A state prediction method and device for a six-degree-of-freedom parallel robot

Abstract

The application provides a state prediction method and device of a six-degree-of-freedom parallel robot, and belongs to the technical field of parallel robot state monitoring. The method provided by the application comprises the following steps: acquiring operation data of the six-degree-of-freedom parallel robot; constructing a digital twin model; calculating a basic prediction pose and a prediction error compensation amount according to the digital twin model, superimposing the basic prediction pose and the prediction error compensation amount to obtain a twin prediction pose sequence; determining a three-source real and virtual residual error sequence in a sliding time window based on the operation data and the twin prediction pose sequence; inputting the three-source real and virtual residual error sequence into a trained space-time feature extraction model to obtain an error evolution feature, calculating a health degradation index according to the error evolution feature, and determining a degradation level of the six-degree-of-freedom parallel robot according to the health degradation index. The state prediction method and device of the six-degree-of-freedom parallel robot are used to realize six-degree-of-freedom parallel robot fault type identification, degradation degree quantification and early warning information output.

Description

Technical Field

[0001] This application relates to the field of parallel robot condition monitoring technology, and in particular to a method and apparatus for predicting the condition of a six-degree-of-freedom parallel robot. Background Technology

[0002] Six-degree-of-freedom (DOF) parallel robots consist of a static platform, a moving platform, and multiple drive chains connecting them. They possess advantages such as high rigidity, strong load-bearing capacity, fast dynamic response, and small cumulative error, and are widely used in motion simulation, equipment testing, precision machining, flight simulators, and medical robotics. During long-term service, these robots are inevitably affected by multiple factors, including structural parameter deviations, assembly errors, chain wear, servo lag, joint clearances, load disturbances, periodic vibrations, and measurement noise. This inevitably leads to nonlinear, time-varying, and multi-source coupled errors between the actual and desired end-effector poses. As operating time increases, these errors accumulate, potentially causing decreased positioning accuracy, deterioration in motion stability, and degradation in dynamic response performance. In severe cases, this can even lead to equipment failure or unplanned downtime. Therefore, continuous monitoring of the operating status of six-DOF parallel robots, accurate detection of early degradation, and timely identification of potential failure modes are critical technical requirements for ensuring their safe and reliable operation.

[0003] Currently, methods for condition monitoring and fault diagnosis of six-DOF parallel robots mainly fall into three categories. The first category is error analysis methods based on kinematic models. These methods establish forward and inverse kinematic models of the robot and use branch length feedback or end-effector pose measurement results to calculate and compensate for pose errors. This type of method relies on accurate mechanism geometry parameters and kinematic calibration results. The second category is threshold judgment methods based on sensor signals. These methods monitor changes in physical quantities such as drive motor current, vibration amplitude, and temperature, and compare them with preset thresholds to trigger an alarm. This type of method is simple, intuitive, and computationally inexpensive. The third category is data-driven fault identification methods. These methods utilize machine learning or deep learning models to automatically learn fault characteristics from large amounts of historical operating data and perform classification and identification. This type of method does not require precise system modeling and is suitable for fault diagnosis of complex nonlinear systems. In addition, in recent years, digital twin technology has begun to be introduced into the field of equipment condition monitoring. By constructing virtual mirror models corresponding to physical entities, real-time mapping and health assessment of equipment operating status can be achieved.

[0004] However, existing technologies still have many shortcomings. First, traditional kinematic error analysis and threshold judgment methods are difficult to simultaneously characterize the dynamic deviations between the physical robot, the virtual model, and the desired target, leading to the coupling and ineffective differentiation of control tracking errors, physical degradation errors, and model prediction errors. Second, data-driven fault identification methods lack physical model constraints, are sensitive to changes in operating conditions, and the fault diagnosis results are difficult to explain the source of the fault, making it difficult to accurately distinguish different types of fault modes such as structural parameter degradation, drive response lag, periodic vibration anomalies, and measurement link anomalies. Third, most existing digital twin diagnostic solutions are geared towards serial robots or general rotating machinery, lacking a dedicated residual characterization system for six-DOF parallel robots, especially lacking a joint residual analysis mechanism for branches and poses that utilizes the strongly nonlinear mapping relationship of parallel mechanisms. Fourth, existing online monitoring solutions lack health state gating constraints during model updates. When the robot experiences real degradation or early faults, the digital twin model parameters continue to track the actual pose for adaptive correction, causing degradation features to be absorbed by the model update process, masking the true degradation trend and easily leading to missed and false alarms. Summary of the Invention

[0005] In view of this, this application provides a state prediction method and apparatus for a six-DOF parallel robot to solve the problems of existing six-DOF parallel robot state monitoring methods, which are difficult to simultaneously characterize the dynamic deviations between the physical robot, the virtual model and the desired target, difficult to distinguish between control tracking error, physical degradation deviation and model prediction deviation, difficult to identify the fault types corresponding to multi-source errors, difficult to quantify health degradation trends, and may mistakenly correct real degradation as model parameter drift during online model updates.

[0006] Specifically, this application is implemented through the following technical solution:

[0007] The first aspect of this application provides a state prediction method for a six-degree-of-freedom parallel robot, the method comprising:

[0008] The operation data of a six-DOF parallel robot is obtained, and the operation data includes at least the expected pose sequence, the actual pose sequence, the six branch length data, and the drive state data.

[0009] A digital twin model is constructed based on the coordinates of the hinge points of the static platform, the coordinates of the hinge points of the dynamic platform, the initial length of the driving branch, the platform coordinate system parameters, and the driving response parameters. The digital twin model includes a geometric structure sub-model, a kinematic sub-model, a driving response sub-model, and an error mapping sub-model.

[0010] Based on the six-branch length data, the basic predicted pose is solved by the kinematic sub-model. Based on the historical running data window, the prediction error compensation amount is obtained by the error mapping sub-model. The basic predicted pose and the prediction error compensation amount are superimposed to obtain the twin predicted pose sequence.

[0011] Based on the running data and the twin predicted pose sequence, a three-source real and virtual residual sequence is determined within a sliding time window;

[0012] The three-source real and virtual residual sequences are input into the trained spatiotemporal feature extraction model to obtain error evolution features. The health degradation index is calculated based on the error evolution features, and the degradation level of the six-degree-of-freedom parallel robot is determined based on the health degradation index.

[0013] A second aspect of this application provides a state prediction device for a six-degree-of-freedom parallel robot, the device comprising an acquisition module, a processing module, and a prediction module;

[0014] The acquisition module is used to acquire the operation data of the six-degree-of-freedom parallel robot. The operation data includes at least the expected pose sequence, the actual pose sequence, the six-branch length data, and the drive state data.

[0015] The processing module is used to construct a digital twin model based on the coordinates of the static platform hinge point, the coordinates of the moving platform hinge point, the initial length of the driving branch, the platform coordinate system parameters, and the driving response parameters. The digital twin model includes a geometric structure sub-model, a kinematic sub-model, a driving response sub-model, and an error mapping sub-model.

[0016] The processing module is also used to solve the basic predicted pose based on the six branch length data through the kinematic sub-model, obtain the prediction error compensation amount based on the historical running data window through the error mapping sub-model, and superimpose the basic predicted pose and the prediction error compensation amount to obtain the twin predicted pose sequence.

[0017] The processing module is also used to determine the three-source real and virtual residual sequence within a sliding time window based on the running data and the twin predicted pose sequence;

[0018] The prediction module is used to input the three-source real and virtual residual sequences into the trained spatiotemporal feature extraction model to obtain error evolution features, calculate the health degradation index based on the error evolution features, and determine the degradation level of the six-degree-of-freedom parallel robot based on the health degradation index.

[0019] The state prediction method and apparatus for a six-DOF parallel robot provided in this application achieve synchronous virtual mapping of the motion and error states of the six-DOF parallel robot by constructing a digital twin model containing four sub-models: geometry, kinematics, drive response, and error mapping. This provides a physically constrained virtual benchmark for subsequent residual analysis. Based on this, the basic predicted pose is solved using the six-branch length data, and error compensation is superimposed to obtain a twin predicted pose sequence. This establishes a three-source correspondence between the desired pose, the actual pose, and the twin predicted pose at the same sampling time, enabling effective differentiation of control tracking error, entity degradation error, and model prediction error in the subsequent residual construction stage. This avoids the problem of mutual coupling and untraceable sources of the three types of errors in traditional methods. Furthermore, by determining the three-source real and virtual residual sequences within a sliding time window and inputting them into a spatiotemporal feature extraction model to extract error evolution features, the residual data can be fully exploited. The system analyzes the local fluctuation characteristics, multi-degree-of-freedom coupling characteristics, time-dependent characteristics, and degradation evolution characteristics of the original residual signal, transforming it into a high-dimensional abstract feature that can characterize the fault type and degradation degree. Based on the error evolution characteristics, a health degradation index is calculated by weighting and fusing five degradation factors: error amplitude, trend, vibration anomaly, twin deviation, and drive hysteresis. Combined with a preset threshold set, the degradation level is determined. This allows the quantitative assessment of health status to no longer rely on a single physical quantity or simple threshold judgment, but rather integrates multi-dimensional and multi-modal degradation information, effectively improving the sensitivity to early degradation trends and robustness to instantaneous noise interference. Taking a six-degree-of-freedom parallel robot as an example, the system fully considers its structural characteristics of multi-branch closed-loop coupling and strong nonlinear mapping between branch length and the six-dimensional pose of the moving platform. This enables accurate identification of fault types and reliable quantification of degradation degree, providing systematic technical support for predictive maintenance and health management of six-degree-of-freedom parallel robots. Attached Figure Description

[0020] Figure 1 A flowchart of an embodiment of the state prediction method for a six-DOF parallel robot provided in this application;

[0021] Figure 2 This is a schematic diagram of the second embodiment of the state prediction device for a six-degree-of-freedom parallel robot provided in this application. Detailed Implementation

[0022] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application.

[0023] The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The singular forms “a,” “the,” and “the” used herein are also intended to include the plural forms unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used herein refers to and includes any and all possible combinations of one or more of the associated listed items.

[0024] It should be understood that although the terms first, second, third, etc., may be used in this application to describe various information, such information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. For example, without departing from the scope of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the word "if" as used herein may be interpreted as "when," "when," or "in response to determination."

[0025] The following specific embodiments are given to illustrate the technical solution of this application in detail.

[0026] Figure 1 This is a flowchart of an embodiment of the state prediction method for a six-DOF parallel robot provided in this application. Please refer to... Figure 1 The method provided in this embodiment may include:

[0027] S101. Obtain the operation data of the six-degree-of-freedom parallel robot. The operation data includes at least the expected pose sequence, the actual pose sequence, the six-branch length data, and the drive state data.

[0028] Specifically, a six-DOF parallel robot includes a static platform, a moving platform, and six drive chains connecting the static and moving platforms. These six drive chains coordinate their extension and retraction to achieve three-dimensional translation and rotation of the moving platform. The six-DOF parallel robot can be a Stewart platform, a 6-UPS parallel mechanism, or other six-DOF parallel mechanisms. The desired pose sequence is obtained through a controller; the actual pose sequence is obtained through a pose measurement device; the length data of the six drive chains is obtained through encoders of the six drive chains; and the drive status data is obtained through drive status sensors. The above operational data undergoes time synchronization and coordinate unification preprocessing.

[0029] Furthermore, the expected pose sequence, the actual pose sequence, and the twin predicted pose sequence are all represented by a six-dimensional pose vector. The six-dimensional pose vector includes three-dimensional translational displacement along the X-axis, Y-axis, and Z-axis, and three-dimensional attitude angles around the X-axis, Y-axis, and Z-axis. The operating data also includes at least one of the following: drive motor current, drive motor speed, drive motor acceleration, platform vibration signal, load information, temperature information, sampling time information, and control command information. The preprocessing includes interpolating sensor data with different sampling frequencies to a unified sampling time, and performing outlier removal, filtering, and normalization based on healthy baseline samples on the synchronized operating data.

[0030] Furthermore, in the base coordinate system, let the center position vector of the moving platform be p(t), and the attitude matrix of the moving platform be R(t). Then, the six-dimensional pose vector of the moving platform is expressed as:

[0031] ;

[0032] Where x(t), y(t), and z(t) represent the translational displacements of the moving platform along the X, Y, and Z axes, respectively, and α(t), β(t), and γ(t) represent the attitude angles of the moving platform about the X, Y, and Z axes, respectively. The attitude matrix R(t) can be determined by the attitude angles.

[0033] Let the first The coordinates of the hinge point of the drive chain on the static platform are: The coordinates of the hinge point in the moving platform coordinate system are: ,in Then the first The branch vector of the driving branch in the base coordinate system is:

[0034] ;

[0035] Where p(t) is the center position vector of the moving platform;

[0036] R(t) is the attitude matrix of the moving platform;

[0037] For the first The coordinates of the hinge point of the drive chain on the static platform;

[0038] For the first The coordinates of the hinge point of the driving chain in the moving platform coordinate system.

[0039] No. The length of the driving branch in the base coordinate system is:

[0040] ;

[0041] The corresponding unit direction vector can be expressed as:

[0042] ;

[0043] The aforementioned kinematic relationship establishes a mapping between the six-dimensional pose of the moving platform and the lengths of the six driving branches, which forms the basis for the subsequent generation of twin prediction poses by the digital twin model.

[0044] Furthermore, the desired pose sequence originates from the target motion trajectory planned by the robot control system or input from an external source. It represents the expected spatial position and orientation of the moving platform at each sampling moment, typically generated by the motion planning module according to a preset trajectory. The actual pose sequence is acquired by a pose measurement device installed at the robot's end effector. This device can be an external pose measurement equipment, a vision measurement device, a laser tracking device, an inertial measurement unit, or a calibrated multi-sensor fusion measurement link. The actual pose sequence reflects the true spatial position and orientation of the moving platform during actual operation. The six-branch length data is acquired by encoders installed on each drive branch. The encoders measure the actual extension and retraction length of each branch in real time, and these length data are mapped to the actual pose of the moving platform through kinematic relationships. Drive state data is acquired by drive state sensors and may include information such as drive motor current, drive motor speed, and drive motor acceleration, used to characterize the execution state and response characteristics of the drive branches.

[0045] In this embodiment, the operational data includes at least the desired pose sequence and the actual pose sequence. The desired pose sequence represents the target motion trajectory planned or input by the robot control system, while the actual pose sequence represents the motion trajectory of the moving platform collected during the actual operation of the robot.

[0046] Optionally, the operational data also includes at least one of the following: length changes of the six drive chains, drive motor current, speed, acceleration, platform vibration signal, load information, temperature information, and sampling time information. This data can be acquired by an encoder, pose measurement device, inertial measurement unit, accelerometer, current sensor, temperature sensor, or robot controller. The actual pose sequence can be obtained by an external pose measurement device, vision measurement device, laser tracking device, inertial measurement device, or a calibrated multi-sensor fusion measurement link.

[0047] After synchronization, the running data undergoes coordinate unification, communication delay compensation, outlier removal, filtering, and normalization. Outlier removal can use three times the standard deviation or median filtering, while filtering can use low-pass filtering, wavelet filtering, or moving average. The normalization parameter is taken from a healthy baseline sample. For sensor data with different sampling frequencies, the data is interpolated to a unified sampling time based on the timestamp, and the pose data is transformed to the same base coordinate system.

[0048] S102. Construct a digital twin model based on the coordinates of the hinge point of the static platform, the coordinates of the hinge point of the moving platform, the initial length of the driving branch, the platform coordinate system parameters, and the driving response parameters. The digital twin model includes a geometric structure sub-model, a kinematic sub-model, a driving response sub-model, and an error mapping sub-model.

[0049] Specifically, the digital twin model is used to synchronously map the motion state and error state of a six-DOF parallel robot and output the twin's predicted pose. The digital twin model includes a geometric structure sub-model, a kinematics sub-model, a drive response sub-model, and an error mapping sub-model.

[0050] The geometric sub-model is used to store and update the structural parameters of the six-DOF parallel robot, including the coordinates of the static platform hinge points. Coordinates of the hinge point of the moving platform Initial length of the driving branch , branch installation angle, and parameters of the moving platform coordinate system and the static platform coordinate system.

[0051] The kinematic sub-model is used to describe the mapping relationship between the lengths of the six driving branches and the six-dimensional pose of the moving platform. For a given desired pose... Kinematic sub-model based on and Calculate the theoretical length of each branch; for a given actual branch length or branch state data, the kinematic sub-model solves for the corresponding dynamic platform pose.

[0052] The driver response sub-model is used to describe the response hysteresis between the instruction input and the actual output of the driver branch. In one implementation, the first... The equivalent actual length of a branch can be expressed as:

[0053] ;

[0054] in Indicates the first The theoretical instruction length of a single-driven branch. This represents the equivalent actual length considering response lag. Indicates the first The equivalent lag time of the driving branch.

[0055] The error mapping sub-model is used to describe the impact of structural parameter errors, drive response hysteresis errors, periodic vibration errors, and measurement noise errors on the end-effector pose. In this embodiment, the robot motion error can be expressed as:

[0056] ;

[0057] in, This indicates structural parameter errors, which are mainly caused by manufacturing and assembly deviations, branch length deviations, hinge point position deviations, or platform geometric parameter deviations. This indicates drive response hysteresis error, which is mainly caused by servo response delay, drive chain gap, actuator response attenuation, or control cycle discretization. This indicates periodic vibration error, which is mainly caused by mechanical resonance, transmission periodic error, or external periodic excitation. This indicates measurement noise error, mainly caused by sensor noise, communication jitter, or abnormal acquisition link.

[0058] The above sub-models are combined to form a digital twin model that operates synchronously with the physical six-DOF parallel robot. To ensure the model can be implemented, when solving the pose of the moving platform from the lengths of the six branches, the forward kinematics iterative solution can be constructed as a length residual minimization problem, using the actual pose or twin-predicted pose at the previous sampling time as the initial value, and solved using the Gauss-Newton method, the Levenberg-Marquardt method, or other iterative optimization algorithms. When the iteration fails to converge or the solution result violates the branch stroke, velocity, and attitude constraints, the window is treated as an abnormal window.

[0059] Furthermore, the implementation steps for building a digital twin model include:

[0060] (1) Construct a geometric sub-model based on the coordinates of the hinge point of the moving platform, the coordinates of the hinge point of the static platform, the initial length of the driving chain, the installation angle of the chain, and the parameters of the platform coordinate system;

[0061] Specifically, the geometric sub-model is used to store and manage the fixed structural parameters of the six-DOF parallel robot. The static platform hinge point coordinates refer to the three-dimensional position coordinates of the hinge points where each drive branch connects to the static platform in the base coordinate system. The moving platform hinge point coordinates refer to the three-dimensional position coordinates of the hinge points where each drive branch connects to the moving platform in the moving platform coordinate system. The initial length of each drive branch refers to its original length in the zero-position state. The branch installation angle reflects the orientation of each branch on the platform. The platform coordinate system parameters include the relative pose relationship between the moving platform coordinate system and the static platform coordinate system. These parameters together constitute a complete set of parameters describing the robot's geometric configuration.

[0062] Furthermore, after the robot is installed, the spatial positions of the six hinge points on the static platform are measured using a laser tracker, coordinate measuring machine, or other precision measuring equipment. The three-dimensional coordinates of each hinge point in the static platform's base coordinate system are obtained and stored in the model. The distribution configuration of these six points determines the geometry of the static platform and the arrangement of the branch roots. The six hinge points on the moving platform are also measured to obtain their three-dimensional coordinates in the moving platform's coordinate system. The distribution configuration of these six points determines the geometry of the moving platform and the connection method of the branch tips. It should be noted that the coordinates of the moving platform hinge points are defined in the moving platform's own coordinate system, which moves with the moving platform, rather than being absolute coordinates in a fixed base coordinate system. The original rod lengths of each drive branch in the calibrated zero-position state are entered into the model. The initial lengths serve as the benchmark for calculating the length changes of all subsequent branches. The installation angles of each branch relative to the platform's normal direction are determined. The branch installation angles reflect the spatial attitude of the branches and play a crucial role in subsequent force analysis and motion constraints. Define the initial relative pose of the moving platform coordinate system with respect to the static platform base coordinate system, including the origin offset and coordinate axis rotation. Once all the above parameters are entered, the geometric sub-model is complete.

[0063] (2) A kinematic sub-model is established based on the geometric structure sub-model. The kinematic sub-model is used to solve the six-dimensional pose of the moving platform based on the length of the six branches.

[0064] Specifically, the kinematic sub-model is built upon the geometric sub-model and describes the bidirectional mapping between the lengths of the six driving branches and the six-dimensional pose of the moving platform. In the forward mapping direction, given the six-dimensional pose of the moving platform, the kinematic sub-model can calculate the theoretical lengths of each of the six branches based on the coordinates of each hinge point and the branch connection relationships. In the reverse mapping direction, given the actual lengths of the six branches, the kinematic sub-model can solve for the corresponding six-dimensional pose of the moving platform. This bidirectional mapping capability makes the kinematic sub-model a bridge connecting the branch length space and the moving platform pose space.

[0065] Furthermore, in the construction of the forward mapping, given the six-dimensional pose of the moving platform, it is necessary to first construct the attitude rotation matrix of the moving platform based on the attitude angle information. The rotation matrix describes the attitude change of the moving platform coordinate system relative to the base coordinate system, transforming the coordinates of the moving platform hinge points from the moving platform coordinate system to the base coordinate system. At this point, the coordinates of the static platform hinge points and the moving platform hinge points are in the same base coordinate system, and the distance between the two points is the actual length of the branch in the current pose. Performing this calculation process on each of the six branches yields the theoretical lengths of the six branches in the given pose. This forward mapping relationship is the foundation of kinematic modeling. In the construction of the inverse mapping, given the actual lengths of the six branches, it is necessary to solve the corresponding six-dimensional pose of the moving platform in reverse. This is a problem of solving a nonlinear system of equations, and the solution process cannot directly obtain an analytical solution. Therefore, a numerical iterative solution scheme needs to be constructed. Specifically, the construction method is to construct a length residual objective function using the sum of squares or absolute values ​​of the differences between the theoretical and actual lengths of the six branches. The value of the objective function reflects the closeness between the current pose estimate and the true pose. The Gauss-Newton method or the Levenberg-Marquardt method is chosen as the iterative optimization algorithm. The actual or predicted pose at the previous sampling time is used as the initial value for iteration. The initial residual is calculated using the initial value, and the iterative update direction is calculated using the Jacobian matrix. The pose estimate is gradually adjusted to decrease the residual objective function. The iteration terminates when the residual objective function value is less than a preset convergence threshold. Simultaneously, to prevent iteration divergence or convergence to an incorrect solution, branch stroke boundary constraints, velocity constraints, and attitude boundary constraints are added to the model as judgment conditions. When the iteration result exceeds the above constraint boundaries, the window is marked as abnormal. The establishment of the above forward and reverse mapping relationships makes the kinematic sub-model a two-way bridge connecting the branch length space and the pose space of the moving platform.

[0066] (3) Establish a driving response sub-model based on the response hysteresis parameters, velocity constraints and travel constraints of the six-branch chain;

[0067] Specifically, the drive response sub-model describes the response characteristics of the drive chains from receiving control commands to generating actual actions. In actual operation, the six drive chains are not ideal actuators; there is a time lag between the issuance of the command and the actual arrival of the chain at the designated position. Furthermore, each chain is constrained by its own maximum speed limit and mechanical travel boundary. The drive response sub-model quantifies this delay characteristic through response lag parameters and defines the motion boundaries of the chains through speed and travel constraints.

[0068] Furthermore, while the robot is stationary or moving at slow speed, step commands or sinusoidal scan commands are applied to each drive chain. Simultaneously, the actual position signals fed back by the chain encoders are recorded at a high sampling frequency. The command signals are compared and analyzed with the actual response signals. Based on the time delay of the response signal relative to the command signal, the equivalent hysteresis time constant of each chain is identified. Since the servo driver parameter settings, mechanical wear, and load conditions of each chain may differ, the hysteresis time parameters of each chain usually need to be identified independently. Speed ​​constraint boundaries are set for each drive chain. These boundaries are calculated based on the rated speed of the servo motor, the lead screw, and the mechanical transmission ratio, or can be obtained by consulting the technical specifications of the motor and driver. The speed constraint boundaries limit the maximum extension and retraction of the chain per unit time. When the control command requires the chain to move at a speed exceeding this limit, the drive response sub-model will truncate the command signal according to the speed limit value. Each drive chain has defined travel constraint boundaries, determined by the mechanical structural limits of the chain, including the minimum length when fully retracted and the maximum length when fully extended. When a control command requires the chain to move beyond these travel limits, the drive response sub-model limits the command to these travel boundaries. The aforementioned hysteresis, velocity limiting, and position limiting elements are cascaded according to the signal transmission sequence of the actual physical system, forming a complete response transmission relationship from the command length output by the control system to the equivalent actual length of the drive chain, thus completing the construction of the drive response sub-model. The drive response sub-model enables the digital twin model to move beyond an ideal kinematic model and instead possess execution elements highly consistent with the dynamic response characteristics of the physical robot, thereby ensuring that the twin's predicted pose reflects the true dynamic behavior of the physical robot.

[0069] (4) Establish an error mapping sub-model based on historical operation data and error data.

[0070] Specifically, the error mapping sub-model, built upon historical operational and error data, describes the impact of various error sources on the end-effector pose. The end-effector pose error of a six-DOF parallel robot originates from diverse sources, including structural parameter errors caused by manufacturing and assembly deviations, branch length deviations, or hinge point position deviations; drive response hysteresis errors caused by servo response delays or actuator response attenuation; periodic vibration errors caused by mechanical resonance or external periodic excitation; and measurement noise errors caused by sensor noise or communication jitter. The error mapping sub-model learns the mapping relationship between these various errors and the end-effector pose through historical data, thereby enabling compensation for prediction errors based on the current operational state.

[0071] Furthermore, under normal robot operation, operational data is collected under different trajectory types, movement speeds, load conditions, and temperature environments. This data includes drive state data, actual pose data, branch length data, load information, and temperature information. Simultaneously, the tracking error of the actual pose relative to the desired pose at each moment is recorded as a supervision label, constructing a training dataset containing input features and output labels. The input feature space and output target space are determined. The input feature space needs to include features related to various error sources, including branch length residual statistics reflecting structural parameter deviations, motor current and speed signals reflecting drive response states, frequency domain features of vibration signals reflecting periodic vibrations, load force or torque information reflecting load disturbances, and temperature information reflecting environmental influences. The output target space is the pose error compensation amount at the current moment. The network structure of the error mapping sub-model is selected, employing methods such as multi-layer fully connected neural networks, support vector regression, or ensemble learning. Hyperparameters such as the number of layers, the number of neurons per layer, and the activation function type are determined based on the scale and feature dimensions of the training data. The model is trained using a training dataset. The loss value between the predicted error compensation and the actual error is calculated through forward propagation. Then, the network weights are updated using backpropagation. This process is iterated until the loss function converges to a preset target value. Simultaneously, the generalization performance of the trained model is evaluated using an independent validation dataset to prevent overfitting, thus completing the construction of the error mapping sub-model. This error mapping sub-model can output the predicted error compensation in real time based on historical data windows at the current moment, used to correct the base predicted pose, making the twin predicted pose more closely approximate the actual pose of the physical robot.

[0072] In this way, a complete virtual mirror system was established for the six-DOF parallel robot, from ideal geometric configuration to actual dynamic response, and from ideal kinematic mapping to real error compensation. The four sub-models cooperate with each other and progress layer by layer, together forming a digital twin model system with ideal geometric reference, complete kinematic mapping, real drive response characteristics and adaptive error compensation capabilities. This enables the twin predicted pose to effectively approximate the real pose state of the physical robot, providing an accurate and reliable virtual comparison reference for subsequent degradation perception based on three-source residuals.

[0073] S103. Based on the six-branch length data, the basic predicted pose is solved through the kinematic sub-model. Based on the historical running data window, the prediction error compensation amount is obtained through the error mapping sub-model. The basic predicted pose and the prediction error compensation amount are superimposed to obtain the twin predicted pose sequence.

[0074] Specifically, the six-branch length data are input into the kinematic sub-model, and the basic predicted pose is obtained by inverse mapping; the historical running data window is input into the error mapping sub-model, and the prediction error compensation is output; the basic predicted pose and the prediction error compensation are superimposed in the pose space to obtain the twin predicted pose at each sampling time, thus forming the twin predicted pose sequence.

[0075] Furthermore, the solution for the basic predicted pose is obtained by using a kinematic submodel to perform an inverse mapping from the branch length space to the pose space. A length residual objective function is established between the theoretical and measured lengths of the six branches. Using the actual or predicted pose at the previous sampling moment as the initial value, an iterative optimization algorithm continuously adjusts the pose estimate, gradually bringing the theoretical branch length calculated from this pose closer to the measured branch length by the encoder. The iteration terminates when the length residual objective function meets a preset convergence threshold, and the pose estimate at this point is the basic predicted pose. This solution process fully considers the strong nonlinearity of the kinematics of a six-DOF parallel robot, using the pose information from the previous moment as a priori constraint to ensure the continuity and stability of the solution.

[0076] The prediction error compensation is output by the error mapping sub-model based on a historical operating data window. Since the basic predicted pose obtained solely from the ideal kinematic model cannot reflect various error factors in actual operation, the error mapping sub-model is needed to predict and compensate for system errors. The input to the error mapping sub-model is a historical operating data window containing drive state data, historical pose data, historical residual data, load information, and temperature information. The output is the prediction error compensation at the current moment, which reflects the combined impact of structural parameter errors, drive response hysteresis errors, periodic vibration errors, and measurement noise errors on the end effector pose.

[0077] After obtaining the basic predicted pose and the prediction error compensation, the two are superimposed in the pose space. Specifically, the corresponding dimensional components of the basic predicted pose are added to the corresponding dimensional components of the prediction error compensation to obtain the twin predicted pose at the current sampling moment. The twin predicted pose includes both the pose reference calculated from the ideal kinematic model based on measured branch lengths and the error compensation term predicted based on historical data, thus more accurately approximating the actual pose state of the robot. By sequentially performing the above process for each sampling moment, a twin predicted pose sequence aligned in time with both the desired and actual pose sequences can be obtained.

[0078] The trajectory tracking residual is the residual between the actual pose and the desired pose; the real-virtual deviation residual is the residual between the actual pose and the twin predicted pose; and the model prediction residual is the residual between the twin predicted pose and the desired pose. The trajectory tracking residual is equal to the sum of the real-virtual deviation residual and the model prediction residual. This summation is used for data synchronization verification, measurement anomaly identification, and digital twin prediction anomaly identification. The first-order rate of change of the real-virtual deviation residual is used to characterize the growth rate of the real-virtual deviation, and the second-order rate of change of the real-virtual deviation residual is used to characterize the acceleration of the growth of the real-virtual deviation.

[0079] Furthermore, the steps for solving the basic predicted pose using the kinematic sub-model based on the six branch length data include:

[0080] (1) Establish the objective function of the length residual between the theoretical length of the six-branch chain and the measured length of the six-branch chain;

[0081] Specifically, based on the current six-dimensional pose estimation value, combined with the coordinates of the static platform hinge point and the dynamic platform hinge point in the geometric structure sub-model, the theoretical length of each of the six branches is calculated; the actual lengths of the six branches measured by the encoder are obtained; the theoretical lengths and actual lengths of the six branches are subtracted one by one to obtain the independent length residuals of each branch; and the six independent residuals are combined to construct a scalarized length residual objective function.

[0082] Furthermore, in a six-DOF parallel robot, there is a definite geometric relationship between the six-dimensional pose of the moving platform and the lengths of the six driving branches. Given a pose estimate of the moving platform, the spatial distance from the hinge point of the static platform to the hinge point of the moving platform can be calculated based on the coordinates of the hinge point of the static platform and the hinge point of the moving platform. This distance is the theoretical length of the branch under the current pose estimate. When the pose estimate is exactly equal to the actual pose, the theoretical length of the six branches should be completely consistent with the actual length of the six branches measured by the encoder. However, during the iterative solution process, there is a deviation between the pose estimate and the actual pose, so there must be a difference between the theoretical length and the actual length of the six branches. For each branch, the theoretical length is subtracted from the measured length to obtain the independent length residual of that branch. Since the residuals of the six branches may be positive or negative, directly adding the six residuals will cancel each other out and cannot effectively represent the overall deviation. Therefore, it is necessary to further combine the six independent residuals into a scalarized length residual objective function. The residuals of each branch are squared and summed, or their absolute values ​​are summed, or a more robust loss function is used. The magnitude of the objective function comprehensively reflects the closeness between the current pose estimate and the true pose. The smaller the objective function value, the smaller the overall deviation between the theoretical length and the measured length, and the closer the pose estimate is to the true pose. When the objective function value is zero, it means that the theoretical length and the measured length are completely consistent, that is, the pose estimate equals the true pose. The establishment of this objective function transforms the pose solving problem into a numerical optimization problem, providing a clear objective guide and convergence criterion for subsequent iterative solutions.

[0083] (2) Using the actual or predicted pose at the previous sampling time as the initial value, the six-dimensional pose that makes the objective function of the length residual satisfy the convergence threshold is solved by the iterative optimization algorithm and used as the basic predicted pose.

[0084] Specifically, the actual or predicted pose at the previous sampling time is obtained as the initial pose estimate for the current iteration; the length residual objective function value and Jacobian matrix are calculated at the current initial pose estimate value; the pose update direction and update step size are calculated according to the optimization algorithm, and the pose estimate value is iteratively updated; after each iteration, the length residual objective function value is recalculated and it is determined whether the convergence threshold is met; when the convergence threshold is met, the iteration is terminated and the current pose estimate value is output as the basic predicted pose.

[0085] Furthermore, solving the six-dimensional pose of a six-DOF parallel robot from the lengths of its six branches is an inverse problem of a nonlinear system of equations, which cannot be solved analytically directly and must be solved using numerical iterative methods. This problem is highly nonlinear, and the objective function may have multiple local minima. Therefore, the choice of initial values ​​for iteration has a decisive impact on the convergence and convergence speed of the solution. If the initial values ​​are not chosen properly, the iterative process may converge to incorrect local minima or even diverge. Since the pose change between adjacent sampling times is usually small during normal continuous operation of a six-DOF parallel robot, the actual or predicted pose at the previous sampling time is very close to the true pose at the current time. Using this pose as the initial value for the current iteration is sufficiently reasonable, ensuring the convergence of the iterative process and the continuity of the solution results. After determining the initial values, an iterative optimization algorithm is used for the solution. In each iteration, the length residual objective function is calculated at the current pose estimate, and the Jacobian matrix, composed of the first-order partial derivatives of the objective function with respect to each component of the six-dimensional pose, is also calculated. This matrix describes the local gradient information of the objective function near the current estimate. Based on the Jacobian matrix and the current residual vector, the pose update direction and update step size are calculated according to the adopted optimization algorithm. The updated amount is then superimposed with the current pose estimate to obtain the updated pose estimate, completing one iteration. The length residual objective function value is recalculated at the updated pose estimate and compared with a preset convergence threshold. The convergence threshold is a pre-set, sufficiently small positive number. When the objective function value is less than this threshold, it indicates that the deviation between the theoretical length and the measured length has become acceptable, and the current pose estimate is sufficiently close to the true pose. The iteration terminates, and this pose estimate is output as the base predicted pose at the current moment. If the objective function value is still greater than or equal to the convergence threshold, the next iteration continues, and this cycle repeats until the convergence condition is met or the maximum number of iterations is reached. The solution process makes full use of the physical characteristics of the continuous motion of a six-degree-of-freedom parallel robot, uses historical pose information as a priori constraint, and achieves high-precision and robust inverse mapping from branch length to pose through numerical optimization methods.

[0086] Furthermore, the steps for obtaining the prediction error compensation amount based on the historical operating data window through the error mapping sub-model include:

[0087] (1) Input the historical running data window containing at least one of the following: driving state data, historical pose data, historical residual data, load information and temperature information into the error mapping sub-model;

[0088] Specifically, the error mapping sub-model is a data-driven predictive model. Its input is a time window consisting of historical operational data from the current moment and several past moments, rather than being limited to instantaneous data from the current moment. This is because the errors of a six-DOF parallel robot have memory and time dependence. For example, the hysteresis effect of the drive response requires combining command and response data from several past moments to accurately determine the current hysteresis state. Although structural parameter errors are static in themselves, their pose errors exhibit different patterns as the motion trajectory changes. The phase information of periodic vibration errors requires data from a past period to accurately capture, while instantaneous single-point data is greatly affected by noise and cannot reflect the dynamic characteristics of error evolution. Therefore, a continuous data window needs to be extracted in the time direction as input. The length of the sliding time window is preset according to the design requirements of the error mapping sub-model. For example, it can be set to include data from dozens of past sampling moments. The window setting needs to consider two aspects: if the window length is too short, the input information will be insufficient, and the model will not be able to capture the time evolution and dynamic characteristics of the error; if the window length is too long, the computational load will increase and outdated invalid information may be introduced. The historical operational data collected within the window can include one or more types of data. Drive status data reflects the execution status of the drive chain, including drive motor current, motor speed, and motor acceleration; historical pose data includes the actual pose or twin-predicted pose at several past moments; historical residual data includes trajectory tracking residuals, real-virtual deviation residuals, or model prediction residuals at several past moments; load information reflects the magnitude and direction of the external load currently borne by the robot; temperature information reflects the thermal state of key parts of the robot. Before inputting the above data into the error mapping sub-model, it is necessary to ensure that all data within the window are strictly aligned in time, i.e., the same row of data corresponds to various types of sensor information at the same sampling moment. The aligned window data is constructed into a structured data form that matches the input interface of the error mapping sub-model, for example, organized as a multi-dimensional array, where one dimension is the time direction and the other dimension is various sensor features. Finally, the constructed historical running data window is provided as input to the error mapping sub-model, enabling it to understand the current running state while combining historical information from the past period to comprehensively judge the current error state.

[0089] (2) The error mapping sub-model outputs the predicted error compensation amount based on the mapping relationship between the structural parameter error, drive response hysteresis error, periodic vibration error and measurement noise error represented in the historical operation data window and the end pose.

[0090] Specifically, the error mapping sub-model has learned the mapping rules between various error source characteristics and end-effector pose errors from a large amount of historical data during the training phase. Therefore, after receiving the historical running data window during the inference phase, the model automatically performs a series of calculation operations to complete the conversion from input to output. The mapping relationship constructed by the error mapping sub-model covers the four main error sources of a six-DOF parallel robot. Structural parameter errors are the manifestation of geometric deviations generated during assembly and manufacturing in the motion process, such as the deviation between the actual and nominal lengths of branches, and the deviation between the actual and designed positions of hinge points. These errors exist when the robot is stationary and affect the end-effector accuracy in different ways with changes in pose. In historical data, they are usually reflected as a persistent residual mean bias that changes regularly with the motion trajectory. Drive response hysteresis error originates from the time delay between the servo control system receiving the control command and the actuator actually reaching the specified position. It is particularly significant during high-speed or acceleration / deceleration movements. The key is that there is a correlation between the error at the current moment and the command changes at several past moments. In historical data, it is usually reflected as a time lag between the actual pose and the expected or predicted pose. Periodic vibration error originates from factors such as mechanical resonance, rotational imbalance of transmission components, or external periodic excitation. This error has a stable frequency component and can be characterized by the energy concentration of the signal within a specific frequency band in the historical operating data window. Measurement noise error originates from the electronic noise of the sensor itself and communication jitter in the acquisition link, and is usually reflected in historical data as high-frequency random fluctuations in the residual sequence. During training, the error mapping sub-model has established a complex nonlinear mapping relationship between the feature patterns of the four types of error sources presented in the input window and the six-dimensional pose error of the end effector. This mapping relationship is stored in the form of network weights or parameter matrices within the model. In the inference phase, the model transforms the input historical operating data window layer by layer through forward propagation calculation, extracts the feature patterns related to each type of error source, and integrates these feature patterns into an estimated value of the end effector pose error according to the training-obtained mapping relationship. This value is output in the form of a six-dimensional pose error vector, which is the prediction error compensation amount at the current moment. Its six components correspond to the predicted pose error values ​​in the three translational directions and the three rotational directions, respectively. The prediction error compensation amount will then be superimposed on the basic prediction pose to obtain the corrected twin prediction pose, so that the twin prediction pose can approximate and reflect the real pose state of the physical robot.

[0091] S104. Based on the running data and the twin predicted pose sequence, determine the three-source real and virtual residual sequence within the sliding time window.

[0092] Specifically, at the same sampling time, three types of residuals are calculated based on the expected pose sequence, the actual pose sequence, and the twin predicted pose sequence; the residuals are expanded and combined within the sliding time window to obtain a three-source real and virtual residual sequence.

[0093] Furthermore, the three types of residuals are constructed based on three pose data sources at the same sampling time. The first type of residual is the trajectory tracking residual between the actual pose and the desired pose, obtained by subtracting the desired pose from the actual pose, and is used to characterize the overall tracking error of the physical robot on the desired trajectory. The second type of residual is the real-to-virtual deviation residual between the actual pose and the twin predicted pose, obtained by subtracting the twin predicted pose from the actual pose, and is used to characterize the degree of deviation between the physical robot and the digital twin model. This deviation reflects abnormal deviations of the physical robot caused by degradation and malfunctions that were not predicted by the digital twin model. The third type of residual is the model prediction residual between the twin predicted pose and the desired pose, obtained by subtracting the desired pose from the twin predicted pose, and is used to characterize the prediction deviation of the digital twin model relative to the desired motion.

[0094] Based on this, there is an additive relationship among the three types of residuals, namely, the trajectory tracking residual is equal to the sum of the real-virtual deviation residual and the model prediction residual, which constitutes a data consistency constraint that can be used to identify time synchronization errors, measurement link anomalies, or digital twin prediction anomalies.

[0095] When expanding and combining residuals within a sliding time window, in addition to using the three types of residuals themselves as basic residual channels, it is also necessary to calculate the first and second rates of change for the real-to-virtual deviation residuals. The first rate of change characterizes the growth rate of the real-to-virtual deviation, and the second rate of change characterizes the acceleration of the growth of the real-to-virtual deviation. Simultaneously, local statistical characteristics of various residuals are calculated within the window, including the root mean square value of the residuals, the peak-to-peak value of the residuals, the mean bias of the residuals, the standard deviation of the residuals, the skewness of the residuals, and the kurtosis of the residuals, as well as the frequency domain energy characteristics of the residuals, including the target frequency band energy, the peak value of the dominant frequency, or the proportion of frequency band energy. Organizing all the above channels into a three-dimensional data matrix within the sliding window yields the three-source real-to-virtual residual sequence.

[0096] Furthermore, the steps for determining the three-source real and virtual residual sequence within a sliding time window based on the running data and the twin predicted pose sequence include:

[0097] (1) Calculate the trajectory tracking residual, real-virtual deviation residual and model prediction residual based on the expected pose sequence, actual pose sequence and twin predicted pose sequence;

[0098] Specifically, at each sampling moment, the desired pose vector, the actual pose vector, and the twin predicted pose vector are acquired; the difference between the actual pose vector and the desired pose vector is used to obtain the trajectory tracking residual; the difference between the actual pose vector and the twin predicted pose vector is used to obtain the real-to-virtual deviation residual; the difference between the twin predicted pose vector and the desired pose vector is used to obtain the model prediction residual; the three types of residuals at each moment are arranged in chronological order to form the trajectory tracking residual sequence, the real-to-virtual deviation residual sequence, and the model prediction residual sequence, respectively.

[0099] Furthermore, three types of residuals are constructed based on the desired pose, the actual pose, and the twin predicted pose. The first residual is the trajectory tracking residual of the actual pose relative to the desired pose:

[0100] ;

[0101] The second residual is the real-to-virtual deviation residual of the actual pose relative to the twin-predicted pose:

[0102] ;

[0103] The third residual is the model prediction residual of the twin predicted pose relative to the desired pose:

[0104] ;

[0105] in, This is the actual pose vector. Let be the desired pose vector. Predicting pose for twins.

[0106] The trajectory tracking residual reflects the overall trajectory tracking error of the robot, the real-virtual deviation residual reflects the degree of deviation between the physical robot and the digital twin model, and the model prediction residual reflects the prediction deviation of the digital twin model relative to the desired motion. These three types of residuals are not independent data sources, but rather form a verifiable residual decomposition relationship between the desired target, the physical state, and the virtual predicted state.

[0107] (2) Within the sliding time window, determine the first-order and second-order rates of change of the real-virtual deviation residuals, and combine the trajectory tracking residuals, real-virtual deviation residuals, model prediction residuals, first-order rates of change, second-order rates of change, local statistical features and frequency domain energy features into a three-source real-virtual residual sequence.

[0108] Specifically, within a sliding time window, real and virtual deviation residuals at adjacent sampling times are selected, and the first and second rates of change are calculated. Within the window, local statistical features such as root mean square value, peak-to-peak value, mean bias, standard deviation, skewness, and kurtosis of various residuals are statistically analyzed. The residual sequence within the window is subjected to frequency domain transformation to extract frequency domain energy features such as target frequency band energy, main frequency peak value, and frequency band energy ratio. The trajectory tracking residual, real and virtual deviation residual, model prediction residual, first rate of change, second rate of change, local statistical features, and frequency domain energy features are organized into a three-dimensional data matrix according to the time dimension and feature dimension, forming a three-source real and virtual residual sequence.

[0109] Optionally, the local statistical features include at least one of the following: root mean square residual value, peak-to-peak residual value, mean offset of residual value, standard deviation of residual value, skewness of residual value, kurtosis of residual value, and frequency domain energy of residual value; the frequency domain energy features include at least one of the following: target frequency band energy, peak value of dominant frequency, or frequency band energy percentage.

[0110] Furthermore, to describe the dynamic changes in the real-to-virtual deviation residuals, the first and second rates of change of these residuals are calculated. For detailed calculation procedures, please refer to the relevant technical descriptions; they will not be repeated here. The first rate of change characterizes the growth rate of the real-to-virtual deviation, while the second rate of change characterizes the acceleration of its growth. Local statistical features are numerical indicators obtained by statistically analyzing the three types of residuals within a window. These include the root mean square value of the residuals, reflecting the average error energy within the window; the peak-to-peak value of the residuals, reflecting the maximum amplitude range of error fluctuations; the mean bias of the residuals, reflecting whether there is a systematic shift in the error; the standard deviation of the residuals, reflecting the dispersion and fluctuation amplitude of the error; the skewness of the residuals, reflecting the asymmetry of the error distribution; and the kurtosis of the residuals, reflecting the peak characteristics of the error distribution. These statistical features characterize the distribution pattern and dispersion characteristics of the residuals within the window from different perspectives. Frequency domain energy features are frequency domain information extracted by performing Fourier transform or other frequency domain transforms on the residual sequence within the window. This includes target frequency band energy reflecting the concentration of signal energy within a specific frequency range, the dominant frequency peak reflecting the frequency component with the most concentrated energy in the residual signal and its amplitude, and the frequency band energy proportion reflecting the proportional distribution of energy in each frequency band within the total energy. All the above feature channels are organized according to time and feature dimensions. The time dimension corresponds to the chronological order of sampling times within the window, while the feature dimension corresponds to different data channels such as trajectory tracking residuals, real-virtual deviation residuals, model prediction residuals, first-order rate of change, second-order rate of change, various statistical features, and frequency domain energy features. The resulting three-source real-virtual residual sequence is a three-dimensional data matrix. This matrix contains the time series information, dynamic change information, statistical distribution information, and frequency domain structure information of the original residual signal, providing rich and multi-dimensional input for the spatiotemporal feature extraction model. This allows it to comprehensively capture the evolution and degradation characteristics of errors from multiple perspectives, including the time domain, frequency domain, and statistical domain.

[0111] S105. Input the three-source real and virtual residual sequences into the trained spatiotemporal feature extraction model to obtain error evolution features, calculate the health degradation index based on the error evolution features, and determine the degradation level of the six-degree-of-freedom parallel robot based on the health degradation index.

[0112] Specifically, the three-source real and virtual residual sequences are input into the spatiotemporal feature extraction model, and the model outputs error evolution features; the health degradation index is calculated based on the error evolution features; the health degradation index is compared with a preset threshold set, and the degradation level is determined based on the comparison results.

[0113] Furthermore, the spatiotemporal feature extraction model is a deep learning model capable of simultaneously extracting spatial correlation and temporal dependence. The three-source real and virtual residual sequences are organized into a data matrix with the time window length as rows and the number of feature channels as columns, and input into the model. The convolutional neural network layer in the model extracts local fluctuation features and multi-degree-of-freedom coupling features from the residual sequences along the time dimension. These features reflect the error correlation and mutual influence between different degrees of freedom. The recurrent neural network layer or gated recurrent unit layer in the model further extracts the evolutionary features of the residuals as they continuously increase over time, exhibiting response lag or periodic enhancement. These features characterize the dynamic development trend of the degradation process. The fully connected layer of the model integrates the above spatiotemporal features and outputs the error evolution features.

[0114] The Health Degradation Index is a comprehensive quantitative indicator used to characterize the degree of degradation of a six-DOF parallel robot's current state relative to a health baseline. This index does not rely on a single physical quantity but integrates five degradation factors. The error amplitude degradation factor is calculated based on the deviation of the residual amplitude from the health baseline, reflecting the overall change in error magnitude. The trend degradation factor is calculated based on the growth slope of the residual amplitude over time, reflecting whether degradation is continuously intensifying. The vibration anomaly factor is calculated based on the energy or energy proportion of the residual within the target frequency band, reflecting the presence of abnormal vibration components. The twin deviation factor is calculated based on the average deviation between the actual pose and the twin predicted pose, reflecting the consistency between the entity and the model. The drive hysteresis factor is calculated based on the phase hysteresis between the desired pose and the actual pose, reflecting the degree of delay in the drive response. These five degradation factors are normalized and amplitude-limited, then weighted and fused according to preset weights to obtain a Health Degradation Index with a value ranging from zero to one; a higher value indicates more severe degradation.

[0115] The degradation level is determined by comparing a health degradation index with a preset set of thresholds. This set of thresholds includes multiple thresholds arranged from smallest to largest, each corresponding to a different degradation level boundary. When the health degradation index is less than the first threshold, the robot is considered to be in a healthy state; when the index is between the first and second thresholds, it is considered to be in a slightly degraded state; when the index is between the second and third thresholds, it is considered to be in a moderately degraded state; when the index is between the third and fourth thresholds, it is considered to be in a severely degraded state; and when the index is greater than or equal to the fourth threshold, it is considered to be in a faulty state. These thresholds are predetermined based on the statistical distribution of health samples, historical fault records, or safe operation requirements, thereby achieving a graded and quantitative assessment of the robot's degradation level.

[0116] Furthermore, the fault diagnosis results include at least one of the following: structural parameter degradation fault, drive response lag fault, periodic vibration anomaly fault, measurement link anomaly fault, and composite degradation fault. When the three-source real-virtual residual sequence exhibits a continuously increasing residual mean bias, while the summation consistency is still satisfied and is mainly a low-frequency stable offset, it is determined to be a structural parameter degradation fault. When the actual pose lags behind the expected pose or twin predicted pose and the lag exceeds a preset lag threshold, it is determined to be a drive response lag fault. When the target frequency band energy in the residual spectrum increases or a stable dominant frequency peak appears, it is determined to be a periodic vibration anomaly fault. When the residual high-frequency energy, standard deviation, or kurtosis increases while the residual mean bias and phase lag are not significant, or the summation consistency of the three types of residuals is disrupted, it is determined to be a measurement link anomaly fault. When at least two fault criteria are simultaneously satisfied, it is determined to be a composite degradation fault.

[0117] Furthermore, the spatiotemporal feature extraction model can be trained as follows: Collect operational data of a six-DOF parallel robot under different trajectories, speeds, loads, temperatures, and fault states. Trajectory types include straight lines, circles, spatial ellipses, or composite spatial trajectories. Fault states include normal states, structural parameter degradation, drive response hysteresis, periodic vibration anomalies, measurement link anomalies, and composite degradation. For fault states that are difficult to obtain directly, labeled samples can be constructed through offline simulation, bench fault injection, or historical maintenance records. Construct training real and virtual residual samples based on the expected pose sequence, actual pose sequence, and twin predicted pose sequence, and add fault type labels and degradation level labels to these samples. Input the training real and virtual residual samples into the spatiotemporal feature extraction model, using fault type labels and degradation level labels as supervision information for training. After training, the model can output error evolution features, fault category probabilities, and degradation state representations. During training, cross-entropy loss, mean squared error loss, or a weighted combination of both can be used, and the validation set is used to determine the window length, number of channels, and threshold set.

[0118] Furthermore, the steps for inputting the three-source real and imaginary residual sequences into the trained spatiotemporal feature extraction model to obtain error evolution features include:

[0119] (1) Organize the three-source real and virtual residual sequences into input samples consisting of a time window of length L and C feature channels;

[0120] Specifically, the length L of the sliding time window is determined, where L represents the number of consecutive sampling moments contained within the window; the total number of feature channels C is determined, including a six-dimensional trajectory tracking residual channel, a six-dimensional real-virtual deviation residual channel, a six-dimensional model prediction residual channel, a first-order and second-order rate-of-change channels for real-virtual deviation residuals, various local statistical feature channels, and various frequency domain energy feature channels; within the sliding window, the C-dimensional feature vectors corresponding to the L sampling moments are arranged in chronological order to form a two-dimensional data matrix of dimension L multiplied by C, which serves as the input sample.

[0121] Furthermore, the value of L needs to be determined based on the specific application scenario and model design requirements. Typically, the sampling frequency of the robot control system and the time scale of the error degradation process need to be considered. If the sampling frequency is high, a longer window length is required to cover sufficient degradation evolution information; if the sampling frequency is low, a shorter window length can be chosen. Typically, the value of L ranges from tens to hundreds of sampling points, allowing the window to cover multiple time scales from transient fluctuations to slow degradation trends. The composition of C determines the information dimensions that the model can utilize. The most basic channels include six channels of trajectory tracking residuals in the six degrees of freedom directions of 3D translation and 3D rotation, six channels of real and virtual deviation residuals in the six degrees of freedom directions, and six channels of model prediction residuals in the six degrees of freedom directions. These three original residual sequences already contain basic information about pose deviation. In addition, six channels each of the first and second rates of change of the real and virtual deviation residuals need to be added, reflecting the rate of change and acceleration of the deviation, respectively. In addition, it includes various local statistical feature channels calculated within the window, such as the root mean square value, peak-to-peak value, mean bias, standard deviation, skewness, and kurtosis of the residuals in each degree of freedom direction, as well as various frequency domain energy feature channels, such as target frequency band energy, peak value of the dominant frequency, and frequency band energy ratio. The total number of the above channels is C.

[0122] Furthermore, after determining the window length L and the total number of channels C, for each sampling time point within the sliding window, all C feature values ​​at that time are organized into a C-dimensional feature vector. The feature vectors from the L time points within the window are arranged in chronological order, forming a two-dimensional data matrix with dimensions L multiplied by C. The rows of this matrix represent the time dimension, and the columns represent the feature dimension. Each data element represents the value of a specific feature at a specific time point. This two-dimensional data matrix serves as the input sample for the spatiotemporal feature extraction model. This sample organically integrates time-series information and multi-dimensional feature information into a unified matrix structure, providing a standardized data input format for subsequent convolutional neural network layers and gated recurrent unit layers.

[0123] (2) Input the input sample into the CNN-GRU spatiotemporal feature extraction model, which includes a convolutional neural network layer, a gated recurrent unit layer and a fully connected output layer; the convolutional neural network layer extracts local fluctuation features and multi-degree-of-freedom coupling features in the input sample along the time dimension, the gated recurrent unit layer extracts time-dependent features and degradation evolution features in the input sample, and the fully connected output layer outputs error evolution features.

[0124] Specifically, the input samples are organized into a two-dimensional matrix of length L multiplied by C and then processed by a convolutional neural network (CNN). The core of the CNN layer consists of multiple learnable convolutional kernels, each a small one-dimensional filter whose width covers several time steps and whose height covers all or part of the feature channels. During the convolution operation, the kernels slide along the time dimension on the input matrix, calculating a weighted sum within the kernel's coverage area at each position and generating an output value through an activation function. By sliding the kernels, the CNN layer can detect local fluctuation patterns in the residual signal along the time direction. Unlike single-degree-of-freedom independent analysis, because the kernels can cover multiple feature channels along the height direction, the convolution operation can also simultaneously capture the coupling relationships between different degrees of freedom and different residual types. After processing by the convolutional layer, the time series of the input samples is transformed into a series of feature maps reflecting local fluctuations and coupling relationships.

[0125] Furthermore, the feature sequence output by the convolutional neural network layer is then input into the gated recurrent unit (ROU) layer. The gated recurrent unit is a recurrent neural network structure specifically designed for processing sequential data. Its core advantage lies in effectively solving the gradient vanishing problem in traditional RNNs when processing long sequences through a gating mechanism, enabling the model to learn dependencies over long time spans. The gated recurrent unit contains two gating structures: an update gate and a reset gate. The update gate controls how much information from the previous hidden state is retained in the current time step, allowing the model to remember important information from long ago. The reset gate controls how much information from the previous hidden state is ignored, allowing the model to discard historical information irrelevant to the current time step. Through the coordinated control of these two gates, the gated recurrent unit can read the input features at each time step, combine them with the state information from the previous time step, and output the hidden state at the current time step. Throughout the entire time series, the gated recurrent unit layer progressively reads the entire feature sequence output by the convolutional layers, with the hidden state at the last time step summarizing the key information within the entire time window. At this point, the model has fully captured the dynamic evolution characteristics of the degradation process, such as the trend of continuous increase of error over time in the residual sequence, the cumulative effect of response lag, and the phase evolution of periodic oscillations.

[0126] Furthermore, the hidden state output at the last time step of the gated recurrent unit layer contains complete spatiotemporal information within the entire time window, and this state vector typically has a high dimensionality. The fully connected output layer receives this hidden state vector and, through linear transformations and nonlinear activation functions of one or more fully connected layers, maps this high-dimensional vector into an output vector of a preset dimension. The output of the fully connected output layer is the error evolution feature. This feature vector comprehensively represents the key information extracted from the input residual samples in a compact encoded form, containing discriminative information sufficient to support subsequent health degradation index calculations and fault diagnosis decisions. Its dimensionality is typically much lower than the original input dimension, thus playing a role in feature dimensionality reduction and information condensation.

[0127] Furthermore, the steps for calculating the health degradation index based on the error evolution characteristics include:

[0128] (1) Extract the error amplitude component, trend component, frequency domain energy component, twin deviation component and driving hysteresis component from the error evolution characteristics, and calculate the error amplitude degradation factor according to the degree of deviation of the error amplitude component from the healthy baseline distribution;

[0129] Specifically, the error evolution feature vector output by the spatiotemporal feature extraction model is decoupled into components, separating the error amplitude component, trend component, frequency domain energy component, twin deviation component, and driving hysteresis component. Pre-stored health baseline distribution parameters are retrieved, which are derived from the statistical distribution of the error amplitude component when the robot is in a healthy state. The current error amplitude component is compared with the health baseline distribution to calculate the degree of deviation of the current amplitude relative to the health baseline distribution. The degree of deviation is then mapped to an error amplitude degradation factor.

[0130] Furthermore, the error evolution feature is a multi-dimensional vector output by the spatiotemporal feature extraction model. Different dimensions of this vector encode the attribute information of the error in different dimensions. Specific dimensions or combinations of dimensions correspond to different types of degradation information. Therefore, before calculating each degradation factor, the error evolution feature vector needs to be decoupled to extract the required components. The error amplitude component reflects the overall amplitude level of the current error, embodying the comprehensive magnitude of the error energy; the trend component reflects the direction and rate of error change over time, embodying the direction and speed of the degradation process; the frequency domain energy component reflects the energy distribution of different frequency components in the error, embodying the characteristics of periodic and vibrational errors; the twin deviation component reflects the degree of deviation between the physical robot and the twin model, embodying the consistency between the digital twin and reality; and the drive hysteresis component reflects the delay between the expected command and the actual response, embodying the response performance of the drive system.

[0131] After obtaining the error amplitude components, they are compared with a pre-stored health baseline distribution. The health baseline distribution is derived from historical data of the robot in a healthy operating state; that is, a large amount of normal data is collected during the period when the robot is calibrated and operating well. The error amplitude components at each moment are extracted, and their mean and standard deviation are calculated to establish the health baseline distribution. The error amplitude component at the current moment is compared with the health baseline mean to calculate the deviation of the current amplitude from the baseline mean. This deviation is then normalized using the baseline standard deviation to obtain the relative position of the current amplitude relative to the normal fluctuation range. The greater the deviation, the more severely the current error amplitude deviates from the normal level under healthy conditions. The deviation is converted into an error amplitude degradation factor ranging from zero to one using a preset mapping function. The closer the factor value is to one, the more severe the amplitude degradation; the closer it is to zero, the closer the amplitude is to a healthy state. This degradation measurement method based on the health baseline statistical distribution can adaptively determine whether the current error amplitude is abnormal, effectively solving the problem of poor applicability of fixed thresholds under different operating conditions.

[0132] (2) Calculate the trend degradation factor based on the growth slope of the residual amplitude as represented by the trend component over time;

[0133] Specifically, the growth slope information of the residual amplitude over time within the current time window is extracted from the trend component of the error evolution characteristics; the direction and rate of degradation trend are determined based on the magnitude and sign of the growth slope; and the growth slope is converted into a trend degradation factor through a preset mapping relationship.

[0134] Furthermore, the trend degradation factor focuses on assessing the degree of continuous change in error over time. The core quantity of interest is the growth slope of the residual amplitude over time, which reflects the change in error amplitude per unit time. If the growth slope is positive and large, it indicates that the error amplitude is continuously increasing over time, suggesting that the robot's performance is continuously degrading. If the growth slope is close to zero, it indicates that the error amplitude remains stable, and the degradation trend is not obvious or has not yet formed. If the growth slope is negative, it indicates that the error amplitude is decreasing, possibly due to changes in operating conditions or error recovery. After extracting the growth slope from the trend component of the error evolution characteristics, it is converted into a trend degradation factor through a preset mapping relationship. The design principle of the mapping relationship is to make the trend degradation factor corresponding to a growth slope of zero or negative close to zero, indicating the absence of a continuous degradation trend; to make the trend degradation factor corresponding to a small positive growth slope an intermediate value, indicating a slow degradation trend; and to make the trend degradation factor corresponding to a large positive growth slope close to one, indicating a rapidly escalating degradation trend. The introduction of this factor allows degradation assessment to focus not only on the current magnitude of the error, but also on the dynamic trend of the error. This enables early warnings to be given based on the continuously rising trend when degradation is still in its early stages and the error amplitude has not yet exceeded the alarm threshold.

[0135] (3) Calculate the vibration anomaly factor based on the frequency domain energy of the residual characterized by the frequency domain energy components in the target frequency band;

[0136] Specifically, the frequency domain energy component is extracted from the error evolution characteristics; the target frequency band range is determined, which corresponds to the frequency interval where the robot's mechanical resonance frequency or the characteristic frequency of the drive system is located; the energy value of the residual within the target frequency band is obtained; the target frequency band energy is compared with the total energy or the target frequency band energy under a healthy baseline, and the vibration anomaly factor is calculated.

[0137] Furthermore, the frequency domain energy components encode the energy distribution information of the residual signal in the frequency domain, reflecting the contribution of different frequency components to the total error. For a six-DOF parallel robot, when the mechanical structure becomes loose, worn, or fatigued, the system's resonance characteristics change, manifesting as an abnormal energy enhancement near the mechanical resonance frequency. When rotational imbalance of transmission components or bearing damage occurs, stable periodic components are generated at specific frequencies. These abnormal vibration components may be difficult to detect in the time domain due to being submerged by the large-amplitude main motion signal, but in the frequency domain, they manifest as a significant energy enhancement within the target frequency band. The calculation of the vibration anomaly factor is based on this mechanism. Extracting the energy value within the target frequency band from the frequency domain energy components requires pre-setting the target frequency band range based on the specific robot's mechanical structure and transmission characteristics. For example, it can cover the robot platform's inherent resonance frequency, the rotation frequency of the drive motor, and its harmonics. After obtaining the energy value of the residual within the target frequency band in the current window, it needs to be compared with a benchmark value. The benchmark value can be the proportion of the target frequency band in the total residual energy within the current window, or the statistical mean of the target frequency band energy under healthy conditions. The higher the proportion of the target frequency band energy, the greater the proportion of abnormal vibration components in the total error, and the more severe the vibration anomaly. This comparison result is mapped to a vibration anomaly factor with a value between zero and one. The closer the factor value is to one, the more severe the abnormal vibration. The introduction of this factor enables the method to effectively identify periodic vibration anomaly faults. These faults usually manifest as periodic fluctuations with small amplitudes in the time-domain residuals and are easily ignored as normal noise, but can be accurately captured through frequency domain analysis.

[0138] (4) Calculate the twin deviation factor based on the average deviation between the actual pose sequence represented by the twin deviation component and the twin predicted pose sequence;

[0139] Specifically, twin deviation components are extracted from error evolution characteristics. These twin deviation components encode the average deviation information between the actual pose sequence and the twin predicted pose sequence. The average deviation between the physical robot and the digital twin model within the current time window is obtained. The average deviation is compared with a preset normal deviation range to calculate the twin deviation factor.

[0140] Furthermore, the twin deviation component reflects the degree of consistency between the physical robot and the digital twin model during operation. The digital twin model is a virtual mirror constructed based on ideal geometric configuration and historical error data. When the physical robot is in a healthy state, this model should be able to predict the actual pose well; that is, the deviation between the actual pose and the twin-predicted pose should remain within a small, normal range. When the physical robot experiences structural parameter degradation, such as wear at the branch hinge points leading to changes in the effective link length or deformation of the platform structure, these changes are not captured by the digital twin model. Therefore, the model will predict according to the original structural parameters, while the actual behavior of the physical robot has deviated from the kinematic laws under the original parameters, resulting in a significant increase in the deviation between the actual pose and the twin-predicted pose. The twin deviation factor calculates the average deviation between the actual pose sequence and the twin-predicted pose sequence within a window. This deviation can be measured by the average of the absolute values ​​of the differences between the two sequences at each time step, or by more robust measures such as the median or quantiles. After obtaining the average deviation, it is compared with a preset normal deviation range, which is typically determined by the statistical distribution of twin deviations under healthy conditions. A greater deviation indicates a more severe inconsistency between the physical robot and the digital twin model, and a higher likelihood of structural parameter degradation. The deviation is mapped to a twin deviation factor ranging from zero to one. The unique value of this factor lies in its independence from changes in the desired trajectory. Even when the robot is operating in a constant position or at a slow speed, the twin deviation factor can capture any deviation as long as the physical structure changes, making it particularly sensitive to structural parameter degradation faults.

[0141] (5) Calculate the driving hysteresis factor based on the phase hysteresis between the desired pose sequence and the actual pose sequence as represented by the driving hysteresis component;

[0142] Specifically, the driving hysteresis component encodes the phase hysteresis information between the desired pose sequence and the actual pose sequence; the phase hysteresis amount between the desired pose and the actual pose within the current time window is obtained; the phase hysteresis amount is compared with a preset hysteresis threshold to calculate the driving hysteresis factor.

[0143] Furthermore, the drive hysteresis component reflects the delay characteristics between the receiving of the desired command and the actual output response of the drive system. The six drive chains of a six-DOF parallel robot are driven by servo motors. Servo control systems inevitably experience response delays. When the robot moves at high speeds or frequently accelerates and decelerates, this delay causes the actual pose to lag behind the desired pose on the time axis, manifesting as phase hysteresis. Under healthy conditions, the drive response hysteresis should remain within a normal range, determined by the bandwidth and control cycle of the servo system. When the drive chain degrades, such as due to decreased servo motor response performance, increased clearance in the transmission mechanism, or increased friction caused by deteriorated lubrication, the hysteresis time of the drive response will increase significantly, leading to a greater phase hysteresis between the desired and actual pose sequences. The drive hysteresis factor calculates the phase hysteresis between the desired and actual pose sequences. This hysteresis is usually estimated through cross-correlation analysis of the two sequences; the delay time corresponding to the peak of the cross-correlation function is the phase hysteresis. After obtaining the phase lag, it is compared with a preset lag threshold, which is determined based on the maximum allowable lag time under healthy conditions. A larger phase lag indicates more severe degradation in the response performance of the drive system. The ratio of the phase lag to the threshold is mapped to a drive lag factor ranging from zero to one. The introduction of this factor allows the method to directly quantify the dynamic performance degradation of the drive system, a degradation that is difficult to reflect in static errors and only manifests during dynamic motion.

[0144] (6) After normalizing and limiting the error amplitude degradation factor, trend degradation factor, vibration anomaly factor, twin deviation factor and driving lag factor respectively, they are weighted and fused according to preset weights to obtain the health degradation index.

[0145] Specifically, the five degradation factors described above characterize the health degradation state of a six-DOF parallel robot from five different dimensions: error amplitude, trend of change, vibration characteristics, twin consistency, and dynamic response of the drive. However, the calculation methods and original scales of each factor are different, requiring unified preprocessing before fusion. Numerical checks are performed on each degradation factor. Since abnormal data may cause values ​​outside the normal range during calculation, factor values ​​less than zero are truncated to zero, and factor values ​​greater than one are truncated to one, ensuring that all factor values ​​are within the valid range of zero to one. Normalization is then performed on each factor. Since the five factors have already been mapped to the zero-to-one range during the original calculation, this step mainly confirms that all factors have a unified scale and dimension, ensuring that the subsequent weighted sum has reasonable mathematical meaning. After normalization and amplitude limiting, the five factors are weighted and summed according to preset fusion weights. The sum of each fusion weight is a fixed value, and the weight allocation is determined based on the degree of influence of each degradation factor on the overall health state and the requirements of the specific application scenario. For example, in precision machining scenarios with extremely high accuracy requirements, the weights of the error amplitude degradation factor and twin deviation factor can be appropriately increased. Similarly, in motion simulation scenarios with high requirements for dynamic response performance, the weight of the drive hysteresis factor can be appropriately increased. The specific values ​​of each weight can be determined through expert experience or through statistical analysis and optimization algorithms of historical fault data. The result obtained after weighted summation is the health degradation index, which also ranges from zero to one; a larger value indicates a more severe degree of degradation. This health degradation index integrates degradation information from five different dimensions, comprehensively and balancedly reflecting the overall health status of the robot, providing a reliable quantitative basis for subsequent degradation level determination and fault diagnosis.

[0146] After normalizing and limiting the amplitude of the five factors, they are weighted and fused into a single health degradation index according to preset weights. This fusion strategy improves the comprehensiveness and robustness of the evaluation results through multi-dimensional information complementarity, avoiding the failure or false alarm of a single index under specific working conditions. On the other hand, the weighting mechanism enables the evaluation system to flexibly adjust the focus according to the differentiated needs of accuracy, dynamism or stability in different application scenarios. Thus, it provides a comprehensive quantitative evaluation scheme for the health status of six-degree-of-freedom parallel robots with multi-source degradation decoupling capability, early degradation sensitivity and scenario adaptability.

[0147] Furthermore, the fault diagnosis results of the six-DOF parallel robot are determined based on error evolution characteristics, health degradation index, and degradation level. These fault diagnosis results include at least one of the following: structural parameter degradation fault, drive response lag fault, periodic vibration anomaly fault, measurement link anomaly fault, and composite degradation fault. Fault criteria include: a structural parameter degradation fault is identified when the residual mean bias continuously increases and exhibits a stable low-frequency offset; a drive response lag fault is identified when the actual pose lags behind the expected pose or twin predicted pose by more than a threshold; a periodic vibration anomaly fault is identified when the target frequency band energy increases or a stable dominant frequency peak appears; a measurement link anomaly fault is identified when high-frequency energy, standard deviation, or kurtosis increases, and the mean bias and phase lag are not significant; and a composite degradation fault is identified when at least two fault criteria are simultaneously met.

[0148] Furthermore, the method provided in this embodiment also includes:

[0149] (1) Continuously calculate the deviation between the actual pose sequence and the twin predicted pose sequence;

[0150] Specifically, at each sampling moment, the actual pose vector and the twin predicted pose vector are acquired; the actual pose vector and the twin predicted pose vector are subtracted component by component at the same moment to obtain a six-dimensional deviation vector, which corresponds to the deviation in the directions of the three translational degrees of freedom and the three rotational degrees of freedom, respectively; the sum of squares of each component of the deviation vector is taken as the square root to calculate the comprehensive deviation value; the comprehensive deviation value is statistically analyzed within the sliding time window to determine the average deviation or maximum deviation of the current window.

[0151] (2) When the deviation is greater than or equal to the preset model update threshold and the health degradation index of the current window is less than the preset warning threshold, the geometric structure parameters, driving response parameters, error mapping parameters or health evaluation parameters in the digital twin model are updated according to the deviation.

[0152] Specifically, the overall deviation value of the current window is compared with the preset model update threshold; the health degradation index of the current window is compared with the preset warning threshold; when the overall deviation value is greater than or equal to the model update threshold and the health degradation index is less than the warning threshold, it is determined that the current deviation belongs to model parameter drift rather than actual degradation, and the model update process is initiated; according to the specific distribution characteristics of the deviation, one or more of the geometric structure parameters, driving response parameters, error mapping parameters, or health evaluation parameters are selectively corrected; after the update, the twin predicted pose is made to approximate the actual pose again.

[0153] Furthermore, during long-term operation, the geometric parameters, drive response parameters, and error mapping parameters stored in the digital twin model may slightly deviate from the current state of the physical robot due to factors such as changes in environmental temperature, mechanical break-in, and minor wear. This deviation is normal parameter drift rather than device degradation. If the model is not updated in a timely manner, the twin's predicted pose will continuously deviate from the actual pose, causing subsequent real-virtual deviation residuals and health degradation indices to be falsely amplified, leading to false alarms. However, if the robot does experience genuine degradation, the model should not blindly track the actual pose for updates; otherwise, the degradation characteristics will be absorbed and masked by the model, resulting in missed alarms. Therefore, a precise update gating mechanism is needed.

[0154] The update requires two conditions to be met simultaneously. The first condition is that the overall deviation value is greater than or equal to a preset model update threshold. This threshold is a value slightly larger than the allowable error range corresponding to the health degradation index. Physically, it means that the deviation between the twin model and reality has accumulated to a level that cannot be ignored and must be eliminated through parameter correction. The second condition is that the health degradation index of the current window is less than a preset warning threshold. This threshold corresponds to the lower boundary of a slight degradation state. When the health degradation index is below this value, it indicates that the robot is still in a healthy state, and the current deviation is not caused by degradation but by the slow drift of model parameters with the environment. Only when the deviation is sufficiently large and the health state is determined to be healthy is the current deviation considered to be model parameter drift rather than actual degradation, at which point the model update process is initiated.

[0155] During the update process, based on the specific distribution characteristics of the deviation in the six degrees of freedom and its changing pattern over time, geometric parameters, driving response parameters, error mapping parameters, or health evaluation parameters are selectively modified. For example, when the deviation manifests as a stable bias error in certain degrees of freedom under a specific trajectory, corrections to geometric parameters such as hinge point coordinates or branch lengths can be triggered; when the deviation manifests as a time delay in following the desired motion, corrections to driving response parameters such as equivalent lag time can be triggered; when the distribution characteristics of the deviation are consistent with a certain pattern in historical data, incremental updates or retraining of the error mapping sub-model can be triggered; when the deviation manifests as an overall shift in the root mean square value of the comprehensive error, updates to the baseline values ​​in the health evaluation parameters can be triggered. After the update, the prediction accuracy of the digital twin model is restored, the twin predicted pose reapproaches the actual pose, and the real-virtual deviation residual returns to normal levels.

[0156] (3) When the health degradation index of the current window exceeds the warning threshold, the update is paused. During the update process, at least one of the regularization term, physical boundary constraint and update amplitude constraint is used to suppress the excessive correction of parameters caused by short-term abnormal data.

[0157] Specifically, when the health degradation index reaches or exceeds the warning threshold, the updating of geometric structure parameters and driving response parameters is suspended. If a small compensation is still needed for the error mapping parameters, their update gain is reduced. A regularization term is introduced into the optimization objective function of the model update to constrain the parameter update magnitude. Physical boundary constraints for parameter updates are set to ensure that the updated parameter values ​​do not exceed the physically feasible range determined by the mechanical structure. A maximum magnitude limit for a single update is set to suppress parameter mutations caused by short-term abnormal data.

[0158] Furthermore, when the health degradation index reaches or exceeds the warning threshold, it indicates that the robot has entered a state of slight or more severe degradation. At this point, the real-virtual deviation residual contains true degradation information. If the geometric structure parameters or drive response parameters continue to be updated according to the normal drift logic, the digital twin model will use the updated parameters to fit the already degraded actual pose, causing degradation features to be absorbed into the model parameters. Subsequent health degradation indices will then fail to accurately reflect the degree of degradation, resulting in missed detections. Therefore, it is necessary to pause the updates of geometric structure parameters and drive response parameters, or significantly reduce their update gain, allowing only small-scale online compensation for error mapping parameters to ensure that the model's ability to perceive degradation remains unaffected.

[0159] To prevent overcorrection caused by short-term abnormal data during model updates, multiple constraint mechanisms are needed. The regularization term is an additional penalty term added to the parameter update optimization objective function. This term consists of the sum of squares or absolute values ​​of the deviations between the parameters to be updated and the initial parameters. Its function is to penalize large changes in parameters during optimization, making parameter updates tend to be as small as possible while maintaining fitting accuracy, thereby suppressing excessive parameter adjustments. Physical boundary constraints are the feasible domains of parameters determined based on the robot's actual physical structure. For example, hinge point coordinates are limited by the platform's geometry and cannot exceed the platform's range; the length of the drive chain is limited by the mechanical structure and cannot exceed mechanical limits; the response lag time is limited by the servo system's bandwidth and cannot increase indefinitely. During parameter updates, any update results exceeding the physical boundaries will be forcibly truncated to the boundary values, ensuring that the model parameters always have physical rationality. The update magnitude constraint sets a maximum limit on the change of each parameter in a single update. This means that no matter how large the update amount calculated by the optimization algorithm, the actual change applied to the parameters must not exceed the preset limit. This constraint effectively suppresses parameter mutations caused by anomalous data at a certain moment. These three constraints work together at different levels to ensure the robustness and reliability of the model update process. Even if short-term anomalies are occasionally mixed into the input data, the model parameters will not fluctuate drastically, thus ensuring the stability of the digital twin model in long-term operation.

[0160] The online update mechanism constructs a health gating constraint by comparing the health degradation index with the warning threshold. When the health degradation index does not reach the warning threshold, the parameters of the digital twin model are updated to eliminate normal parameter drift. When the health degradation index exceeds the warning threshold, the update is paused to prevent the real degradation from being absorbed and masked by the model. This effectively solves the core problem of traditional online update methods that mistakenly correct real degradation as model parameter drift. At the same time, through regularization terms, physical boundary constraints, and update magnitude constraints, the mechanism works together to suppress excessive parameter correction caused by short-term abnormal data from three levels: objective function, physical feasible region, and single change amount. This ensures the robustness of the model update process and that the parameters always have physical rationality. Thus, in long-term operation, it can maintain the twin model's ability to accurately track the health status and ensure its sensitive perception of real degradation characteristics.

[0161] The state prediction method for a six-DOF parallel robot provided in this embodiment achieves synchronous virtual mapping of the robot's motion state and error state by constructing a digital twin model that includes four sub-models: geometry, kinematics, drive response, and error mapping. This provides a physically constrained virtual benchmark for subsequent residual analysis. Based on this, the basic predicted pose is solved using the six-branch length data, and error compensation is superimposed to obtain the twin predicted pose sequence. This establishes a three-source correspondence between the expected pose, the actual pose, and the twin predicted pose at the same sampling time. This allows control tracking error, entity degradation error, and model prediction error to be effectively distinguished in the subsequent residual construction stage, avoiding the problem of mutual coupling and untraceable sources of the three types of errors in traditional methods. By determining the three-source real and virtual residual sequences within a sliding time window and inputting them into a CNN-GRU spatiotemporal feature extraction model to extract error evolution features, the local fluctuation features, multi-degree-of-freedom coupling features, time-dependent features, and degradation evolution features contained in the residual data are fully explored. The original residual signal is transformed into high-dimensional abstract features that can characterize the fault type and degradation degree. Based on the error evolution features, a health degradation index is calculated by weighting and fusing five degradation factors: error amplitude, trend, vibration anomaly, twin deviation, and driving hysteresis. The degradation level is determined by combining the index with a preset threshold set. This allows the quantitative assessment of health status to integrate multi-dimensional and multi-modal degradation information, effectively improving the sensitivity to early degradation trends and the robustness to transient noise interference. Furthermore, a health-gated online update mechanism, constructed using a health degradation index and an early warning threshold, updates model parameters in a timely manner to eliminate normal parameter drift during healthy states and pauses updates during degraded states to prevent the model from absorbing and masking actual degradation. Triple constraints—regularization terms, physical boundary constraints, and update amplitude constraints—suppress over-correction caused by short-term anomalies, ensuring long-term operational stability and reliable degradation perception. This application fully considers the structural characteristics of a six-DOF parallel robot, including multi-branch closed-loop coupling and a strongly nonlinear mapping between branch length and the six-dimensional pose of the moving platform. It enables accurate identification of fault types and reliable quantification of degradation levels, providing systematic technical support for predictive maintenance and health management of six-DOF parallel robots.

[0162] Corresponding to the aforementioned embodiment of a state prediction method for a six-degree-of-freedom parallel robot, this application also provides an embodiment of a state prediction device for a six-degree-of-freedom parallel robot.

[0163] Figure 2 This is a schematic diagram of the second embodiment of the state prediction device for the six-DOF parallel robot provided in this application. Please refer to... Figure 2 The apparatus provided in this embodiment includes an acquisition module 210, a processing module 220, and a prediction module 230.

[0164] The acquisition module 210 is used to acquire the operation data of the six-degree-of-freedom parallel robot. The operation data includes at least the expected pose sequence, the actual pose sequence, the six-branch length data, and the drive state data.

[0165] The processing module 220 is used to construct a digital twin model based on the coordinates of the static platform hinge point, the coordinates of the moving platform hinge point, the initial length of the driving branch, the platform coordinate system parameters, and the driving response parameters. The digital twin model includes a geometric structure sub-model, a kinematic sub-model, a driving response sub-model, and an error mapping sub-model.

[0166] The processing module 220 is further configured to solve the basic predicted pose based on the six-branch length data through the kinematic sub-model, obtain the prediction error compensation amount based on the historical running data window through the error mapping sub-model, and superimpose the basic predicted pose and the prediction error compensation amount to obtain the twin predicted pose sequence.

[0167] The processing module 220 is also used to determine the three-source real and virtual residual sequence within a sliding time window based on the running data and the twin prediction pose sequence;

[0168] The prediction module 230 is used to input the three-source real and virtual residual sequences into the trained spatiotemporal feature extraction model to obtain error evolution features, calculate the health degradation index based on the error evolution features, and determine the degradation level of the six-degree-of-freedom parallel robot based on the health degradation index.

[0169] The apparatus of this embodiment can be used to perform... Figure 1 The steps of the method embodiment shown are similar in principle and process, and will not be repeated here.

[0170] The specific implementation process of the functions and roles of each unit in the above device can be found in the implementation process of the corresponding steps in the above method, and will not be repeated here.

[0171] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this application according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0172] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the state of a six-degree-of-freedom parallel robot, characterized in that, The method includes: The operation data of a six-DOF parallel robot is obtained, and the operation data includes at least the expected pose sequence, the actual pose sequence, the six branch length data, and the drive state data. A digital twin model is constructed based on the coordinates of the hinge points of the static platform, the coordinates of the hinge points of the dynamic platform, the initial length of the driving branch, the platform coordinate system parameters, and the driving response parameters. The digital twin model includes a geometric structure sub-model, a kinematic sub-model, a driving response sub-model, and an error mapping sub-model. Based on the six-branch length data, the basic predicted pose is solved by the kinematic sub-model. Based on the historical running data window, the prediction error compensation amount is obtained by the error mapping sub-model. The basic predicted pose and the prediction error compensation amount are superimposed to obtain the twin predicted pose sequence. Based on the running data and the twin predicted pose sequence, a three-source real and virtual residual sequence is determined within a sliding time window; The three-source real and virtual residual sequences are input into the trained spatiotemporal feature extraction model to obtain error evolution features. The health degradation index is calculated based on the error evolution features, and the degradation level of the six-degree-of-freedom parallel robot is determined based on the health degradation index.

2. The method according to claim 1, characterized in that, The construction of the digital twin model based on the coordinates of the static platform hinge point, the coordinates of the moving platform hinge point, the initial length of the drive branch, the platform coordinate system parameters, and the drive response parameters includes: A geometric sub-model is constructed based on the coordinates of the hinge point of the moving platform, the coordinates of the hinge point of the static platform, the initial length of the drive chain, the installation angle of the chain, and the platform coordinate system parameters. A kinematic sub-model is established based on the geometric structure sub-model, and the kinematic sub-model is used to solve the six-dimensional pose of the moving platform based on the length of the six branches; A driving response sub-model is established based on the response hysteresis parameters, velocity constraints, and travel constraints of the six-branch chain; An error mapping sub-model is established based on historical operational data and error data.

3. The method according to claim 1, characterized in that, The process of solving the basic predicted pose using the kinematic sub-model based on the six branch length data includes: Establish a length residual objective function between the theoretical length of the six-branch chain and the measured length of the six-branch chain; Using the actual or predicted pose at the previous sampling time as the initial value, the six-dimensional pose that satisfies the convergence threshold of the length residual objective function is solved by an iterative optimization algorithm, and this pose is used as the basic predicted pose.

4. The method according to claim 1, characterized in that, The prediction error compensation amount obtained through the error mapping sub-model based on the historical operating data window includes: Input a historical running data window containing at least one of the following: drive state data, historical pose data, historical residual data, load information, and temperature information, into the error mapping sub-model; The error mapping sub-model outputs the predicted error compensation amount based on the mapping relationship between the structural parameter error, drive response hysteresis error, periodic vibration error, and measurement noise error represented in the historical operation data window and the end pose.

5. The method according to claim 1, characterized in that, The step of determining the three-source real and virtual residual sequence within a sliding time window based on the running data and the twin predicted pose sequence includes: Based on the expected pose sequence, actual pose sequence, and twin predicted pose sequence, calculate the trajectory tracking residual, real-virtual deviation residual, and model prediction residual; Within the sliding time window, the first-order and second-order rates of change of the real-virtual deviation residuals are determined, and the trajectory tracking residuals, real-virtual deviation residuals, model prediction residuals, first-order rates of change, second-order rates of change, local statistical features, and frequency domain energy features are combined into a three-source real-virtual residual sequence.

6. The method according to claim 5, characterized in that, The local statistical features include at least one of the following: root mean square residual value, peak-to-peak residual value, mean offset of residual value, standard deviation of residual value, skewness of residual value, kurtosis of residual value, and frequency domain energy of residual value; the frequency domain energy features include at least one of the following: target frequency band energy, peak value of dominant frequency, or frequency band energy percentage.

7. The method according to claim 1, characterized in that, The step of inputting the three-source real and virtual residual sequences into the trained spatiotemporal feature extraction model to obtain error evolution features includes: The three-source real and virtual residual sequences are organized into input samples consisting of a time window of length L and C feature channels; The input sample is fed into the CNN-GRU spatiotemporal feature extraction model, which includes a convolutional neural network layer, a gated recurrent unit layer, and a fully connected output layer. The convolutional neural network layer extracts local fluctuation features and multi-degree-of-freedom coupling features from the input sample along the time dimension. The gated recurrent unit layer extracts time-dependent features and degradation evolution features from the input sample. The fully connected output layer outputs error evolution features.

8. The method according to claim 1, characterized in that, The calculation of the health degradation index based on the error evolution characteristics includes: The error amplitude component, trend component, frequency domain energy component, twin deviation component, and driving hysteresis component are extracted from the error evolution characteristics, and the error amplitude degradation factor is calculated based on the degree of deviation of the error amplitude component from the healthy baseline distribution. The trend degradation factor is calculated based on the growth slope of the residual magnitude represented by the trend component over time. The vibration anomaly factor is calculated based on the frequency domain energy of the residual characterized by the frequency domain energy components within the target frequency band. The twin deviation factor is calculated based on the average degree of deviation between the actual pose sequence and the twin predicted pose sequence represented by the twin deviation component. The driving hysteresis factor is calculated based on the phase hysteresis between the desired pose sequence and the actual pose sequence, as represented by the driving hysteresis component. After normalizing and limiting the error amplitude degradation factor, trend degradation factor, vibration anomaly factor, twin deviation factor, and driving lag factor respectively, they are weighted and fused according to preset weights to obtain the health degradation index.

9. The method according to claim 1, characterized in that, The method further includes: The deviation between the actual pose sequence and the twin predicted pose sequence is continuously calculated; When the deviation is greater than or equal to a preset model update threshold, and the health degradation index of the current window is less than a preset warning threshold, the geometric structure parameters, driving response parameters, error mapping parameters, or health evaluation parameters in the digital twin model are updated according to the deviation. When the health degradation index of the current window exceeds the warning threshold, the update is paused. During the update process, at least one of the regularization term, physical boundary constraint and update amplitude constraint is used to suppress the overcorrection of parameters caused by short-term abnormal data.

10. A state prediction device for a six-degree-of-freedom parallel robot, characterized in that, The device includes an acquisition module, a processing module, and a prediction module; The acquisition module is used to acquire the operation data of the six-degree-of-freedom parallel robot. The operation data includes at least the expected pose sequence, the actual pose sequence, the six-branch length data, and the drive state data. The processing module is used to construct a digital twin model based on the coordinates of the static platform hinge point, the coordinates of the moving platform hinge point, the initial length of the driving branch, the platform coordinate system parameters, and the driving response parameters. The digital twin model includes a geometric structure sub-model, a kinematic sub-model, a driving response sub-model, and an error mapping sub-model. The processing module is also used to solve the basic predicted pose based on the six branch length data through the kinematic sub-model, obtain the prediction error compensation amount based on the historical running data window through the error mapping sub-model, and superimpose the basic predicted pose and the prediction error compensation amount to obtain the twin predicted pose sequence. The processing module is also used to determine the three-source real and virtual residual sequence within a sliding time window based on the running data and the twin predicted pose sequence; The prediction module is used to input the three-source real and virtual residual sequences into the trained spatiotemporal feature extraction model to obtain error evolution features, calculate the health degradation index based on the error evolution features, and determine the degradation level of the six-degree-of-freedom parallel robot based on the health degradation index.

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