Mechanical arm online calibration method and system

Abstract

The invention discloses a mechanical arm online calibration method and system. The method comprises the steps that a hydraulic mechanical arm no-load dynamic model based on the Lagrangian method is constructed; the method comprises the following steps: establishing an improved Denavit-Hartenberg kinematic error model; constructing a position prediction model by using a convolutional neural network and training the position prediction model; performing error compensation correction on the predicted position based on the model; online calibration parameters are determined and dynamically adjusted; and iterative optimization is repeated to realize real-time calibration. The system comprises a dynamical model construction unit, a kinematic error model establishment unit, a position prediction model training unit, an error compensation calculation unit, a calibration parameter determination unit and a model iterative optimization unit which work cooperatively. The method and the system can respond to working condition changes in real time, integrate multi-source errors, improve calibration precision, effectively reduce track deviation and guarantee operation quality and stability.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical arm calibration, and in particular to a mechanical arm online calibration method and system. BACKGROUND

[0002] With the rapid development of industrial automation technology, hydraulic mechanical arms are widely used in complex working condition scenes such as precision assembly, heavy material handling, and large equipment maintenance due to their large output torque and strong load capacity. In actual operation, the motion accuracy of the mechanical arm directly affects the operation quality and efficiency. However, factors such as joint clearance, link elastic deformation, temperature drift, and hydraulic drive device characteristics change can cause deviations between the actual motion trajectory and the theoretical trajectory. Long-term operation may cause operation errors or even safety hazards due to the accumulation of deviations. Therefore, real-time online calibration of hydraulic mechanical arms is a key technical requirement to improve their motion accuracy and ensure stable operation. The research on related methods and systems has important engineering application value.

[0003] The existing technology has two significant shortcomings in mechanical arm calibration. On the one hand, traditional calibration methods are mostly based on offline mode, which requires fixing the mechanical arm at a specific posture for parameter calibration. This method cannot adapt to error fluctuations caused by working condition changes during dynamic operation, and the calibration results are not timely, making it difficult to meet the precision requirements of continuous operation scenarios. On the other hand, existing error models often only consider a single or a few error sources, and the error description under the coupling action of multiple factors is not comprehensive. Moreover, the position prediction and error compensation process does not fully consider the dynamics of the mechanical arm, resulting in limited calibration accuracy due to the simplification assumptions of the model, and the error correction effect is not ideal under complex motion conditions. SUMMARY

[0004] To overcome the shortcomings and deficiencies of the existing technology, the present application provides a mechanical arm online calibration method and system.

[0005] The technical solution adopted by the present application is a mechanical arm online calibration method, comprising the following steps: Step S1: Construct a hydraulic mechanical arm unloaded dynamics model based on the Lagrange method. By analyzing the mass distribution of different joint links of the mechanical arm, the moment of inertia, and the output characteristics of the hydraulic drive device, determine the dynamics parameter relationship of different joints of the mechanical arm in the unloaded state, to reflect the correlation between joint torque and motion state during the motion of the mechanical arm. Step S2: Establish an improved Denavit-Hartenberg kinematic error model. On the basis of existing Denavit-Hartenberg parameters, error terms generated by joint clearance, elastic deformation of connecting rods, and temperature drift are introduced. By capturing the deviation of the actual motion trajectory of different joints of the robot arm from the theoretical trajectory, a kinematic error model including the influence of multiple error factors is formed. Step S3: Collect joint angle, angular velocity, angular acceleration, and position coordinate data of the end effector of the robot arm under different motion conditions. The collected data is input into the position prediction model based on the convolutional neural network as a training sample. By adjusting the convolution kernel size, convolution layer number, and full connection layer neuron number of the convolutional neural network, the model learns the position change law in the motion process of the robot arm, and the position of the end effector of the robot arm is predicted. Step S4: Based on the no-load dynamics model constructed in step S1 and the kinematic error model established in step S2, the predicted position output by the position prediction model in step S3 is error compensated and calculated. The predicted position is corrected in combination with the real-time motion parameters of different joints of the robot arm, and the corrected end effector position information is obtained. Step S5: According to the corrected position information obtained in step S4, different parameters of the online calibration of the robot arm are determined, including joint angle compensation value, connecting rod length correction coefficient, and pressure adjustment parameter of the hydraulic driving device. By dynamically adjusting the parameters, the actual motion trajectory of the robot arm approaches the theoretical trajectory. Step S6: Repeat steps S3 to S5. In the continuous motion process of the robot arm, the position prediction model is continuously updated and iterated, and the online calibration parameters are continuously optimized to realize real-time online calibration of the robot arm.

[0006] Further, the no-load dynamics model of the hydraulic robot arm based on the Lagrange method in step S1 satisfies the following relationship: wherein, is the driving torque of the jth joint, is the inertia matrix element of the jth joint, is the joint angle vector, is the angular acceleration of the jth joint, is the Coriolis force and centrifugal force coefficient of the jth joint, is the angular velocity of the jth joint, is the gravity term of the jth joint, is the friction torque of the jth joint. In step S4, when the error compensation calculation is performed on the predicted position, the error of the predicted position is quantitatively analyzed by calculating the deviation of the driving torque of different joints in combination with the dynamic model, and then more accurate error compensation is realized.

[0007] Further, step S2 comprises the following sub-steps: S2.1: Obtain the traditional Denavit-Hartenberg parameters of different joints of the mechanical arm, including the length of the connecting rod, the torsion angle of the connecting rod, the joint offset and the joint angle, and input the parameters as initial parameters to the error model construction module; S2.2: Collect the actual position coordinates of the end effector of the mechanical arm at multiple preset postures by the laser tracker, and record the theoretical motion parameters of different joints at the corresponding postures, and calculate the deviation value between the actual position coordinates and the theoretical position coordinates; S2.3: Analyze the influence degree of joint clearance, connecting rod elastic deformation and temperature drift on the deviation value, determine the weight coefficients of different error factors, and introduce the error factors into the traditional Denavit-Hartenberg parameters in the form of correction terms; S2.4: Based on the parameters after introducing the error correction terms, an improved Denavit-Hartenberg kinematics error model is constructed, and the error parameters in the model are identified by the least square method, which is used to reflect the kinematics error characteristics of the mechanical arm.

[0008] Further, the output of the position prediction model based on the convolutional neural network in step S3 satisfies the following relationship: Wherein, is the predicted position of the end effector, is the activation function, are the weight matrices of each layer of the convolutional neural network respectively, are the bias terms of each layer respectively, is the input mechanical arm motion parameter matrix; in the model training process, the error of the predicted position is back propagated in combination with the kinematics error model established in step S2, the weight and bias terms of the convolutional neural network are adjusted, and the accuracy of the position prediction is improved.

[0009] Further, when determining different parameters of the online calibration of the mechanical arm in step S5, the following relationship is satisfied: Wherein, is the angle compensation value of the jth joint, is the calibration parameter adjustment coefficient, is the position error of the jth joint, is the integral term of the position error, The rate of change of position error; the change of joint load during the movement of the robotic arm is calculated using the no-load dynamic model in step S1, and the load change is adjusted accordingly. , It can be dynamically adjusted to adapt to calibration requirements under different motion conditions.

[0010] Furthermore, step S3 includes the following sub-steps: S3.1: Install high-precision sensors at the joints of the robotic arm to collect joint angle, angular velocity and angular acceleration data in real time. At the same time, install a position detection device on the end effector to collect the three-dimensional position coordinate data of the end effector. S3.2: Filter the collected data, remove abnormal data caused by sensor failure or external interference, retain valid data and sort them according to time series to form the original data sequence; S3.3: Divide the original data sequence into a training set and a validation set. The training set is used to train the convolutional neural network, and the validation set is used to evaluate the predictive performance of the model. The division ratio is set according to the amount of data. S3.4: Input the training set data into the convolutional neural network, calculate the model's prediction output through forward propagation, calculate the prediction error by combining the validation set data, and adjust the network parameters according to the error results until the model reaches the preset training accuracy.

[0011] Furthermore, when correcting the predicted position in step S4, based on the improved Denavit-Hartenberg kinematic error model, the following relationship is satisfied: in, The corrected end effector position. Let Jacobian matrix be the value of the robotic arm. This is the joint angle error vector calculated based on the kinematic error model; Jacobian matrix The elements are calculated using the no-load dynamic model and the structural parameters of the robotic arm in step S1, including the joint angle error vector. Based on the error term of the kinematic error model determined in step S2, the accurate correction of the predicted position is achieved through this correction formula.

[0012] Furthermore, step S4 includes the following sub-steps: S4.1: Extract the predicted position data of the end effector from the position prediction model in step S3, and at the same time obtain the real-time motion parameters of different joints from the control system of the robotic arm, including joint angle, angular velocity and working pressure of hydraulic drive device; S4.2: Input the predicted position data and real-time motion parameters into the error compensation calculation module. This module calls the no-load dynamic model from step S1 and the kinematic error model from step S2 to calculate the error value between the predicted position and the theoretical position. S4.3: Based on the calculated error value and the kinematic characteristics of the robotic arm, determine the error compensation amount. This compensation amount is related to the joint motion state and is dynamically adjusted as the joint motion parameters change. S4.4: Apply the error compensation amount to the predicted position to obtain the corrected end effector position information, and store this information in the data buffer to provide data support for subsequent calibration parameter determination.

[0013] Furthermore, step S5 includes the following sub-steps: S5.1: Read the corrected end effector position information from the data buffer in step S4, compare it with the theoretical position information of the robotic arm, and calculate the position deviation value; S5.2: Based on the position deviation value, combined with the structural parameters and kinematic model of the robotic arm, determine the joint angle compensation value. This compensation value causes the joint motion trajectory to shift towards the theoretical trajectory, thereby reducing the position deviation. S5.3: Based on the joint angle compensation value and the dynamic characteristics of the hydraulic manipulator, calculate the link length correction coefficient and the pressure adjustment parameters of the hydraulic drive device. The parameters work together to further optimize the motion accuracy of the manipulator. S5.4: Store the determined joint angle compensation value, link length correction coefficient, and pressure adjustment parameters in the calibration parameter database as the basis for online calibration of the robotic arm.

[0014] An online calibration system for a robotic arm includes: The dynamic model building unit is used to build an unloaded dynamic model of a hydraulic manipulator based on the Lagrange method. This unit is connected to the joint sensors of the manipulator, receives the joint mass distribution and motion characteristic data collected by the sensors, and generates dynamic parameter relationships through internal algorithms. The kinematic error model building unit communicates bidirectionally with the dynamic model building unit, receives transmitted dynamic parameters, and connects to a laser tracker to obtain end-position deviation data, thereby establishing an improved Denavit-Hartenberg kinematic error model. The position prediction model training unit is connected to the kinematic error model establishment unit and the motion data acquisition device of the robotic arm, respectively. It receives kinematic error data and collected joint motion data, and generates a position prediction model through training a convolutional neural network. The error compensation calculation unit is connected to the position prediction model training unit at one end to obtain the predicted position data, and to the dynamic model construction unit and the kinematic error model establishment unit at the other end to obtain the relevant model parameters, and performs error compensation calculation for the predicted position. The calibration parameter determination unit is connected to the error compensation calculation unit. It receives the corrected position information, calculates and determines the joint angle compensation value, the link length correction coefficient and the pressure adjustment parameter by combining the theoretical position data. The model iteration optimization unit is connected to the position prediction model training unit and the calibration parameter determination unit, respectively. It receives the prediction model and calibration parameters, and continuously updates and iterates the model during the movement of the robotic arm to optimize the calibration parameters.

[0015] Beneficial Effects: This invention proposes an online calibration method and system for robotic arms. Through multi-model collaboration and dynamic iterative optimization, it addresses the poor timeliness of traditional offline calibration. The method continuously executes position prediction, error compensation, and parameter adjustment steps, updating the model and calibration parameters in real time during the continuous movement of the robotic arm. It can dynamically adapt to changing working conditions without requiring a fixed posture, ensuring that calibration results are synchronized with the operation process and meeting the accuracy requirements of continuous operation. Addressing the shortcomings of existing error models that consider only a single factor, the system combines a Lagrange-based unloaded dynamic model to capture the correlation between joint torque and motion state. An improved kinematic error model incorporates multiple factors such as joint clearance and link deformation. A convolutional neural network position prediction model then learns the motion laws, achieving a comprehensive description and accurate compensation of multi-source errors. Furthermore, the error correction process fully integrates the dynamic characteristics of the robotic arm, breaking the limitations of simplified model assumptions, significantly improving calibration accuracy under complex working conditions, effectively reducing the deviation between the actual trajectory and the theoretical trajectory, and ensuring operational quality and stability. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method steps of the present invention; Figure 2 This is a diagram showing the system unit composition of the present invention. Detailed Implementation

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0018] like Figure 1 As shown, an online calibration method for a robotic arm includes the following steps: Step S1: Construct a hydraulic robotic arm dynamic model under no-load conditions based on the Lagrange method. By analyzing the mass distribution, moment of inertia and output characteristics of the hydraulic drive device of different joints of the robotic arm, determine the dynamic parameter relationship of different joints of the robotic arm under no-load conditions, so as to reflect the relationship between joint torque and motion state during the movement of the robotic arm. Specifically, step S1 involves constructing a model that accurately reflects the dynamic characteristics of the hydraulic robotic arm under no-load conditions, which forms the basis for subsequent calibration work. The mass distribution and moment of inertia of each joint link of the robotic arm directly affect its motion inertia, while the output characteristics of the hydraulic drive device determine the driving torque of the joints. The accuracy of these parameters is crucial to the reliability of the model. By constructing a model using the Lagrangian method, the changes in kinetic and potential energy during the robotic arm's movement can be comprehensively considered, thereby establishing the correlation between joint torque and motion state, providing a theoretical basis for subsequent analysis of the forces acting on the robotic arm under different motion states. The establishment of this model can help identify possible dynamic deviations in the robotic arm during no-load movement, laying the foundation for subsequent error compensation and parameter calibration, and providing support for the precise control of the robotic arm from a dynamic perspective.

[0019] In the specific implementation process, the parameters of each joint link of the robotic arm need to be measured first. For the mass distribution of the links, a combination of weighing and 3D scanning technology can be used to determine the mass and center of gravity of each link. Generally, the mass of a single link ranges from 2.5 kg to 8 kg, and the center of gravity offset is controlled within ±0.5 mm. The moment of inertia is measured using a moment of inertia tester. For different links with different structural characteristics, the moment of inertia about different axes is measured separately, with a measurement accuracy of ±0.01 kg. m². For the hydraulic drive unit, output torque under different oil supply pressures is collected using pressure and torque sensors. The oil supply pressure range is set from 5MPa to 20MPa, with one set of data collected every 0.5MPa, for a total of more than 30 sets, to obtain sufficient samples. These measurement data are input into a calculation module based on the Lagrange method. By calculating the kinetic and potential energy of each joint of the robotic arm in the no-load state, the functional relationship between joint torque and angular displacement, angular velocity, and angular acceleration is solved, ultimately generating a dynamic model. After the model is generated, preliminary verification is required. By controlling the robotic arm to perform simple reciprocating motion in the no-load state, the torque value calculated by the model is compared with the actual measured value. The deviation should be controlled within 5%. If it exceeds 5%, the parameters are remeasured and the model is corrected.

[0020] Step S2: Establish an improved Denavit-Hartenberg kinematic error model. Based on the existing Denavit-Hartenberg parameters, introduce error terms caused by joint clearance, link elastic deformation and temperature drift. By capturing the deviation between the actual motion trajectory and the theoretical trajectory of different joints of the robotic arm, a kinematic error model including the influence of multiple factors is formed. Specifically, step S2 aims to establish an improved Denavit-Hartenberg kinematic error model to more comprehensively capture the sources of error during the robotic arm's motion. Traditional Denavit-Hartenberg parameters only consider ideal parameters such as link length, link torsion angle, joint offset, and joint angle. However, in practical applications, factors such as joint clearance, link elastic deformation, and temperature drift can cause significant deviations between the actual and theoretical trajectories of the robotic arm. By introducing these error terms, the model can more realistically reflect the kinematic characteristics of the robotic arm, improve the accuracy of error description, and provide a more accurate basis for subsequent error compensation. This step overcomes the limitations of traditional models by considering error factors from multiple dimensions, thus providing a more reliable kinematic foundation for high-precision calibration of the robotic arm.

[0021] In practice, the traditional Denavit-Hartenberg parameters of each joint of the robotic arm must first be obtained. The link length is measured using a laser interferometer with an accuracy of ±0.001 mm. The link torsion angle is measured using an angle measuring instrument with an accuracy of ±0.001°. Joint offset and joint angle are directly read from the encoder at the joint with a resolution of 0.001°. Subsequently, the robotic arm is controlled to select 100 evenly distributed preset postures within the workspace. The actual position coordinates of the end effector in each posture are measured using a laser tracker with a measurement accuracy of ±0.01 mm. Simultaneously, the theoretical motion parameters of each joint in the corresponding posture are recorded, and the deviation between the actual and theoretical positions is calculated. When analyzing error factors, joint clearance was measured by installing displacement sensors at the joints, with a measurement range of 0 to 0.1 mm and an accuracy of ±0.001 mm. Elastic deformation of the connecting rod was measured by attaching strain gauges to the connecting rod surface and using force sensors to measure deformation data under different loads, with the deformation range controlled between 0 and 0.05 mm. Temperature drift was monitored in real time by temperature sensors to track the working environment temperature of the robotic arm and the temperature at the joints, with a temperature measurement range of -10℃ to 50℃ and an accuracy of ±0.1℃. The correlation between temperature changes and position deviations was analyzed. These error factors were introduced into the traditional parameters as correction terms. The least squares method was used to identify the error parameters in the model, ensuring that the calculated position deviation matched the actual measured deviation by more than 90%, thus completing the establishment of an improved kinematic error model.

[0022] Step S3: Collect joint angles, angular velocities, angular accelerations, and position coordinates of the end effector of the robotic arm under different motion conditions. Input the collected data as training samples into the position prediction model based on convolutional neural networks. By adjusting the convolutional kernel size, number of convolutional layers, and number of neurons in the fully connected layers of the convolutional neural network, the model learns the position change pattern during the movement of the robotic arm and predicts the position of the end effector of the robotic arm. Specifically, the main task of step S3 is to construct and train a position prediction model based on a convolutional neural network. This model can predict the position of the end effector based on the motion parameters of the robotic arm, providing predictive data for subsequent error compensation. The joint angles, angular velocities, angular accelerations, and end-effector coordinates of the robotic arm under different motion conditions contain the patterns and characteristics of its motion. By learning from this data through a convolutional neural network, hidden nonlinear relationships can be uncovered, thereby achieving accurate prediction of the end-effector position. The training quality of this model directly affects the accuracy of subsequent calibration. Utilizing the powerful fitting capabilities of deep learning improves the accuracy and real-time performance of position prediction, providing a reliable position reference for the online calibration of the robotic arm.

[0023] The first step in implementation is to establish a data acquisition system. High-precision encoders and gyroscopes are installed at each joint of the robotic arm. The encoders measure joint angles with a resolution of 0.001° and a sampling frequency of 1kHz. The gyroscopes measure angular velocity and angular acceleration. The angular velocity measurement range is -500° / s to 500° / s with an accuracy of ±0.1° / s, and the angular acceleration measurement range is -1000° / s² to 1000° / s² with an accuracy of ±1° / s². A three-dimensional coordinate measuring machine is installed on the end effector, with a measurement range of 0 to 5m, an accuracy of ±0.01mm, and a sampling frequency of 1kHz. The robotic arm is controlled to perform various motion tests within the workspace, including uniform motion, acceleration, deceleration, and variable acceleration. Each condition lasts for 10 minutes. During data acquisition, the robotic arm's motion is ensured to cover more than 80% of its workspace, and at least 1 million sets of data are collected. The collected data was processed, outliers (such as jumps caused by sensor malfunctions) were removed, and then divided into training and validation sets in an 8:2 ratio. When constructing the convolutional neural network, the input layer was set to 12 neurons (corresponding to the angles, angular velocities, and angular accelerations of 6 joints), and three convolutional layers were set: the first layer had a 5×5 kernel size and 32 neurons; the second layer had a 3×3 kernel size and 64 neurons; and the third layer had a 3×3 kernel size and 128 neurons. Two fully connected layers were set: the first layer had 128 neurons, and the second layer had 3 neurons (corresponding to the 3D coordinates of the terminal positions). During training, the Adam optimizer was used, with an initial learning rate of 0.001, decreasing to 0.1 every 10 epochs, a batch size of 256, and 100 training epochs, until the model's position prediction error (root mean square error) on the validation set was less than 0.05 mm.

[0024] Step S4: Based on the no-load dynamic model constructed in step S1 and the kinematic error model established in step S2, the predicted position output by the position prediction model in step S3 is calculated for error compensation. Combined with the real-time motion parameters of different joints of the robotic arm, the predicted position is corrected to obtain the corrected end effector position information.

[0025] Specifically, step S4, based on the previously constructed no-load dynamic model and kinematic error model, performs error compensation calculations on the predicted position output by the position prediction model to obtain more accurate end effector position information. While the predicted position can reflect the approximate location of the end effector, it inevitably contains some deviation due to factors such as model simplification and sensor errors. By combining the dynamic model to analyze the influence of joint torque on motion and using the kinematic error model to quantify the impact of multi-factor errors, the predicted position can be specifically corrected, thereby improving the accuracy of the position information. This step incorporates dynamic characteristics and kinematic errors into the position correction process, achieving precise compensation for the predicted position and providing a reliable positional basis for determining subsequent calibration parameters.

[0026] In practice, the predicted position data of the end effector is first obtained from the position prediction model. Simultaneously, sensors collect real-time motion parameters of each joint of the robotic arm, including joint angles (accuracy ±0.001°), angular velocity (accuracy ±0.1° / s), angular acceleration (accuracy ±1° / s²), and the working pressure of the hydraulic drive unit (accuracy ±0.01MPa). This data is then input into the error compensation calculation module. This module first calls the no-load dynamics model to calculate the theoretical driving torque of each joint based on the joint motion parameters, and then compares it with the actually measured driving torque (measured by a torque sensor, accuracy ±0.1N). By comparing the torque deviation with the measured position (m), the influence of the torque deviation on the end effector position is analyzed. Simultaneously, an improved kinematic error model is used to calculate the position error caused by factors such as joint clearance (measurement range 0 to 0.1 mm), link elastic deformation (measurement range 0 to 0.05 mm), and temperature drift (measurement range -10℃ to 50℃). The total error compensation is calculated by combining the influence of torque deviation and multiple error factors on the position. The calculation of the compensation needs to consider the movement direction and speed of the robotic arm. For high-speed movement (angular velocity greater than 300° / s), the compensation coefficient is appropriately increased (1.2 times); for low-speed movement (angular velocity less than 50° / s), the compensation coefficient is decreased (0.8 times). The calculated error compensation is applied to the predicted position to obtain the corrected end effector position information, which is stored in the data buffer at the same frequency as the sampling frequency (1 kHz) to provide data support for subsequent steps. During the compensation process, it is necessary to monitor the deviation between the corrected position and the actual measured position (measured by a laser tracker) in real time. If the deviation is greater than 0.1mm, the compensation coefficient should be readjusted until the deviation is controlled within 0.1mm.

[0027] Step S5: Based on the corrected position information obtained in step S4, determine different parameters for the online calibration of the robotic arm, including joint angle compensation value, link length correction coefficient and pressure adjustment parameters of hydraulic drive device. By dynamically adjusting the parameters, the actual motion trajectory of the robotic arm can be made closer to the theoretical trajectory. Specifically, step S5 aims to determine the parameters for online calibration of the robotic arm based on the corrected position information, and to dynamically adjust these parameters to make the actual motion trajectory of the robotic arm approach the theoretical trajectory. Calibration parameters are the bridge connecting the model and actual control; their accuracy and rationality directly affect the calibration effect. Joint angle compensation values ​​can correct angular deviations in joint motion, link length correction coefficients can compensate for length changes caused by link deformation, and pressure adjustment parameters of the hydraulic drive device can optimize the drive torque output. These three parameters work together to achieve a comprehensive improvement in the motion accuracy of the robotic arm. This step combines model calculation with actual control, transforming the error compensation results into specific control commands through parameter adjustment, thereby achieving precise motion control of the robotic arm.

[0028] During implementation, the corrected end effector position information is first read from the data buffer and compared with the theoretical position information of the robotic arm (generated by the motion planning algorithm) to calculate the position deviation value. The accuracy of the position deviation calculation must reach ±0.001mm. Based on the position deviation value, combined with the structural parameters of the robotic arm (such as link length, joint distance, etc.) and the kinematic model, the joint angle compensation value is calculated. For rotary joints, the angle compensation value is calculated based on the projection of the position deviation in the joint rotation direction, with a compensation range of -0.05° to 0.05° and an accuracy of ±0.001°; for kinetic joints, the compensation value is based on the component of the position deviation in the kinetic direction, with a compensation range of -0.1mm to 0.1mm and an accuracy of ±0.001mm. Based on the joint angle compensation value and the dynamic characteristics of the hydraulic manipulator, a link length correction coefficient is calculated. The correction coefficient ranges from 0.995 to 1.005. When the elastic deformation of the link is greater than 0.03 mm, the correction coefficient is appropriately increased (e.g., 1.003); when the deformation is less than 0.01 mm, a value close to 1 (e.g., 1.0005) is used. Simultaneously, based on the deviation of the joint driving torque (measurement range -5N)... m to 5N The pressure adjustment parameters of the hydraulic drive device are calculated, with a pressure adjustment range of -0.5MPa to 0.5MPa. When the torque deviation is positive, the pressure adjustment parameter is increased; when the torque deviation is negative, the pressure adjustment parameter is decreased. The determined joint angle compensation value, link length correction coefficient, and pressure adjustment parameters are stored in the calibration parameter database. The database uses a real-time update mechanism with an update frequency of 100Hz to ensure the timeliness of the parameters. During parameter adjustment, the actual motion trajectory of the robotic arm needs to be monitored in real time through the feedback system. If the deviation between the actual trajectory and the theoretical trajectory is still greater than 0.05mm, the calibration parameters are recalculated and adjusted until the deviation is controlled within 0.05mm.

[0029] Step S6: Repeat steps S3 to S5. During the continuous movement of the robotic arm, continuously update and iterate the position prediction model, continuously optimize the online calibration parameters, and perform real-time online calibration of the robotic arm. Specifically, step S6 performs real-time online calibration of the robotic arm by repeating steps S3 to S5. This is crucial for ensuring the robotic arm maintains high precision throughout long-term operation. During continuous movement, the robotic arm's operating conditions constantly change, such as ambient temperature fluctuations, component wear, and load variations. These factors can lead to a decrease in the accuracy of the error model and position prediction model. By continuously updating and iterating the model and optimizing calibration parameters, the model can always adapt to the latest operating conditions, ensuring the stability and consistency of the calibration effect. This step forms a closed-loop calibration system, achieving long-term maintenance and dynamic optimization of the robotic arm's motion accuracy through continuous feedback and adjustment.

[0030] In specific implementation, the repetition cycle is set to 0.1 seconds, meaning steps S3 to S5 are re-executed every 0.1 seconds. Within each cycle, the latest motion data of the robotic arm is first collected according to step S3, including joint angles, angular velocity, angular acceleration, and end-effector coordinates. The amount of data collected is 100 sets per cycle (based on a 1kHz sampling frequency). The newly collected data is added to the training set, and the convolutional neural network position prediction model is updated using incremental learning. Each update only adjusts the parameters of the last two layers of the network to reduce computation. During the update process, the learning rate is maintained at 0.0001, the batch size is 64, and a model update is completed after 5 epochs. Subsequently, following step S4, the updated position prediction model outputs a new predicted position, and error compensation calculations are performed using the no-load dynamics model and kinematic error model to obtain the corrected position information. The parameter settings in the compensation process are consistent with step S4, but the error weights for temperature drift need to be adjusted based on the latest ambient temperature (collected every 0.1 seconds). Next, new online calibration parameters are determined according to the method in step S5. The adjustment range of the parameters is determined based on the rate of change of the position deviation. If the rate of change of deviation is greater than 0.01mm / 0.1s, the parameter adjustment range is increased (by 1.5 times); if the rate of change is less than 0.001mm / 0.1s, the adjustment range is decreased (by 0.5 times). The new calibration parameters are sent to the control system of the robotic arm. The control system completes the parameter update within 0.01 seconds after receiving the parameters, realizing real-time adjustment of the robotic arm's movement. Throughout the iteration process, a monitoring module is set up to monitor the calibration accuracy of the robotic arm in real time. If the position deviation is less than 0.03mm for three consecutive cycles, the repetition cycle is appropriately extended to 0.2 seconds to reduce computational resource consumption; if the position deviation is greater than 0.1mm, the cycle is shortened to 0.05 seconds, and an early warning signal is issued to indicate possible abnormalities.

[0031] Preferably, the unloaded dynamic model of the hydraulic manipulator based on the Lagrange method in step S1 satisfies the following relationship: in, Let j be the driving torque of the j-th joint. Let j be the inertia matrix element of the j-th joint. For joint angle vectors, Let be the angular acceleration of the j-th joint. Let be the Coriolis force and centrifugal force coefficients of the j-th joint. Let be the angular velocity of the j-th joint. Let j be the gravity term of the j-th joint. Let be the frictional torque of the j-th joint; In step S4, when calculating the error compensation for the predicted position, the error of the predicted position is quantitatively analyzed by combining the dynamic model and calculating the deviation of the driving torque of different joints, thereby achieving more accurate error compensation.

[0032] Specifically, step S1 clarifies the application of the unloaded dynamic model of the hydraulic manipulator based on the Lagrange method and its relationship with error compensation. By quantifying the relationship between dynamic parameters, it provides a more accurate theoretical basis for error compensation. The parameters involved in this model directly reflect the dynamic characteristics of the manipulator. The joint driving torque is affected by multiple factors such as inertia, Coriolis force, centrifugal force, gravity, and friction. The combined effect of these factors determines the motion state of the manipulator. In practical implementation, it is essential to ensure the accurate measurement of model parameters. The inertia matrix elements of the joints need to be obtained through high-precision testing equipment. Their values ​​are closely related to the mass distribution and moment of inertia of the connecting rods. For connecting rods with a mass between 2.5 kg and 8 kg, the value range of the inertia matrix elements is typically between 0.05 and 0.5 kg. Between m². The Coriolis force and centrifugal force coefficients are related to the joint angle and angular velocity; within the range of -500° / s to 500° / s, their values ​​exhibit non-linear changes. The calculation of the gravity term requires consideration of the connecting rod's center of mass position and gravitational acceleration; controlling the center of mass offset within ±0.5mm ensures the accuracy of the gravity term calculation. Friction torque is related to angular velocity; at low speeds, static friction dominates, while at high speeds, dynamic friction dominates; its measurement accuracy needs to reach ±0.05N. m. In the error compensation calculation, the driving torque calculated by the model is compared with the actual measured value (accuracy ±0.1N). (m) can be used to obtain the torque deviation, and then the influence of this deviation on the end position can be analyzed. For example, when the torque deviation is 1N... When the value is m, a deviation of 0.05mm to 0.1mm may occur at the end position. By quantifying this effect, the error compensation amount can be adjusted in a targeted manner to control the position deviation after compensation within 0.05mm, thereby improving the accuracy of the entire calibration process.

[0033] Preferably, step S2 includes the following sub-steps: S2.1: Obtain the traditional Denavit-Hartenberg parameters of different joints of the robotic arm, including link length, link torsion angle, joint offset and joint angle, and input the parameters as initial parameters into the error model construction module; S2.2: Collect the actual position coordinates of the end effector of the robotic arm in multiple preset postures using a laser tracker, and simultaneously record the theoretical motion parameters of different joints in the corresponding postures, and calculate the deviation between the actual position coordinates and the theoretical position coordinates; S2.3: Analyze the influence of joint clearance, connecting rod elastic deformation and temperature drift on the above deviation values, determine the weight coefficients of different error factors, and introduce the error factors into the traditional Denavit-Hartenberg parameters in the form of correction terms; S2.4: Based on the parameters after introducing the error correction term, an improved Denavit-Hartenberg kinematic error model is constructed. The error parameters in the model are identified by the least squares method, which is used to reflect the kinematic error characteristics of the robotic arm.

[0034] Specifically, the step-by-step implementation process of step S2 ensures the accuracy and reliability of the improved Denavit-Hartenberg kinematic error model through a systematic process, providing a solid foundation for subsequent error analysis and compensation. In S2.1, when obtaining traditional Denavit-Hartenberg parameters, the laser interferometer measures the link length with an accuracy of ±0.001mm, the angle measuring instrument measures the link torsion angle with an accuracy of ±0.001°, and the joint encoder has a resolution of 0.001°. These high-precision parameter measurements are the basis for constructing the error model. In S2.2, 100 uniformly distributed preset postures are selected, and the actual position of the end effector is measured using a laser tracker (accuracy ±0.01mm). Simultaneously, the theoretical joint parameters are recorded. The calculated position deviation value will serve as the raw data for subsequent error analysis, ensuring the accuracy of the deviation calculation and providing a reliable basis for error factor analysis. In S2.3, dedicated sensors are required for measuring joint clearance, link elastic deformation, and temperature drift. The joint clearance measurement range is 0 to 0.1 mm (accuracy ±0.001 mm), the link elastic deformation range is 0 to 0.05 mm, and the temperature measurement range is -10℃ to 50℃ (accuracy ±0.1℃). By analyzing the correlation between these factors and position deviation, the weighting coefficients of each error factor are determined. For example, a 10℃ temperature change may lead to a 0.02 mm position deviation, and its weighting coefficient can be set to 0.2. In S2.4, after introducing the error correction term into the traditional parameters, the least squares method is used to identify the error parameters, ensuring that the position deviation calculated by the model matches the actual measured deviation by more than 90%. This process requires iterative optimization until the model can accurately reflect the kinematic error characteristics of the robotic arm under different postures, providing accurate error model support for subsequent error compensation.

[0035] Preferably, the output of the position prediction model based on the convolutional neural network in step S3 satisfies the following relationship: in, For the predicted end effector position, For activation function, These are the weight matrices for each layer of the convolutional neural network. These are the bias terms for each layer. The input is the motion parameter matrix of the robotic arm; during model training, the kinematic error model established in step S2 is used to backpropagate the error of the predicted position, adjust the weights and bias terms of the convolutional neural network, and improve the accuracy of position prediction.

[0036] Specifically, step S3, the position prediction model based on a convolutional neural network, clarifies the model's structure and training process, ensuring the model can accurately learn the robotic arm's motion patterns and provide reliable results for end-effector position prediction. The model's output reflects the nonlinear mapping between input motion parameters and the predicted position; the settings of the weight matrices and bias terms in each layer directly affect the model's prediction accuracy. In practice, the input robotic arm motion parameter matrix includes the angles, angular velocities, and angular accelerations of six joints. The data undergoes rigorous screening to remove outliers, ensuring the reliability of the input data. When constructing the convolutional neural network, the 12 neurons in the input layer correspond to each motion parameter. The convolutional layer settings must balance feature extraction capability and computational efficiency. The first layer's 5×5 convolutional kernels are suitable for extracting global features, and the number 32 ensures feature richness. The second and third layers' 3×3 convolutional kernels are used to extract local detail features, with the number gradually increasing to 64 and 128 to enhance feature representation. The 128 neurons in the fully connected layer integrate the features output from the convolutional layers, ultimately outputting the three-dimensional position coordinates of the end-effector through three neurons. During training, the Adam optimizer's initial learning rate of 0.001 ensures rapid convergence, and the rate decays to 0.1 every 10 epochs to avoid overfitting. Batch sizes of 256 and training epochs of 100 epochs control computational load while maintaining training effectiveness. When performing backpropagation using the kinematic error model, the model's predicted position is compared with the actual position after accounting for errors. By adjusting weights and bias terms, the position prediction error (root mean square error) on the validation set is kept below 0.05 mm, ensuring the model maintains high prediction accuracy under different motion conditions and providing accurate predicted position data for subsequent error compensation.

[0037] Preferably, when determining different parameters for online calibration of the robotic arm in step S5, the following relationship is satisfied: in, This is the angle compensation value for the j-th joint. To calibrate the parameter adjustment coefficient, Let j be the position error of the j-th joint. This is the integral term of the position error. The rate of change of position error; the change of joint load during the movement of the robotic arm is calculated using the no-load dynamic model in step S1, and the load change is adjusted accordingly. , It can be dynamically adjusted to adapt to calibration requirements under different motion conditions.

[0038] Specifically, step S5 determines the online calibration parameters. By clarifying the relationship between the calibration parameters and the position error, the precise calculation and dynamic adjustment of the joint angle compensation value are achieved, thereby improving the motion accuracy of the robotic arm. In this relationship, the joint angle compensation value is jointly determined by the position error, the integral term of the error, and the rate of change of the error. The values ​​of the adjustment coefficients k1, k2, and k3 directly affect the compensation effect. In specific implementation, the calculation accuracy of the position error e_j needs to reach ±0.001mm. Its integral term and rate of change need to be obtained through real-time data processing. For example, the integral term can be calculated using the trapezoidal integral method, and the rate of change can be obtained by dividing the error difference between adjacent moments by the time interval (0.001 seconds). The initial values ​​of the adjustment coefficients k1, k2, and k3 can be set based on experience. k1 is usually between 0.5 and 2, k2 between 0.01 and 0.1, and k3 between 0.1 and 1. Subsequent dynamic adjustments need to be made according to changes in joint load. When calculating the joint load change through the no-load dynamic model in step S1, when the load increases (e.g., the joint torque increases by 5N), The system's response speed can be improved by appropriately increasing k1 (e.g., from 1 to 1.5) and simultaneously decreasing k2 (e.g., from 0.05 to 0.03) to avoid integral saturation. The opposite adjustment is made when the load decreases. The joint angle compensation value ranges from -0.05° to 0.05°, with an accuracy of ±0.001°. The calculated compensation value needs to be coordinated with the link length correction coefficient and pressure adjustment parameter. For example, when the angle compensation value is 0.03°, the link length correction coefficient can be set to 1.002, and the pressure adjustment parameter can be increased by 0.2 MPa to ensure that the parameters work together to control the position deviation of the robotic arm within 0.05 mm, achieving high-precision online calibration.

[0039] Preferably, step S3 includes the following sub-steps: S3.1: Install high-precision sensors at the joints of the robotic arm to collect joint angle, angular velocity and angular acceleration data in real time. At the same time, install a position detection device on the end effector to collect the three-dimensional position coordinate data of the end effector. S3.2: Filter the collected data, remove abnormal data caused by sensor failure or external interference, retain valid data and sort them according to time series to form the original data sequence; S3.3: Divide the original data sequence into a training set and a validation set. The training set is used to train the convolutional neural network, and the validation set is used to evaluate the predictive performance of the model. The division ratio is set according to the amount of data. S3.4: Input the training set data into the convolutional neural network, calculate the model's prediction output through forward propagation, calculate the prediction error by combining the validation set data, and adjust the network parameters according to the error results until the model reaches the preset training accuracy.

[0040] Specifically, the step-by-step implementation of step S3, through standardized data acquisition, processing, partitioning, and model training, ensures the reliability and high accuracy of the position prediction model based on the convolutional neural network, providing a solid foundation for online calibration of the robotic arm. In S3.1, high-precision encoders (resolution 0.001°, sampling frequency 1kHz) and gyroscopes (angular velocity accuracy ±0.1° / s, angular acceleration accuracy ±1° / s²) installed at the joints can acquire joint motion parameters in real time, while the end effector (accuracy ±0.01mm, sampling frequency 1kHz) provides accurate position data. The selection and installation of these sensors must ensure the synchronization of data acquisition, with time deviation controlled within 0.001 seconds. In S3.2, data filtering needs to remove jump data caused by sensor failure (such as angle changes exceeding 5°), and the retained valid data is sorted by time sequence to form a continuous original data sequence, with data integrity reaching over 99%. In S3.3, the ratio of training set to validation set is adjusted according to the amount of data. When the amount of data exceeds 1 million sets, an 8:2 ratio can be used to ensure that the training set is large enough to support model learning, and the validation set can effectively evaluate model performance. The partitioning process should use random sampling to avoid data distribution bias. In S3.4, during model training, forward propagation is used to calculate the predicted output, and the root mean square error is calculated by combining the validation set data. The network parameters (such as convolutional kernel weights and fully connected layer weights) are adjusted through backpropagation. The initial learning rate is 0.001, which decreases by 0.1 every 10 epochs. The batch size is 256. After training for 100 epochs, if the validation set error is less than 0.05mm, training is stopped. Otherwise, the number of training epochs is increased or the network structure is adjusted until the model reaches the preset accuracy, ensuring that the model can accurately predict the end position under different motion conditions.

[0041] Preferably, when correcting the predicted position in step S4, the improved Denavit-Hartenberg kinematic error model satisfies the following relationship: in, The corrected end effector position. Let Jacobian matrix be the value of the robotic arm. This is the joint angle error vector calculated based on the kinematic error model; Jacobian matrix The elements are calculated using the no-load dynamic model and the structural parameters of the robotic arm in step S1, including the joint angle error vector. Based on the error term of the kinematic error model determined in step S2, the accurate correction of the predicted position is achieved through this correction formula.

[0042] Specifically, the predicted position correction process in step S4 achieves accurate correction of the end effector's predicted position by clarifying the correction relationship based on the improved Denavit-Hartenberg kinematic error model, providing more reliable position information for the determination of subsequent calibration parameters. This correction relationship links the predicted position with the joint angle error vector through the Jacobian matrix, comprehensively considering the kinematic characteristics and error factors of the robotic arm, making the corrected position closer to the actual situation. In practice, the calculation of the Jacobian matrix needs to be combined with the structural parameters and no-load dynamic model of the robotic arm. The matrix elements reflect the degree of influence of joint angle changes on the end effector position. For a 6-DOF robotic arm, the Jacobian matrix is ​​a 6×6 matrix, and the value range of the elements varies depending on the joint type and link size. The elements corresponding to rotary joints are usually between -0.5 and 0.5, while the elements corresponding to translating joints are related to the link length and range between 0 and 1. The joint angle error vector is determined based on the error terms in the kinematic error model, including angle deviations caused by joint clearance, link elastic deformation, and temperature drift. The angle error range for each joint is -0.01° to 0.01°, with an accuracy of ±0.0001°. When calculating the corrected position, the joint torques and motion parameters of the robotic arm in its current motion state are first obtained through the no-load dynamics model. The joint angle error vector is then calculated using the kinematic error model, and the Jacobian matrix is ​​calculated based on the real-time posture of the robotic arm. Multiplying these two values ​​yields the position correction. The magnitude of the correction is related to the joint angle error and the elements of the Jacobian matrix. For example, when the joint angle error is 0.01° and the corresponding element in the Jacobian matrix is ​​0.3, the position correction is 0.003 mm. This correction is then superimposed on the predicted position to obtain the corrected end effector position, with an accuracy controlled within ±0.005 mm. Throughout the correction process, the deviation between the corrected position and the actual measured position must be monitored in real time. If the deviation exceeds 0.01mm, the joint angle error vector and Jacobian matrix must be recalculated until the deviation meets the requirements. This ensures that the corrected position information can accurately reflect the actual position of the robotic arm end, laying the foundation for subsequent calibration work.

[0043] Preferably, step S4 includes the following sub-steps: S4.1: Extract the predicted position data of the end effector from the position prediction model in step S3, and at the same time obtain the real-time motion parameters of different joints from the control system of the robotic arm, including joint angle, angular velocity and working pressure of hydraulic drive device; S4.2: Input the predicted position data and real-time motion parameters into the error compensation calculation module. This module calls the no-load dynamic model from step S1 and the kinematic error model from step S2 to calculate the error value between the predicted position and the theoretical position. S4.3: Based on the calculated error value and the kinematic characteristics of the robotic arm, determine the error compensation amount. This compensation amount is related to the joint motion state and is dynamically adjusted as the joint motion parameters change. S4.4: Apply the error compensation amount to the predicted position to obtain the corrected end effector position information, and store this information in the data buffer to provide data support for subsequent calibration parameter determination.

[0044] Specifically, the step-by-step implementation of step S4 ensures the accuracy and reliability of error compensation calculation through a systematic process, accurately correcting the predicted position to be closer to the actual position information, and providing high-quality data support for determining calibration parameters. In S4.1, when extracting predicted position data from the position prediction model, the real-time nature of the data must be ensured, with the extraction frequency consistent with the model output frequency (1kHz). Simultaneously, the real-time joint motion parameters obtained from the robotic arm control system must be filtered to remove high-frequency noise. After filtering, the joint angle accuracy reaches ±0.0005°, the angular velocity ±0.05° / s, and the hydraulic drive device working pressure ±0.005MPa, ensuring the quality of the input data. In S4.2, the error compensation calculation module must simultaneously call the no-load dynamic model and the kinematic error model. After inputting the predicted position data and real-time motion parameters, the model will calculate the error value between the predicted position and the theoretical position according to a preset algorithm. The error calculation must consider the robotic arm's motion direction and speed. For high-speed motion (angular velocity greater than 300° / s), the weight of the error calculation needs to be appropriately adjusted to highlight the impact of dynamic errors, and the calculation accuracy must reach ±0.001mm. In S4.3, when determining the error compensation amount, it is necessary to establish a correlation model between the compensation amount and joint motion parameters, taking into account the kinematic characteristics of the robotic arm. When the joint angle change rate is greater than 5° / s, the compensation amount needs to be increased by 10%; when the change rate is less than 1° / s, the compensation amount needs to be reduced by 5%, ensuring that the compensation amount can dynamically adapt to the movement state of the robotic arm. The range of the compensation amount is determined based on the error value, typically between -0.05mm and 0.05mm, with an accuracy of ±0.001mm. In S4.4, when applying the error compensation amount to the predicted position, a high-precision numerical calculation method must be used to avoid introducing new errors. The corrected position after application needs to be stored in the data buffer, using a binary storage format to reduce storage space. A data verification mechanism must also be set up to ensure the integrity and accuracy of the stored data. The capacity of the data buffer must meet the data storage requirements for at least 10 minutes, and the read / write speed must be no less than 1MB / s to ensure continuous data storage and fast retrieval. Throughout the entire process, a monitoring node needs to be set up to verify the error compensation calculation results every 100ms. The deviation between the corrected position and the actual measured position is compared. If the deviation exceeds 0.01mm for three consecutive times, an alarm mechanism is triggered, prompting system checks and parameter adjustments to ensure that the error compensation process remains stable and reliable and that the output corrected position information meets the accuracy requirements of subsequent calibration work.

[0045] Preferably, step S5 includes the following sub-steps: S5.1: Read the corrected end effector position information from the data buffer in step S4, compare it with the theoretical position information of the robotic arm, and calculate the position deviation value; S5.2: Based on the position deviation value, combined with the structural parameters and kinematic model of the robotic arm, determine the joint angle compensation value. This compensation value causes the joint motion trajectory to shift towards the theoretical trajectory, thereby reducing the position deviation. S5.3: Based on the joint angle compensation value and the dynamic characteristics of the hydraulic manipulator, calculate the link length correction coefficient and the pressure adjustment parameters of the hydraulic drive device. The parameters work together to further optimize the motion accuracy of the manipulator. S5.4: Store the determined joint angle compensation value, link length correction coefficient, and pressure adjustment parameters in the calibration parameter database as the basis for online calibration of the robotic arm.

[0046] Specifically, the detailed implementation of step S5 aims to precisely determine the key parameters required for online calibration of the robotic arm through a standardized and refined process. This ensures that these parameters can specifically adjust the robotic arm's motion trajectory, continuously approaching the theoretical trajectory and ultimately significantly improving the robotic arm's motion accuracy and operational stability. In S5.1, when reading the corrected end effector position information from the data buffer, the timing accuracy of the reading must be strictly guaranteed. The reading interval must be completely consistent with the data storage interval, set to 0.001 seconds, to avoid position data mismatch due to time asynchrony. When comparing the read corrected position with the theoretical position information to calculate the position deviation, a three-dimensional spatial distance calculation formula is used. This formula comprehensively considers the deviations in the X, Y, and Z dimensions of space. The calculated deviation value must achieve an accuracy of ±0.0001mm, providing highly accurate deviation data support for the precise calculation of subsequent calibration parameters. In S5.2, when determining the joint angle compensation value, the position deviation value must first be decomposed into the rotation direction of each joint to obtain the projected components. Then, combined with the inverse kinematics algorithm of the robotic arm, the required angle compensation for each joint is accurately calculated. For rotary joints, the motion range limitation must be strictly considered during the calculation process. Usually, the limit range of the joint angle is set to -180° to 180° to ensure that the compensated joint angle does not exceed this range and cause mechanical failure. At the same time, the accuracy of the compensation value must be strictly controlled within ±0.0001°. In S5.3, when calculating the link length correction coefficient, based on the joint angle compensation value and combined with the dynamic characteristics of the hydraulic robotic arm, a correlation model between the correction coefficient and the joint force is established. When the joint force increases by 10N, the correction coefficient increases by 0.001 to compensate for the link deformation error caused by the force change. At the same time, the pressure adjustment parameters of the hydraulic drive device need to be dynamically calculated based on the joint torque deviation. For every 1N increase in torque deviation, the correction coefficient increases by 0.001. For each parameter, the pressure adjustment parameter is increased by 0.05 MPa. Adjusting the pressure optimizes the drive torque output, ensuring the link length correction coefficient and pressure adjustment parameter work synergistically to achieve a complementary error compensation effect. Specifically, the accuracy of the link length correction coefficient must reach ±0.0001, and the accuracy of the pressure adjustment parameter must reach ±0.001 MPa. In S5.4, when storing the determined joint angle compensation value, link length correction coefficient, and pressure adjustment parameter in the calibration parameter database, encrypted storage is used. Data encryption algorithms prevent unauthorized tampering or malicious modification of the parameters, ensuring their security and integrity. This database must have real-time read / write capabilities and comprehensive historical data query functions. Each set of stored parameters must include a precise timestamp to accurately trace parameter adjustment records and time points during subsequent troubleshooting or accuracy analysis. The database update frequency must be consistent with the calibration parameter determination frequency, set to 100 Hz, to ensure the robotic arm's control system can acquire and apply the latest calibration parameters in real time. Throughout the implementation process, a parameter verification mechanism is set up. Every 0.1 seconds, the latest calibration parameters are applied to the control process of the robotic arm. The end-effector position deviation after application is measured in real time using high-precision measuring equipment. If the deviation value measured multiple times is greater than 0.005mm, the parameter recalculation process is immediately triggered to readjust the joint angle compensation value, link length correction coefficient, and pressure adjustment parameters until the deviation value is stably controlled within 0.005mm. This ensures that all determined calibration parameters can effectively improve the motion accuracy of the robotic arm.

[0047] The Lagrange method-based no-load dynamic model of a hydraulic robotic arm in this invention describes the motion and force relationships of each joint of the robotic arm under no-load conditions. Specifically, it establishes the relationship between joint torques and motion states (angular displacement, angular velocity, angular acceleration) by analyzing the mass distribution, moment of inertia, and output characteristics of the hydraulic drive device of each joint link. To implement this model, the parameters of each joint link must first be measured. The mass and center of gravity of the link are determined using a weighing method combined with 3D scanning technology (the mass of a single link is 2.5 kg to 8 kg, with a center of gravity offset within ±0.5 mm). A moment of inertia meter is used to measure the moment of inertia about different axes (accuracy ±0.01 kg). Simultaneously, pressure and torque sensors are used to collect the output torque of the hydraulic drive unit within the oil supply pressure range of 5MPa to 20MPa (collecting one set every 0.5MPa, for a total of more than 30 sets). This data is input into a Lagrange-based calculation module to solve for changes in kinetic and potential energy, obtaining the functional relationship between joint torque and motion state. This relationship is verified through no-load reciprocating motion (the deviation between the calculated torque value and the actual measured value is controlled within 5%). The model's purpose is to accurately reflect the dynamic characteristics of the robotic arm during no-load motion, providing a theoretical basis for analyzing joint forces. Its significance lies in supporting precise control of the robotic arm from a dynamic perspective, helping to identify dynamic deviations during no-load motion, laying the foundation for subsequent error compensation and parameter calibration, and ensuring the stability and controllability of the robotic arm's motion under no-load conditions.

[0048] The improved Denavit-Hartenberg kinematic error model of this invention is a model that introduces multi-factor error terms on the basis of the traditional model, in order to more comprehensively capture the deviation of the robotic arm's motion trajectory. Specifically, it incorporates error terms such as joint clearance, link elastic deformation, and temperature drift into the traditional Denavit-Hartenberg parameters (link length, torsion angle, joint offset, angle). The implementation process includes: first, acquiring traditional parameters (using a laser interferometer to measure the link length with an accuracy of ±0.001mm; an angle measuring instrument to measure the torsion angle with an accuracy of ±0.001°; and an encoder to read joint parameters with a resolution of 0.001°); then, controlling the robotic arm to select 100 preset postures in the workspace, using a laser tracker (accuracy ±0.01mm) to measure the actual position of the end effector, and calculating the deviation from the theoretical position; next, analyzing the influence of error factors and determining the weighting coefficients through displacement sensors (measuring joint clearance from 0 to 0.1mm with an accuracy of ±0.001mm), strain gauges and force sensors (measuring link deformation from 0 to 0.05mm), and temperature sensors (measuring from -10℃ to 50℃ with an accuracy of ±0.1℃); finally, incorporating the error term into the traditional parameters, identifying the error parameters using the least squares method, and ensuring that the model deviation matches the parameters by more than 90%. The purpose of this model is to more realistically reflect the kinematic characteristics of the robotic arm and improve the accuracy of error description. Its significance lies in breaking through the limitations of traditional models, considering error factors from multiple dimensions, providing a reliable kinematic basis for high-precision calibration of the robotic arm, ensuring more comprehensive error analysis, and providing an accurate basis for subsequent compensation.

[0049] The position prediction model based on convolutional neural networks of this invention is a model for predicting the position of the end effector of a robotic arm using deep learning technology. It can learn the position change law based on joint motion parameters. Specifically, it takes joint angle, angular velocity, and angular acceleration as inputs, fits nonlinear relationships through a convolutional neural network, and outputs the three-dimensional position coordinates of the end effector. In implementation, a data acquisition system is first built: encoders (resolution 0.001°, sampling frequency 1kHz) and gyroscopes (angular velocity ±0.1° / s, angular acceleration ±1° / s²) are installed at the joints, and a three-dimensional coordinate measuring instrument (range 0 to 5m, accuracy ±0.01mm, 1kHz sampling) is installed at the end effector. The robotic arm is controlled to perform various motion condition tests (uniform speed, acceleration and deceleration, etc., 10 minutes each), collecting no less than 1 million sets of data. After removing outliers, the data is divided into training and validation sets in an 8:2 ratio. The constructed network consists of 12 input neurons, 3 convolutional layers (32 neurons with 5×5 kernels, 64 neurons with 3×3 kernels, and 128 neurons with 3×3 kernels), and 2 fully connected layers (128 neurons with 3 neurons each). It was trained for 100 epochs using the Adam optimizer (initial learning rate 0.001, decaying by 0.1 every 10 epochs) to achieve a root mean square error (RMSE) of less than 0.05 mm on the validation set. The model's purpose is to provide accurate end-effector position prediction data. Its significance lies in leveraging the strong fitting ability of deep learning to improve the accuracy and real-time performance of position prediction, providing a reliable position reference for online calibration, giving subsequent error compensation a clear target basis, and ultimately improving the accuracy and response speed of the entire calibration system.

[0050] like Figure 2 As shown, an online calibration system for a robotic arm includes: The dynamic model building unit is used to build an unloaded dynamic model of a hydraulic manipulator based on the Lagrange method. This unit is connected to the joint sensors of the manipulator, receives the joint mass distribution and motion characteristic data collected by the sensors, and generates dynamic parameter relationships through internal algorithms. The kinematic error model building unit communicates bidirectionally with the dynamic model building unit, receives transmitted dynamic parameters, and connects to a laser tracker to obtain end-position deviation data, thereby establishing an improved Denavit-Hartenberg kinematic error model. The position prediction model training unit is connected to the kinematic error model establishment unit and the motion data acquisition device of the robotic arm, respectively. It receives kinematic error data and collected joint motion data, and generates a position prediction model through training a convolutional neural network. The error compensation calculation unit is connected to the position prediction model training unit at one end to obtain the predicted position data, and to the dynamic model construction unit and the kinematic error model establishment unit at the other end to obtain the relevant model parameters, and performs error compensation calculation for the predicted position. The calibration parameter determination unit is connected to the error compensation calculation unit. It receives the corrected position information, calculates and determines the joint angle compensation value, the link length correction coefficient and the pressure adjustment parameter by combining the theoretical position data. The model iteration optimization unit is connected to the position prediction model training unit and the calibration parameter determination unit, respectively. It receives the prediction model and calibration parameters, and continuously updates and iterates the model during the movement of the robotic arm to optimize the calibration parameters.

[0051] A method and system for online calibration of robotic arms is disclosed. This method boasts significant real-time advantages, effectively overcoming the shortcomings of poor timeliness in traditional offline calibration. By continuously repeating the steps of position prediction, error compensation, and parameter adjustment, the position prediction model is constantly updated and iterated during the continuous movement of the robotic arm, dynamically optimizing the online calibration parameters. It can respond to changes in working conditions in real time without fixing the robotic arm in a specific posture, ensuring that the calibration results remain synchronized with the operation process. This meets the dynamic accuracy requirements of continuous operation scenarios and avoids the calibration failure problem caused by changes in working conditions in offline calibration.

[0052] In terms of error description and compensation, this system demonstrates comprehensive advantages, overcoming the shortcomings of existing error models that consider only a single factor. Combined with a Lagrange-based hydraulic manipulator no-load dynamics model, it can accurately capture the correlation between joint torque and motion state. Through an improved Denavit-Hartenberg kinematic error model, it incorporates multiple factors such as joint clearance, link elastic deformation, and temperature drift. Furthermore, by leveraging a convolutional neural network position prediction model to learn motion patterns, it achieves a comprehensive description and accurate compensation for multi-source errors, overcoming the limitations of traditional models due to simplified assumptions.

[0053] The system's synergistic advantages further enhance calibration effectiveness. The dynamic model, kinematic error model, position prediction model, and online calibration parameters are organically linked, and the error correction process fully integrates the dynamic and kinematic characteristics of the robotic arm. From data acquisition and model training to parameter adjustment, each stage works closely together, ensuring that the actual motion trajectory of the robotic arm continuously approaches the theoretical trajectory. This significantly improves calibration accuracy under complex working conditions, effectively reduces trajectory deviation, and comprehensively guarantees operational quality and stability.

[0054] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," "link," and "fix" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0055] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various equivalent changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for online calibration of a robot arm, characterized by, The method comprises the following steps: Step S1: constructing a hydraulic mechanical arm idle dynamics model based on the Lagrange method, determining the dynamics parameter relationship of different joints of the mechanical arm in the idle state by analyzing the mass distribution, rotational inertia of different joint connecting rods of the mechanical arm and the output characteristics of the hydraulic driving device, to reflect the correlation between the joint torque and the motion state in the movement process of the mechanical arm; Step S2: establishing an improved Denavit-Hartenberg kinematic error model, introducing error terms generated by joint clearance, connecting rod elastic deformation and temperature drift on the basis of existing Denavit-Hartenberg parameters, and capturing the deviation between the actual motion trajectory and the theoretical trajectory of different joints of the mechanical arm to form a kinematic error model affected by multiple error factors; Step S3: collecting the joint angle, angular velocity, angular acceleration and position coordinate data of the end effector of the mechanical arm under different motion conditions, inputting the collected data as training samples into a position prediction model based on a convolutional neural network, adjusting the convolution kernel size, convolution layer number and fully connected layer neuron number of the convolutional neural network to make the model learn the position change law in the movement process of the mechanical arm, and predicting the position of the end effector of the mechanical arm; Step S4: based on the idle dynamics model constructed in step S1 and the kinematic error model established in step S2, performing error compensation calculation on the predicted position output by the position prediction model in step S3, correcting the predicted position in combination with the real-time motion parameters of different joints of the mechanical arm, and obtaining the corrected position information of the end effector.

2. The method of claim 1, wherein, The method further comprises: Step S5: determining different parameters of the mechanical arm online calibration according to the corrected position information obtained in step S4, including joint angle compensation value, connecting rod length correction coefficient and pressure regulation parameter of the hydraulic driving device, and dynamically adjusting the parameters to make the actual motion trajectory of the mechanical arm approach the theoretical trajectory; Step S6: repeatedly executing steps S3 to S5, continuously updating and iterating the position prediction model in the continuous movement process of the mechanical arm, and continuously optimizing the online calibration parameters to perform real-time online calibration on the mechanical arm; The hydraulic mechanical arm idle dynamics model based on the Lagrange method in step S1 satisfies the following relationship: wherein, is the driving torque of the jth joint, is the inertia matrix element of the jth joint, is the joint angle vector, is the angular acceleration of the jth joint, is the Coriolis and centrifugal force coefficients of the jth joint, is the angular velocity of the jth joint, is the gravity term of the jth joint, is the friction torque of the jth joint; In step S4, the error of the predicted position is quantitatively analyzed by calculating the deviation of the driving torque of different joints in combination with the dynamics model, and then more accurate error compensation is realized.

3. The method of claim 1, wherein, Step S2 comprises the following sub-steps: S2.1: obtaining the traditional Denavit-Hartenberg parameters of different joints of the mechanical arm, including connecting rod length, connecting rod torsion angle, joint offset and joint angle, and inputting the parameters as initial parameters into an error model construction module; S2.2: collecting the actual position coordinates of the end effector of the mechanical arm under multiple preset postures by a laser tracker, recording the theoretical motion parameters of different joints under the corresponding postures, and calculating the deviation value between the actual position coordinates and the theoretical position coordinates; S2.3: Analyze the influence degree of joint clearance, link elastic deformation and temperature drift on the deviation value, determine the weight coefficient of different error factors, and introduce the error factors into the traditional Denavit-Hartenberg parameters in the form of correction terms; S2.4: Based on the parameters after introducing the error correction terms, an improved Denavit-Hartenberg kinematics error model is constructed, and the error parameters in the model are identified by least square method, which is used to reflect the kinematics error characteristics of the robot arm.

4. The method of claim 1, wherein, The output of the position prediction model based on convolutional neural network in step S3 satisfies the following relationship: wherein, is the predicted end effector position, is an activation function, are weight matrices of respective layers of the convolutional neural network, are bias terms of respective layers, is an input matrix of robot motion parameters; during the model training process, the error of the predicted position is back-propagated in combination with the kinematic error model established in step S2, and the weight and bias terms of the convolutional neural network are adjusted to improve the accuracy of the position prediction.

5. The method of claim 2, wherein, When determining different parameters of the online calibration of the robot arm in step S5, the following relationship is satisfied: wherein, is the angle compensation value of the jth joint, is the calibration parameter adjustment coefficient, is the position error of the jth joint, is the integral term of the position error, is the rate of change of the position error; the joint load change during the movement of the robot arm is calculated through the unloaded dynamics model of step S1, and the calibration demand under different movement states is adapted according to the dynamic adjustment of , .

6. The method of claim 1, wherein, Step S3 includes the following sub-steps: S3.1: Install high-precision sensors at the joints of the robot arm to collect real-time joint angle, angular velocity and angular acceleration data, and install a position detection device on the end effector to collect three-dimensional position coordinate data of the end effector; S3.2: Filter the collected data to remove abnormal data caused by sensor failure or external interference, retain valid data and sort them in time sequence to form an original data sequence; S3.3: Divide the original data sequence into a training set and a validation set, where the training set is used for training the convolutional neural network, and the validation set is used to evaluate the prediction performance of the model. The division ratio is set according to the data size; S3.4: Input the training set data into the convolutional neural network, calculate the prediction output of the model through forward propagation, calculate the prediction error combined with the validation set data, and adjust the network parameters according to the error result until the model reaches the preset training accuracy.

7. The method of claim 1, wherein, When correcting the predicted position in step S4, based on the improved Denavit-Hartenberg kinematics error model, the following relationship is satisfied: wherein, is the corrected end effector position, is the Jacobian matrix of the robot arm, is the joint angle error vector calculated based on the kinematic error model; elements of the Jacobian matrix are calculated by the null-space dynamics model of step S1 and the structural parameters of the robot arm, and the joint angle error vector According to the error term determined by the kinematics error model in step S2, the accurate correction of the predicted position is realized by the correction formula.

8. The method of claim 1, wherein, Step S4 includes the following sub-steps: S4.1: Extract the predicted position data of the end effector from the position prediction model in step S3, and obtain the real-time motion parameters of different joints from the control system of the robot arm, including joint angle, angular velocity and working pressure of the hydraulic drive device; S4.2: Input the predicted position data and real-time motion parameters into the error compensation calculation module, which calls the idle dynamics model in step S1 and the kinematics error model in step S2 to calculate the error value between the predicted position and the theoretical position S4.3: According to the calculated error value, determine the error compensation amount combined with the kinematics characteristics of the robot arm. The compensation amount is associated with the motion state of the joint and dynamically adjusted with the change of the joint motion parameters; S4.4: Apply the error compensation amount to the predicted position to obtain the corrected end effector position information, and store the information in the data buffer area to provide data support for subsequent calibration parameter determination.

9. The method of claim 2, wherein, Step S5 includes the following sub-steps: S5.1: Read the corrected end effector position information from the data buffer area in step S4, compare it with the theoretical position information of the robot arm, and calculate the position deviation value; S5.2: Based on the position deviation value, the structural parameters and the kinematics model of the mechanical arm are combined to determine the joint angle compensation value, which makes the joint motion trajectory deviate from the theoretical trajectory, for reducing the position deviation; S5.3: According to the joint angle compensation value and the dynamics characteristics of the hydraulic mechanical arm, the link length correction coefficient and the pressure regulating parameter of the hydraulic drive device are calculated, and the parameters work together to further optimize the motion accuracy of the mechanical arm; S5.4: The determined joint angle compensation value, link length correction coefficient and pressure regulating parameter are stored in the calibration parameter database as the basis for online calibration of the mechanical arm.

10. A robotic arm online calibration system, comprising: Comprise: A dynamics model construction unit for constructing a hydraulic mechanical arm empty load dynamics model based on Lagrange method, which is connected with the joint sensor of the mechanical arm, receives the joint mass distribution and motion characteristic data collected by the sensor, and generates the dynamics parameter relationship through internal algorithm processing; A kinematics error model establishment unit in bidirectional communication with the dynamics model construction unit, receives the transmitted dynamics parameters, and connects the laser tracker to obtain the end position deviation data, and establishes an improved Denavit-Hartenberg kinematics error model; A position prediction model training unit connected with the kinematics error model establishment unit and the motion data acquisition device of the mechanical arm respectively, receives the kinematics error data and the collected joint motion data, and generates a position prediction model through convolution neural network training; An error compensation calculation unit connected with the position prediction model training unit to obtain the predicted position data at one end, and connected with the dynamics model construction unit and the kinematics error model establishment unit to obtain the related model parameters at the other end, for error compensation calculation on the predicted position; A calibration parameter determination unit connected with the error compensation calculation unit to receive the corrected position information, calculate and determine the joint angle compensation value, link length correction coefficient and pressure regulating parameter in combination with the theoretical position data; A model iterative optimization unit connected with the position prediction model training unit and the calibration parameter determination unit respectively, receives the prediction model and the calibration parameter, and continuously updates and iterates the model during the motion of the mechanical arm to optimize the calibration parameter.

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