A high-precision position holding method and device for multi-dimensional motor cooperative control and a storage medium

Abstract

The application discloses a high-precision position keeping method and device for multi-dimensional motor cooperative control and a storage medium, and is used for keeping high-precision position of multi-dimensional motor. The application comprises the following steps: constructing a multi-dimensional data set; performing standardization processing on the multi-dimensional data set to obtain standard data; calculating a covariance matrix based on the standard data and performing eigenvalue decomposition; determining a plurality of principal component feature vectors according to cumulative variance contribution rates to form a principal component space; projecting the standard data into the principal component space to form a reduced dimension data set; inputting the reduced dimension data set into a pre-trained deep belief network, outputting a comprehensive feature vector through hierarchical features of a restricted Boltzmann machine; inputting the comprehensive feature vector into a deep deterministic policy gradient algorithm model to construct a reward function; outputting a real-time adjustment strategy based on the reward function to obtain optimized control parameters; and realizing high-precision position keeping of the plurality of motors according to the optimized control parameters.

Description

Technical Field

[0001] This application relates to the field of industrial automation control, and in particular to a high-precision position holding method, device and storage medium for multi-dimensional motor cooperative control. Background Technology

[0002] In high-precision control fields such as industrial automation, robotics, and aerospace, multi-dimensional motor cooperative systems are widely used in complex motion control scenarios, such as multi-joint robotic arms, precision machining platforms, and satellite attitude adjustment systems. These systems typically require multiple motors to maintain micron-level or even sub-micron-level positional accuracy under complex conditions such as dynamic loads and environmental disturbances, while simultaneously meeting multiple constraints including energy optimization and synchronization control. Traditional single-motor control methods cannot satisfy the coupling effects and cooperative requirements between multiple motors; therefore, multi-dimensional motor cooperative control technology has become a core research direction.

[0003] Currently, multi-dimensional motor collaborative control only collects data in limited dimensions such as position, speed, and current. This data, after undergoing linear dimensionality reduction processing such as traditional low-pass filtering or principal component analysis, is input into a preset motor mathematical model or a PID control algorithm with fixed parameters to generate control commands. Control algorithms based on preset models lack adaptive capabilities. When faced with complex operating conditions such as dynamic load changes and environmental parameter fluctuations, parameters must be manually readjusted. They cannot autonomously optimize current, speed, and position loop parameters through real-time data-driven methods. Ultimately, this leads to a gradual accumulation of position errors during long-term operation, making it difficult to meet the stringent requirements of high-precision position maintenance in advanced equipment.

[0004] Furthermore, ignoring the impact of temperature and humidity changes on the motor winding resistance, as well as the mechanical resonance risk reflected by vibration sensor data, can easily lead to the control strategy failing to fully perceive the system state, and linear dimensionality reduction methods are difficult to effectively handle the nonlinear characteristics in motor operating data. Summary of the Invention

[0005] This application discloses a high-precision position holding method, device, and storage medium for multi-dimensional motor cooperative control, used to maintain the high-precision position of multi-dimensional motors.

[0006] The first aspect of this application discloses a high-precision position-keeping method for multi-dimensional motor cooperative control, including:

[0007] Real-time acquisition of position data, speed data, torque data, environmental data, vibration data, and current data of multiple motors;

[0008] The location data, rotational speed data, torque data, environmental data, vibration data, and current data are aligned based on timestamps to construct a multidimensional dataset;

[0009] The multidimensional dataset is standardized to obtain standard data;

[0010] Calculate the covariance matrix and perform eigenvalue decomposition based on the standard data;

[0011] Multiple principal component eigenvectors are determined based on the cumulative variance contribution rate, forming a principal component space;

[0012] The standard data is projected into the principal component space to form a dimensionality-reduced dataset.

[0013] The dimensionality reduction dataset is input into a pre-trained deep belief network, and a comprehensive feature vector is output through the hierarchical features of a restricted Boltzmann machine. The comprehensive feature vector is used to characterize the dynamic characteristics of the position error of multiple motors, the load torque coupling relationship, the environmental disturbance response characteristics, and the dynamic compensation parameters required for the coordinated control of multiple motors.

[0014] The comprehensive feature vector is input into the deep deterministic policy gradient algorithm model to construct the reward function;

[0015] Based on the reward function, a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors is output to obtain optimized control parameters.

[0016] Based on the optimized control parameters, the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors are adjusted in real time to achieve high-precision position holding of multiple motors.

[0017] Optionally, after obtaining optimized control parameters by outputting a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors based on the reward function, and before adjusting the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors in real time according to the optimized control parameters to achieve high-precision position holding of multiple motors, the method further includes:

[0018] Calculate the deviation between the actual position and the target position of multiple motors to form a position deviation sequence;

[0019] Based on the position deviation sequence, a comprehensive error index is calculated;

[0020] If the comprehensive error index exceeds a preset threshold, the reward function correction mechanism is triggered;

[0021] The current multidimensional dataset is input into the deep belief network, which outputs the current comprehensive feature vector. Combined with the preset fault feature library, the source of error is analyzed.

[0022] Based on the aforementioned error sources, the reward function in the deep deterministic policy gradient algorithm model is dynamically corrected;

[0023] The modified reward function is input into the deep deterministic policy gradient algorithm model to regenerate the adjustment strategies for multiple motors and obtain new optimized control parameters.

[0024] Optionally, the step of inputting the comprehensive feature vector into the deep deterministic policy gradient algorithm model to construct the reward function includes:

[0025] The comprehensive feature vector is input into the deep deterministic strategy gradient algorithm model to generate initial control parameters, which include the motor's current loop parameters, speed loop compensation coefficient, and position loop parameters.

[0026] Based on the initial control parameters, multiple motors are controlled to operate, and the actual position data of multiple motors, the synchronization data between multiple motors, and the energy consumption data of multiple motors are collected in real time to generate actual control parameters;

[0027] Based on the actual control parameters, the position error, synchronization error, and energy consumption are calculated respectively, and a reward function that includes position error, synchronization error, and energy consumption optimization is constructed.

[0028] Optionally, the real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors output based on the reward function to obtain optimized control parameters includes:

[0029] The operating status of multiple motors under actual control parameters is evaluated based on the reward function, and the evaluation results are output.

[0030] Based on the evaluation results, optimized control parameters are generated using an adjustment strategy based on a deep deterministic policy gradient algorithm.

[0031] Optionally, based on the actual control parameters, the step of calculating the position error, synchronization error, and energy consumption respectively, and constructing a reward function that includes position error, synchronization error, and energy consumption optimization, includes:

[0032] The penalty term for the position error is designed using an exponential decay function, and the formula is as follows:

[0033]

[0034] in, This is the position error sensitivity coefficient. This refers to the actual position of the motor. The target position of the motor;

[0035] The penalty term for the synchronization error is designed using a Gaussian kernel function, and the formula is as follows:

[0036]

[0037] Where M represents the number of motors. The synchronization error sensitivity coefficient, and These are the actual positions of motors i and j;

[0038] The optimization term for the energy consumption is designed using the current-square integral form, and the formula is as follows:

[0039]

[0040] in, Energy consumption weighting coefficient This represents the motor current.

[0041] Optionally, after aligning the position data, rotational speed data, torque data, environmental data, and current data based on timestamps to construct a multidimensional dataset, and before standardizing the multidimensional dataset to obtain standard data, the method further includes:

[0042] Wavelet transform is used to perform multi-scale decomposition on the multidimensional dataset to remove high-frequency noise.

[0043] Optionally, the step of performing multi-scale decomposition of the multidimensional dataset using wavelet transform to remove high-frequency noise includes:

[0044] The multidimensional data is decomposed into different decomposition layers by using wavelet basis functions at multiple scales.

[0045] An adaptive threshold is used to reduce noise in the different decomposition layers;

[0046] The high-frequency coefficients in the different decomposition layers are processed by a soft thresholding function to obtain the denoised coefficients.

[0047] The noise-reduced coefficients are reconstructed with the low-frequency approximation coefficients to complete the high-frequency noise removal.

[0048] A second aspect of this application provides a high-precision position holding device for multi-dimensional motor cooperative control, comprising:

[0049] The data acquisition unit is used to collect position data, speed data, torque data, environmental data, vibration data, and current data of multiple motors in real time.

[0050] An alignment unit is used to align the position data, rotational speed data, torque data, environmental data, vibration data, and current data based on timestamps to construct a multidimensional dataset.

[0051] The processing unit is used to standardize the multidimensional dataset to obtain standard data.

[0052] The decomposition unit is used to calculate the covariance matrix and perform eigenvalue decomposition based on the standard data.

[0053] Forming units are used to determine multiple principal component eigenvectors based on the cumulative variance contribution rate, forming the principal component space;

[0054] A projection unit is used to project the standard data into the principal component space to form a dimension-reduced dataset.

[0055] The output unit is used to input the dimensionality reduction dataset into a pre-trained deep belief network and output a comprehensive feature vector through the hierarchical features of the restricted Boltzmann machine. The comprehensive feature vector is used to characterize the dynamic characteristics of the position error of multiple motors, the load torque coupling relationship, the environmental disturbance response characteristics, and the dynamic compensation parameters required for the coordinated control of multiple motors.

[0056] The construction unit is used to input the comprehensive feature vector into the deep deterministic policy gradient algorithm model to construct the reward function;

[0057] The acquisition unit is used to output a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients and position loop parameters of multiple motors based on the reward function, so as to obtain optimized control parameters.

[0058] The holding unit is used to adjust the current loop parameters, the speed loop compensation coefficient, and the position loop parameters of multiple motors in real time according to the optimized control parameters, so as to achieve high-precision position holding of multiple motors.

[0059] A third aspect of this application provides a high-precision position holding device for multi-dimensional motor cooperative control, comprising:

[0060] Processor, memory, input / output units, and bus;

[0061] The processor is connected to memory, input / output units, and a bus;

[0062] The memory holds a program, which the processor calls to execute, as in the first aspect and any optional method of the first aspect.

[0063] The fourth aspect of this application provides a computer-readable storage medium on which a program is stored, which, when executed on a computer, performs the methods of the first aspect and any optional methods of the first aspect.

[0064] As can be seen from the above technical solutions, the embodiments of this application have the following advantages:

[0065] First, this application constructs a full-dimensional dataset containing multi-source data such as position, speed, torque, environmental parameters, and current. Compared with the limitations of traditional methods that rely only on basic data such as position and current, the newly added torque data can accurately reflect load changes, while temperature, humidity, and vibration sensor data can capture environmental interference in real time. This constructs a complete dataset containing motor operating status, load characteristics, and environmental interference. By adjusting the current loop parameters in real time through temperature data, errors are reduced and accuracy is improved.

[0066] Secondly, a fusion mechanism of principal component analysis (PCA) dimensionality reduction and deep belief network (DBN) hierarchical feature extraction is adopted to overcome the bottleneck of traditional linear dimensionality reduction methods in handling nonlinear features. PCA first removes data redundancy, and then uses the nonlinear transformation of a restricted Boltzmann machine to mine the deep coupling features between multi-source data, effectively handling the nonlinear laws in motor operation.

[0067] Finally, a multi-objective optimization intelligent decision-making mechanism is constructed using a deep deterministic policy gradient algorithm. Position error, synchronization error, and energy consumption optimization are the joint optimization objectives, enabling autonomous dynamic adjustment of control parameters. Through real-time interaction with the motor's operating environment, the deep deterministic policy gradient algorithm automatically learns the optimal control strategy under different operating conditions, handling complex scenarios such as sudden load changes and environmental fluctuations without manual intervention. Furthermore, through closed-loop control of "acquisition-decision-execution-feedback," position deviation is continuously monitored, and error sources are analyzed using a data fusion model. The reward function is then specifically modified to suppress the cumulative effect of errors, ensuring the system maintains positional stability during long-term operation and meeting the stringent requirements of high-precision and high-reliability equipment. Attached Figure Description

[0068] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0069] Figure 1 This is a schematic diagram of an embodiment of a high-precision position holding method for multi-dimensional motor cooperative control according to this application;

[0070] Figure 2 This is a schematic diagram of an embodiment of the adjustment strategy based on the real-time error dynamic optimization method of this application;

[0071] Figure 3 A schematic diagram of an embodiment of the method for constructing the reward function in this application;

[0072] Figure 4 This is a schematic diagram of an embodiment of the method for obtaining optimized control parameters according to this application;

[0073] Figure 5 This is a schematic diagram of an embodiment of the method in this application that uses wavelet transform to perform multi-scale decomposition of a multidimensional dataset and remove high-frequency noise.

[0074] Figure 6 This is a schematic diagram of an embodiment of the high-precision position holding device for multi-dimensional motor cooperative control according to this application;

[0075] Figure 7 This is a schematic diagram of one embodiment of the high-precision position holding device for multi-dimensional motor coordinated control according to this application. Detailed Implementation

[0076] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0077] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0078] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0079] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0080] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0081] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not an embodiment," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0082] Based on this, this application discloses a high-precision position holding method, device and storage medium for multi-dimensional motor cooperative control, used to maintain the high-precision position of multi-dimensional motors.

[0083] The technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0084] The method of this application can be applied to servers, devices, terminals, or other devices with logical processing capabilities; therefore, this application does not limit its application. For ease of description, the following description uses a system as the executing entity.

[0085] Please see Figure 1 This application provides an embodiment of a high-precision position holding method for multi-dimensional motor cooperative control, comprising:

[0086] 101. Real-time acquisition of position data, speed data, torque data, environmental data, vibration data, and current data of multiple motors;

[0087] 102. Align position data, rotational speed data, torque data, environmental data, vibration data, and current data based on timestamps to construct a multidimensional dataset;

[0088] In step 101, various sensors are installed on the motor equipment to collect key data in real time during the operation of multiple motors. Encoders accurately acquire the motor's position and speed data, torque sensors monitor the output torque data, environmental sensors for temperature, humidity, and air pressure collect data on the motor's operating environment, vibration sensors capture the vibration of the motor casing, and a current detection module in the motor drive circuit records current data. These sensors and detection modules work together to continuously and uninterruptedly collect data, ensuring complete and timely acquisition of comprehensive information about the motor's operation.

[0089] Because the timing and frequency of data collection from various sensors in step 101 may differ, step 102 aligns the collected position data, speed data, torque data, environmental data, vibration data, and current data based on timestamps. Using a unified time reference, different types of data at the same moment are integrated together, ensuring consistency and correlation between data in the time dimension. After data alignment, data from different dimensions are combined to construct a multidimensional dataset. This multidimensional dataset covers various aspects of information, including motor operating status and working environment.

[0090] 103. Standardize the multidimensional dataset to obtain standard data;

[0091] 104. Calculate the covariance matrix and perform eigenvalue decomposition based on standard data;

[0092] 105. Determine multiple principal component eigenvectors based on the cumulative variance contribution rate to form the principal component space;

[0093] 106. Project the standard data into the principal component space to form a dimensionality-reduced dataset;

[0094] In step 103, standardization is performed on the multidimensional dataset to eliminate differences in dimensions and magnitudes between different types of data. Specifically, for each dimension of data, the mean and standard deviation are calculated first, then the mean is subtracted from the original data, and then the result is divided by the standard deviation to obtain the standardized data.

[0095] In step 104, the covariance matrix is ​​calculated based on standard data. The covariance matrix primarily reflects the correlation between data in different dimensions. Eigenvalue decomposition of the covariance matrix yields a series of eigenvalues ​​and corresponding eigenvectors. The magnitude of the eigenvalues ​​indicates the variance of the data along the corresponding eigenvector direction; the larger the variance, the more data information is contained in that direction.

[0096] The formula for calculating the covariance matrix is:

[0097]

[0098] in For standard sample vectors, The mean of the sample;

[0099] The eigenvalues ​​of the covariance matrix obtained by the QR iterative algorithm are: The corresponding feature vector is: .

[0100] The formula for calculating the cumulative variance contribution rate in step 105 is as follows:

[0101]

[0102] Dynamic selection to satisfy The values ​​are used as principal component eigenvectors to form the principal component space.

[0103] In step 106, the standard data is projected onto the principal component space determined in step 105. Specifically, this involves performing matrix multiplication between the original data and the principal component eigenvectors, thereby mapping the high-dimensional data to the low-dimensional principal component space, ultimately forming a dimensionality-reduced dataset.

[0104] 107. Input the dimensionality-reduced dataset into the pre-trained deep belief network, and output a comprehensive feature vector through the hierarchical features of the restricted Boltzmann machine. The comprehensive feature vector is used to characterize the dynamic characteristics of the position error of multiple motors, the load torque coupling relationship, the environmental disturbance response characteristics, and the dynamic compensation parameters required for the coordinated control of multiple motors.

[0105] 108. Input the comprehensive feature vector into the deep deterministic policy gradient algorithm model to construct the reward function;

[0106] 109. Based on the reward function, a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors is developed to obtain optimized control parameters.

[0107] 110. Based on the optimized control parameters, adjust the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors in real time to achieve high-precision position holding of multiple motors.

[0108] In step 107, the dimensionality-reduced dataset obtained in the previous steps is input into the pre-trained deep belief network. The deep belief network is composed of multiple stacked Restricted Boltzmann Machines (RBMs), each of which can perform layer-by-layer training and feature learning on the input data. Through hierarchical feature extraction, complex nonlinear relationships in multiple motor operating data are automatically captured. The final output comprehensive feature vector fully characterizes the dynamic characteristics of the motor's position error, the coupling relationship between load torque, environmental disturbance response characteristics, and the dynamic compensation parameters required for coordinated control.

[0109] After layer-by-layer training and feature learning on the input data using a Restricted Boltzmann Machine, the formula for outputting the comprehensive feature vector is:

[0110]

[0111] in, For the first Layer weight matrix, This is the output of the hidden layer above. For bias vectors, is the activation function, and L is the number of network layers.

[0112] In step 108, the comprehensive feature vector obtained in step 107 is input into the deep deterministic policy gradient algorithm model to construct the reward function. Specifically, the reward function is constructed based on the comprehensive feature vector. By appropriately setting the reward function, multiple objectives of motor control can be transformed into quantifiable numerical indicators, guiding the algorithm to learn towards the desired control effect.

[0113] The deep deterministic policy gradient algorithm model in step 109 optimizes the control strategy by maximizing the reward function. After training, the model outputs real-time adjustment strategies for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors. The optimized control parameters are dynamically generated by the algorithm based on the current motor operating state and environmental conditions, fully considering the cooperative relationship between motors and the influence of various disturbance factors. In this way, intelligent mapping from data features to control parameters is achieved, providing accurate parameter support for high-precision motor control.

[0114] In step 110, based on the obtained optimized control parameters, the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors are adjusted in real time. In actual motor control systems, the current loop, speed loop, and position loop are the core components for achieving precise control. By adjusting these parameters in real time, a complete closed-loop control system is formed. The system can continuously adjust the control strategy according to the actual operating state of the motors, promptly compensate for various errors and disturbances, thereby achieving high-precision position holding of multiple motors and ensuring stable and accurate operation of the motors even under complex working conditions.

[0115] In this embodiment, firstly, a full-dimensional dataset containing multi-source data such as position, speed, torque, environmental parameters, and current is constructed. Compared with the limitations of traditional methods that only rely on basic data such as position and current, the newly added torque data can accurately reflect load changes, while temperature, humidity, and vibration sensor data can capture environmental interference in real time. A complete dataset containing motor operating status, load characteristics, and environmental interference is constructed. The current loop parameters are adjusted in real time through temperature data to reduce errors and improve accuracy.

[0116] Secondly, a fusion mechanism of principal component analysis (PCA) dimensionality reduction and deep belief network (DBN) hierarchical feature extraction is adopted to overcome the bottleneck of traditional linear dimensionality reduction methods in handling nonlinear features. PCA first removes data redundancy, and then uses the nonlinear transformation of a restricted Boltzmann machine to mine the deep coupling features between multi-source data, effectively handling the nonlinear laws in motor operation.

[0117] Finally, a multi-objective optimization intelligent decision-making mechanism is constructed using a deep deterministic policy gradient algorithm. Position error, synchronization error, and energy consumption optimization are the joint optimization objectives, enabling autonomous dynamic adjustment of control parameters. Through real-time interaction with the motor's operating environment, the deep deterministic policy gradient algorithm automatically learns the optimal control strategy under different operating conditions, handling complex scenarios such as sudden load changes and environmental fluctuations without manual intervention. Furthermore, through closed-loop control of "acquisition-decision-execution-feedback," position deviation is continuously monitored, and error sources are analyzed using a data fusion model. The reward function is then specifically modified to suppress the cumulative effect of errors, ensuring the system maintains positional stability during long-term operation and meeting the stringent requirements of high-precision and high-reliability equipment.

[0118] Please see Figure 2 This application provides an embodiment of an adjustment strategy dynamically optimized based on real-time error, comprising:

[0119] 201. Calculate the deviation between the actual position and the target position of multiple motors to form a position deviation sequence;

[0120] Using a high-precision encoder mounted on the motor drive shaft, the actual position data of each motor is collected in real time and compared with the preset target position. Specifically, the position deviation value within each sampling period is obtained through subtraction, and recorded sequentially in chronological order to form a position deviation sequence. This sequence reflects the dynamic error trend of the motor's position control during operation.

[0121] 202. Calculate the comprehensive error index based on the position deviation sequence;

[0122] Based on the position deviation sequence obtained in step 201, a comprehensive error index is calculated using a combination of statistical analysis and weighted calculation. The comprehensive error index integrates multiple dimensions of the deviation, including the mean, variance, and maximum peak value. Through weighted summation, different weights are assigned to long-term cumulative errors and instantaneous drastic fluctuation errors, thus comprehensively reflecting the stability and accuracy of the motor position control. The comprehensive error index allows for a quantitative assessment of the effectiveness of the current control strategy, providing a quantitative basis for system decision-making.

[0123] 203. If the overall error index exceeds the preset threshold, the reward function correction mechanism will be triggered;

[0124] A threshold range for the comprehensive error index is preset, and the preset threshold is determined based on the motor control accuracy requirements and system operation stability requirements. When the comprehensive error index calculated in step 202 exceeds the preset threshold, it indicates that the current control strategy can no longer meet the high-precision position holding requirements, and the system automatically triggers the reward function correction mechanism to start the subsequent dynamic optimization process.

[0125] 204. Input the current multidimensional dataset into the deep belief network, output the current comprehensive feature vector, and analyze the sources of error by combining it with the preset fault feature library;

[0126] The currently collected multidimensional dataset is input into a pre-trained deep belief network. The deep belief network extracts features from the multidimensional dataset using a multi-layer restricted Boltzmann machine, outputting a comprehensive feature vector that characterizes the motor's operating state. This comprehensive feature vector is then matched against a pre-defined fault feature library, which stores feature patterns corresponding to different types of errors (such as mechanical wear, electromagnetic interference, and parameter mismatch). Through similarity calculation and pattern recognition algorithms, the specific causes of excessive errors are quickly located, and the sources of error are analyzed.

[0127] 205. Based on the source of error, dynamically adjust the reward function in the deep deterministic policy gradient algorithm model;

[0128] Based on the error sources identified in step 204, the reward function in the deep deterministic policy gradient algorithm model is dynamically adjusted. For example, when the error originates from torque fluctuations caused by sudden changes in motor load, the weight of torque stability-related parameters in the reward function is increased; when changes in ambient temperature affect motor performance, environmental parameters are included in the reward function's considerations. By dynamically adjusting the reward function, it can reflect the control objective under the current operating conditions in real time, guiding the deep deterministic policy gradient algorithm to generate control strategies that better meet actual needs.

[0129] 206. Input the corrected reward function into the deep deterministic policy gradient algorithm model to regenerate the adjustment strategies of multiple motors, obtain new optimized control parameters, and form closed-loop control.

[0130] The corrected reward function is re-input into the deep deterministic policy gradient algorithm model. This algorithm, based on reinforcement learning principles, continuously iterates through trial and error to output adjustment strategies for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors, forming new optimized control parameters. These parameters directly affect the closed-loop control system of the motor driver, enabling real-time adjustment of the motor current, speed, and position. This constructs a complete closed-loop control system of "data acquisition - error assessment - strategy correction - parameter adjustment," ensuring that the motor maintains high-precision position synchronization under complex operating conditions.

[0131] In this embodiment, by calculating the position deviation in real time and dynamically adjusting the control strategy, the system can automatically compensate for position errors caused by factors such as load changes, mechanical wear, and environmental interference, ensuring that multiple motors always maintain high-precision synchronous operation and reducing position tracking errors. The combination of deep belief networks and fault feature databases enables intelligent identification of error root causes, shortening fault diagnosis time and improving production efficiency compared to manual inspection. Adjusting the reward function weights according to the real-time error sources enables the reinforcement learning algorithm to quickly adapt to different working conditions.

[0132] The design of the comprehensive error index takes into account multiple dimensions of position deviation, such as mean and variance. While ensuring position accuracy, it effectively suppresses system jitter and overshoot, achieving synergistic optimization of stability and speed, and improving dynamic response speed. The entire correction mechanism forms a complete closed loop, allowing the system to run continuously without human intervention and exhibiting strong adaptability to unknown disturbances and time-varying parameters.

[0133] Please see Figure 3 This application provides an embodiment of a method for constructing a reward function, including:

[0134] 301. Input the comprehensive feature vector into the deep deterministic strategy gradient algorithm model to generate initial control parameters, including the motor's current loop parameters, speed loop compensation coefficients, and position loop parameters;

[0135] 302. Based on the initial control parameters, control the operation of multiple motors, and collect the actual position data of multiple motors, the synchronization data between multiple motors, and the energy consumption data of multiple motors in real time to generate actual control parameters;

[0136] 303. Based on the actual control parameters, calculate the position error, synchronization error and energy consumption respectively, and construct a reward function that includes position error, synchronization error and energy consumption optimization.

[0137] This embodiment is based on the deep deterministic policy gradient algorithm model, and constructs a reward function that includes position error, synchronization error, and energy consumption optimization. Specifically, an exponential decay function is used to design the penalty term for position error, as shown in the formula:

[0138]

[0139] in, This is the position error sensitivity coefficient. This refers to the actual position of the motor. The target position of the motor;

[0140] The Gaussian kernel function is used to design the penalty term for synchronization error, and the formula is as follows:

[0141]

[0142] Where M represents the number of motors. The synchronization error sensitivity coefficient, and These are the actual positions of motors i and j;

[0143] The energy consumption optimization term is designed using the current-square integral form, and the formula is:

[0144]

[0145] in, Energy consumption weighting coefficient This represents the motor current.

[0146] By dynamically weighting and balancing position error, synchronization error, and energy consumption optimization, the formula is:

[0147] The constraints are as follows: .

[0148] In this embodiment, by inputting the comprehensive feature vector into the algorithm model to generate initial control parameters, the traditional method of relying on manual experience to set parameters is changed. This makes the initial values ​​of the current loop, speed loop, and position loop parameters more closely match the actual operating state of the motor, effectively improving the efficiency and accuracy of parameter setting. During actual control, multi-dimensional operating data is collected in real time to generate actual control parameters, comprehensively capturing motor operating information and ensuring precise control. In the reward function construction stage, position error, synchronization error, and energy consumption are integrated for optimization, enabling the algorithm to balance accuracy, synchronization, and energy consumption during operation. This avoids performance imbalances caused by single-objective optimization and improves the overall performance and applicability of the motor cooperative control system.

[0149] Please see Figure 4 This application provides an embodiment of a method for obtaining optimized control parameters, comprising:

[0150] 401. Evaluate the operating status of multiple motors under actual control parameters based on the reward function, and output the evaluation results;

[0151] Will Figure 3 The actual control parameters obtained are substituted into the reward function to evaluate the operating status of multiple motors. The reward function comprehensively considers multiple dimensions of indicators such as position error, synchronization error, and energy consumption. By quantifying these indicators, a specific evaluation result is obtained. The evaluation result can intuitively reflect the performance of the current motor control system.

[0152] 402. Based on the evaluation results, generate optimized control parameters by adjusting the strategy based on the deep deterministic policy gradient algorithm.

[0153] Based on the evaluation results of the operating status, the control strategy is adjusted accordingly using a deep deterministic policy gradient algorithm. This algorithm possesses powerful adaptive learning capabilities, dynamically adjusting control parameters based on the current evaluation results to maximize the reward function. Specifically, the algorithm analyzes the gaps between various indicators in the evaluation results and the expected targets, and then optimizes the current loop parameters, speed loop compensation coefficients, and position loop parameters accordingly. Through continuous iteration and learning, an optimal set of control parameters is found, enabling the motor to achieve the best balance in terms of position accuracy, synchronization performance, and energy consumption. The final optimized control parameters are then applied to the motor control system to achieve precise regulation of the motor's operating status.

[0154] In this embodiment, the motor operating state is quantitatively evaluated through a reward function. This transforms multiple objectives such as position accuracy, synchronization, and energy consumption into measurable indicators, avoiding the problem of performance degradation in other areas due to optimization of a single indicator. This achieves a comprehensive evaluation of the motor operating state, providing an objective and accurate basis for control strategy optimization. Based on a deep deterministic strategy gradient algorithm, optimized control parameters are dynamically generated, endowing the system with strong adaptive capabilities. The current loop, speed loop, and position loop parameters are rapidly adjusted according to real-time evaluation results, enabling the motor control system to quickly adapt to complex operating conditions such as load changes and environmental disturbances. This reduces control lag or deviation caused by fixed parameters, improving the dynamic response speed and steady-state accuracy of motor control.

[0155] Please see Figure 5 This application provides an embodiment of a method for removing high-frequency noise by performing multi-scale decomposition of a multidimensional dataset using wavelet transform, comprising:

[0156] 501. Multi-scale decomposition of multidimensional data using wavelet basis functions yields different decomposition layers;

[0157] 502. Adaptive thresholding is used to reduce noise in different decomposition layers;

[0158] 503. High-frequency coefficients in different decomposition layers are processed using a soft thresholding function to obtain the denoised coefficients;

[0159] 504. Reconstruct the noise-reduced coefficients with the low-frequency approximation coefficients to complete the high-frequency noise removal.

[0160] Step 501 uses wavelet basis functions to process multidimensional data, achieving multi-scale decomposition. In the context of motor data, signals such as position and current are decomposed into low-frequency and high-frequency components. The low-frequency component mainly contains the essential characteristics of the signal, such as the actual operating trend of the motor; while the high-frequency component contains noise and some detailed information. Decomposing the multidimensional data makes data processing faster and more efficient.

[0161] In step 502, an adaptive thresholding method is used for noise reduction on the different decomposition layers obtained in step 501. The adaptive threshold dynamically determines an appropriate threshold based on the specific characteristics of the data in each decomposition layer. For high-frequency layers with more noise, a relatively high threshold is set to effectively remove noise; while for low-frequency layers containing important signals, a lower threshold is set to avoid accidentally deleting useful information. This adaptive thresholding method enables more accurate identification and removal of noise.

[0162] Step 503 uses a soft thresholding function to process the high-frequency coefficients in different decomposition layers. High-frequency coefficients contain both noise components and potentially valuable signal details. Therefore, by processing the high-frequency coefficients in the decomposition layers using a soft thresholding function, when the absolute value of a high-frequency coefficient is less than a set threshold, it is set to zero to remove noise; when the absolute value of a high-frequency coefficient is greater than the threshold, it undergoes a certain degree of shrinkage processing instead of directly retaining the original value. This approach effectively removes noise while preserving signal details, avoiding over-processing that could lead to signal distortion.

[0163] Step 504 reconstructs the noise-reduced coefficients obtained after processing and the low-frequency approximation coefficients. Through this reconstruction operation, an approximate version of the original signal can be recovered, and this approximate signal has effectively removed high-frequency noise. In motor control, the reconstructed clean signal provides a more reliable basis for subsequent data analysis, fault diagnosis, and control decisions, helping to improve the accuracy and stability of the motor control system.

[0164] In this embodiment, multi-scale decomposition of multi-dimensional data using wavelet basis functions expands the original data at different frequencies and time scales, accurately separating high-frequency noise from low-frequency effective signals, thus avoiding signal feature loss problems that may occur with traditional filtering methods. Secondly, adaptive threshold denoising combined with a soft threshold function processes high-frequency coefficients, dynamically adjusting the denoising intensity based on data characteristics. This effectively suppresses high-frequency noise caused by current fluctuations and environmental interference while preserving key signal details such as position and speed to the maximum extent, improving the signal-to-noise ratio of the data. Finally, the reconstruction of the denoised coefficients and low-frequency approximation coefficients achieves high-quality data recovery, improving the accuracy and stability of the motor control strategy, reducing control deviations caused by data noise, facilitating high-precision position holding and coordinated control of multiple motors, and enhancing the system's adaptability and anti-interference capabilities under complex operating conditions.

[0165] Please see Figure 6 This application provides an embodiment of a high-precision position holding device with multi-dimensional motor cooperative control, comprising:

[0166] The acquisition unit 601 is used to acquire position data, speed data, torque data, environmental data, vibration data, and current data of multiple motors in real time.

[0167] Alignment unit 602 is used to align position data, rotational speed data, torque data, environmental data, vibration data, and current data based on timestamps to construct a multidimensional dataset;

[0168] Optionally, a removal unit 603 is also included, for:

[0169] Wavelet transform is used to perform multi-scale decomposition on the multidimensional dataset to remove high-frequency noise.

[0170] Optionally, the removal unit 603 is also used for:

[0171] Multi-dimensional data is decomposed into different decomposition layers by using wavelet basis functions at multiple scales.

[0172] An adaptive threshold is used to reduce noise for different decomposition layers;

[0173] High-frequency coefficients in different decomposition layers are processed using a soft thresholding function to obtain the denoised coefficients.

[0174] The noise-reduced coefficients are reconstructed with the low-frequency approximation coefficients to complete the removal of high-frequency noise.

[0175] Processing unit 604 is used to standardize the multidimensional dataset to obtain standard data;

[0176] Decomposition unit 605 is used to calculate the covariance matrix and perform eigenvalue decomposition based on standard data;

[0177] Forming unit 606 is used to determine multiple principal component eigenvectors based on the cumulative variance contribution rate, forming a principal component space;

[0178] Projection unit 607 is used to project standard data into the principal component space to form a dimension-reduced dataset.

[0179] The output unit 608 is used to input the dimensionality reduction dataset into the pre-trained deep belief network and output a comprehensive feature vector through the hierarchical features of the restricted Boltzmann machine. The comprehensive feature vector is used to characterize the dynamic characteristics of the position error of multiple motors, the load torque coupling relationship, the environmental disturbance response characteristics, and the dynamic compensation parameters required for the coordinated control of multiple motors.

[0180] The building unit 609 is used to input the comprehensive feature vector into the deep deterministic policy gradient algorithm model to construct the reward function;

[0181] Optionally, building block 609 is also used for:

[0182] The comprehensive feature vector is input into the deep deterministic policy gradient algorithm model to generate initial control parameters, including the motor's current loop parameters, speed loop compensation coefficients, and position loop parameters.

[0183] Based on the initial control parameters, multiple motors are controlled to operate, and the actual position data of multiple motors, the synchronization data between multiple motors, and the energy consumption data of multiple motors are collected in real time to generate actual control parameters;

[0184] Based on actual control parameters, position error, synchronization error, and energy consumption are calculated respectively, and a reward function that includes position error, synchronization error, and energy consumption optimization is constructed.

[0185] The first acquisition unit 610 is used to output a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients and position loop parameters of multiple motors based on the reward function, so as to obtain optimized control parameters.

[0186] Optionally, the first obtaining unit 610 is also used for:

[0187] The operating status of multiple motors under actual control parameters is evaluated based on the reward function, and the evaluation results are output.

[0188] Based on the evaluation results, the adjustment strategy based on the deep deterministic policy gradient algorithm is used to generate optimized control parameters.

[0189] Optionally, it also includes a first computing unit 611, used for:

[0190] Calculate the deviation between the actual position and the target position of multiple motors to form a position deviation sequence;

[0191] Optionally, a second computing unit 612 is also included, for:

[0192] Calculate the comprehensive error index based on the position deviation sequence;

[0193] Optionally, a trigger unit 613 is also included, for:

[0194] If the overall error index exceeds the preset threshold, the reward function correction mechanism will be triggered.

[0195] Optionally, an analysis unit 614 is also included, for:

[0196] Input the current multidimensional dataset into the deep belief network, output the current comprehensive feature vector, and combine it with the preset fault feature library to analyze the source of error;

[0197] Optionally, a correction unit 615 is also included, for:

[0198] Based on the source of error, dynamically adjust the reward function in the deep deterministic policy gradient algorithm model;

[0199] Optionally, a generation unit 616 is also included, for:

[0200] The modified reward function is input into the deep deterministic policy gradient algorithm model to regenerate the adjustment strategies for multiple motors and obtain new optimized control parameters.

[0201] The holding unit 617 is used to adjust the pulse duty cycle and current vector of multiple motors in real time according to optimized control parameters, so as to achieve high-precision position holding of multiple motors.

[0202] For detailed implementation methods, please refer to... Figures 1 to 5 Examples are not detailed here.

[0203] Please see Figure 7 This application provides a high-precision position holding device for multi-dimensional motor cooperative control, comprising:

[0204] Processor 701, memory 702, input / output unit 704, and bus 703.

[0205] The processor 701 is connected to the memory 702, the input / output unit 704, and the bus 703.

[0206] The memory 702 stores a program, and the processor 701 calls the program to execute it, such as... Figure 1 , Figure 2 , Figure 3 , Figure 4 as well as Figure 5 The method in the middle.

[0207] This application provides a computer-readable storage medium on which a program is stored, and when the program is executed on a computer, it performs the following... Figure 1 , Figure 2 , Figure 3 , Figure 4 as well as Figure 5 The method in the middle.

[0208] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0209] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection between apparatuses or units through some interfaces, and may be electrical, mechanical, or other forms.

[0210] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0211] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0212] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A high-precision position holding method for multi-dimensional motor cooperative control, characterized in that, include: Real-time acquisition of position data, speed data, torque data, environmental data, vibration data, and current data of multiple motors; The location data, rotational speed data, torque data, environmental data, vibration data, and current data are aligned based on timestamps to construct a multidimensional dataset; The multidimensional dataset is standardized to obtain standard data; Calculate the covariance matrix and perform eigenvalue decomposition based on the standard data; Multiple principal component eigenvectors are determined based on the cumulative variance contribution rate, forming a principal component space; The standard data is projected into the principal component space to form a dimensionality-reduced dataset. The dimensionality reduction dataset is input into a pre-trained deep belief network, and a comprehensive feature vector is output through the hierarchical features of a restricted Boltzmann machine. The comprehensive feature vector is used to characterize the dynamic characteristics of the position error of multiple motors, the load torque coupling relationship, the environmental disturbance response characteristics, and the dynamic compensation parameters required for the coordinated control of multiple motors. The comprehensive feature vector is input into the deep deterministic policy gradient algorithm model to construct the reward function; Based on the reward function, a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors is output to obtain optimized control parameters. Based on the optimized control parameters, the current loop parameters, the speed loop compensation coefficient, and the position loop parameters of multiple motors are adjusted in real time to achieve high-precision position holding of multiple motors; The comprehensive feature vector is input into the deep deterministic policy gradient algorithm model to construct the reward function, including: The comprehensive feature vector is input into the deep deterministic strategy gradient algorithm model to generate initial control parameters, which include the motor's current loop parameters, speed loop compensation coefficient, and position loop parameters. Based on the initial control parameters, multiple motors are controlled to operate, and the actual position data of multiple motors, the synchronization data between multiple motors, and the energy consumption data of multiple motors are collected in real time to generate actual control parameters; Based on the actual control parameters, the position error, synchronization error, and energy consumption are calculated respectively, and a reward function that includes position error, synchronization error, and energy consumption optimization is constructed. Based on the actual control parameters, the position error, synchronization error, and energy consumption are calculated respectively, and a reward function that includes position error, synchronization error, and energy consumption optimization is constructed, including: The penalty term for the position error is designed using an exponential decay function, and the formula is as follows: in, This is the position error sensitivity coefficient. This refers to the actual position of the motor. The target position of the motor; The penalty term for the synchronization error is designed using a Gaussian kernel function, and the formula is as follows: Where M represents the number of motors. The synchronization error sensitivity coefficient, and These are the actual positions of motors i and j; The optimization term for the energy consumption is designed using the current-square integral form, and the formula is as follows: in, Energy consumption weighting coefficient This represents the motor current.

2. The high-precision position holding method according to claim 1, characterized in that, After obtaining optimized control parameters by outputting a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors based on the reward function, and before adjusting the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors in real time according to the optimized control parameters to achieve high-precision position holding of multiple motors, the method further includes: Calculate the deviation between the actual position and the target position of multiple motors to form a position deviation sequence; Based on the position deviation sequence, a comprehensive error index is calculated; If the comprehensive error index exceeds a preset threshold, the reward function correction mechanism is triggered; The current multidimensional dataset is input into the deep belief network, which outputs the current comprehensive feature vector. Combined with the preset fault feature library, the source of error is analyzed. Based on the aforementioned error sources, the reward function in the deep deterministic policy gradient algorithm model is dynamically corrected; The modified reward function is input into the deep deterministic policy gradient algorithm model to regenerate the adjustment strategies for multiple motors and obtain new optimized control parameters.

3. The high-precision position holding method according to claim 1, characterized in that, The real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients, and position loop parameters of multiple motors, based on the reward function, yields optimized control parameters, including: The operating status of multiple motors under actual control parameters is evaluated based on the reward function, and the evaluation results are output. Based on the evaluation results, optimized control parameters are generated using an adjustment strategy based on a deep deterministic policy gradient algorithm.

4. The high-precision position holding method according to claim 1, characterized in that, After aligning the location data, rotational speed data, torque data, environmental data, and current data based on timestamps to construct a multidimensional dataset, and before standardizing the multidimensional dataset to obtain standardized data, the method further includes: Wavelet transform is used to perform multi-scale decomposition on the multidimensional dataset to remove high-frequency noise.

5. The high-precision position holding method according to claim 4, characterized in that, The step of using wavelet transform to perform multi-scale decomposition on the multidimensional dataset to remove high-frequency noise includes: The multidimensional data is decomposed into different decomposition layers by using wavelet basis functions at multiple scales. An adaptive threshold is used to reduce noise in the different decomposition layers; The high-frequency coefficients in the different decomposition layers are processed by a soft thresholding function to obtain the denoised coefficients. The noise-reduced coefficients are reconstructed with the low-frequency approximation coefficients to complete the high-frequency noise removal.

6. A high-precision position holding device with multi-dimensional motor cooperative control, characterized in that, For performing the method as described in any one of claims 1 to 5, comprising: The data acquisition unit is used to collect position data, speed data, torque data, environmental data, vibration data, and current data of multiple motors in real time. An alignment unit is used to align the position data, rotational speed data, torque data, environmental data, vibration data, and current data based on timestamps to construct a multidimensional dataset. The processing unit is used to standardize the multidimensional dataset to obtain standard data. The decomposition unit is used to calculate the covariance matrix and perform eigenvalue decomposition based on the standard data. Forming units are used to determine multiple principal component eigenvectors based on the cumulative variance contribution rate, forming the principal component space; A projection unit is used to project the standard data into the principal component space to form a dimension-reduced dataset. The output unit is used to input the dimensionality reduction dataset into a pre-trained deep belief network and output a comprehensive feature vector through the hierarchical features of the restricted Boltzmann machine. The comprehensive feature vector is used to characterize the dynamic characteristics of the position error of multiple motors, the load torque coupling relationship, the environmental disturbance response characteristics, and the dynamic compensation parameters required for the coordinated control of multiple motors. The construction unit is used to input the comprehensive feature vector into the deep deterministic policy gradient algorithm model to construct the reward function; The acquisition unit is used to output a real-time adjustment strategy for the current loop parameters, speed loop compensation coefficients and position loop parameters of multiple motors based on the reward function, so as to obtain optimized control parameters. The holding unit is used to adjust the current loop parameters, the speed loop compensation coefficient, and the position loop parameters of multiple motors in real time according to the optimized control parameters, so as to achieve high-precision position holding of multiple motors.

7. A high-precision position holding device with multi-dimensional motor cooperative control, characterized in that, include: The processor, memory, input / output unit, and bus are connected to the memory, the input / output unit, and the bus. The memory stores a program, and the processor calls the program to execute the high-precision position-keeping method as described in any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium contains a program that, when executed on a computer, performs the high-precision position-keeping method as described in any one of claims 1 to 5.

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