A hand-eye calibration method suitable for a 5-axis hybrid mechanical arm

Abstract

The application discloses a hand-eye calibration method suitable for a 5-axis hybrid mechanical arm, which comprises the following steps: analyzing coordinate conversion error distribution characteristics according to initial hand-eye calibration matrix calculation results, separating total error into two components, i.e., translation error and rotation error, through an error vector decomposition algorithm, and obtaining distribution rules and variation trends of the error in different spatial directions; establishing a calibration accuracy evaluation system according to verification results, calculating the repeat positioning accuracy and the absolute positioning accuracy of the system through statistical analysis of position deviation data obtained in multiple tests, and obtaining system performance indexes in the current calibration state; and establishing an adaptive updating mechanism for the system performance indexes, automatically triggering local updating of calibration parameters when detecting that the environmental temperature changes or the mechanical structure slightly deforms, and adjusting a compensation model through an incremental learning mode to avoid overall recalibration.

Description

Technical Field

[0001] This invention relates to the field of robot vision system technology, and in particular to a hand-eye calibration method suitable for a 5-axis hybrid robotic arm. Background Technology

[0002] In robot vision systems, hand-eye calibration is a crucial step in determining the relationship between the camera coordinate system and the robot's end effector coordinate system. Traditional hand-eye calibration methods for tandem 6-axis robotic arms typically rely on the precise motion of the robot's end effector. Using a series of known robot poses and image data acquired by the camera, mathematical optimization algorithms are employed to solve for the transformation matrix between the camera and the robot's end effector. As a core technology in modern intelligent manufacturing, robot vision systems play an irreplaceable role in key applications such as industrial automation, precision assembly, and quality inspection. This technology combines robot maneuvering capabilities with visual perception capabilities, achieving high-precision automated operations and serving as a significant driving force for the intelligent transformation of the manufacturing industry.

[0003] Current mainstream hand-eye calibration methods mainly rely on complex mathematical modeling and the collection of a large amount of calibration data. In practical applications, these methods often face problems such as unstable calibration accuracy, demanding environmental requirements, and cumbersome calibration processes. Traditional calibration methods usually require precise initial parameter settings and high professional skills from operators, making it difficult to meet the requirements of rapid deployment and high precision in industrial settings. The fundamental challenge facing robot vision systems lies in the difficulty of establishing a precise transformation relationship between the camera coordinate system and the robot coordinate system.

[0004] Due to factors such as mechanical assembly errors and thermal deformation, the initial hand-eye calibration matrix obtained through measuring tools often has significant deviations. This initial error directly affects the accuracy of all subsequent vision-guided operations. The existence of initial calibration errors further leads to the problem of cumulative errors during coordinate transformation. When the coordinates of the target point detected by the camera are transformed into the robot's base coordinate system, the transformation error will amplify with the increase of the operating distance and angle. The cumulative error problem makes it impossible for the robot to accurately reach the target position specified by the vision system, which seriously restricts the operational accuracy and reliability of the entire system. Especially in precision assembly and inspection tasks that require high-precision positioning, this error is often unacceptable.

[0005] Therefore, how to achieve high-precision registration between the camera coordinate system and the robot coordinate system and eliminate the cumulative error in the coordinate transformation process under the condition of initial measurement error has become the key issue for robot vision systems to achieve high-precision operation. Summary of the Invention

[0006] This invention provides a hand-eye calibration method suitable for a 5-axis hybrid robotic arm, mainly including the following steps:

[0007] Step 1) Use a multi-point sampling calibration algorithm to obtain the coordinate data of the robot end effector in different positions and postures. Simultaneously collect the coordinates of the corresponding image feature points through the camera to establish an initial hand-eye calibration matrix. If the number of sampling points is less than the preset threshold, continue to increase the sampling points until the matrix calculation accuracy requirements are met.

[0008] Step 2) Analyze the coordinate transformation error distribution characteristics based on the initial hand-eye calibration matrix calculation results. Use the error vector decomposition algorithm to separate the total error into two components: translation error and rotation error, and obtain the distribution law and trend of error in different spatial directions.

[0009] Step 3) Establish a dynamic compensation model based on the error change trend, and use the least squares method to fit the functional relationship between the error and the robot's operating distance and angle. If the fitting residual exceeds the preset accuracy range, adjust the fitting order and recalculate until a compensation function that meets the accuracy requirements is obtained.

[0010] Step 4) The original hand-eye calibration matrix is ​​corrected in real time by using the correction parameters calculated by the compensation function. The corresponding error compensation amount is determined according to the current robot position and the distance to the target point. The compensation amount is then superimposed on the coordinate transformation process to obtain the corrected target coordinates.

[0011] Step 5) Verify the corrected coordinate transformation results using an iterative optimization algorithm. Obtain the deviation data between the actual reached position and the theoretical target position by having the robot perform standard test actions. If the deviation exceeds the allowable range, return to step 3 to readjust the compensation model parameters.

[0012] Step 6) Establish a calibration accuracy evaluation system based on the verification results. Calculate the repeatability and absolute positioning accuracy of the system by statistically analyzing the position deviation data from multiple tests, and obtain the system performance indicators under the current calibration state.

[0013] Step 7) Establish an adaptive update mechanism for system performance indicators. When a change in ambient temperature or a slight deformation of the mechanical structure is detected, the calibration parameters are automatically updated locally. The compensation model is adjusted through incremental learning to avoid full recalibration.

[0014] Step 8) By monitoring the changes in coordinate transformation accuracy during the robot's operation in real time, the sliding window algorithm is used to analyze the positioning error trend of the most recent operations. If the error shows a systematic increase, the automatic optimization process of calibration parameters is started to ensure the long-term stable operation of the system. Beneficial effects

[0015] This invention establishes an initial hand-eye calibration matrix by collecting coordinate data of the robot's end effector at different positions and the coordinates of corresponding image feature points. For coordinate transformation errors, this invention analyzes their distribution characteristics and establishes a dynamic compensation model. It uses the least squares method to fit the functional relationship between the error and the robot's operating parameters, and performs real-time correction of the original calibration matrix using a compensation function. An iterative optimization algorithm is then used to verify the correction results. This invention also establishes a calibration accuracy evaluation system and an adaptive update mechanism, which can automatically trigger local parameter updates based on environmental changes and initiate an automatic optimization process by monitoring accuracy changes in real time. This method significantly improves the accuracy and stability of robot hand-eye calibration, achieving long-term reliable operation. Detailed Implementation

[0016] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] A hand-eye calibration method applicable to a 5-axis hybrid robotic arm may specifically include the following steps:

[0018] Step 1) Use a multi-point sampling calibration algorithm to obtain the coordinate data of the robot end effector in different positions and postures. Simultaneously collect the coordinates of the corresponding image feature points through the camera to establish an initial hand-eye calibration matrix. If the number of sampling points is less than the preset threshold, continue to increase the sampling points until the matrix calculation accuracy requirements are met.

[0019] Specifically, a multi-point sampling calibration algorithm is used to acquire coordinate data of the robot's end effector at different positions and postures. Simultaneously, the coordinates of corresponding image feature points are acquired using a camera to obtain an initial dataset. The initial dataset is then processed using the least squares method to construct a hand-eye calibration matrix and determine the initial matrix parameters. If the calculation error of the initial matrix exceeds a preset threshold, an iterative optimization algorithm is used to adjust the sampling point positions, acquire new coordinate data and feature point coordinates, and update the hand-eye calibration matrix based on the newly acquired coordinate data and feature point coordinates to obtain an optimized matrix. The optimized matrix is ​​then decomposed using a singular value decomposition algorithm to extract the main feature vectors and determine whether the matrix accuracy meets the requirements. If the matrix accuracy is lower than the preset threshold, the sampling point distribution strategy is adjusted based on the distribution characteristics of the feature vectors to acquire supplementary coordinate data. The hand-eye calibration matrix is ​​then reconstructed using the supplementary coordinate data to obtain the final calibration result.

[0020] In one possible implementation of the present invention, the robot end effector coordinate data is obtained through a multi-point sampling calibration algorithm. The core is to ensure that the sampling points cover the diversity of the workspace. For example, in an industrial assembly scenario, the robot end effector can select 10 different positions in the workspace, such as spatial coordinates (100, 200, 300) mm, (150, 250, 350) mm, etc., and combine them with different attitude angles, such as rotation around the Z-axis at 0°, 45°, and 90°, to obtain three-dimensional coordinate data. At the same time, the camera synchronously collects image feature points, such as circular markers on the workpiece, and records pixel coordinates such as (320, 240) and (400, 300). These data constitute the initial dataset, providing the foundation for subsequent calibration. A diverse distribution of sampling points improves the robustness of the calibration matrix and reduces the bias from sampling in a single region. Specifically, the least squares method is used to process the initial dataset and construct the hand-eye calibration matrix. For example, based on 10 sets of coordinate data and corresponding feature points, the transformation matrix from the robot's end effector to the camera coordinate system is calculated. The initial matrix parameters may include rotation and translation components, such as the rotation matrix R and the displacement vector T. Error evaluation is performed by comparing the deviation between the predicted feature point positions and the actual positions. If the average error exceeds a preset threshold of 0.5 mm, optimization is required. The least squares method improves the initial accuracy of the matrix by optimizing the sum of squared residuals, laying the foundation for subsequent iterations.

[0021] In one embodiment of the present invention, if the initial matrix error exceeds the standard, the iterative optimization algorithm can adjust the sampling point positions. For example, if the initial sampling points are concentrated in the central area of ​​the workspace, the error may be too high due to insufficient boundary data. Through optimization using a genetic algorithm, boundary points such as (50, 50, 50) mm and (200, 300, 400) mm are reselected to obtain new coordinates and feature point data. This strategy can effectively cover the workspace boundary, improve the matrix's adaptability to complex postures, and reduce the error of the updated hand-eye calibration matrix to 0.3 mm, significantly improving calibration accuracy. For example, the singular value decomposition algorithm decomposes the optimized matrix and extracts the main eigenvectors to evaluate the matrix accuracy. After decomposition, if the distribution of the main eigenvectors shows that the matrix does not adequately describe the transformation in certain directions, such as a small eigenvalue in the Z-axis direction, it indicates that the sampling points are insufficiently distributed in the Z-axis direction. In this case, the adjustment strategy can increase the sampling points in the Z-axis direction, such as (100, 200, 400) mm, and reconstruct the matrix after supplementing the data. This method accurately locates the root cause of the problem through eigenvector analysis, ensuring that the matrix accuracy meets the requirement of 0.2 mm. The preset threshold for mm.

[0022] In one possible implementation of this invention, the hand-eye calibration matrix is ​​reconstructed after supplementing coordinate data to obtain the final calibration result. For example, after adding 5 sets of sampling points, the translation error of the updated matrix is ​​reduced to 0.15 mm, and the rotation error is reduced to 0.1°. The final calibration result is applied to robot vision-guided tasks, such as precise workpiece grasping, improving positioning accuracy by 30% and significantly reducing the positioning failure rate in production. The strategy of supplementing data ensures that the matrix fully covers the workspace, enhancing the stability and reliability of the system in complex environments. It should be noted that the above method forms a closed-loop calibration process through multi-point sampling, iterative optimization, and feature vector analysis. Each step supports each other, ensuring that the accuracy of the calibration matrix is ​​gradually improved, ultimately achieving high-precision hand-eye coordination. The advantage of this method is its strong adaptability, which can cope with different robot and camera configurations and is widely applicable to industrial automation scenarios.

[0023] Step 2) Analyze the coordinate transformation error distribution characteristics based on the initial hand-eye calibration matrix calculation results. Use the error vector decomposition algorithm to separate the total error into two components: translation error and rotation error, and obtain the distribution law and trend of error in different spatial directions.

[0024] Coordinate transformation error data is obtained through an initial hand-eye calibration matrix. Translation and rotation errors are separated using an error vector decomposition algorithm to obtain error components. The distribution characteristics of translation and rotation errors in the spatial coordinate system are extracted from the error components to determine the error distribution characteristics. If the error distribution characteristics exceed a preset threshold, spatial direction decomposition is performed on the translation and rotation errors to obtain the spatial direction distribution. The magnitude of the error vector in each direction is calculated based on the spatial direction distribution to obtain the distribution law extraction results. Principal component analysis is used to perform dimensionality reduction processing on the distribution law extraction results to obtain change trend analysis data. The error change curve is fitted through the change trend analysis data to determine the change trend of the error in the spatial direction. Key feature points are extracted from the change trend to generate a feature description of the spatial direction error distribution.

[0025] Specifically, in hand-eye calibration scenarios, obtaining coordinate transformation error data through an initial hand-eye calibration matrix is ​​fundamental to achieving high-precision robot operation. For example, in an industrial robot assembly scenario, the robotic arm locates a target object using a vision system. The calibration matrix associates the camera coordinate system with the robotic arm coordinate system. Coordinate transformation error data is typically obtained by repeatedly measuring the deviation between the actual and theoretical positions. Assuming the robotic arm positions a workpiece in space with theoretical coordinates of (100, 200, 300) mm and actual measured coordinates of (102, 199, 301) mm, the error vector is (2, -1, 1) mm. This process can be achieved by collecting multiple sets of data using high-precision sensors to generate an error dataset. A key step is to use an error vector decomposition algorithm to separate translation and rotation errors. Translation error refers to positional deviation, and rotation error refers to attitude deviation. For example, in the above example, the error vector is (2, -1, 1). mm can be directly considered as translation error, while rotation error can be calculated using the Euler angle deviation of the attitude matrix. Assuming the calibration matrix indicates that the robotic arm's rotation deviation around the Z-axis is 0.5 degrees and around the X and Y axes is 0.2 degrees, the error components can be separated using a vector decomposition algorithm. This separation helps to analyze the impact of translation and rotation on system accuracy separately, improving calibration optimization efficiency. Extracting spatial distribution characteristics from the error components requires analyzing the error's pattern in the three-dimensional coordinate system. Specifically, statistical analysis can be used to calculate the mean and variance of translation error along the X, Y, and Z axes. For example, after collecting 100 sets of data, it is found that the mean translation error on the X-axis is 2 mm with a variance of 0.5 mm², and the mean on the Y-axis is -1 mm with a variance of 0.3 mm², indicating that the X-axis error distribution is more dispersed. A similar analysis of rotation error can be performed, analyzing the deviation distribution around each axis. If the error distribution characteristics exceed a preset threshold (e.g., the mean translation error exceeds 3...), further analysis can be conducted. (For errors exceeding 1 mm or rotational error exceeding 1 degree), further decomposition of the spatial distribution is necessary. For example, projecting the translation error along the X, Y, and Z axes yields the magnitude of the error vector in each direction. Analyzing its distribution pattern identifies the main error sources. Principal component analysis (PCA) is then used to reduce the dimensionality of the distribution results, effectively extracting the trend. For instance, PCA reveals that X-axis translational error and Z-axis rotational error contribute 80% of the error variation, indicating that optimization should focus on these two directions. The dimensionality-reduced data can be used to fit the error variation curve. For example, the fitting result shows that the X-axis error increases linearly with the workpiece position, with a slope of 0.02 mm / mm. This curve reveals the variation of error with spatial position, aiding in error behavior prediction. Extracting key feature points from the trend to generate an error distribution feature description is the final step.For example, feature points can include error peak points, inflection points, etc. Suppose that the fitted curve shows that the X-axis error reaches a peak of 3.5 mm at the workpiece position (150, 200, 300) mm. This feature point can be used to optimize the calibration algorithm, adjust the robot arm's motion path, and reduce errors at specific positions. This method significantly improves the robot's positioning accuracy and reduces the assembly failure rate. It should be noted that the above process, through decomposition, analysis, and dimensionality reduction, gradually focuses on the key sources of error, optimizes the calibration matrix, and ensures high-precision operation. Each step supports each other, forming a complete error analysis and optimization chain, which significantly improves system stability and production efficiency.

[0026] Step 3) Establish a dynamic compensation model based on the error change trend, and use the least squares method to fit the functional relationship between the error and the robot's operating distance and angle. If the fitting residual exceeds the preset accuracy range, adjust the fitting order and recalculate until a compensation function that meets the accuracy requirements is obtained.

[0027] The robot acquires its operating distance and angle data, and uses sensors to collect real-time operating parameters. Noise is removed through data preprocessing to obtain a standardized operating dataset. Based on this dataset, an initial fitting function for the operating distance, angle, and error is constructed using the least squares method, determining the initial fitting parameters. For this initial fitting function, the fitting residuals are calculated, and compared with a preset accuracy threshold to determine if the accuracy requirements are met. If the residuals exceed the threshold, the fitting order is adjusted, and the least squares method is used again to calculate the fitting function, resulting in updated fitting parameters. Based on these updated parameters, a dynamic error compensation model is constructed, generating a compensation function. This compensation function is used to correct errors in the real-time operating distance and angle data, obtaining the corrected operating parameters. These corrected parameters are then used to update the robot control commands, resulting in an optimized motion trajectory.

[0028] For example, in the process of collecting distance and angle data for robot operations, sensors are key equipment, typically using LiDAR or ultrasonic sensors to acquire high-precision real-time data. Suppose that in a scenario where an industrial robot is grasping a workpiece, the LiDAR collects distance and angle data at a frequency of 100 times per second, resulting in a raw dataset containing noise. In the data preprocessing stage, outliers are removed using median filtering; for example, abrupt changes exceeding 5% of the normal range in the distance data are eliminated, resulting in a smooth, standardized operational dataset. This preprocessing ensures the reliability of the data in subsequent analysis and avoids noise interference with the fitting results. Specifically, when constructing the initial fitting function based on the standardized dataset, the least squares method is used to establish a model of the relationship between distance, angle, and error. For example, in the movement of a robot arm, assuming the operating distance range is 0.5 meters to 2 meters and the angle range is -45 degrees to 45 degrees, a quadratic function is fitted using the least squares method to initially determine parameters such as the distance coefficient and angle offset. In the residual analysis stage, the difference between the predicted value and the actual value of the fitted function is calculated. Assuming the mean residual is 0.02 meters and the standard deviation is 0.01 meters, if the preset accuracy threshold is 0.015 meters, the residual exceeds the limit. In this case, the fitted function is adjusted to a cubic function, and after recalculation, the mean residual decreases to 0.01 meters, meeting the accuracy requirements. In one embodiment, a dynamic error compensation model is constructed based on the updated fitted parameters. For example, by analyzing the residual distribution, it is found that the error increases non-linearly at greater distances, and a compensation function can be designed to dynamically adjust the control parameters. Assuming the error is 0.03 meters at a distance of 1.8 meters, the compensation function corrects this error to within 0.005 meters. The corrected parameters are directly used to update the robot control commands, such as adjusting the joint angles of the robotic arm and optimizing the motion trajectory, thereby improving the positioning accuracy of the workpiece gripping to 0.002 meters. This dynamic compensation significantly improves the stability of robot operation. For example, in scenarios involving updating the motion trajectory, the corrected parameters can be used to adjust the path planning of the robot's end effector. Suppose a robot needs to complete a circular trajectory movement within a plane. The original trajectory has a radius deviation of 0.05 meters due to errors, which is reduced to 0.01 meters after correction. This optimized trajectory ensures repeatability in workpiece grasping, improving production efficiency. It's important to note that the real-time nature of error correction relies on the high-frequency acquisition and rapid computation capabilities of sensors, which is particularly crucial in high-precision assembly tasks. Specifically, the advantage of the above method lies in its data-driven approach, dynamically adapting to different operating scenarios. For example, the error distribution may change with different workpiece sizes or weights; the dynamic compensation model can adjust parameters based on real-time data to maintain high precision. This flexibility makes it applicable to various industrial robot tasks, such as welding, assembly, or handling, significantly improving operational consistency and reliability.

[0029] Step 4) The original hand-eye calibration matrix is ​​corrected in real time by using the correction parameters calculated by the compensation function. The corresponding error compensation amount is determined according to the current robot position and the distance to the target point. The compensation amount is then superimposed on the coordinate transformation process to obtain the corrected target coordinates.

[0030] Specifically, correction parameters are calculated using an error compensation function, and the position error is obtained from the distance between the robot's current position and the target point. If the position error exceeds a preset threshold, correction parameters are generated based on the error compensation function. The correction parameters are used to adjust the hand-eye calibration matrix in real time, resulting in an adjusted calibration matrix. A coordinate system transformation is performed based on the adjusted calibration matrix to obtain initial transformed coordinates. The error compensation amount is calculated from the initial transformed coordinates and the distance to the target point. If the error compensation amount meets the dynamic adjustment conditions, a compensation vector is generated. The compensation vector is superimposed onto the initial transformed coordinates to obtain the corrected target coordinates. The corrected target coordinates are used to update the robot's motion control parameters, generate control commands, drive the robot's movement according to the control commands, obtain real-time position feedback, and determine whether the position error meets the accuracy requirements.

[0031] For example, during robot hand-eye calibration, when calculating correction parameters using the error compensation function, the distance between the current position and the target point can first be obtained based on sensor data. Assuming the robot's current coordinates are (100, 200, 50) mm and the target point's coordinates are (105, 205, 55) mm, the calculated position error is (5, 5, 5) mm. If the preset threshold is 3 mm, the error exceeds the threshold, triggering the error compensation function. The error compensation function can generate correction parameters based on historical calibration data and a linear interpolation method. For example, an adjustment coefficient of 0.8 would generate a correction vector of (4, 4, 4) mm. This method uses historical data analysis to ensure that the correction parameters are consistent with the actual error trend. In one possible implementation, when adjusting the hand-eye calibration matrix, the correction parameters can be used to update the matrix parameters. Assume the original calibration matrix is ​​a 4×4 homogeneous transformation matrix containing rotation and translation components. The translation components are adjusted by modifying parameters, for example, updating the translation vector from (10, 20, 30) mm to (14, 24, 34) mm. The adjusted matrix can more accurately describe the relative positional relationship between the camera and the robot's end effector, thereby improving the accuracy of coordinate transformation. Specifically, when performing coordinate system transformation, the initial transformed coordinates can be calculated using the adjusted calibration matrix. For example, if the target point's coordinates in the camera coordinate system are (50, 60, 70) mm, after transformation, the initial transformed coordinates in the robot coordinate system are (48, 58, 68) mm. Then, the error compensation is calculated based on the distance to the target point, assuming the compensation is (2, 2, 2) mm. If the dynamic adjustment requires the compensation to be less than 5 mm, a compensation vector of (2, 2, 2) mm is generated and superimposed on the initial transformed coordinates to obtain the corrected target coordinates (50, 60, 70) mm. This method, through multiple iterative optimizations, ensures that the coordinate transformation result closely approximates the target point. For example, when updating robot motion control parameters, control commands can be generated based on the corrected target coordinates. Assuming the robot uses joint angle control, the corrected coordinates (50, 60, 70) mm can be converted into joint angle adjustments, such as joint 1 rotating 2 degrees and joint 2 rotating 1.5 degrees. After the control command drives the robot's movement, real-time position feedback is obtained through a laser sensor. Assuming the feedback coordinates are (50.1, 60.2, 69.9) mm, the calculated position error is (0.1, 0.2, -0.1) mm. If the preset accuracy requirement is less than 0.5 mm, the requirement is met, indicating that the control command is effective. This process verifies the accuracy of the compensation vector through real-time feedback. In one possible implementation, if the position error does not meet the accuracy requirement, the compensation function can be further optimized.For example, by introducing a weighting factor to adjust the compensation vector, the correction weight for the key axis can be increased. For instance, a weight of 1.2 can be assigned to the Z-axis error to generate a new compensation vector of (2, 2, 2.4) mm. This method improves the stability of robot motion by dynamically adjusting the weights to adapt to the error characteristics in different directions. Specifically, the design of the feedback mechanism can be combined with multi-sensor fusion. For example, a laser sensor provides high-precision distance data, and a vision sensor provides angle information. After fusion, a comprehensive position feedback is generated. This method improves the robustness of error judgment through the complementarity of multi-source data, thereby optimizing the generation efficiency of control commands.

[0032] Step 5) Verify the corrected coordinate transformation results using an iterative optimization algorithm. Obtain the deviation data between the actual reached position and the theoretical target position by having the robot perform standard test actions. If the deviation exceeds the allowable range, return to Step 3 to readjust the compensation model parameters.

[0033] The robot performs standard test actions to acquire actual arrival position data and theoretical target position data. The deviation between the two is calculated, and an iterative optimization algorithm is used to process the deviation data, generating a position deviation analysis result. It is determined whether the deviation exceeds a preset threshold. If the deviation exceeds the preset threshold, a gradient descent algorithm is used to adjust the compensation model parameters, generating updated compensation model parameters. The coordinate transformation is then re-executed using the updated compensation model parameters to generate a new coordinate transformation result. The robot performs the standard test actions again to acquire new actual arrival position data, and the deviation from the theoretical target position is calculated. If the new deviation data is still outside the preset threshold, the gradient descent algorithm is repeatedly executed to adjust the compensation model parameters, obtaining optimized compensation model parameters. The final coordinate transformation is then performed using the optimized compensation model parameters, generating a verification result output.

[0034] In one possible implementation of this invention, the process of obtaining actual arrival position data and theoretical target position data by having a robot perform standard test actions can be understood as a fundamental step in accuracy verification. For example, assuming an industrial robot needs to complete a point-to-point movement task in a two-dimensional plane, the standard test action can be designed to move from the origin (0,0) to the target point (100,100) mm. The actual arrival position is recorded as (99.5,100.2) mm by a high-precision laser rangefinder, while the theoretical target position is (100,100) mm. The deviation data is calculated by comparing the two coordinates, i.e., the x-axis deviation is -0.5 mm and the y-axis deviation is 0.2 mm. The acquisition of this deviation data provides a basis for subsequent analysis, emphasizing the importance of high-precision measuring equipment in data acquisition. For example, when using an iterative optimization algorithm to process the deviation data, an optimization method based on the least squares method can be selected. Specifically, the system will summarize the deviation data of multiple test actions, for example, the x-axis deviations of 10 tests are -0.5, -0.4, -0.6 mm, etc., forming a deviation dataset. The iterative optimization algorithm analyzes this data to determine the distribution pattern of the deviation and generates position deviation analysis results. If the analysis results show that the average x-axis deviation exceeds a preset threshold of 0.3 mm, subsequent adjustments to the compensation model are triggered. This method ensures the comprehensiveness of the deviation analysis and helps to identify systematic errors. In one embodiment of the invention, if the deviation exceeds the preset threshold, the gradient descent algorithm is used to adjust the compensation model parameters. For example, the initial parameters of the compensation model may include a coordinate transformation scaling factor and an offset of 1.0 and 0 mm, respectively. Based on the deviation data, the gradient descent algorithm iteratively adjusts the scaling factor to 1.005 and the offset to -0.2 mm. This adjustment process gradually optimizes and reduces the deviation, ensuring that the model is closer to the actual motion characteristics. The optimized parameters improve the accuracy of the coordinate transformation. Specifically, when re-performing the coordinate transformation with the updated compensation model parameters, the robot calculates the target coordinates based on the new scaling factor and offset. For example, if the input target point is (100, 100) mm, the adjusted model may output coordinates as (100.5, 99.8) mm. This new coordinate transformation result is closer to actual needs, reflecting the effectiveness of model optimization. For example, when the robot performs a standard test action again to verify the new model, the actual position reached may be recorded as (100.1, 100.0) mm. The calculated new deviation is 0.1 mm on the x-axis and 0.0 mm on the y-axis, both within the preset threshold of 0.3 mm. This verification process confirms the reliability of the model adjustment and reduces the need for repeated optimization. In one possible implementation of this invention, if the new deviation data still exceeds the threshold, the gradient descent algorithm is repeatedly executed. For example, when the x-axis deviation is 0.4 mm, the system further fine-tunes the scaling factor to 1.006 and the offset to -0.25 mm.This iterative optimization ensures that the deviation gradually converges, improving the robustness of the system. Finally, the final coordinate transformation is performed through the optimized compensation model parameters to generate the verification result output. For example, the robot moves to (100.05, 99.95) mm based on the final parameters, with a deviation of only 0.05 mm, meeting the high precision requirements. This method, through multiple rounds of verification and optimization, ensures the stability and accuracy of the coordinate transformation, providing reliable support for robot motion control.

[0035] Step 6) Establish a calibration accuracy evaluation system based on the verification results. Calculate the repeatability and absolute positioning accuracy of the system by statistically analyzing the position deviation data from multiple tests, and obtain the system performance indicators under the current calibration state.

[0036] Position deviation data is collected from multiple tests using sensors. The mean and standard deviation are used to calculate the data distribution characteristics. Based on these characteristics, a normal distribution model is used to analyze the position deviation data and determine the statistical characteristics of repeatability accuracy. If the statistical characteristics of repeatability accuracy exceed a preset threshold, the calibration parameters are optimized using the least squares method to obtain an adjusted calibration model. Using this adjusted calibration model, test data collection is repeated to obtain new position deviation data. Based on this new data, analysis of variance is used to calculate the trend of absolute positioning accuracy. If the trend of absolute positioning accuracy does not meet a preset standard, the calibration parameters are further optimized using a gradient descent algorithm to obtain an optimized calibration model. Finally, using this optimized calibration model, final test data collection is performed to obtain system performance indicators.

[0037] In one possible implementation of the present invention, collecting position deviation data from multiple tests using sensors is a fundamental step in ensuring the accuracy of robot motion control. For example, when an industrial robot is performing a point-to-point movement task, the sensor can be a high-precision encoder installed at the robot's joints to record the actual position of each movement. Suppose that the robot moves 100 mm from the origin to the target point, and the sensor continuously collects test data 10 times, recording the actual positions as 99.8 mm, 100.1 mm, 99.7 mm, etc. This data acquisition method emphasizes the stability and high-frequency sampling capability of the sensor, which helps to capture subtle changes in positional deviation and provides a reliable data foundation for subsequent analysis. For example, when analyzing data distribution characteristics using the mean and standard deviation calculation method, the system summarizes the deviation data from multiple tests. Assuming the deviation data from 10 tests are -0.2 mm, 0.1 mm, -0.3 mm, etc., the calculated mean is -0.1 mm and the standard deviation is 0.15 mm. These statistical indicators reflect the central tendency and dispersion of the deviation. The mean indicates a slight negative bias in the system, while the standard deviation shows the fluctuation range of the data. This method provides an intuitive basis for subsequent modeling by quantifying the deviation distribution. In another possible implementation, when analyzing positional deviation data based on a normal distribution model, the system assumes that the deviation data conforms to the characteristics of a normal distribution. For example, based on the aforementioned mean of -0.1 mm and standard deviation of 0.15 mm, the system can plot the probability density curve of the deviation and determine whether the deviation range within the 95% confidence interval meets the preset threshold of 0.2 mm. If the deviation range is found to exceed the threshold... This indicates insufficient repeatability in positioning accuracy. This analysis method reveals the regularity of the deviation through statistical models, providing theoretical support for optimizing calibration parameters. For example, when optimizing calibration parameters using the least squares method, the system adjusts the model parameters based on the deviation dataset. Assuming the calibration model includes a scaling factor with an initial value of 1.0, the system iteratively calculates using the least squares method based on the deviation data to adjust the scaling factor to 1.003. This method ensures that the calibration model is closer to the actual motion characteristics by minimizing the sum of squared deviations. The optimized calibration model can reduce systematic errors and improve positioning stability. In one possible implementation, when re-executing test data acquisition, the robot uses the adjusted calibration model. For example, the target point remains 100 mm, but the new actual positions recorded by the sensors are 99.9 mm, 100.0 mm, etc. The deviation data is significantly reduced. This re-acquisition process verifies the effectiveness of the calibration model and provides data support for further analysis. For example, when using the analysis of variance method to calculate the trend of absolute positioning accuracy, the system compares the variance of the deviations from multiple tests.Assuming the variance of the new deviation data decreases from 0.0225 to 0.01, it indicates that the positioning accuracy is stabilizing. This analysis method clearly demonstrates the effect of calibration model optimization by quantifying the dispersion of the deviation. In one possible implementation, if the absolute positioning accuracy is not met, the system further optimizes the calibration parameters using a gradient descent algorithm. For example, based on the new deviation data, the scaling factor is fine-tuned from 1.003 to 1.004. This iterative optimization method gradually converges the deviation by adjusting the parameters step by step, ensuring the robustness of the model. For instance, if the final test data is based on the optimized calibration model, the deviation data recorded by the sensor may be 0.05 mm, -0.03 mm, etc., and the system performance indicators show that the deviations are all within 0.1 mm. This result verifies the high accuracy of the optimized model and provides a reliable guarantee for robot motion control.

[0038] Step 7) Establish an adaptive update mechanism for system performance indicators. When a change in ambient temperature or a slight deformation of the mechanical structure is detected, the calibration parameters are automatically updated locally. The compensation model is adjusted through incremental learning to avoid full recalibration.

[0039] Ambient temperature and mechanical structure deformation data are acquired in real time by sensors. The rate of temperature change and the degree of deformation are calculated to obtain environmental change characteristics. If the environmental change characteristics exceed a preset threshold, an adaptive calibration process is triggered to determine the set of calibration parameters that need to be updated. An incremental learning algorithm is used to update the compensation model, extracting feature vectors from the calibration parameter set to obtain updated model parameters. The compensation model is adjusted using the updated model parameters to generate a new control signal, which is output to the system execution unit. Feedback data is obtained from the system execution unit, performance index deviation is calculated, and it is determined whether the stable control requirements are met. If the performance index deviation exceeds a preset range, the calibration parameters are iteratively optimized to obtain new environmental change characteristics. Based on the new environmental change characteristics, the above process is repeated to output the final system control signal.

[0040] For example, in precision machining scenarios, real-time acquisition of ambient temperature and mechanical deformation data via sensors can effectively capture dynamic changes during system operation. Ambient temperature data is typically collected by high-precision thermocouple sensors. Assuming a machining equipment is operating, the ambient temperature rises from 20°C to 25°C, with a temperature change rate of 0.5°C / minute. Simultaneously, mechanical deformation data is measured by a laser displacement sensor, detecting a spindle deformation of 0.02 mm. These data together constitute the environmental change characteristics, reflecting the potential impact of temperature on mechanical precision. It should be noted that the temperature change rate and deformation degree are key indicators for evaluating system stability. If the temperature change rate exceeds 0.3°C / minute or the deformation exceeds 0.015 mm, the system may experience machining errors due to thermal expansion or mechanical stress. In one possible implementation, if the environmental change characteristics exceed a preset threshold, such as a temperature change rate reaching 0.4°C / minute, an adaptive calibration process is triggered. The calibration parameter set may include the spindle's thermal compensation coefficient and the servo motor's control gain. Assuming analysis determines that the thermal compensation coefficient needs to be adjusted from 0.8 to 0.85 to offset the expansion caused by temperature increases, when updating the compensation model using an incremental learning algorithm, the system extracts feature vectors from historical data, such as the correlation coefficient between the temperature change rate and deformation, to generate new model parameters. The advantage of this approach is its ability to dynamically adapt to environmental changes and avoid frequent recalibration. For example, after adjusting the compensation model with the updated model parameters, a new control signal is generated to drive the servo motor to adjust the spindle position. Assuming the spindle offset decreases from 0.02 mm to 0.01 mm after adjustment, it indicates that the control signal effectively reduces the impact of deformation. After obtaining feedback data from the system execution unit, the performance index deviation is calculated; for example, the workpiece dimensional error decreases from 0.03 mm to 0.01 mm, meeting the stable control requirements. If the deviation still exceeds the standard, for example, the dimensional error is 0.02 mm, then the calibration parameters are iteratively optimized, and the environmental change characteristics are recalculated. More preferably, the iterative optimization can be based on the temperature-deformation mapping relationship in historical data, adjusting the compensation coefficient to 0.87 to further reduce the error. In one embodiment, the new environmental change characteristics may show that the temperature change rate drops to 0.2°C / min and the deformation stabilizes at 0.01 mm. At this time, the system repeats the above process and outputs the final control signal to ensure long-term stability of processing accuracy. The advantage of this method is that through continuous monitoring and dynamic adjustment, the system can maintain high-precision operation in complex environments, significantly improving processing quality and equipment reliability.

[0041] Step 8) By monitoring the changes in coordinate transformation accuracy during the robot's operation in real time, the sliding window algorithm is used to analyze the positioning error trend of the most recent operations. If the error shows a systematic increase, the automatic optimization process of calibration parameters is started to ensure the long-term stable operation of the system.

[0042] The robot's coordinate transformation data during operation is collected in real time by sensors and stored as a time series dataset to obtain the original coordinate dataset. A sliding window algorithm is used to process the original coordinate dataset, calculating the mean and standard deviation of the positioning error within a specified time window to determine the error statistical characteristics. If the mean of the error statistical characteristics exceeds a preset threshold and the standard deviation continues to increase, it is determined that the error is showing a systematic increase, generating a trigger signal. Based on the trigger signal, initial values ​​of calibration parameters are obtained from a preset parameter library, and the calibration parameters are optimized using a gradient descent algorithm to obtain an optimized parameter set. The robot's coordinate transformation model is updated using the optimized parameter set, and the positioning error is recalculated to obtain updated error data. The sliding window algorithm is used to analyze the updated error data. If the mean error is lower than a preset threshold, it is confirmed that the system has returned to a stable operating state. The optimized operating state is continuously monitored through time series analysis. If a new error growth trend is detected, the above optimization process is repeated to obtain a stable system operating state.

[0043] For example, during robot operations, real-time acquisition of coordinate transformation data by sensors is fundamental to the entire process. Sensors can be deployed on key joints or moving parts of the robot to continuously record changes in position coordinates, forming a time-series dataset. For instance, suppose an industrial robot is used for precision positioning tasks on an assembly line. The sensors acquire coordinate data 10 times per second, recording the three-dimensional coordinate values ​​of the robot's end effector. This data is stored as a time-series dataset, providing the initial basis for subsequent analysis. It is understood that the completeness and accuracy of the time-series data are crucial for subsequent error analysis. In one embodiment, when processing the original coordinate dataset using a sliding window algorithm, a time window can be set to 5 seconds, covering 50 data points. The sliding window algorithm calculates the mean and standard deviation of the positioning error within each window by successively moving the window. For example, the mean error recorded within a certain window is 0.5 mm, and the standard deviation is 0.2 mm. Of course, it should be noted that the mean reflects the overall level of error deviation, while the standard deviation indicates the degree of error dispersion. If the mean gradually increases and the standard deviation continues to expand, it may mean that the robot positioning system is affected by external factors or internal parameter drift. For example, if the mean in the error statistics exceeds the preset threshold of 0.4 mm, and the standard deviation increases from 0.2 mm to 0.3 mm and continues to rise, then it is judged that the error shows a systematic increase. The systematic increase may be due to factors such as environmental vibration, load changes, or mechanical wear. In one possible implementation of the present invention, the system generates a trigger signal to indicate that the coordinate transformation model needs to be adjusted. Understandably, timely detection of a systematic error growth trend helps prevent further deterioration in positioning accuracy. In one embodiment, when obtaining initial values ​​of calibration parameters from a preset parameter library, a suitable parameter set can be selected based on the robot's current task type. For example, for high-precision assembly tasks, the initial values ​​stored in the parameter library may be empirical values ​​derived from historical calibration data, such as joint angle offset of 0.1 degrees and coordinate scaling factor of 1.02. When these parameters are optimized using the gradient descent algorithm, the system gradually adjusts the parameter values, causing the positioning error to gradually decrease. Understandably, the gradient descent algorithm helps to quickly converge to a suitable parameter set by iteratively finding the optimal solution to the error.For example, after updating the robot coordinate transformation model with the optimized parameter set, the positioning error is recalculated. Assuming the average error within a certain time window decreases from 0.5 mm to 0.3 mm, below the preset threshold of 0.4 mm, it should be noted that the decrease in the average error indicates that the coordinate transformation model has better adapted to the current operating state. In one possible implementation, the system continuously analyzes the updated error data using a sliding window algorithm to confirm that the average error is stable at around 0.3 mm and the standard deviation no longer increases significantly, indicating that the system has returned to stable operation. In one embodiment of the invention, time series analysis is used to continuously monitor the optimized operating state; for example, the system... The system generates an error trend report every minute, observing changes in the mean and standard deviation of the error. If a new error growth trend is detected, such as the mean increasing from 0.3 mm to 0.45 mm and the standard deviation increasing from 0.15 mm to 0.25 mm, it indicates that there may be new interfering factors. It should be noted that continuous monitoring can promptly identify potential problems and trigger a new round of optimization processes. For example, the system retrieves initial values ​​from the parameter library again, combines them with the current error data for optimization, and adjusts the coordinate transformation model until the mean error is lower than the threshold again. It can be understood that the above process forms a closed-loop mechanism through real-time data acquisition, error analysis, parameter optimization, and continuous monitoring. For example, the data collected by the sensors provides a basis for error analysis, the sliding window algorithm extracts error features, triggers a signal to start the optimization process, the gradient descent algorithm adjusts the parameters, and after updating the model, the stability is verified by time series analysis. In one possible implementation, if the robot operates in a high-temperature or high-load environment for a long time, the system can dynamically adjust the threshold according to historical data, such as adjusting the average error threshold from 0.4 mm to 0.5 mm to adapt to environmental changes. It should be noted that this adaptive mechanism can flexibly cope with the positioning needs under different working conditions.

[0044] Obviously, those skilled in the art can make various modifications and variations to the embodiments of this application without departing from the spirit and scope of the embodiments of this application. Therefore, if these modifications and variations to the embodiments of this application fall within the scope of the claims of this application and their equivalents, this application also intends to include these modifications and variations.

Claims

1. A hand-eye calibration method suitable for a 5-axis hybrid robotic arm, characterized in that, The method includes: Step 1) Using a multi-point sampling calibration algorithm to obtain coordinate data of the robot end effector at different positions and postures, synchronously collecting the coordinates of corresponding image feature points through a camera, establishing an initial hand-eye calibration matrix, and if the number of sampling points is less than a preset threshold, continuing to increase the sampling points until the matrix calculation accuracy requirements are met. Step 2) Analyze the coordinate transformation error distribution characteristics based on the initial hand-eye calibration matrix calculation results. Use the error vector decomposition algorithm to separate the total error into two components: translation error and rotation error, and obtain the distribution law and trend of error in different spatial directions. Step 3) Establish a dynamic compensation model based on the error change trend, and use the least squares method to fit the functional relationship between the error and the robot's operating distance and angle. If the fitting residual exceeds the preset accuracy range, adjust the fitting order and recalculate until a compensation function that meets the accuracy requirements is obtained. Step 4) The original hand-eye calibration matrix is ​​corrected in real time by using the correction parameters calculated by the compensation function. The corresponding error compensation amount is determined according to the current robot position and the distance to the target point. The compensation amount is then superimposed on the coordinate transformation process to obtain the corrected target coordinates. Step 5) Verify the corrected coordinate transformation results using an iterative optimization algorithm. Obtain the deviation data between the actual reached position and the theoretical target position by having the robot perform standard test actions. If the deviation exceeds the allowable range, return to Step 3) to readjust the compensation model parameters. Step 6) Establish a calibration accuracy evaluation system based on the verification results. Calculate the repeatability and absolute positioning accuracy of the system by statistically analyzing the position deviation data from multiple tests, and obtain the system performance indicators under the current calibration state. Step 7) Establish an adaptive update mechanism for system performance indicators. When a change in ambient temperature or a slight deformation of the mechanical structure is detected, the calibration parameters are automatically updated locally. The compensation model is adjusted through incremental learning to avoid full recalibration. Step 8) By monitoring the changes in coordinate transformation accuracy during the robot's operation in real time, the sliding window algorithm is used to analyze the positioning error trend of the most recent operations. If the error shows a systematic increase, the automatic optimization process of calibration parameters is started to ensure the long-term stable operation of the system.

2. The hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 1, characterized in that, Step 1) further includes: obtaining coordinate data of the robot end effector at different positions and postures through a multi-point sampling calibration algorithm, and simultaneously using a camera to collect the coordinates of corresponding image feature points to obtain an initial dataset; The initial dataset was processed using the least squares method to construct a hand-eye calibration matrix and determine the initial matrix parameters; If the calculation error of the initial matrix exceeds a preset threshold, the sampling point position is adjusted through an iterative optimization algorithm to obtain new coordinate data and feature point coordinates; Based on the newly acquired coordinate data and feature point coordinates, the hand-eye calibration matrix is ​​updated to obtain the optimized matrix; The optimization matrix is ​​decomposed using the singular value decomposition algorithm, the main eigenvectors are extracted, and it is determined whether the matrix accuracy meets the requirements. If the matrix precision is lower than the preset threshold, the sampling point distribution strategy is adjusted according to the distribution characteristics of the feature vector to obtain supplementary coordinate data; The hand-eye calibration matrix was reconstructed by supplementing the coordinate data, and the final calibration result was obtained.

3. The hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 1, characterized in that, Step 2) further includes: obtaining coordinate transformation error data through the initial hand-eye calibration matrix, and using the error vector decomposition algorithm to separate translation error and rotation error to obtain error components; Extract the distribution characteristics of translation and rotation errors in the spatial coordinate system from the error components to determine the error distribution characteristics; If the error distribution characteristics exceed the preset threshold, then the translation error and rotation error are decomposed into spatial directions to obtain the spatial direction distribution. The magnitude of the error vector in each direction is calculated based on the spatial directional distribution to obtain the distribution pattern extraction result; Principal component analysis algorithm is used to reduce the dimensionality of the extracted distribution pattern to obtain data for trend analysis. By analyzing the trend of change, the error variation curve is fitted to the data to determine the trend of error change in the spatial direction. Key feature points are extracted from the changing trends to generate a feature description of the spatial orientation error distribution.

4. The hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 1, characterized in that, Step 3) further includes: acquiring robot operation distance and angle data, using sensors to collect real-time operation parameters, removing noise through data preprocessing, and obtaining a standardized operation dataset; Based on the standardized operation dataset, the least squares method is used to construct an initial fitting function for the operation distance, angle, and error, and the initial fitting parameters are determined. For the initial fitting function, calculate the fitting residual value, and compare the fitting residual value with the preset accuracy threshold to determine whether the accuracy requirement is met; If the fitting residual value exceeds the preset accuracy threshold, the fitting order is adjusted, and the least squares method is used again to calculate the fitting function to obtain the updated fitting parameters. Based on the updated fitting parameters, construct a dynamic error compensation model and generate a compensation function; The real-time operating distance and angle data are corrected using a compensation function to obtain the corrected operating parameters. By using the corrected operating parameters, the robot control commands are updated to obtain the optimized motion trajectory.

5. A hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 1, 2, or 3, characterized in that, Step 4) includes: calculating correction parameters through an error compensation function, and obtaining the position error based on the robot's current position and the distance to the target point; If the position error exceeds the preset threshold, correction parameters are generated based on the error compensation function; The calibration matrix is ​​adjusted in real time using correction parameters to obtain the adjusted calibration matrix; Perform coordinate system transformation based on the adjusted calibration matrix to obtain the initial transformed coordinates; The error compensation amount is calculated from the initial transformed coordinates and the distance to the target point; If the error compensation amount meets the dynamic adjustment conditions, then a compensation vector is generated; The corrected target coordinates are obtained by superimposing the compensation vector onto the initial transformed coordinates; The robot's motion control parameters are updated by correcting the target coordinates, and control commands are generated. Drive the robot to move according to control commands, obtain real-time position feedback, and determine whether the position error meets the accuracy requirements.

6. The hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 5, characterized in that, Step 5) includes: performing standard test actions by the robot to obtain actual arrival position data and theoretical target position data, and calculating the deviation data between the two. An iterative optimization algorithm is used to process the deviation data, generate position deviation analysis results, and determine whether the deviation exceeds a preset threshold. If the deviation exceeds the preset threshold, the gradient descent algorithm is used to adjust the compensation model parameters and generate updated compensation model parameters. The coordinate transformation is re-executed using the updated compensation model parameters to generate new coordinate transformation results. The robot is used to perform the standard test action again to obtain new actual arrival position data and calculate the deviation data from the theoretical target position; If the new deviation data is still outside the preset threshold, the gradient descent algorithm is repeated to adjust the compensation model parameters to obtain the optimized compensation model parameters. The final coordinate transformation is performed using the optimized compensation model parameters to generate the verification results output.

7. A hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 2, characterized in that, Step 6) further includes: collecting position deviation data from multiple tests using sensors, and obtaining data distribution characteristics by using mean and standard deviation calculation methods; Based on the data distribution characteristics, a normal distribution model is used to analyze the position deviation data and determine the statistical characteristics of repeatability accuracy. If the statistical characteristics of the repeatability accuracy exceed the preset threshold, the calibration parameters are optimized by the least squares method to obtain the adjusted calibration model. Using the adjusted calibration model, test data acquisition was re-executed to obtain new position deviation data. Based on the new position deviation data, the variation trend of absolute positioning accuracy is calculated using the analysis of variance method. If the trend of absolute positioning accuracy does not reach the preset standard, the calibration parameters are further optimized by gradient descent algorithm to obtain the optimized calibration model. By using the optimized calibration model, the final test data is collected to obtain the system performance indicators.

8. A hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 7, characterized in that, Step 7) further includes: acquiring ambient temperature data and mechanical structure deformation data in real time through sensors, calculating the temperature change rate and deformation degree, and obtaining environmental change characteristics; If the environmental change characteristics exceed the preset threshold, the adaptive calibration process is triggered to determine the set of calibration parameters that need to be updated. An incremental learning algorithm is used to update the compensation model, extracting feature vectors from the calibration parameter set to obtain the updated model parameters; The compensation model is adjusted by updating the model parameters, new control signals are generated, and output to the system execution unit. The system execution unit obtains feedback data, calculates performance index deviations, and determines whether the stability control requirements are met. If the performance index deviation exceeds the preset range, the calibration parameters are iteratively optimized to obtain new environmental change characteristics; Based on the new environmental changes, repeat the above process to output the final system control signal.

9. A hand-eye calibration method for a 5-axis hybrid robotic arm according to claim 5, characterized in that, Step 8) further includes: collecting coordinate transformation data in real time during the robot's operation through sensors, storing it as a time series dataset, and obtaining the original coordinate dataset; The original coordinate dataset is processed using a sliding window algorithm. The mean and standard deviation of the positioning error within a specified time window are calculated to determine the statistical characteristics of the error. If the mean of the error statistics exceeds the preset threshold and the standard deviation continues to increase, it is determined that the error is showing a systematic increase, and a trigger signal is generated. Based on the trigger signal, the initial values ​​of the calibration parameters are obtained from the preset parameter library, and the calibration parameters are optimized using the gradient descent algorithm to obtain the optimized parameter set. The robot coordinate transformation model is updated by optimizing the parameter set, and the positioning error is recalculated to obtain the updated error data. The updated error data is analyzed using a sliding window algorithm. If the mean error is lower than a preset threshold, the system is confirmed to have returned to a stable operating state. By continuously monitoring the optimized operating status through time series analysis, if a new error growth trend is detected, the above optimization process is repeated to obtain a stable system operating status.