompensation.

[0115] Specifically, first calculate the norm of the error prediction residual vector at the current moment k, ||E(k)|| = , and set the error prediction residual threshold . When ||E(k)|| > , the system increases the update step size of the feedforward compensation gain matrix to accelerate the compensation adjustment speed; when ||E(k)|| < , the system reduces the update step size to make the control more stable and prevent oscillation; when ||E(k)|| continuously remains below the threshold, the system enters the fine-tuning mode and only makes small-range adjustments to improve the compensation accuracy. Through this adaptive adjustment mechanism, the compensation gain matrix will not be updated significantly when the error is small, and at the same time, it can enhance the compensation ability in a timely manner when the error is large, thereby improving the stability and accuracy of the control system.

[0116] According to the gradient descent method, the update law of the feedforward compensation gain matrix is:

[0117]

[0118] wherein, is the learning rate.

[0119] Preferably, the feedback control is a closed-loop control based on the state estimator. The feedback controller calculates the state feedback control law according to the deviation between the system state estimator and the given state command value, and drives the actuator in real time to make the state of the robotic arm system approach the expected value; the state feedback control law includes proportional-integral-derivative (PID) control and optimal linear quadratic regulator (LQR) control. Taking PID control as an example, its mathematical model is:

[0120]

[0121] wherein, is the output of the moment feedback controller, is the state command value at the moment, , , are the proportional, integral, and differential coefficients respectively;

[0122] Furthermore, the outputs of the feedforward compensation controller and the feedback controller are superimposed to obtain the total output of the compensation control strategy :

[0123]

[0124] The above formula indicates that the core of the compensation control strategy is to combine the mechanical arm system state estimation error and the predicted value of the state estimation error with real-time feedback correction, so as to achieve a balance between dynamic response and steady-state performance. By suppressing the inherent lag of the system through feedforward compensation and resisting random disturbances through feedback control, the comprehensive performance index of the control system can be significantly improved.

[0125] In summary, the compensation control strategy proposed in this embodiment is based on high-speed dynamic state estimation and multi-scale error analysis and prediction, and integrates multiple control means such as feedforward compensation control, closed-loop feedback control, and adaptive gain correction. It realizes the accurate analysis, adaptive modeling, and active suppression of complex system errors in terms of function, and constitutes an adaptive and data-driven closed-loop control system in terms of architecture, with significant real-time, robustness, and intelligent characteristics; compared with the traditional single feedback control method, the solution of this embodiment can more fully explore the value of the mechanical arm system state information and error data, characterize and estimate the error from two dimensions of time domain and frequency domain, and adaptively optimize the structure and parameters of the compensation control, so as to obtain an ideal trade-off between dynamic performance and steady-state index.

[0126] Step S4, the feedforward compensation control quantity based on state estimation and the closed-loop control quantity based on state feedback are comprehensively used to obtain the total control output U(k), and a unified execution instruction is output. After the execution instruction is processed by dynamic amplitude limiting, the actuator is driven to achieve stable control of the robotic arm system; at the same time, the real-time collected state information is fed back to step S1 to form a closed-loop control.

[0127] Preferably, based on the aforementioned dynamic state estimation, multi-scale error analysis, error prediction, and compensation control strategy, a real-time execution architecture is constructed to ensure the online real-time operation of various algorithms; the real-time execution architecture is a three-layer task scheduling model, which from top to bottom are the decision-making layer, the management layer, and the execution layer;

[0128] The decision-making layer is responsible for receiving operator instructions and status feedback, formulating the working mode and task objectives of the robotic arm system, and outputting task instructions and constraint conditions to be passed to the management layer;

[0129] The management layer is mainly responsible for planning and coordinating the execution of various control tasks. Its core is the task scheduler, which adopts a priority-based dynamic scheduling strategy. According to the time constraints, error prediction trends, logical order, and resource requirements of tasks, it dynamically adjusts the computing resource allocation and task priorities to ensure that the refined error compensation strategy is preferentially executed when the error is large, while reducing the computing load when the error is small, reasonably allocating computing resources, and improving the system response efficiency; the scheduling process can be modeled and analyzed using a timed Petri net, and the scheduling algorithms include the earliest deadline first (EDF) algorithm, the lowest slack first (LSF) algorithm, etc.; the management layer sends the scheduling results to the execution layer;

[0130] The execution layer directly faces the control object and is responsible for the specific operations of the control algorithms. Its core modules include a state estimator, an error predictor, and a compensation controller, which respectively implement the EKF algorithm, ARMA prediction, and compensation control. These modules execute in parallel according to the time and logical order planned by the management layer, and their input and output data are shared and synchronized through a cache and a real-time database; the execution layer feeds back the calculation results to the management layer and the decision-making layer, and passes the control instructions to the actuator.

[0131] In this embodiment, through the three-layer task scheduling model from top to bottom, the decision-making planning, task coordination, and algorithm execution are organically combined to ensure the real-time performance of the control system; at the same time, through measures such as safety inspection, precise timing, and highly reliable transmission of control instructions, the reliability and robustness of the execution process are further strengthened; compared with the conventional hierarchical control system, this solution can more closely coordinate the data interaction and task synchronization between different levels, reducing interface delays and scheduling overhead; compared with the centralized control system, this solution adopts a modular and hot-pluggable deployment mode, which can significantly improve the flexibility, maintainability, and scalability of the system. This real-time execution solution can fully exert the superior performance of the multi-scale error analysis and prediction and compensation control algorithms, improve the output response speed of complex dynamic systems, strongly enhance the technical level of robotic arm motion control equipment, and can be widely applied to high-precision robotic arm control systems, providing an important support for improving the technical level of industrial automation equipment.

[0132] Other embodiments of the present invention will be readily apparent to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention, which follow the general principles of the invention and include known common general knowledge or conventional technical means in the technical field not disclosed by the present invention. The specification and examples are only to be considered as exemplary, and the true scope and spirit of the invention are pointed out by the claims. It should be understood that the present invention is not limited to the exact structures described above and shown in the drawings, and various modifications and changes can be made without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. A manipulator control method based on multi-scale dynamic state estimation and error compensation, characterized in that Including: Step S1: Perform real-time fusion on multi-sensor data. By constructing an extended Kalman filter, dynamically estimate the state of the robotic arm system and output a state estimate; Step S2: Based on the state estimate, conduct multi-scale error analysis in the time domain and frequency domain. Based on the error analysis results, construct an autoregressive moving average model to predict the error in the future time period and output an error prediction result; The multi-scale error analysis includes using the state estimate as the center and determining the ellipsoid interface with the covariance matrix of the posterior state estimation error as the confidence interval of the true state of the robotic arm system. Discretize the interface of the ellipsoid into a series of points to obtain a high-confidence sampling set of the true state; Calculate the energy distribution of the state estimation error of the robotic arm system on different frequency components based on the high-confidence sampling set; Step S3: Based on the state estimate and the error prediction result, formulate a multi-link compensation control strategy including feedforward compensation, adaptive correction, and feedback control to perform precise compensation control on the robotic arm system; The controller output of the feedforward compensation consists of the times of the current state estimator, the predicted value of the output of the future feedback control, and the cumulative effect of the predicted error value at the future moment; for the adaptive correction, the feedforward compensation gain matrix is updated through the error prediction residual to obtain the feedforward compensation control quantity ; the feedback control adopts proportional-integral-derivative control or linear quadratic control to obtain the closed-loop control quantity of the closed-loop control based on the state estimator ; Superimpose the output of the feedforward compensation and the feedback control to obtain the total output of the compensation control strategy : ; Step S4: Use the total output as a unified execution instruction. After dynamic amplitude limiting processing, drive the actuator to perform stable control on the robotic arm system, and at the same time collect the state information of the robotic arm system as the new round of the multi-sensor data to form a closed-loop control.

2. The robotic arm control method based on multi-scale dynamic state estimation and error compensation according to claim 1, wherein The error prediction is to construct an error prediction model based on the multi-scale error analysis to predict the state estimation error of the robotic arm system at a future time. Use an autoregressive moving average model as the error prediction model to predict the state estimation error. Assume that the state estimation error at a future time is represented by a linear combination of the state estimation errors at several past times and random noise. The calculation formula is as follows: ， wherein is the state estimation error at the moment, is the historical state estimation error, and are the orders of the autoregressive term and the moving average term respectively, and is the random noise at the moment.

3. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 2, characterized in that, Based on the autoregressive moving average model, recursively predict the state estimation error of the robotic arm system at the future moments to obtain N error prediction values as the error prediction result, as follows: ， Among them, represents the prediction value of the state estimation error at moment for the moment.

4. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 1, characterized in that Based on the state estimator and the error prediction result, set the feedforward compensation controller as: , where is the output of the feedforward compensation controller at time is the feedforward compensation gain matrix, is the predicted value of the state estimator at the next time instants, denoted as the state prediction value.

5. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 4, characterized in that, Express the state prediction value as the sum of the current state estimate and the error prediction value. The expression is: ， Among them, and are the state transition matrix and the control input matrix of the robotic arm system respectively, is the output of the feedback controller at time, substituting it into the controller of the feedforward compensation gives: 。 6. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 1, characterized in that, The adaptive correction updates the feedforward compensation gain matrix based on the error prediction residual, and defines the error prediction residual vector at time as: ， Among them, represents the predicted value of the time error at the moment; correspondingly, the gradient direction of the feedforward compensation gain matrix is defined as: ； According to the gradient descent method, the update law of the feedforward compensation gain matrix is as follows: , where is the learning rate.

7. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 1, characterized in that The feedback control is a closed-loop control based on the state estimate. The feedback controller calculates the state feedback control law according to the deviation between the state estimate and the given state command value, and drives the actuator in real time to make the state of the robotic arm system approach the expected value; The state feedback control law includes proportional-integral-derivative control or optimal linear quadratic control. When using proportional-integral-derivative control, its mathematical model is: ， Among them, is the output of the feedback controller at time is the state command value at time , , are the proportional, integral, and differential coefficients, respectively.

8. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 1, characterized in that Based on the high-confidence sampling set, calculate the energy distribution of the state estimation error of the robotic arm system on different frequency components through the spectral analysis method of discrete Fourier transform, including: Calculate the deviation between each state sample in the high-confidence sampling set and the state estimator to obtain a high-confidence error sample set of the state estimation error at the moment; Conduct statistical analysis on the error sample set to obtain the mean, covariance matrix, and other higher-order statistical quantities of the state estimation error of the robotic arm system at time k.

9. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 8, characterized in that, The calculation of the energy distribution of the state estimation error of the robotic arm system on different frequency components also includes: Arrange the error samples within a period window in chronological order to form an error time series, perform DFT transformation on the error time series to obtain its spectral function, calculate the energy distribution of the state estimation error of the robotic arm system on different frequency components according to the spectral function to obtain the power spectral density, and perform normalization processing on the power spectral density to obtain the probability density function of the frequency domain distribution of the state estimation error; By analyzing the shape characteristics of the probability density function curve of the frequency domain distribution, including peak value, peak width, mean value, and variance, to judge the main components and distribution rules of the state estimation error of the robotic arm system in the frequency domain.

10. A manipulator control method based on multi-scale dynamic state estimation and error compensation according to claim 1, characterized in that Based on the dynamic state estimation, the multi-scale error analysis, the error prediction, and the compensation control strategy, construct a real-time execution architecture, and the real-time execution architecture is a three-layer task scheduling model, which is the decision-making layer, the management layer, and the execution layer from top to bottom in turn.

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