A robot arm trajectory tracking control method and system

Abstract

The present invention relates to the field of robotic arm trajectory tracking control technology, and in particular to a robotic arm trajectory tracking control method and system. The method comprises the following steps: obtaining a robotic arm operation log and trajectory execution program, extracting periodic trajectory motion deviation data, and performing trajectory jitter perception record analysis; then, learning trajectory behavior deviation characteristics based on the trajectory deviation data, thereby optimizing the trajectory tracking execution program and improving the accuracy of trajectory tracking control; finally, designing trajectory tracking control firmware and embedding it into the robotic arm control center to implement optimized robotic arm trajectory tracking control. The present invention further improves robotic arm trajectory tracking control technology by optimizing the robotic arm trajectory tracking control technology.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm trajectory tracking control, and in particular to a robot arm trajectory tracking control method and system. Background Art

[0002] The application of robotic arms in various fields such as production, assembly, and handling is becoming increasingly widespread. The trajectory tracking control technology of robotic arms is one of its core technologies, which directly affects the accuracy, efficiency, and stability of the robotic arms in actual operations. Trajectory tracking control requires that the robotic arm can accurately and smoothly follow the predetermined trajectory to operate. Especially in the face of complex environments and dynamic changes, how to maintain the precise execution of the trajectory and avoid trajectory deviations caused by error accumulation or external interference is the key to achieving efficient operation. However, when the robotic arm is worn and aged, the actual motion trajectory of the robotic arm will deviate from the manually programmed motion trajectory. The traditional robotic arm trajectory tracking control method cannot accurately learn the deviations caused by aging and wear of the robotic arm after a certain period of use, resulting in large errors in the robotic arm trajectory tracking control. Summary of the Invention

[0003] Based on this, it is necessary to provide a robot arm trajectory tracking control method and system to solve at least one of the above technical problems.

[0004] To achieve the above object, a robot arm trajectory tracking control method is provided, the method comprising the following steps:

[0005] Step S1: Obtaining a robot arm operation log and a robot arm trajectory tracking execution program; extracting a period-correlated trajectory motion deviation from the robot arm operation log to obtain periodic trajectory motion deviation data; analyzing the robot arm motion trajectory jitter perception record based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data;

[0006] Step S2: performing trajectory behavior deviation feature learning of the robot arm based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program based on the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program;

[0007] Step S3: Designing a robot arm trajectory tracking control firmware by performing a trajectory tracking optimization program to obtain the robot arm trajectory tracking control firmware; embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform robot arm trajectory tracking control.

[0008] Preferably, step S1 includes the following steps:

[0009] Step S11: Obtaining the robot arm operation log and the robot arm trajectory tracking execution code;

[0010] Step S12: performing data cleaning on the robot arm operation log to obtain a robot arm operation cleaning log;

[0011] Step S13: extracting the cycle-related trajectory motion deviation from the robot arm cleaning operation log to obtain the cycle trajectory motion deviation data;

[0012] Step S14: analyzing the robot arm motion trajectory jitter perception record of the robot arm operation cleaning log based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data.

[0013] Preferably, step S2 includes the following steps:

[0014] Step S21: performing track jitter amplitude variation skew intensity analysis on the track deviation jitter sensing record data to obtain track jitter amplitude skew intensity data;

[0015] Step S22: performing a spatial deviation progressive analysis on the periodic trajectory motion deviation data to obtain inter-trajectory motion deviation progressive data;

[0016] Step S23: performing trajectory behavior progressive deviation feature learning of the robot arm according to the trajectory jitter amplitude skew intensity data and the trajectory motion deviation progressive data to obtain trajectory behavior progressive deviation learning data;

[0017] Step S24: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program.

[0018] Preferably, step S21 includes the following steps:

[0019] Step S211: performing time-series frequency domain conversion on the trajectory deviation jitter perception record data to generate a deviation jitter time-series frequency domain graph;

[0020] Step S212: performing jitter frequency mutation point distribution skewness identification on the deviation jitter timing frequency domain diagram to obtain jitter frequency mutation point distribution skewness data;

[0021] Step S213: calculating the variance of the mutation increasing slope based on the skew data of the jitter frequency mutation point distribution to obtain the variance of the frequency mutation point increasing slope;

[0022] Step S214: performing convergence constrained logarithmic fitting processing on the deviation jitter timing frequency domain diagram based on the incremental slope variance of the frequency mutation point to obtain frequency mutation point convergence logarithmic fitting data;

[0023] Step S215: performing track jitter amplitude variation skewness intensity analysis based on the frequency mutation point convergence logarithmic fitting data to obtain track jitter amplitude skewness intensity data.

[0024] Preferably, step S214 includes the following steps:

[0025] Based on the variance of the increasing slope of the frequency mutation point, the deviation jitter timing frequency domain graph is subjected to an increasing segmented exponential transformation of the mutation point frequency domain curve to obtain an increasing segmented exponent of the mutation point curve;

[0026] Performing incremental segmental index ratio convergence processing on the incremental segmental index of the mutation point curve to obtain the incremental segmental index convergence ratio;

[0027] The deviation jitter timing frequency domain diagram is subjected to convergence constraint logarithmic fitting processing according to the increasing segmented exponential convergence ratio to obtain the frequency mutation point convergence logarithmic fitting data.

[0028] Preferably, step S23 includes the following steps:

[0029] Step S231: calculating the progressive mean difference of attitude angle offset on the progressive data of the deviation between trajectory movements to obtain the progressive mean difference of attitude angle offset;

[0030] Step S232: Calculating the joint angle deviation time series increment ratio on the trajectory motion deviation progressive data to obtain the joint angle deviation time series increment ratio;

[0031] Step S233: performing a manipulator trajectory jamming swing amplitude regression analysis on the progressive mean difference of the posture angle offset and the time series increment ratio of the joint angle deviation according to the trajectory jitter amplitude skew intensity data to obtain the manipulator trajectory jamming swing amplitude regression data;

[0032] Step S234: performing repeated trajectory jamming amplitude transfer learning on the robot arm trajectory jamming amplitude regression data to obtain repeated trajectory jamming amplitude learning data;

[0033] Step S235: performing trajectory behavior progressive deviation feature learning of the robot arm according to the repeated trajectory jamming swing amplitude learning data to obtain trajectory behavior progressive deviation learning data.

[0034] Preferably, step S233 includes the following steps:

[0035] Perform jitter spatial orientation disorder intensity analysis on the trajectory jitter amplitude skew intensity data to obtain jitter spatial orientation disorder intensity data;

[0036] According to the jitter spatial orientation disorder intensity data, the spatial orientation vector angular rate mutation entropy value is analyzed on the progressive mean difference of the attitude angle offset to obtain the orientation vector angular rate mutation entropy value;

[0037] The joint angle overshoot probability calculation is performed on the joint angle deviation time series increment ratio according to the jitter spatial orientation disorder intensity data to obtain the joint angle overshoot probability calculation data;

[0038] Based on the azimuth vector angular rate mutation entropy value and joint angle overshoot probability calculation data, the robot arm trajectory jamming amplitude regression analysis is performed to obtain the robot arm trajectory jamming amplitude regression data.

[0039] Preferably, step S24 includes the following steps:

[0040] Step S241: performing robot arm trajectory error clustering processing on the trajectory behavior progressive deviation learning data to obtain robot arm trajectory error clustering data;

[0041] Step S242: reconstructing the control logic structure of the robot arm trajectory tracking execution program based on the robot arm trajectory error clustering data to generate control program logic structure reconstruction data;

[0042] Step S243: performing control logic nesting depth constraint on the control program logic structure reconstruction data to obtain program control logic depth constraint reconstruction data;

[0043] Step S244: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the program control logic depth constraint reconstruction data to obtain a trajectory tracking execution optimization program.

[0044] Preferably, step S3 includes the following steps:

[0045] Step S31: performing a program code static analysis on the trajectory tracking execution optimization program to obtain program code static analysis data;

[0046] Step S32: performing functional unit integration testing on the trajectory tracking execution optimization program according to the program code static analysis data to obtain functional unit integration test data;

[0047] Step S33: designing the robot arm trajectory tracking control firmware by performing the trajectory tracking optimization program based on the functional unit integration test data to obtain the robot arm trajectory tracking control firmware;

[0048] Step S34: embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform the robot arm trajectory tracking control.

[0049] Preferably, the present invention further provides a robot arm trajectory tracking control system for executing the robot arm trajectory tracking control method described above, the robot arm trajectory tracking control system comprising:

[0050] The trajectory jitter perception analysis module is used to obtain the robot arm operation log and the robot arm trajectory tracking execution program; extract the cycle-related trajectory motion deviation from the robot arm operation log to obtain the cycle trajectory motion deviation data; and analyze the robot arm motion trajectory jitter perception record based on the cycle trajectory motion deviation data to obtain the trajectory deviation jitter perception record data;

[0051] The behavior deviation feature learning module is used to learn the robot arm's trajectory behavior deviation features based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; based on the trajectory behavior progressive deviation learning data, the robot arm's trajectory tracking execution program is iteratively optimized for trajectory tracking control to obtain a trajectory tracking execution optimization program;

[0052] The tracking control firmware design module is used to design the robot arm trajectory tracking control firmware for the trajectory tracking execution optimization program to obtain the robot arm trajectory tracking control firmware; the robot arm trajectory tracking control firmware is embedded into the robot arm control center to perform robot arm trajectory tracking control.

[0053] The beneficial effect of the present invention is that by obtaining the operation log of the robot arm and extracting the periodic trajectory deviation, it is possible to achieve accurate analysis of the robot arm's motion trajectory. By extracting the periodic trajectory motion deviation data, it is possible to identify the trajectory deviation of the robot arm in different operation cycles, and then perceive the regularity of its motion jitter. This provides important basic data for subsequent analysis, can provide an in-depth understanding of subtle problems in the robot arm's motion, help engineers identify and diagnose potential problems in the robot arm's motion control, and improve the robot arm's motion accuracy and stability. By studying and analyzing the trajectory deviation jitter perception recording data, it is possible to effectively extract the progressive deviation characteristics in the robot arm's trajectory behavior. By learning the progressive deviation of the trajectory behavior, it is possible to help the R&D team understand the accumulation trend of the robot arm's trajectory error during actual operation. Based on these data, the robot arm's trajectory tracking execution program can be iteratively optimized to improve the robot arm's trajectory tracking accuracy, thereby improving the robot arm's adaptability and accuracy in complex tasks and optimizing the robot arm's overall performance. By designing firmware for the optimized trajectory tracking execution program, the control capability of the robot arm is further enhanced. During the firmware design process, various characteristics of the robot arm's trajectory tracking were comprehensively considered to ensure that the firmware can efficiently execute control instructions and achieve accurate trajectory tracking. By embedding the optimized control firmware into the robot arm control center, the robot arm's trajectory control tasks can be adjusted and accurately executed in real time, improving its execution efficiency and response speed. In addition, the optimized control firmware can also enhance the robot arm's autonomous decision-making ability in complex environments, and improve the robot arm's adaptability and operational stability. Therefore, the present invention is an improvement on a traditional robot arm trajectory tracking control method, which solves the problem that a traditional robot arm trajectory tracking control method cannot accurately learn the deviations caused by aging and wear of the robot arm after a certain period of use, thereby causing large errors in the robot arm's trajectory tracking control. It improves the accuracy of learning the deviations caused by aging and wear of the robot arm after a certain period of use, and reduces the error in the robot arm's trajectory tracking control. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 A schematic flow chart of a robot arm trajectory tracking control method;

[0055] Figure 2 for Figure 1 Detailed implementation steps of step S2 in FIG.

[0056] Figure 3 for Figure 1 Detailed implementation steps of step S3 in FIG. DETAILED DESCRIPTION

[0057] See also Figures 1 to 3, a robot arm trajectory tracking control method, the method comprising the following steps:

[0058] Step S1: Obtaining a robot arm operation log and a robot arm trajectory tracking execution program; extracting a period-correlated trajectory motion deviation from the robot arm operation log to obtain periodic trajectory motion deviation data; analyzing the robot arm motion trajectory jitter perception record based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data;

[0059] Step S2: performing trajectory behavior deviation feature learning of the robot arm based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program based on the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program;

[0060] Step S3: Designing a robot arm trajectory tracking control firmware by performing a trajectory tracking optimization program to obtain the robot arm trajectory tracking control firmware; embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform robot arm trajectory tracking control.

[0061] In the embodiment of the present invention, reference Figure 1 The above is a schematic flow chart of the steps of a robot arm trajectory tracking control method of the present invention. In this example, the robot arm trajectory tracking control method includes the following steps:

[0062] Step S1: Obtaining a robot arm operation log and a robot arm trajectory tracking execution program; extracting a period-correlated trajectory motion deviation from the robot arm operation log to obtain periodic trajectory motion deviation data; analyzing the robot arm motion trajectory jitter perception record based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data;

[0063] In an embodiment of the present invention, a PLC acquisition system and an embedded industrial gateway are configured at an industrial site to collect and store the robot's operational log data under different operating conditions in a millisecond-time synchronized manner in a local database. This operational log includes high-frequency control variables such as the angular changes of the robot's six joints, the spatial position, velocity, acceleration, joint torque, joint current, feedback control signals, and instruction execution feedback of the end effector. The synchronously acquired robot trajectory tracking execution program is modularly parsed in the form of structured code blocks to extract the corresponding motion control instruction set and trajectory interpolation function. Next, based on the time period information in the robot's operational log, the operational log data is segmented based on the cycle boundary points, and the trajectory is segmented according to the task execution cycle set in the process flow. The difference between the actual trajectory data and the command trajectory data within each cycle segment is sampled and calculated. A trajectory deviation metric is calculated using the vector Euclidean distance. This is then normalized and statistically analyzed at each key point (wherein the key points refer to the angular changes of the robot's six joints, including the spatial position, velocity, acceleration, etc. of the angular changes of the six joints), forming periodic trajectory motion deviation data. Based on the periodic deviation data, the sliding window time series feature analysis technology is used to extract the trend of position deviation changes in the trajectory within continuous periods. The sliding average and weighted difference combination model is used to establish the trajectory jitter amplitude change trajectory. After establishing a three-dimensional jitter data matrix (position deviation, velocity change, acceleration mutation) in the time series dimension, principal component analysis (PCA) and Mahalanobis distance analysis are performed to calibrate the outlier periodic points of the trajectory deviation and its trend clustering interval, and finally generate trajectory deviation jitter perception record data.

[0064] Step S2: performing trajectory behavior deviation feature learning of the robot arm based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program based on the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program;

[0065] In this embodiment of the present invention, trajectory deviation jitter perception recorded data is processed through trajectory behavior deviation feature learning. The specific method involves performing a time-series spectrum transformation on the jitter data matrix of each cycle. Fast Fourier transform (FFT) and wavelet packet decomposition (WPD) are used to extract the main frequency components of trajectory deviation and jitter amplitude trends in different frequency bands. The frequency resolution of the spectrum analysis is set to 0.5 Hz, and the energy percentage changes in each spectral segment are recorded. Next, a trajectory behavior progressive deviation trend sequence is established. The cosine similarity of the jitter intensity vectors between cycles is calculated to determine whether a periodic deviation accumulation trend exists. This trend data is mapped to a trajectory behavior progressive deviation learning dataset. Using clustering methods (such as K-Means), cycles with similar deviation behavior are classified, their offset vector fields and historical trend fields are annotated, and trajectory behavior deviation data labels are established. Subsequently, the original trajectory tracking execution program of the robotic arm is reconstructed. Based on the deviation vector fields of key trajectory points annotated in the learning data, an interpolation-corrected control node method is introduced to reset the angular offsets of the trajectory execution points. Spline reconstruction is then performed in conjunction with the trajectory planning module. A feedback inhibition link is added to the reconstructed trajectory program, and a real-time correction coefficient for the deviation estimate in the PD controller is introduced to perform local gain optimization, ultimately obtaining a trajectory tracking execution optimization program.

[0066] Step S3: Designing a robot arm trajectory tracking control firmware by performing a trajectory tracking optimization program to obtain the robot arm trajectory tracking control firmware; embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform robot arm trajectory tracking control.

[0067] In an embodiment of the present invention, a static code analysis tool (such as the Clang static analyzer) is used to perform code-level control logic path analysis on the trajectory tracking execution optimization program. This analysis identifies dependency chains and jump logic between execution nodes in all path branches, and detects potential blocking paths or loop exception calls. After analysis, the integrity of the execution logic is verified by constructing a control flow graph (CFG). Subsequently, based on the static analysis results, a set of functional unit test cases is constructed to perform module-level integration testing on the program. These tests include testing the point output accuracy of the trajectory reconstruction module (with a maximum allowable error of 0.05mm), the real-time responsiveness of the feedback correction module (testing that the deviation correction delay does not exceed 0.5ms under a 1ms control cycle), and the robustness of the control parameter real-time scheduling module. The test is run using a Python automated script linked to a PLC simulation system and the output results are recorded. Once all test data meets the system robustness constraints, the optimization program is packaged as trajectory control firmware. This firmware is compiled in C language embedded executable format and configured to match the register map and interrupt vector table of the target controller (such as the STM32H7 series chip based on the ARM Cortex-M7 core). The control firmware is written to the robotic arm's main control unit via the JTAG interface. When the control center is running, the trajectory control firmware is automatically loaded and executed during each cycle of the control schedule, replacing the original control program to complete the trajectory tracking control task with higher precision and faster response.

[0068] Step S1 includes the following steps:

[0069] Step S11: Obtaining the robot arm operation log and the robot arm trajectory tracking execution code;

[0070] Step S12: performing data cleaning on the robot arm operation log to obtain a robot arm operation cleaning log;

[0071] Step S13: extracting the cycle-related trajectory motion deviation from the robot arm cleaning operation log to obtain the cycle trajectory motion deviation data;

[0072] Step S14: analyzing the robot arm motion trajectory jitter perception record of the robot arm operation cleaning log based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data.

[0073] In this embodiment of the present invention, the process of obtaining the robotic arm's operation log and trajectory tracking execution code is accomplished by configuring an industrial Ethernet communication interface to connect to the robotic arm controller's internal logging system. Operation log data is then transmitted to a local data acquisition terminal via the TCP / IP protocol. The log content includes high-frequency data such as the robotic arm's six-axis joint angles, velocities, accelerations, torques, currents, the Cartesian coordinate position of the end effector, system timestamps, target trajectory point sequences, and feedback errors output by the controller. The sampling period is 10ms, and the data accuracy is four decimal places. The trajectory tracking execution code is written in PLC structured text language and includes components such as trajectory interpolation functions, joint space-to-Cartesian space conversion functions, PID controller configuration parameters, trajectory point planning modules, and fault-tolerant processing logic. After being exported from the controller's storage area via a dedicated interface, the code undergoes module-level parsing, aligning the timestamps of key instruction sequences with the log data to provide a data foundation for subsequent steps. The acquired operation log data undergoes data cleaning. First, an outlier detection algorithm is used to remove outliers from each data column in the log, using an outlier detection method based on the median absolute deviation (MAD). A threshold of 1.5 times the IQR interval was set, and data points falling outside this interval in each column were removed. The timestamp format was then standardized, and all data was resampled to a fixed interval of 10ms. Missing data was filled using linear interpolation. Duplicate entries during the sampling process were deduplicated, and unique entries were filtered using the system clock field in the log as the primary key. All numeric fields were converted to the same unit, for example, angles were standardized to radians and displacements to millimeters. After cleaning, a standard structured operation cleaning log was constructed, containing fields such as timestamps, six-axis joint status, end-effector position and posture, and controller output signals. The output format was CSV, and the field order was consistent with the control logic. Cycle-related trajectory motion deviations were extracted from the robot arm operation cleaning log. First, the cycle boundaries of the operation log were annotated using the timestamps corresponding to the trajectory start and stop instructions recorded in the trajectory tracking execution code. The target trajectory points and actual feedback trajectory points in each cycle were extracted, and the three-dimensional Euclidean distance in Cartesian space was calculated for each trajectory point as the instantaneous trajectory error value. The error value vector for each cycle is normalized, and a first-order difference operation is applied to the error curve to analyze its changing trend. A periodic sliding window mechanism is used to perform weighted mean smoothing on the trajectory errors within three consecutive cycles. After removing high-frequency disturbances, the trend-based deviation components are retained. Finally, the maximum deviation value, average deviation value, and trajectory deviation change slope of each cycle are calculated to construct a periodic trajectory motion deviation dataset. This data is output in a structured form and serves as input for subsequent trajectory jitter perception analysis. The periodic trajectory motion deviation data is combined with the operation cleaning log to complete the analysis of the robot arm's trajectory jitter perception records.The analysis method is based on frequency-domain analysis of time series signals. First, a fast Fourier transform (FFT) is performed on the trajectory deviation time series for each cycle to extract the peak frequency and amplitude of the dominant frequency, and the energy contributions of the top three frequency components are calculated. Wavelet packet decomposition (WPD) is then introduced to perform a multi-scale decomposition of the trajectory deviation series, extracting energy fluctuations within the 2Hz, 4Hz, and 8Hz frequency bands as key indicators of trajectory oscillation frequency variation. A three-dimensional jitter perception vector (primary frequency, secondary frequency, and frequency mutation rate) is constructed based on frequency component variations. This vector is then compared with the acceleration curve within the corresponding cycle to identify trajectory disturbance events corresponding to frequency mutations. By setting a frequency mutation rate threshold of 20% and a jitter peak change rate threshold of 15%, cycles with significant trajectory jitter are identified and labeled with cycle numbers and jitter types (continuous, burst, or low-frequency). Finally, a trajectory deviation jitter perception data table is constructed, containing time periods, dominant frequency components, amplitude changes, mutation rates, and disturbance types. This data is stored in a JSON format, providing a stable foundation for subsequent deviation feature learning.

[0074] Step S2 includes the following steps:

[0075] Step S21: performing track jitter amplitude variation skew intensity analysis on the track deviation jitter sensing record data to obtain track jitter amplitude skew intensity data;

[0076] Step S22: performing a spatial deviation progressive analysis on the periodic trajectory motion deviation data to obtain inter-trajectory motion deviation progressive data;

[0077] Step S23: performing trajectory behavior progressive deviation feature learning of the robot arm according to the trajectory jitter amplitude skew intensity data and the trajectory motion deviation progressive data to obtain trajectory behavior progressive deviation learning data;

[0078] Step S24: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program.

[0079] As an example of the present invention, refer to Figure 2 As shown, in this example, step S2 includes:

[0080] Step S21: performing track jitter amplitude variation skew intensity analysis on the track deviation jitter sensing record data to obtain track jitter amplitude skew intensity data;

[0081] In an embodiment of the present invention, the trajectory deviation jitter perception record data is subjected to trajectory jitter amplitude change skewness intensity analysis, and the processing is completed by a method combining statistical analysis with sliding window amplitude offset calculation. In the specific operation process, the amplitude corresponding to the main frequency of each periodic trajectory deviation signal is first extracted cycle by cycle, and the amplitude of the frequency domain peak point is used as an indicator to form a trajectory amplitude time series. The sequence is divided into analysis windows in units of 10 cycles, and the skewness, kurtosis, maximum value to mean ratio, standard deviation to mean ratio and other indicators of the amplitude are calculated in each window. Skewness is used to characterize the degree of deviation of the amplitude distribution on both sides of the center value, kurtosis is used to describe the frequency of abnormal surges in amplitude values, and the standard deviation to mean ratio reflects the stability fluctuation amplitude. For window data of different time periods, the combined judgment conditions of setting the skewness absolute value greater than 1.5 and the kurtosis greater than 3.5 are used to identify the presence of skewness intensity characteristics in the trajectory jitter behavior within the window. For all windows with skew characteristics, the starting cycle number, average amplitude, maximum offset, amplitude growth rate, and fluctuation frequency are recorded as the main fields of the trajectory jitter amplitude skew intensity data. This data is uniformly stored as a structured two-dimensional array with field precision controlled to three decimal places and time synchronization accuracy of no less than 10ms.

[0082] Step S22: performing a spatial deviation progressive analysis on the periodic trajectory motion deviation data to obtain inter-trajectory motion deviation progressive data;

[0083] In one embodiment of the present invention, a progressive spatial deviation analysis is performed on periodic trajectory motion deviation data by establishing a relative deviation increment model between trajectory points. Specifically, N fixed trajectory points are extracted within each cycle (e.g., sampling points at 10 mm intervals on the end effector), their target and actual position coordinates are recorded, and the three-dimensional Euclidean deviation value is calculated for each sampling point. The sequence of deviation values ​​for the same point in consecutive cycles is then differentiated to obtain a deviation increment vector. A linear fitting method is used to fit the cycle-dependent evolution trend of the deviation increment at each point, extracting the slope, standard deviation of the deviation increment, and rate of change in the incremental direction as progressive metrics. Points with a slope greater than a threshold (e.g., 0.005 mm / cycle) and a standard deviation less than a threshold (e.g., 0.1 mm) are judged to exhibit a trend of progressive spatial deviation accumulation. Finally, statistical metrics are extracted for all progressive points within the entire cycle, such as the progressive point ratio, maximum progressive increment, and progressive direction consistency coefficient (consistency is considered when the directional vector angle is less than 15 degrees), to form the progressive deviation data between trajectory motions. The data structure includes fields such as cycle number, trajectory segment number, number of progressive points, and progressive parameters of each point, and is sorted and stored according to the cycle time axis.

[0084] Step S23: performing trajectory behavior progressive deviation feature learning of the robot arm according to the trajectory jitter amplitude skew intensity data and the trajectory motion deviation progressive data to obtain trajectory behavior progressive deviation learning data;

[0085] In this embodiment of the present invention, the robot arm's trajectory behavior progressive deviation features are learned based on trajectory jitter amplitude skew intensity data and progressive deviation data between trajectory motions. Features are extracted through multivariate trajectory behavior vector encoding and principal component cluster analysis. First, a trajectory behavior vector is constructed for each cycle, containing five dimensions: amplitude dominant frequency, amplitude skew intensity, progressive slope, progressive direction consistency, and maximum progressive increment. All vectors form a behavior data matrix. After normalization, all field values ​​are scaled to the [0, 1] range, and a covariance matrix is ​​calculated. Principal component analysis is performed on this matrix, extracting the top two principal components with a cumulative contribution exceeding 95%. The reduced behavior vectors are then input into a density-based clustering method (DBSCAN) for unsupervised cluster analysis, with a minimum sample size of 5 and a density threshold of 0.3. Different categories of behavioral deviation patterns are identified. For each category, the typical period segment number is labeled, and representative behavioral parameter values ​​are recorded. This generates trajectory behavior progressive deviation learning data, including fields such as principal component distribution, behavior cluster identifier, representative period, and behavioral indicator mean and variance. The data is output as a CSV file and is used to guide the optimization direction of the control program.

[0086] Step S24: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program.

[0087] In an embodiment of the present invention, trajectory tracking control is iteratively optimized for the robot arm trajectory tracking execution program based on the trajectory behavior progressive deviation learning data. This is achieved by combining controller parameter adjustment with trajectory interpolation strategy adjustment. First, the controller PID parameter configuration is analyzed for each periodic segment corresponding to each type of deviation behavior, and the historical setting values ​​of the three parameters P, I, and D and the corresponding deviation performance are recorded. For periodic segments with progressive deviation, the P parameter value is increased to enhance the controller's responsiveness, while the I parameter value is reduced to suppress integral accumulation lag. The adjustment step size is set to 5% of the initial value. For periodic segments with high-frequency jitter characteristics, the D parameter value is reduced to suppress the oscillation effect. At the same time, the trajectory point spacing is optimized, and the interpolation point distribution is adjusted to an encrypted style to achieve smoother end-point posture changes. After all parameters are adjusted, the trajectory interpolation function segment and PID controller configuration segment in the control program code are overwritten and updated, and the historical adjustment version is retained for comparative experimental basis. Finally, the modified code is executed and verified in a simulation environment, and the trajectory error and jitter index changes of each cycle after optimization are recorded. After confirming the performance improvement, the code version is solidified to form a trajectory tracking execution optimization program. All control parameters in the program are encapsulated in the form of structures, recording the version number and parameter source cycle number for traceability analysis and subsequent iterations.

[0088] Step S21 includes the following steps:

[0089] Step S211: performing time-series frequency domain conversion on the trajectory deviation jitter perception record data to generate a deviation jitter time-series frequency domain graph;

[0090] Step S212: performing jitter frequency mutation point distribution skewness identification on the deviation jitter timing frequency domain diagram to obtain jitter frequency mutation point distribution skewness data;

[0091] Step S213: calculating the variance of the mutation increasing slope based on the skew data of the jitter frequency mutation point distribution to obtain the variance of the frequency mutation point increasing slope;

[0092] Step S214: performing convergence constrained logarithmic fitting processing on the deviation jitter timing frequency domain diagram based on the incremental slope variance of the frequency mutation point to obtain frequency mutation point convergence logarithmic fitting data;

[0093] Step S215: performing track jitter amplitude variation skewness intensity analysis based on the frequency mutation point convergence logarithmic fitting data to obtain track jitter amplitude skewness intensity data.

[0094] In this embodiment of the present invention, the recorded trajectory deviation jitter sensing data is converted from the time series to the frequency domain. The discrete Fourier transform (DFT) method is used to perform frequency domain mapping on the trajectory deviation displacement sequence of the manipulator end within each cycle. Specifically, the trajectory deviation data collected within each cycle is organized into a real number sequence with equal time intervals. 1024 sampling points are taken per cycle at a sampling frequency of 1000 Hz. A fast Fourier transform (FFT) algorithm is applied to this time series to obtain the corresponding frequency-amplitude spectrum, with a frequency range of 0 Hz to 500 Hz. The frequency domain graph is stored as a two-dimensional array with frequency as the horizontal axis and amplitude as the vertical axis. Each element in the array contains a frequency value and its corresponding amplitude, with precision set to three decimal places. The time series frequency domain graphs are numbered according to the cycle number and archived in a unified directory structure. The jitter frequency mutation point distribution skewness is identified in the deviation jitter time series frequency domain graphs using a combination of first-order difference mutation point detection and peak counting. Specifically, a first-order difference is performed on the frequency domain graph of each cycle on the frequency axis, identifying the frequency locations where the differential amplitude exceeds a set threshold (e.g., 0.15) as the mutation point locations. Subsequently, a local peak determination is performed on the three frequency components before and after each mutation point, with the current amplitude being greater than the previous and next amplitudes and at least twice the average amplitude of the full spectrum. The frequency distribution of the mutation point locations for each cycle is statistically analyzed, and a frequency histogram of the mutation frequency locations is plotted, with its skewness and kurtosis calculated. A skewness greater than 1 indicates that the distribution deviates from the low-frequency concentration, while a kurtosis greater than 4 indicates that the mutation frequency is concentrated in a certain frequency band. The skewness and kurtosis are combined into a structure to represent the skewness data of the jitter frequency mutation point distribution for each cycle. This structure contains a list of mutation point frequency values, average amplitude value, frequency skewness value, and frequency kurtosis value.

[0095] The variance of the incremental slope of jitter frequency mutation points is calculated based on the skewed distribution data. This is processed using a mathematical statistics method combining slope fitting and variance analysis. A linear fit is performed on the amplitude evolution trend of the same mutation point frequency over multiple consecutive cycles to obtain a series of amplitude incremental slopes for each mutation point frequency. The standard deviation of this slope series is calculated to determine the intensity of the incremental slope fluctuation at that frequency mutation point. To improve analysis accuracy, the mutation frequency range is divided into 10Hz intervals, and the mean and variance of the slopes of the mutation points within each interval are calculated. If the variance exceeds a preset threshold (e.g., 0.05), the frequency band is considered to have a strong incremental slope fluctuation. The slope variance values ​​corresponding to all mutation frequency bands constitute a frequency mutation point incremental slope variance dataset, which includes fields such as the frequency band start and end values, slope variance, number of mutation frequency points, and average incremental amplitude. Based on the frequency mutation point incremental slope variance, a convergence-constrained logarithmic fit is performed on the frequency domain graph of the deviation jitter timing series, using a logarithmic fitting curve and residual convergence constraint strategy. Frequency domain data for each cycle within the mutation frequency band with high variance values ​​was selected. A data series showing the amplitude evolution of the mutation point over the cycle was extracted, and fitted data pairs were constructed between the cycle number and the amplitude. Fitting was performed using the natural logarithm, and the least squares method was used to determine the logarithmic function parameters. The fitting residual was constrained to not exceed 0.1 to control convergence error. Convergence was determined by determining that the absolute value of the derivative of the fitting curve was continuously less than 0.01 over the last five cycles. The frequency bands and corresponding fitting parameters that met this condition were recorded as the frequency mutation point convergence logarithmic fitting data. The data structure included the frequency band range, fitting constant parameter, maximum residual, and fitting convergence cycle number. The skewness of the trajectory jitter amplitude variation was analyzed using frequency-weighted integration and the extraction of the proportion of high-amplitude points. Within each frequency band's fitting convergence cycle, the corresponding amplitude growth rate was extracted and normalized to serve as the amplitude variation rate factor. The number of points in each frequency band with an amplitude greater than twice the overall mean was counted, and the proportion of high-amplitude points was calculated using the total number of points as the denominator. Finally, the skewness intensity index for that frequency band is calculated using a weighted integration method, combining the amplitude growth rate factor and the proportion of high-amplitude points. The skewness intensity index data for all frequency bands is merged and indexed by frequency band number and corresponding cycle number to form a trajectory jitter amplitude skewness intensity dataset. This data is accurate to three decimal places and contains fields such as frequency band range, skewness intensity value, maximum amplitude value, high amplitude ratio, and fitting residuals.

[0096] Step S214 includes the following steps:

[0097] Based on the variance of the increasing slope of the frequency mutation point, the deviation jitter timing frequency domain graph is subjected to an increasing segmented exponential transformation of the mutation point frequency domain curve to obtain an increasing segmented exponent of the mutation point curve;

[0098] Performing incremental segmental index ratio convergence processing on the incremental segmental index of the mutation point curve to obtain the incremental segmental index convergence ratio;

[0099] The deviation jitter timing frequency domain diagram is subjected to convergence constraint logarithmic fitting processing according to the increasing segmented exponential convergence ratio to obtain the frequency mutation point convergence logarithmic fitting data.

[0100] In this embodiment of the present invention, the deviation jitter timing frequency domain graph is subjected to an incremental piecewise exponential transformation of the frequency domain curve at the frequency mutation point based on the variance of the incremental slope at the frequency mutation point. Nonlinear enhanced representation of frequency domain fluctuations is achieved by performing piecewise exponential fitting on the frequency domain amplitude sequence corresponding to each cycle within the mutation point frequency segment. Specifically, the frequency interval of the frequency mutation point is first determined. For example, if the mutation point frequency is 135Hz, the interval [125Hz, 145Hz] with ±10Hz above and below it is used as the analysis range. The amplitude sequence of this frequency interval over N = 10 consecutive cycles is divided into three segments, each containing the amplitude sequence corresponding to the same frequency point. Each segment is fitted using a power exponential fitting function, and the fitting parameters are determined using the least squares method. The rate of change of the exponential portion serves as the incremental exponent value for that segment. The incremental exponents of each fitted segment are recorded separately, and their corresponding period and frequency ranges are annotated. This forms a data structure for the incremental segmental exponents of the catastrophe point curve, which contains fields such as the frequency start and end values, period start and end values, fitting exponent parameters, sum of squares of fitting residuals, and the location of the maximum frequency domain amplitude point. The incremental segmental exponents of the catastrophe point curve are processed for convergence. The stability of the frequency domain fluctuation intensity is tested using the segmental exponent ratio decrement determination and the analysis of the rate of change within the convergence window. Specifically, the ratio of the incremental exponents of two adjacent segments is calculated. For example, if the index of the first segment is α1 and the index of the second segment is α2, α2 / α1 is calculated as the ratio of the comparison segment. If the ratio is less than 1 within two consecutive segments and the change amplitude is less than a set threshold (e.g., 0.05), a convergence trend is determined. The absolute value of the rate of change of the ratio is calculated within the three-segment sliding window. If the maximum rate does not exceed 0.03, the incremental exponent value is considered to be stable. Frequency bands and period ranges that meet this condition are marked as incremental exponential convergence regions. Increasing segmented exponential convergence ratio data is output, including fields such as intra-segment exponential value, inter-segment ratio, convergence period window number, ratio stabilization rate, and residual ratio fluctuation range. Based on the incremental segmented exponential convergence ratio, convergence-constrained logarithmic fitting is performed on the deviation jitter timing frequency domain graph. The convergence weight is adjusted using the logarithmic fitting algorithm to improve the accuracy of the convergence model for energy changes at frequency mutation points.In the implementation, for all frequency bands identified as regions of increasing exponential convergence, the amplitude change sequence at the same frequency point during the periodic evolution is extracted. A fitting dataset is constructed with the period number as the independent variable and the amplitude as the dependent variable. Fitting is performed using a natural logarithmic function, y = a × ln(t) + b, where t is the period number, i.e., the number of trajectory execution cycles. y represents the frequency-domain amplitude response at a specific frequency point; the variation of y with t indicates the evolution trend of the robot arm trajectory jitter amplitude at that frequency over consecutive cycles. a represents the rate of increase or decrease of the amplitude with the number of cycles, and b represents the baseline amplitude offset (initial logarithmic amplitude) at t = 1. To ensure convergence, segments with smaller rate of change are given higher fitting weights. The logarithmic function parameters are determined using a weighted least squares fitting method. After the fit is completed, the residuals of all fitted curves are statistically analyzed. If the residual mean square value is less than 0.08 and the amplitude change within the last three cycles is less than 0.01, the fit result is considered a valid converged fit curve. The final output is a frequency mutation point convergence logarithmic fitting dataset. The data structure includes fields such as frequency range, cycle start and end numbers, fitting parameters, weight coefficients, residual mean square, and fitting stability window cycle number. This data is used to extract the characteristics of the trajectory control deviation's stable change over time during the trajectory behavior deviation modeling phase.

[0101] In another embodiment, the variance data of the incremental slope of frequency mutation points is divided into 24 time windows in chronological order, each window being 5 seconds long. The frequency domain data within each time window is subjected to an exponential transformation with a base of 2.718, mapping the frequency values ​​into an exponential space. Mutation points are extracted from the exponential space, and the threshold for determining mutation points is set to 1.5 times the local mean. The exponential mean of the mutation points is calculated for each time window, forming a sequence of 24 exponential means. The exponential mean sequence is segmented, with segmentation points set at locations where the rate of change in the exponential value exceeds 30%. Linear regression is performed on each segment of data to obtain the segmented slope. The segmented slopes, exponential means, and number of mutation points for the 24 time windows are combined into a feature vector to form the incremental segmented index of the mutation point curve. The incremental segmented index of the mutation point curve is normalized to a range of 0-1. A sequence of ratios of the exponential values ​​between adjacent segments is calculated. The ratio convergence threshold was set to 0.85, and convergence was considered when the rate of change of three consecutive ratios was less than 15%. Unconverged segments were iterated, halving the segment length at each iteration and recalculating the exponential ratio. The maximum number of iterations was set to 8. The ratio sequence and convergence status of each iteration were recorded. The final converged ratio sequence, convergence position, and iteration number were integrated into feature data to obtain the increasing segmented exponential convergence ratio. Logarithmic fitting constraints were established based on the increasing segmented exponential convergence ratio, including a maximum fitting error of 0.1, a minimum convergence ratio of 0.8, and a maximum number of 12 iterations. The original frequency domain data was segmented into 5-second time windows. The baseline drift was subtracted from each segment, and the baseline was obtained using a 60-point sliding median filter. A logarithmic function was fitted to the baseline-free data, and the trust region method was used to determine the optimal fitting parameters. The convergence ratio was used as a weight in the fitting process, with a higher weight being assigned to a higher convergence ratio. Fitting was terminated when the fitting error fell below the threshold or the maximum number of iterations was reached. All segmented fitting results are spliced ​​along the time dimension to obtain the frequency mutation point convergence logarithmic fitting data.

[0102] Step S23 includes the following steps:

[0103] Step S231: calculating the progressive mean difference of attitude angle offset on the progressive data of the deviation between trajectory movements to obtain the progressive mean difference of attitude angle offset;

[0104] Step S232: Calculating the joint angle deviation time series increment ratio on the trajectory motion deviation progressive data to obtain the joint angle deviation time series increment ratio;

[0105] Step S233: performing a manipulator trajectory jamming swing amplitude regression analysis on the progressive mean difference of the posture angle offset and the time series increment ratio of the joint angle deviation according to the trajectory jitter amplitude skew intensity data to obtain the manipulator trajectory jamming swing amplitude regression data;

[0106] Step S234: performing repeated trajectory jamming amplitude transfer learning on the robot arm trajectory jamming amplitude regression data to obtain repeated trajectory jamming amplitude learning data;

[0107] Step S235: performing trajectory behavior progressive deviation feature learning of the robot arm according to the repeated trajectory jamming swing amplitude learning data to obtain trajectory behavior progressive deviation learning data.

[0108] In one embodiment of the present invention, the progressive mean difference of attitude angle offsets is calculated for the inter-trajectory motion deviation data, and the characteristics of the end-effector attitude angle change per cycle are obtained through statistical methods. The specific process is as follows: a sequence of attitude angle (Euler angles around the X, Y, and Z axes) offset values ​​for each sampling point within 20 consecutive cycles is extracted from the inter-trajectory motion deviation data set. A sliding window analysis is applied to each of the three angular directions, with a window length of 5 cycles and a step size of 1 cycle. The mean offset is calculated for each angular direction within the window, and the mean difference of the deviation is extracted (i.e., the mean difference between the absolute value of the attitude angle offset within the window and the window mean). The mean difference values ​​for each window are aggregated over the entire time period, and their mean and standard deviation are calculated. The result is the progressive mean difference of attitude angle offsets, expressed in degrees with an accuracy of three decimal places. The corresponding trajectory segment number and cycle number are recorded and output in CSV format. The time-series incremental ratio of joint angle deviation is calculated for the inter-trajectory motion deviation data, and the cumulative trend of joint angle error is revealed through normalization. The specific method involves extracting a 20-cycle sequence of deviation values ​​for each sampling endpoint of six joints from the dataset. For each joint, the time series increment (i.e., the difference between adjacent cycle deviations) is calculated, resulting in a sequence of 19 increment values. For each joint, the increment sequence is rounded to positive absolute value, and the percentage ratio of each increment to the maximum increment in the joint sequence is calculated. The average increment ratio and variance for each joint are then calculated to form the joint angle deviation time series increment ratio data. The data format includes fields such as cycle number, joint number, average increment ratio, increment variance, and maximum increment cycle number, with accuracy to three decimal places. Based on the trajectory jitter amplitude skewness intensity data, trajectory jitter amplitude regression analysis is performed on the progressive mean difference of attitude angle offset and the joint angle deviation time series increment ratio to identify jitter behavior characteristics. A jitter amplitude prediction model is established using a multivariate linear regression method. The independent variables include amplitude skewness intensity, progressive mean difference of attitude angle, and average increment ratio for each joint, and the dependent variable is the end-effector posture jitter amplitude (unit: millimeter). The dataset comes from multiple periodic segments, and 200 sets of data were selected for training from the 7th to the 27th period. The least squares method was used to estimate the regression coefficient, and the model R2R^2R2 value and parameter significance p-value were calculated. The regression coefficient corresponding to each independent variable must satisfy the p-value < 0.05 and R^2 greater than 0.85; outliers with residuals exceeding twice the standard deviation were eliminated during the regression process. The regression results are output as the robot trajectory jamming amplitude regression data, and the format includes the regression coefficient, p-value, R^2, residual standard deviation, and sampling period range. Repeated trajectory jamming amplitude transfer learning is performed on the robot trajectory jamming amplitude regression data to extract the similarity of jamming and swing behaviors of previous runs and realize behavioral migration feature extraction. The specific method is: the jamming amplitude regression data collected from multiple trajectory runs are classified according to trajectory type, such as multiple runs of the same processing path.For each trajectory data set, dynamic time warping (DTW) was used to align and compare the regression coefficient time series of each run. The DTW distance between each pair was calculated, and repeated trajectories were considered similar if the distance was less than a threshold (e.g., 0.2). Trajectories with more than three similarities within each category were counted, and the corresponding regression model average coefficient and standard deviation were extracted to form repeated trajectory stuttering amplitude learning data. The data included the trajectory ID, average regression coefficient, coefficient variance, number of similarities, and mean DTW distance. The robot's trajectory stuttering amplitude learning data was used to learn the progressive deviation features of the robot's trajectory behavior. The identified stuttering amplitude features were mapped to the underlying deviation patterns of the trajectory behavior. Unsupervised clustering was performed on the stuttering amplitude learning data corresponding to different trajectory IDs using cluster analysis. Ward's hierarchical clustering method was used to calculate the Euclidean distance between data points and construct a cluster tree. The number of clusters in the clustering results was set between 3 and 5, and the optimal number of clusters was determined using inter-class sum-of-squares error analysis (Elbow method). For each cluster, the center point is calculated. This center point is the feature vector of the progressive deviation of the trajectory behavior of that type, and the cluster is assigned a label. This ultimately generates a trajectory behavior progressive deviation learning dataset, including fields such as trajectory cluster ID, central regression coefficient, intra-cluster variance, cluster member period range, and similarity score. This data is formatted as a JSON structure and serves as a basis for the subsequent trajectory tracking control optimization program design.

[0109] In another embodiment, periodic trajectory motion deviation data is first retrieved. During a complete task cycle, frame sequences are sampled based on the angular errors of the six joints of the manipulator. The sampling frequency is set to 1000 Hz, the trajectory segment length is 5 seconds, and a total of 5000 trajectory frames are sampled. The difference between the expected and actual trajectory of the six-axis end effector posture within adjacent trajectory execution cycles is converted to Euler angles to calculate the corresponding attitude angle error vector. The mean growth of the attitude difference vector along the three attitude angle axes (pitch, yaw, and roll) is then calculated for each adjacent execution cycle. The change in the mean difference is calculated by sliding a window of 10 cycles over the data blocks. The trend is then smoothed using an autoregressive moving average filter. The progressive mean difference is calculated for all data blocks, and the change index is recorded. Finally, a sequence of progressive mean differences in attitude angle offset is output as a three-dimensional array. Each axis includes statistics such as the frame number, the mean difference of consecutive cycles, the mean increase rate, and the index of the local extreme value. The progressive trajectory motion deviation data corresponding to step S231 is processed using joint angle deviation time series increments. Specifically, the angle error values ​​for each joint of the manipulator are treated as a time series, and first-order differences are performed between adjacent frames to obtain an angle increment sequence. This increment is then divided by the theoretical angle change in the previous frame to obtain the increment ratio. Each frame is then subjected to a sliding window process, with the window set to 100 frames (corresponding to 100 milliseconds). The mean and variance of the joint angle deviation increment relative to the theoretical velocity within this window are calculated. Parts exceeding a set threshold (e.g., ±15%) are filtered and marked as sensitive sites. Finally, a joint angle deviation time series increment ratio sequence is generated, containing data fields such as joint number, frame number, deviation increment ratio, local mutation point location, and mutation index. This sequence is used to determine the response inconsistency rate between control commands and feedback execution. Using trajectory jitter amplitude skewness intensity data as a modulation factor, the progressive mean difference of the posture angle offset and the joint angle deviation time series increment ratio data are combined to construct a regression analysis system for manipulator trajectory jitter amplitude. The regression analysis method utilizes a multivariate linear regression enhanced model. The main process uses the identified abnormal jitter intensity segments in each cycle as target labels, and the mean posture difference and offset ratio in the corresponding cycle as independent variables. An attribution threshold of 0.75 is set to determine whether the correlation joint degree of the results meets the fitting conditions. The Bayesian Information Criterion (BIC) is also embedded in the regression model to conditionally filter each dependent variable and eliminate non-significant variables. The final output targets include regression residuals, a list of fitted linear equations, variable weight ranking, regression goodness of fit, anomaly discrimination rate, and a cycle span mapping index. These fields describe the relationship between jitter and swing caused by structural disturbances and control lag in a specific frequency domain. A repeated trajectory jitter and swing transfer learning process is performed based on trajectory jitter and swing regression data generated over multiple historical cycles.This step uses a statistical learning method to construct typical feature templates. Using jam data from long-term running trajectories, the temporal distribution of key change points, axial contribution weights, and structural variations between periodicities are extracted to establish a trajectory behavior feature migration mapping structure. In specific implementation, verified jam amplitude features from multiple historical trajectory files are projected into a unified time domain and normalized. A K-means clustering algorithm is then used to identify several typical attitude offset templates and angular response misalignment feature clusters. The total number of clusters is typically set between 7 and 10, and the optimal configuration is selected based on the Davies–Bouldin metric. After iterative convergence, the underlying trajectory period mapping relationships representing the locations of recurring jams are accurately identified. The jam amplitude learning data for recurring trajectories is output, including the feature cluster mean vector, cluster center ID, feature sequence period position number, and corresponding error contribution index. The jam amplitude learning data for recurring trajectories is then fed into the feature learning module. Specifically, sequences exhibiting recurring jams are sequentially selected from all cycles, and the corresponding attitude angle progressive change curves are time-normalized to generate a standard periodic deviation waveform template. The dynamic time warping (DTW) method is then used to measure the degree of time offset matching between all cycles, with the waveform point with the largest deviation being designated as the progressive deviation point. The energy value of the deviation waveform integrated over the entire time axis and the degree of periodic offset are then used as two target indicators, labeled as a behavioral deviation energy intensity sequence. The final output is trajectory behavior progressive deviation learning data, whose key fields include feature vectors such as trajectory segment identification code, aggravation frequency, amplitude accumulated energy, periodic progressive delay rate, and waveform structure stability. This provides a classification of variation patterns for subsequent optimization model updates of the trajectory tracking control system. This processing, based on an open-loop trajectory command and feedback error statistical method, identified 88 significant deviation segments from 1600 training cycles, detecting an average of 7.2 deviation points per cycle. The total processing time was 14 seconds, and the error goodness-of-fit R² reached 0.94, demonstrating high trajectory recognition accuracy and a stable monitoring foundation.

[0110] Step S233 includes the following steps:

[0111] Perform jitter spatial orientation disorder intensity analysis on the trajectory jitter amplitude skew intensity data to obtain jitter spatial orientation disorder intensity data;

[0112] According to the jitter spatial orientation disorder intensity data, the spatial orientation vector angular rate mutation entropy value is analyzed on the progressive mean difference of the attitude angle offset to obtain the orientation vector angular rate mutation entropy value;

[0113] The joint angle overshoot probability calculation is performed on the joint angle deviation time series increment ratio according to the jitter spatial orientation disorder intensity data to obtain the joint angle overshoot probability calculation data;

[0114] Based on the azimuth vector angular rate mutation entropy value and joint angle overshoot probability calculation data, the robot arm trajectory jamming amplitude regression analysis is performed to obtain the robot arm trajectory jamming amplitude regression data.

[0115] In an embodiment of the present invention, the jitter amplitude skew intensity data is analyzed for jitter spatial orientation disorder intensity. To perform this analysis, the jitter amplitude skew intensity data is first mapped to the displacement deviation direction of the robotic arm end effector in three-dimensional space. The deviation signals and their corresponding amplitude intensity values ​​along the X, Y, and Z axes are extracted and treated as sampling points of the three-dimensional vector field. The spatial direction of each sampling point within a continuous cycle is divided into unit spaces, with a cube with a side length of 10 mm as a unit grid. The number and intensity distribution of deviation vectors within each grid are counted. For each grid, a disorder intensity index is calculated based on the vector direction distribution within it. This involves traversing all deviation vectors within the grid, calculating the absolute value of the angle between them and the average direction within the grid, and calculating the standard deviation of the angle as the disorder intensity value for the grid. The disorder intensity values ​​of all grids constitute a jitter spatial orientation disorder intensity data structure, with fields including the grid center coordinates, the number of vectors, the average amplitude, and the standard deviation of the angle, with accuracy to three decimal places, and output as a structured table. The spatial orientation vector angular rate mutation entropy analysis is performed on the progressive mean difference of attitude angle offsets based on the jitter spatial orientation disorder intensity data. First, the progressive mean difference of attitude angle offsets is spatially and temporally aligned with the spatial disorder intensity data. For each sampling period, the disorder intensity value of the corresponding sampling grid is extracted as a weight. Next, the mutation rate of the angular rate in the three spatial axes of the average attitude angle offset vector in that period is calculated. This is done by calculating the rate of change in direction between adjacent timestamps and weighting the disorder intensity value of that period to obtain a weighted angular rate mutation sequence. Shannon entropy is then calculated on this sequence, which calculates the entropy value after calculating the probability of the distribution of the angular rate mutation value intervals. This entropy value reflects the complexity of the change in the attitude angle offset direction. Output fields include the period number, the average disorder intensity value, the angular rate mutation entropy value, and the maximum directional change interval. The probability of joint angle overshoot (i.e., the angle change exceeds the target or expected) is calculated based on the time series increment ratio of the joint angle deviation based on the jitter spatial orientation disorder intensity data. This step first segments the joint angle deviation time series increment ratio data by joint number, with each segment containing 20 consecutive cycles. For each joint data segment, the frequency of events where the increment ratio exceeds a critical value (set to 0.8, representing 80% of the maximum increment ratio) is counted. This is combined with the spatial disorder intensity value of the corresponding cycle to calculate the conditional probability of angle increment overshoot in a highly disordered grid. This probability is then smoothed using a sliding window (window length 5 cycles) along the time dimension to form a joint angle overshoot probability curve. The output fields are joint number, cycle number, and overshoot probability. A regression analysis of the robot's trajectory jitter amplitude is performed based on the angular velocity mutation entropy values ​​of the orientation vector and the calculated joint angle overshoot probability data. This analysis utilizes a multivariate generalized linear regression method, with the angular velocity mutation entropy values ​​and the overshoot probability of each joint as independent variables and the actual end-effector jitter amplitude as the dependent variable.The regression process uses 30 trajectory execution cycles as a sample window, iteratively estimating the regression coefficients. Ridge regression is used to address collinearity, with the regularization parameter set to 0.01 to ensure stability. The regression results include the individual coefficients, standard errors, p-values, and residual variances. The regression model was evaluated using ten-fold cross-validation, with the average prediction error kept within 0.1 mm. The final output of the robot arm trajectory lag amplitude regression data includes fields such as cycle number, independent variable value, independent variable coefficient, predicted value, residual value, and R-squared value.

[0116] In another embodiment, the trajectory jitter amplitude skew intensity data is decomposed into X, Y, and Z components according to three-dimensional spatial coordinates, with a sampling frequency of 200 Hz. A Hilbert transform is performed on the amplitude data in each direction to obtain the instantaneous phase, with a phase resolution of 0.01 radians. The phase difference between adjacent sampling points is calculated to construct a phase difference sequence. Autocorrelation analysis is performed on the phase difference sequence, with delay times ranging from 1 to 100 sampling points. The first zero crossing point of the autocorrelation function is extracted as the correlation length. The cross-correlation coefficient matrix of the amplitudes in the three directions is calculated. Singular value decomposition is performed on the cross-correlation matrix, and the largest three singular values ​​are taken. The correlation length, singular values, and phase difference statistics are combined to form jitter spatial orientation disorder intensity data. The attitude angle offset progressive mean difference data is resampled to 200 Hz and aligned with the jitter spatial orientation disorder intensity data. The angular velocity sequences of the six joints are calculated using a five-point central difference method. The angular velocity sequences are segmented, with each segment consisting of 1000 sampling points. Angular velocity mutation points were detected within each segment, with the mutation threshold set at 2.5 times the local standard deviation. The number and temporal distribution of mutation points within each segment were counted. The angular velocity change at the mutation point was calculated, and a weighted entropy value was calculated based on the jitter spatial orientation disorder intensity data. The weight coefficient was determined by the singular value of the disorder intensity. The entropy sequence, mutation statistics, and angular velocity change characteristics of each segment were integrated to obtain the azimuth vector angular velocity mutation entropy. The joint angle deviation time series incremental proportional data was segmented, with a segment length of 2 seconds. Angle threshold boundaries were set within each segment, with an upper limit of the mean plus 2 times the standard deviation and a lower limit of the mean minus 2 times the standard deviation. Data points exceeding the threshold boundaries were counted, and the overshoot time fraction was calculated. Overshoot events were weighted using the jitter spatial orientation disorder intensity data, with the weight proportional to the disorder intensity. Probability density estimation was performed on the weighted overshoot sequence using kernel density estimation with a bandwidth of 0.1. Calculate the overshoot probability distribution parameters for each joint, including mean, variance, skewness, and kurtosis. Combine the probability distribution parameters with the overshoot statistics to generate joint angle overshoot probability calculation data. Use the azimuth vector angular rate mutation entropy and joint angle overshoot probability calculation data as input features to construct a support vector regression model. Use the radial basis kernel function with the kernel parameter gamma set to 0.01 and the penalty factor C set to 10. The dataset is divided chronologically, with the first 80% used for training and the last 20% for testing. Normalize the features to the interval [-1, 1]. Train the support vector regression model and use grid search to determine the optimal hyperparameters. Predictions are performed on the test set, and prediction error statistics are calculated. The prediction results, model parameters, and error statistics are combined to generate the robot trajectory sway amplitude regression data.

[0117] Step S24 includes the following steps:

[0118] Step S241: performing robot arm trajectory error clustering processing on the trajectory behavior progressive deviation learning data to obtain robot arm trajectory error clustering data;

[0119] Step S242: reconstructing the control logic structure of the robot arm trajectory tracking execution program based on the robot arm trajectory error clustering data to generate control program logic structure reconstruction data;

[0120] Step S243: performing control logic nesting depth constraint on the control program logic structure reconstruction data to obtain program control logic depth constraint reconstruction data;

[0121] Step S244: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the program control logic depth constraint reconstruction data to obtain a trajectory tracking execution optimization program.

[0122] In an embodiment of the present invention, when clustering the trajectory error of a robot arm using the trajectory behavior progressive deviation learning data, the trajectory behavior progressive deviation learning data is first segmented according to time windows, with each segment containing trajectory data for 20 control cycles. Three types of error indicators are extracted from each cycle: spatial displacement error, attitude angle offset, and end-effector offset. After error normalization, a sample set is constructed in the form of a three-dimensional error vector, and unsupervised classification is performed using the Density Peak Clustering algorithm. The error trends are divided into three categories: stable deviation type, periodic deviation type, and sudden deviation type. The local density threshold is set to 0.4 and the distance threshold is set to 0.6 during clustering. Finally, a set of labeled error clustering data is obtained, each category containing its cluster center coordinates, the corresponding data index, and the average offset vector, which is used to characterize the deviation distribution pattern of the trajectory behavior. When reconstructing the control logic structure of the robot trajectory tracking execution program based on robot trajectory error clustering data, the trajectory execution code segments corresponding to each error type are extracted. Control logic paths with a frequency greater than 0.8 in the stable deviation type are identified. Conditional structures with frequent loops are expanded and replaced with branching structures driven by a state transition matrix. The control logic corresponding to the periodic deviation type clusters uses periodic conditional jump optimization technology to optimize the original time-based deterministic formula into a phase-locked trajectory rhythm conditional control structure. The code segments corresponding to the sudden deviation type clusters are enhanced with exception jump capture, and high-priority error event interrupt response logic is inserted. This generates structured control program logic structure reconstruction data, including a logic tree structure, a conditional path table, and a mapping table for triggering exception handling logic. To constrain the control logic nesting depth of the control program logic structure reconstruction data, the multi-level nested conditional structures in all control logic trees are analyzed, and three dimensional parameters are extracted: the number of logic layers, the complexity of each conditional layer, and the number of nested paths. The maximum number of nested layers is set to 5. When more than 5 nested paths are detected in the control structure, the control segment is automatically split into two sub-process modules. The original deeply nested logic is reconstructed into a linear structure in a state jump manner using a logic callback mechanism, reducing the number of nested layers to less than 3. At the same time, a Boolean expression simplification strategy is introduced, and the Karnaugh map method is used to simplify the complex conditional judgment logic to ensure that the total number of control logic paths does not exceed 128. After processing, the program control logic depth constraint reconstruction data is formed. The data format includes the control block identifier, the reconstructed path depth value, and the corresponding trigger response structure description. When the trajectory tracking control of the robot arm trajectory tracking execution program is iteratively optimized based on the program control logic depth constraint reconstruction data, a control logic version management chain is established to generate an independent version identifier for the control program after each logical structure adjustment.For each version, the actual robotic arm executes 100 typical trajectories (such as circular trajectories, figure-eight trajectories, and rectangular paths) to obtain real-time error data. A trajectory error feedback matrix is ​​constructed, and the error convergence trend is extracted by comparing the mean trajectory error feedback of the current version with the difference between the previous version. If the error decreases by less than 5% in the current version, the control weight adjustment module is activated to fine-tune the proportional gain and integral feedback terms in the current control program, with a step size of 0.01 to ensure that the control program achieves the minimum step size tuning in the convergence direction. The final output trajectory tracking execution optimization program includes the optimization version number, error convergence rate indicator, and the updated control logic structure mapping table.

[0123] Step S3 includes the following steps:

[0124] Step S31: performing a program code static analysis on the trajectory tracking execution optimization program to obtain program code static analysis data;

[0125] Step S32: performing functional unit integration testing on the trajectory tracking execution optimization program according to the program code static analysis data to obtain functional unit integration test data;

[0126] Step S33: designing the robot arm trajectory tracking control firmware by performing the trajectory tracking optimization program based on the functional unit integration test data to obtain the robot arm trajectory tracking control firmware;

[0127] Step S34: embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform the robot arm trajectory tracking control.

[0128] As an example of the present invention, refer to Figure 3 As shown, in this example, step S3 includes:

[0129] Step S31: performing a program code static analysis on the trajectory tracking execution optimization program to obtain program code static analysis data;

[0130] In an embodiment of the present invention, static code analysis of a trajectory tracking optimization program utilizes a method combining syntax tree parsing and data flow analysis to analyze the optimized control program source code. First, an abstract syntax tree (ABST) is constructed for the control program using a syntax parser (such as Clang AST), extracting the function call graph, variable definition and usage chains, and semantic context relationships for each control module. A control flow graph (CFG) and data flow graph (DFG) are then constructed to analyze the program for potential issues such as variable escape paths, uninitialized variables, and insufficient branch coverage. Complexity is measured using a static analysis tool, using cyclomatic complexity to assess the number of control paths for each function. Functions exceeding 20 are labeled as high-complexity. In this example, analysis of the program module containing the trajectory control main loop revealed three conditional jump statements with incomplete path coverage and the risk of uninitialized use of the integral error variable in a joint PID controller. The resulting static code analysis data includes a control path graph, a variable usage table, a code complexity report, and a list of potential error warnings.

[0131] Step S32: performing functional unit integration testing on the trajectory tracking execution optimization program according to the program code static analysis data to obtain functional unit integration test data;

[0132] In this embodiment of the present invention, a functional unit-level verification mechanism based on a test-driven development framework is employed when performing functional unit integration testing on a trajectory tracking execution optimization program based on program code static analysis data. First, a functional unit test checklist is constructed based on the function call dependency graph generated by static analysis. Independent test modules are constructed for each key control function (such as the trajectory generation function, the error feedback processing function, and the position-velocity-acceleration command fusion function). An industrial control-grade simulation platform (such as Matlab Simulink with TargetLink) is used to establish a simulation environment, and standard trajectory data is injected for closed-loop execution testing. Test parameters include a trajectory sampling period of 5ms, a maximum command position step size of 0.02rad, and an error injection range of ±1mm. Boundary value tests, abnormal input tests, and instruction jump tests are performed for each functional unit to verify its robustness. The resulting functional unit integration test data includes input and output consistency verification results for each function, logic path coverage (required to be above 95%), execution latency statistics (maximum limit of 1ms), and output response error statistics.

[0133] Step S33: designing the robot arm trajectory tracking control firmware by performing the trajectory tracking optimization program based on the functional unit integration test data to obtain the robot arm trajectory tracking control firmware;

[0134] In an embodiment of the present invention, when designing the robotic arm trajectory tracking control firmware based on the trajectory tracking execution optimization program based on functional unit integration test data, the firmware design process is completed using a real-time embedded system development platform (such as the TI C2000 series or STM32H7). The tested trajectory control program is compiled into target instruction code (.hex or .bin format) using a cross-compiler. During the compilation process, interrupt priorities are configured, the trajectory control main loop is assigned to the periodic interrupt service function, and the high-frequency data acquisition function is set to DMA drive mode to reduce CPU load. Independent timer resources and PWM output modules are allocated for different joint channels. The system clock is configured in the startup code, with the main frequency set to 400MHz to meet the 5ms control cycle requirement. A firmware interface protocol is designed to communicate with the host computer via RS485 or CAN bus, defining the communication frame structure for trajectory update commands, joint status queries, and emergency stop control. The final output robotic arm trajectory tracking control firmware is a binary file that can be burned into the target controller, accompanied by a hardware resource mapping table and register initialization table.

[0135] Step S34: embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform the robot arm trajectory tracking control.

[0136] In an embodiment of the present invention, the robot arm trajectory tracking control firmware is embedded into the robot arm control center to execute the robot arm trajectory tracking control, and the generated firmware is written into the FLASH storage area of ​​the control mainboard using an industrial burning device. After the burning is completed, the control system is powered on and the hardware and software are debugged together. The controller status is monitored online through the JTAG interface, and the joint drive output is captured using an oscilloscope to verify whether the trajectory control cycle is strictly 5ms, whether the PWM output waveform is continuous, and whether the current instruction changes are smooth and jitter-free. A three-dimensional position tracker (such as the OptiTrack system) is used to monitor the trajectory execution trajectory of the robot arm end in real time, and the error is compared and analyzed with the theoretical trajectory. The trajectory execution error of each joint is recorded, requiring the average deviation to be no more than 1.5mm and the maximum deviation to be no more than 2.5mm. After debugging is completed, the firmware configuration data is written into the EEPROM as a startup configuration file, and the robot arm control center enters the working state and starts to execute trajectory tracking control.

[0137] The present invention also provides a robot arm trajectory tracking control system for executing the robot arm trajectory tracking control method described above, the robot arm trajectory tracking control system comprising:

[0138] The trajectory jitter perception analysis module is used to obtain the robot arm operation log and the robot arm trajectory tracking execution program; extract the cycle-related trajectory motion deviation from the robot arm operation log to obtain the cycle trajectory motion deviation data; and analyze the robot arm motion trajectory jitter perception record based on the cycle trajectory motion deviation data to obtain the trajectory deviation jitter perception record data;

[0139] The behavior deviation feature learning module is used to learn the robot arm's trajectory behavior deviation features based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; based on the trajectory behavior progressive deviation learning data, the robot arm's trajectory tracking execution program is iteratively optimized for trajectory tracking control to obtain a trajectory tracking execution optimization program;

[0140] The tracking control firmware design module is used to design the robot arm trajectory tracking control firmware for the trajectory tracking execution optimization program to obtain the robot arm trajectory tracking control firmware; the robot arm trajectory tracking control firmware is embedded into the robot arm control center to perform robot arm trajectory tracking control.

[0141] The foregoing description is intended only to provide specific embodiments of the present invention, which will enable those skilled in the art to understand and implement the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not intended to be limited to the embodiments shown herein, but is to be construed in the widest possible manner consistent with the principles and novel features disclosed herein.

Claims

1. A robot arm trajectory tracking control method, characterized in that: The following steps are involved: Step S1: Obtain the robot arm operation log and the robot arm trajectory tracking execution program; The robot arm operation log is used to extract the use-cycle associated trajectory motion deviation to obtain periodic trajectory motion deviation data; the robot arm motion trajectory jitter perception record analysis is performed based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data; wherein, the trajectory deviation jitter perception record data is based on the periodic trajectory motion deviation data through the sliding window time series feature analysis technology, extracting the trajectory position deviation change trend in the continuous period, using the sliding average and weighted difference combination model to establish the trajectory jitter amplitude change trajectory, and establishing a three-dimensional jitter data matrix in the time series dimension, wherein the three-dimensional jitter data matrix includes position deviation, speed change, acceleration mutation, and performs principal component analysis (PCA) and Mahalanobis distance analysis to calibrate the outlier periodic points of the trajectory deviation and its trend clustering interval, and finally generate the trajectory deviation jitter perception record data; Step S2: performing trajectory behavior deviation feature learning of the robot arm based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program based on the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program; Step S3: Designing a robot arm trajectory tracking control firmware by performing a trajectory tracking optimization program to obtain the robot arm trajectory tracking control firmware; embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform robot arm trajectory tracking control.

2. The robot arm trajectory tracking control method according to claim 1, characterized in that: Step S1 includes the following steps: Step S11: Obtaining the robot arm operation log and the robot arm trajectory tracking execution code; Step S12: performing data cleaning on the robot arm operation log to obtain a robot arm operation cleaning log; Step S13: extracting the cycle-related trajectory motion deviation from the robot arm cleaning operation log to obtain the cycle trajectory motion deviation data; Step S14: analyzing the robot arm motion trajectory jitter perception record of the robot arm operation cleaning log based on the periodic trajectory motion deviation data to obtain trajectory deviation jitter perception record data.

3. The robot arm trajectory tracking control method according to claim 1, characterized in that: Step S2 includes the following steps: Step S21: performing track jitter amplitude variation skew intensity analysis on the track deviation jitter sensing record data to obtain track jitter amplitude skew intensity data; Step S22: performing a spatial deviation progressive analysis on the periodic trajectory motion deviation data to obtain trajectory motion spatial deviation progressive data; Step S23: performing trajectory behavior progressive deviation feature learning of the robot arm according to the trajectory jitter amplitude skew intensity data and the trajectory motion space deviation amount progressive data to obtain trajectory behavior progressive deviation learning data; Step S24: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the trajectory behavior progressive deviation learning data to obtain a trajectory tracking execution optimization program.

4. The robot arm trajectory tracking control method according to claim 3, characterized in that: Step S21 includes the following steps: Step S211: performing time-series frequency domain conversion on the trajectory deviation jitter perception record data to generate a deviation jitter time-series frequency domain graph; Step S212: performing jitter frequency mutation point distribution skewness identification on the deviation jitter timing frequency domain diagram to obtain jitter frequency mutation point distribution skewness data; Step S213: calculating the variance of the mutation increasing slope based on the skew data of the jitter frequency mutation point distribution to obtain the variance of the frequency mutation point increasing slope; Step S214: performing convergence constrained logarithmic fitting processing on the deviation jitter timing frequency domain diagram based on the incremental slope variance of the frequency mutation point to obtain frequency mutation point convergence logarithmic fitting data; Step S215: performing track jitter amplitude variation skewness intensity analysis based on the frequency mutation point convergence logarithmic fitting data to obtain track jitter amplitude skewness intensity data.

5. The robot arm trajectory tracking control method according to claim 4, characterized in that: Step S214 includes the following steps: Based on the variance of the increasing slope of the frequency mutation point, the deviation jitter timing frequency domain graph is subjected to an increasing segmented exponential transformation of the mutation point frequency domain curve to obtain an increasing segmented exponent of the mutation point curve; Performing incremental segmental index ratio convergence processing on the incremental segmental index of the mutation point curve to obtain the incremental segmental index convergence ratio; The deviation jitter timing frequency domain diagram is subjected to convergence constraint logarithmic fitting processing according to the increasing segmented exponential convergence ratio to obtain the frequency mutation point convergence logarithmic fitting data.

6. The robot arm trajectory tracking control method according to claim 3, characterized in that: Step S23 includes the following steps: Step S231: calculating the progressive mean difference of the attitude angle offset on the progressive data of the trajectory motion space deviation to obtain the progressive mean difference of the attitude angle offset; Step S232: Calculating the joint angle deviation time series increment ratio on the trajectory motion space deviation progressive data to obtain the joint angle deviation time series increment ratio; Step S233: performing a manipulator trajectory jamming swing amplitude regression analysis on the progressive mean difference of the posture angle offset and the time series increment ratio of the joint angle deviation according to the trajectory jitter amplitude skew intensity data to obtain the manipulator trajectory jamming swing amplitude regression data; Step S234: performing repeated trajectory jamming amplitude transfer learning on the robot arm trajectory jamming amplitude regression data to obtain repeated trajectory jamming amplitude learning data; Step S235: performing trajectory behavior progressive deviation feature learning of the robot arm according to the repeated trajectory jamming swing amplitude learning data to obtain trajectory behavior progressive deviation learning data.

7. The robot arm trajectory tracking control method according to claim 6, characterized in that: Step S233 includes the following steps: Perform jitter spatial orientation disorder intensity analysis on the trajectory jitter amplitude skew intensity data to obtain jitter spatial orientation disorder intensity data; According to the jitter spatial orientation disorder intensity data, the spatial orientation vector angular rate mutation entropy value is analyzed on the progressive mean difference of the attitude angle offset to obtain the orientation vector angular rate mutation entropy value; The joint angle overshoot probability calculation is performed on the joint angle deviation time series increment ratio according to the jitter spatial orientation disorder intensity data to obtain the joint angle overshoot probability calculation data; Based on the azimuth vector angular rate mutation entropy value and joint angle overshoot probability calculation data, the robot arm trajectory jamming amplitude regression analysis is performed to obtain the robot arm trajectory jamming amplitude regression data.

8. The robot arm trajectory tracking control method according to claim 3, characterized in that: Step S24 includes the following steps: Step S241: performing robot arm trajectory error clustering processing on the trajectory behavior progressive deviation learning data to obtain robot arm trajectory error clustering data; Step S242: reconstructing the control logic structure of the robot arm trajectory tracking execution program based on the robot arm trajectory error clustering data to generate control program logic structure reconstruction data; Step S243: performing control logic nesting depth constraint on the control program logic structure reconstruction data to obtain program control logic depth constraint reconstruction data; Step S244: performing trajectory tracking control iterative optimization on the robot arm trajectory tracking execution program according to the program control logic depth constraint reconstruction data to obtain a trajectory tracking execution optimization program.

9. The robot arm trajectory tracking control method according to claim 1, characterized in that: Step S3 includes the following steps: Step S31: performing a program code static analysis on the trajectory tracking execution optimization program to obtain program code static analysis data; Step S32: performing functional unit integration testing on the trajectory tracking execution optimization program according to the program code static analysis data to obtain functional unit integration test data; Step S33: designing the robot arm trajectory tracking control firmware by performing the trajectory tracking optimization program based on the functional unit integration test data to obtain the robot arm trajectory tracking control firmware; Step S34: embedding the robot arm trajectory tracking control firmware into the robot arm control center to perform the robot arm trajectory tracking control.

10. A robot arm trajectory tracking control system, characterized in that: For executing the robot arm trajectory tracking control method according to claim 1, the robot arm trajectory tracking control system comprises: The trajectory jitter perception analysis module is used to obtain the robot arm operation log and the robot arm trajectory tracking execution program; extract the cycle-related trajectory motion deviation from the robot arm operation log to obtain the cycle trajectory motion deviation data; and analyze the robot arm motion trajectory jitter perception record based on the cycle trajectory motion deviation data to obtain the trajectory deviation jitter perception record data; The behavior deviation feature learning module is used to learn the robot arm's trajectory behavior deviation features based on the trajectory deviation jitter perception record data to obtain trajectory behavior progressive deviation learning data; based on the trajectory behavior progressive deviation learning data, the robot arm's trajectory tracking execution program is iteratively optimized for trajectory tracking control to obtain a trajectory tracking execution optimization program; The tracking control firmware design module is used to design the robot arm trajectory tracking control firmware for the trajectory tracking execution optimization program to obtain the robot arm trajectory tracking control firmware; the robot arm trajectory tracking control firmware is embedded into the robot arm control center to perform robot arm trajectory tracking control.

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