Dual-vector collaborative compensation method and system for multi-degree-of-freedom motion errors of computer axis

Abstract

The present invention provides a dual-vector collaborative compensation method and system for multi-degree-of-freedom motion errors in a computer axis. The method comprises the following steps: synchronously collecting the axis's translation and rotation vectors through sensors, unifying the translation and rotation vector data to the same spatiotemporal reference; constructing a coupled error model for the translation and rotation vectors, and integrating the translation and rotation vector data into a unified six-degree-of-freedom error value; and dynamically allocating translation and rotation vector compensation weights within the time domain using a feedforward-feedback mechanism, generating a real-time adjustment compensation value through rolling time-domain optimization. This method eliminates the need for complex parameter identification processes associated with traditional axis physical models and achieves six-degree-of-freedom error collaborative compensation solely through sensor data synchronization and a dynamic optimization algorithm. The method is applicable to computer axis systems with diverse loads and motion scenarios, significantly improving the motion accuracy and reliability of the device.

Description

Technical Field

[0001] The present invention relates to the technical field of precision electromechanical system motion control, and in particular to a dual-vector collaborative compensation method and system for multi-degree-of-freedom motion errors of a computer shaft. Background Art

[0002] With the rapid development of portable electronic devices and high-density storage technologies, computer hinges, as core moving components in precision devices such as laptop computers and optical drive read / write mechanisms, face a significant impact on device reliability and performance. Six-degree-of-freedom (DOF) positional errors (including axial displacement and rotational attitude deviation) caused by mechanical backlash, load disturbances, and drive nonlinearity during high-speed telescoping and multi-axis rotational compound motion in traditional hinge systems have become a key bottleneck restricting device precision improvement.

[0003] In the existing technology, the compensation methods for axis motion errors are mostly limited to single degree of freedom or static coupling models, which have the following problems:

[0004] The acquisition of translation and rotation vectors often uses independent sensors, without achieving unified time and space references, resulting in distortion in coupling error modeling.

[0005] Traditional feedforward or PID feedback control uses fixed weight distribution and cannot adapt to the dynamically changing error characteristics of the shaft motion stage. Summary of the Invention

[0006] In view of the deficiencies in the prior art, the present invention provides a dual-vector collaborative compensation method and system for multi-degree-of-freedom motion errors of a computer axis to solve the problems raised in the above background technology.

[0007] To achieve the above objectives, the present invention is implemented through the following technical solutions: A dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis includes the following steps:

[0008] The translation vector and rotation vector of the rotating shaft are synchronously collected by sensors, and the data of the translation vector and rotation vector are unified to the same time and space reference;

[0009] Construct a coupled error model of translation vector and rotation vector, and integrate the data of translation vector and rotation vector into a unified six-degree-of-freedom error;

[0010] Combined with the feedforward-feedback mechanism, the translation vector and rotation vector compensation weights are dynamically allocated in the time domain, and the real-time adjustment compensation amount is generated through rolling time domain optimization;

[0011] The compensation parameters generated by MPC collaborative optimization are used to adjust the compensation amount in real time. The compensation parameters separate the translation and rotation compensation amounts through the motion decoupling algorithm, and the feedforward-feedback compound control is performed in a 10 kHz high-frequency closed loop to dynamically distribute the axial force and torque and suppress the posture error of the rotating shaft.

[0012] As a further preferred embodiment, the process of synchronously collecting the translation vector and the rotation vector of the rotating shaft through the sensor and unifying the data of the translation vector and the rotation vector to the same time-space reference includes:

[0013] Measure translation and rotation vectors based on sensors, and complete hardware synchronization and coordinate system calibration;

[0014] Among them, hardware synchronization uses the IEEE 1588 PTP protocol to achieve sensor clock synchronization. The coordinate system calibration establishes a global coordinate system with the center of mass of the shaft as the origin, and solves the rigid transformation of the sensor local coordinate system through the calibration point set.

[0015] As a further preferred embodiment, the step of constructing a coupled error model of the translation vector and the rotation vector, and integrating the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error value specifically includes:

[0016] Receive translation and rotation vector data unified to the same spatiotemporal reference, verify data integrity and remove outliers, and ensure strict timestamp alignment through dynamic delay compensation;

[0017] Perform interpolation synchronization and dynamic delay compensation for sensor sampling rate differences;

[0018] The global linear velocity is calculated by numerically differentiating the translation vector, and the angular acceleration is obtained by differentiating the rotation vector. A dual-vector coupling error model is constructed, and the coupling error term is defined based on the dual-vector coupling model. The state equation and observation equation are generated through filtering and fusion.

[0019] The coupling error term is defined as:

[0020] , ;

[0021] in, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are experimentally calibrated cross-interference coefficients, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector;

[0022] The state equation is: ;

[0023] The observation equation is: ;

[0024] in, represents the Kalman filter state vector, F represents the state transfer matrix, H represents the observation matrix, and represents process noise and observation noise.

[0025] As a further preferred embodiment, the interpolation synchronization includes performing cubic spline interpolation on the low sampling rate data to generate a sequence synchronized with the laser displacement sensor;

[0026] The calculation formula of the interpolated gyroscope rotation vector is:

[0027] ;

[0028] in, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the residual clock error between sensors, represents the discrete sampling time points of the translation vector, Represents the discrete sampling time points of the rotation vector;

[0029] The calculation formula for the clock residual error is:

[0030] ;

[0031] 𝜏where τ represents the time offset.

[0032] As a further preferred embodiment, the step of dynamically allocating the translation vector and rotation vector compensation weights in the time domain by combining the feedforward-feedback mechanism and generating the real-time adjustment compensation amount by rolling time domain optimization specifically includes:

[0033] A discrete state-space model of the six-degree-of-freedom system is established, with the system state variables defined as translational position, translational velocity, rotational attitude angle, and rotational angular velocity. A dual-vector compensation is set as the control input, with the prediction time domain window and the control time domain window divided. An initial prediction sequence of feedforward compensation is generated based on the reference trajectory.

[0034] The feedforward compensation is calculated based on the reference trajectory and the system disturbance model, and the feedback compensation correction is generated based on the deviation between the real-time measured system state and the predicted state;

[0035] Define a time-varying weight function and , dynamically adjust the optimization priority of translation error and rotation error according to the system motion stage, and construct the rolling time domain optimization objective function;

[0036] Among them, the objective function is:

[0037] ;

[0038] Where J represents the total cost function of the rolling horizon optimization, represents the translation tracking error, represents the rotation tracking error, Indicates the rate of change of the controlled quantity, Indicates the number of prediction time domain steps, represents the number of control time domain steps, represents the time-varying weight matrix of the translation error, A time-varying weight matrix representing the rotation error;

[0039] Add actuator saturation constraints and state variable safety margins as inequality constraints, use numerical optimization solvers to solve the constrained optimization problem online, and obtain the optimal control sequence ;

[0040] Extract the optimal control quantity at the current moment , output dual vector compensation instructions to the actuator;

[0041] The prediction time domain window is updated based on the updated system state measurement value, and the optimization process is repeated to achieve closed-loop dynamic adjustment, integrating the feedforward prediction compensation and feedback correction, and outputting the global six-degree-of-freedom optimization real-time adjustment compensation.

[0042] As a further preferred method, the compensation amount is adjusted in real time based on the compensation parameters generated by MPC collaborative optimization. The compensation parameters separate the translation and rotation compensation amounts through a motion decoupling algorithm, and a feedforward-feedback composite control is performed in a 10 kHz high-frequency closed loop to dynamically distribute the axial force and torque. The process of suppressing the posture error of the rotating shaft includes:

[0043] Based on the compensation parameters generated by MPC collaborative optimization, the Lie group-Lie algebra decoupling algorithm is used to map the compensation parameters to the local coordinate system of the rotating shaft, separating the axial translation force and radial correction force, as well as the torsional torque and tilt correction torque, to eliminate the coupling interference between the degrees of freedom.

[0044] The actual position and posture data of the rotating shaft are synchronized with a 10 kHz microsecond control cycle to calculate the position and angle deviations. Combined with acceleration feedforward compensation and robust feedback correction of the reference trajectory, the linear motor and torque motor are driven to output dynamically distributed force / torque, achieving high-precision closed-loop suppression of the rotating shaft's axial telescopic error and rotational posture deviation.

[0045] As a further preferred embodiment, a dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer axis is provided, which is used to implement the aforementioned dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis, comprising:

[0046] The spatiotemporal calibration module is used to unify the collected data of the axis translation vector and rotation vector to the same spatiotemporal reference;

[0047] The model building module constructs the coupled error model of the translation vector and the rotation vector, and integrates the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error;

[0048] The collaborative optimization module dynamically allocates translation and rotation compensation weights in the time domain by combining a feedforward-feedback mechanism, and generates real-time adjustment compensation through rolling time domain optimization.

[0049] The error compensation module adjusts the compensation amount in real time based on the compensation parameters generated by MPC collaborative optimization, separates the translation and rotation compensation amounts through the motion decoupling algorithm, and performs feedforward-feedback compound control in a 10 kHz high-frequency closed loop to dynamically distribute axial force and torque and suppress the position error of the rotating shaft.

[0050] As a further preferred embodiment, the step of constructing a coupled error model of the translation vector and the rotation vector, and integrating the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error value specifically includes:

[0051] Receive translation and rotation vector data unified to the same spatiotemporal reference, verify data integrity and remove outliers, and ensure strict timestamp alignment through dynamic delay compensation;

[0052] Perform interpolation synchronization and dynamic delay compensation for sensor sampling rate differences;

[0053] The global linear velocity is calculated by numerically differentiating the translation vector, and the angular acceleration is obtained by differentiating the rotation vector. A dual-vector coupling error model is constructed, and the coupling error term is defined based on the dual-vector coupling model. The state equation and observation equation are generated through filtering and fusion.

[0054] The coupling error term is defined as:

[0055] , ;

[0056] in, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are experimentally calibrated cross-interference coefficients, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector;

[0057] The state equation is: ;

[0058] The observation equation is: ;

[0059] in, represents the Kalman filter state vector, represents the state vector of the previous moment k-1, F represents the state transfer matrix, H represents the observation matrix, and represents process noise and observation noise, represents the observation vector.

[0060] As a further preferred embodiment, the interpolation synchronization includes performing cubic spline interpolation on the low sampling rate data to generate a sequence synchronized with the laser displacement sensor;

[0061] The calculation formula of the interpolated gyroscope rotation vector is:

[0062] ;

[0063] in, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the residual clock error between sensors, represents the discrete sampling time points of the translation vector, Represents the discrete sampling time points of the rotation vector;

[0064] The calculation formula for the clock residual error is:

[0065] ;

[0066] 𝜏where τ represents the time offset.

[0067] As a further preferred embodiment, the step of dynamically allocating the translation vector and rotation vector compensation weights in the time domain by combining the feedforward-feedback mechanism, and generating the real-time adjustment compensation amount by rolling time domain optimization specifically includes:

[0068] A discrete state-space model of the six-degree-of-freedom system is established, with the system state variables defined as translational position, translational velocity, rotational attitude angle, and rotational angular velocity. A dual-vector compensation is set as the control input, with the prediction time domain window and the control time domain window divided. An initial prediction sequence of feedforward compensation is generated based on the reference trajectory.

[0069] The feedforward compensation is calculated based on the reference trajectory and the system disturbance model, and the feedback compensation correction is generated based on the deviation between the real-time measured system state and the predicted state;

[0070] Define a time-varying weight function and , dynamically adjust the optimization priority of translation error and rotation error according to the system motion stage, and construct the rolling time domain optimization objective function;

[0071] Among them, the objective function is:

[0072] ;

[0073] Where J represents the total cost function of the rolling horizon optimization, represents the translation tracking error, represents the rotation tracking error, Indicates the rate of change of the controlled quantity, Indicates the number of prediction time domain steps, represents the number of control time domain steps, represents the time-varying weight matrix of the translation error, A time-varying weight matrix representing the rotation error;

[0074] Add actuator saturation constraints and state variable safety margins as inequality constraints, use numerical optimization solvers to solve the constrained optimization problem online, and obtain the optimal control sequence ;

[0075] Extract the optimal control quantity at the current moment , output dual vector compensation instructions to the actuator;

[0076] The prediction time domain window is updated based on the updated system state measurement value, and the optimization process is repeated to achieve closed-loop dynamic adjustment, integrating the feedforward prediction compensation and feedback correction, and outputting the global six-degree-of-freedom optimization real-time adjustment compensation.

[0077] The present invention provides a dual-vector collaborative compensation method and system for multi-degree-of-freedom motion errors of a computer axis, which has the following beneficial effects:

[0078] Dynamic coupling error modeling and real-time suppression: Based on a dual-vector coupling model and Kalman filter algorithm, the cross-interference error between the translation vector and the rotation vector is corrected in real time, significantly reducing the combined error of position and attitude. This allows for highly robust error compensation without relying on complex physical modeling.

[0079] Adaptive time-domain optimization and collaborative control: Utilizing model predictive control combined with a feedforward-feedback mechanism, the system dynamically allocates translational and rotational error weights based on the axis's motion phase. This prioritizes oscillation suppression during high-speed telescoping and provides balanced tracking accuracy during precise posture adjustments (such as optical drive laser head positioning). The system achieves millisecond-level compensation response speeds, adapting to complex operating conditions.

[0080] High-frequency decoupling and precise execution: The Lie group-Lie algebra decoupling algorithm separates the global compensation into local axial force and torque. 10 kHz high-frequency closed-loop control drives the linear motor and torque motor, directly eliminating coupling interference between degrees of freedom. This minimizes shaft axial position error and rotational attitude deviation, meeting the stringent nanometer-level positioning requirements of high-density storage devices.

[0081] This method eliminates the complex parameter identification process of traditional shaft physical models and achieves coordinated compensation for six-degree-of-freedom errors through simple sensor data synchronization and dynamic optimization algorithms. It is applicable to computer shafts with diverse loads and motion scenarios, significantly improving the motion accuracy and reliability of the equipment. Furthermore, this method is not limited to specific shaft types and can be extended to suppress multi-degree-of-freedom errors in other precision electromechanical systems, demonstrating its versatility and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] Figure 1 This is a flow chart of the dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer shaft according to the present invention;

[0083] Figure 2 This is a block diagram of the dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer shaft according to the present invention. DETAILED DESCRIPTION

[0084] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and are not to be construed as limiting the present invention.

[0085] The disclosure below provides many different embodiments or examples for realizing different structures of the present invention. In order to simplify the disclosure of the present invention, the components and settings of specific examples are described below. Of course, they are merely examples and are not intended to limit the present invention. In addition, the present invention may repeat reference numbers and / or reference letters in different examples. Such repetition is for the purpose of simplicity and clarity and does not in itself indicate the relationship between the various embodiments and / or settings discussed. In addition, the present invention provides examples of various specific processes and materials, but those skilled in the art will recognize the application of other processes and / or the use of other materials.

[0086] like Figure 1 As shown, an embodiment of the present invention provides a dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis, comprising the following steps:

[0087] S1: Synchronously collect the translation vector and rotation vector of the rotating shaft through the sensor, and unify the data of the translation vector and rotation vector to the same time and space reference;

[0088] Specifically, the process of synchronously collecting the translation vector and rotation vector of the rotating shaft through sensors and unifying the translation vector and rotation vector data to the same time and space reference includes:

[0089] Measure translation and rotation vectors based on sensors, and complete hardware synchronization and coordinate system calibration;

[0090] Among them, hardware synchronization uses the IEEE 1588 PTP protocol to achieve sensor clock synchronization. The coordinate system calibration establishes a global coordinate system with the center of mass of the shaft as the origin, and solves the rigid transformation of the sensor local coordinate system through the calibration point set;

[0091] It should be noted that the translation vector and rotation vector are measured by a laser displacement sensor and a gyroscope, respectively;

[0092] S2: Construct a coupled error model of translation vector and rotation vector, and integrate the data of translation vector and rotation vector into a unified six-degree-of-freedom error;

[0093] Specifically, it receives translation and rotation vector data that are unified to the same spatiotemporal reference, verifies data integrity and removes outliers, and ensures strict timestamp alignment through dynamic delay compensation.

[0094] Perform interpolation synchronization and dynamic delay compensation for sensor sampling rate differences;

[0095] The interpolation synchronization includes performing cubic spline interpolation on the low sampling rate data to generate a sequence synchronized with the laser displacement sensor;

[0096] The calculation formula of the interpolated gyroscope rotation vector is:

[0097] ;

[0098] in, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the residual clock error between sensors, represents the discrete sampling time points of the translation vector, Represents the discrete sampling time points of the rotation vector;

[0099] The calculation formula for the residual clock error between sensors is:

[0100] ;

[0101] 𝜏where τ represents the time offset;

[0102] The global linear velocity is calculated by numerically differentiating the translation vector, and the angular acceleration is obtained by differentiating the rotation vector. A dual-vector coupling error model is constructed, and the coupling error term is defined based on the dual-vector coupling model. The state equation and observation equation are generated through filtering and fusion.

[0103] The coupling error term is defined as:

[0104] , ;

[0105] in, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are experimentally calibrated cross-interference coefficients, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector;

[0106] The state equation is: ;

[0107] The observation equation is: ;

[0108] in, represents the Kalman filter state vector, F represents the state transfer matrix, H represents the observation matrix, and represents process noise and observation noise;

[0109] It should be noted that the Kalman filter state vector including position, attitude, linear velocity and angular velocity is defined, and the coupling error term is compensated into the sensor observation equation to form an observation formula including error correction;

[0110] In this embodiment, after initializing the filter parameters, the state vector is dynamically estimated through a prediction-update cycle. The prediction phase infers the state based on the motion model, and the update phase fuses the sensor observations and uses the coupling error to correct the deviation, while suppressing the influence of process noise and sensor noise.

[0111] Specifically, the global coordinate system position and attitude angle in the filtered state vector are extracted and fused into a unified six-degree-of-freedom error quantity to achieve high-precision spatiotemporal alignment and error integration of dual-vector data.

[0112] S3: Combined with the feedforward-feedback mechanism, the translation and rotation vector compensation weights are dynamically allocated in the time domain, and the real-time adjustment compensation amount is generated through rolling time domain optimization;

[0113] A discrete state-space model of the six-degree-of-freedom system is established, with the system state variables defined as translational position, translational velocity, rotational attitude angle, and rotational angular velocity. A dual-vector compensation is set as the control input, with the prediction time domain window and the control time domain window divided. An initial prediction sequence of feedforward compensation is generated based on the reference trajectory.

[0114] The feedforward compensation is calculated based on the reference trajectory and the system disturbance model to offset the predicted dynamic error caused by the inertial coupling effect. The feedback compensation correction is generated based on the deviation between the real-time measured system state and the predicted state.

[0115] It can be understood that the system state is specifically the measured translation vector and rotation vector data volume, and the predicted state is specifically the estimated value of the system state at the future moment calculated in the prediction time domain;

[0116] Define a time-varying weight function and , dynamically adjust the optimization priority of translation error and rotation error according to the system motion stage, and construct the rolling time domain optimization objective function;

[0117] Among them, the objective function is:

[0118] ;

[0119] Where J represents the total cost function of the rolling horizon optimization, represents the translation tracking error, represents the rotation tracking error, Indicates the rate of change of the controlled quantity, Indicates the number of prediction time domain steps, represents the number of control time domain steps, represents the time-varying weight matrix of the translation error, A time-varying weight matrix representing the rotation error;

[0120] Add actuator saturation constraints and state variable safety margins as inequality constraints, use numerical optimization solvers to solve the constrained optimization problem online, and obtain the optimal control sequence ;

[0121] Extract the optimal control quantity at the current moment , output dual vector compensation instructions to the actuator;

[0122] The prediction time domain window is updated based on the updated system state measurement value, and the optimization process is repeated to achieve closed-loop dynamic adjustment, integrating the feedforward prediction compensation and feedback correction, and outputting the global six-degree-of-freedom optimization real-time adjustment compensation.

[0123] In this embodiment, the time-varying weight function and According to the dynamic adjustment of the system acceleration stage and steady-state stage, the rotation error weight is reduced in the acceleration stage to suppress oscillation, and the translation and rotation weights are evenly distributed in the steady-state stage; the dual-vector compensation instruction includes the force vector in the translation direction and the torque vector in the rotation direction, and the two realize six-degree-of-freedom collaborative compensation through dynamic weight distribution.

[0124] S4: The compensation amount is adjusted in real time based on the compensation parameters generated by MPC collaborative optimization. The compensation parameters are separated into translation and rotation compensation amounts through the motion decoupling algorithm. Feedforward-feedback compound control is performed in a 10 kHz high-frequency closed loop to dynamically distribute axial force and torque and suppress the position error of the rotating shaft.

[0125] Specifically, based on the compensation parameters generated by MPC collaborative optimization, the Lie group-Lie algebra decoupling algorithm is used to map the compensation parameters to the local coordinate system of the rotating shaft, separate the axial translation force and radial correction force, as well as the torsional torque and tilt correction torque, and eliminate the coupling interference between the degrees of freedom; then, the actual position data of the rotating shaft is synchronized with a 10 kHz microsecond control cycle, and the position and angular deviations are calculated. Combined with the acceleration feedforward compensation of the reference trajectory (to offset inertia lag) and robust feedback correction (such as sliding mode control), the linear motor and torque motor are driven to output dynamically distributed force / torque, achieving high-precision closed-loop suppression of the axial telescopic error and rotational posture deviation of the rotating shaft.

[0126] like Figure 2 As shown, this embodiment further provides a dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer axis, which is used to implement the aforementioned dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis, including:

[0127] The spatiotemporal calibration module is used to unify the collected data of the axis translation vector and rotation vector to the same spatiotemporal reference;

[0128] The model building module constructs the coupled error model of the translation vector and the rotation vector, and integrates the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error;

[0129] The collaborative optimization module dynamically allocates translation and rotation compensation weights in the time domain by combining a feedforward-feedback mechanism, and generates real-time adjustment compensation through rolling time domain optimization.

[0130] The error compensation module adjusts the compensation amount in real time based on the compensation parameters generated by MPC collaborative optimization. The compensation parameters separate the translation and rotation compensation amounts through the motion decoupling algorithm, and perform feedforward-feedback compound control in a 10 kHz high-frequency closed loop to dynamically distribute the axial force and torque and suppress the posture error of the rotating shaft.

[0131] Among them, the coupled error model of translation vector and rotation vector is constructed, and the data of translation vector and rotation vector are integrated into a unified six-degree-of-freedom error quantity. Specifically, it includes:

[0132] Receive translation and rotation vector data unified to the same spatiotemporal reference, verify data integrity and remove outliers, and ensure strict timestamp alignment through dynamic delay compensation;

[0133] Perform interpolation synchronization and dynamic delay compensation for sensor sampling rate differences;

[0134] The global linear velocity is calculated by numerically differentiating the translation vector, and the angular acceleration is obtained by differentiating the rotation vector. A dual-vector coupling error model is constructed, and the coupling error term is defined based on the dual-vector coupling model. The state equation and observation equation are generated through filtering and fusion.

[0135] The coupling error term is defined as:

[0136] , ;

[0137] in, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are experimentally calibrated cross-interference coefficients, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector;

[0138] The state equation is: ;

[0139] The observation equation is: ;

[0140] in, represents the Kalman filter state vector, F represents the state transfer matrix, H represents the observation matrix, and represents process noise and observation noise.

[0141] Specifically, interpolation synchronization involves performing cubic spline interpolation on low sampling rate data to generate a sequence synchronized with the laser displacement sensor;

[0142] The calculation formula of the interpolated gyroscope rotation vector is:

[0143] ;

[0144] in, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the residual clock error between sensors, represents the discrete sampling time points of the translation vector, Represents the discrete sampling time points of the rotation vector;

[0145] The calculation formula for the residual clock error between sensors is:

[0146] ;

[0147] 𝜏where τ represents the time offset.

[0148] Furthermore, in combination with the feedforward-feedback mechanism, the steps of dynamically allocating the translation vector and rotation vector compensation weights in the time domain and generating the real-time adjustment compensation amount through rolling time domain optimization specifically include:

[0149] A discrete state-space model of the six-degree-of-freedom system is established, with the system state variables defined as translational position, translational velocity, rotational attitude angle, and rotational angular velocity. A dual-vector compensation is set as the control input, with the prediction time domain window and the control time domain window divided. An initial prediction sequence of feedforward compensation is generated based on the reference trajectory.

[0150] The feedforward compensation is calculated based on the reference trajectory and the system disturbance model, and the feedback compensation correction is generated based on the deviation between the real-time measured system state and the predicted state;

[0151] Define a time-varying weight function and , dynamically adjust the optimization priority of translation error and rotation error according to the system motion stage, and construct the rolling time domain optimization objective function;

[0152] Among them, the objective function is:

[0153] ;

[0154] Where J represents the total cost function of the rolling horizon optimization, represents the translation tracking error, represents the rotation tracking error, Indicates the rate of change of the controlled quantity, Indicates the number of prediction time domain steps, represents the number of control time domain steps, represents the time-varying weight matrix of the translation error, A time-varying weight matrix representing the rotation error;

[0155] Add actuator saturation constraints and state variable safety margins as inequality constraints, use numerical optimization solvers to solve the constrained optimization problem online, and obtain the optimal control sequence ;

[0156] Extract the optimal control quantity at the current moment , output dual vector compensation instructions to the actuator;

[0157] The prediction time domain window is updated based on the updated system state measurement value, and the optimization process is repeated to achieve closed-loop dynamic adjustment, integrating the feedforward prediction compensation and feedback correction, and outputting the global six-degree-of-freedom optimization real-time adjustment compensation.

[0158] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis, characterized by: The following steps are involved: The translation vector and rotation vector of the rotating shaft are synchronously collected by sensors, and the data of the translation vector and rotation vector are unified to the same time and space reference; Construct a coupled error model of translation vector and rotation vector, and integrate the data of translation vector and rotation vector into a unified six-degree-of-freedom error; Combined with the feedforward-feedback mechanism, the translation vector and rotation vector compensation weights are dynamically allocated in the time domain, and the real-time adjustment compensation amount is generated through rolling time domain optimization; The compensation parameters generated by MPC collaborative optimization are used to adjust the compensation amount in real time. The compensation parameters are separated into translation and rotation compensation amounts through the motion decoupling algorithm. Feedforward-feedback compound control is performed in a 10 kHz high-frequency closed loop to dynamically distribute the axial force and torque and suppress the posture error of the rotating shaft.

2. The dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis according to claim 1, characterized in that: The process of synchronously collecting the translation vector and rotation vector of the rotating shaft through the sensor and unifying the data of the translation vector and the rotation vector to the same time and space reference includes: Measure translation and rotation vectors based on sensors, and complete hardware synchronization and coordinate system calibration; Among them, hardware synchronization uses the IEEE 1588 PTP protocol to achieve sensor clock synchronization. The coordinate system calibration establishes a global coordinate system with the center of mass of the shaft as the origin, and solves the rigid transformation of the sensor local coordinate system through the calibration point set.

3. The dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis according to claim 1, characterized in that: The construction of the coupled error model of the translation vector and the rotation vector, and integration of the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error specifically includes: Receive translation and rotation vector data unified to the same spatiotemporal reference, verify data integrity and remove outliers, and ensure strict timestamp alignment through dynamic delay compensation; Perform interpolation synchronization and dynamic delay compensation for sensor sampling rate differences; The global linear velocity is calculated by numerically differentiating the translation vector, and the angular acceleration is obtained by differentiating the rotation vector. A dual-vector coupling error model is constructed, and the coupling error term is defined based on the dual-vector coupling model. The state equation and observation equation are generated through filtering and fusion. The coupling error term is defined as: ， ； in, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are experimentally calibrated cross-interference coefficients, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector; The state equation is: ; The observation equation is: ; in, represents the Kalman filter state vector, F represents the state transfer matrix, H represents the observation matrix, and represents process noise and observation noise.

4. The dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis according to claim 3, characterized in that: Interpolation synchronization includes performing cubic spline interpolation on low sampling rate data to generate a sequence synchronized with the laser displacement sensor; The calculation formula of the interpolated gyroscope rotation vector is: ； in, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the residual clock error between sensors, represents the discrete sampling time points of the translation vector, Represents the discrete sampling time points of the rotation vector; The calculation formula for the residual clock error between sensors is: ； 𝜏where τ represents the time offset.

5. The dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis according to claim 1, characterized in that: The steps of dynamically allocating the translation vector and rotation vector compensation weights in the time domain by combining the feedforward-feedback mechanism and generating the real-time adjustment compensation amount by rolling time domain optimization specifically include: A discrete state-space model of the six-degree-of-freedom system is established, with the system state variables defined as translational position, translational velocity, rotational attitude angle, and rotational angular velocity. A dual-vector compensation is set as the control input, with the prediction time domain window and the control time domain window divided. An initial prediction sequence of feedforward compensation is generated based on the reference trajectory. The feedforward compensation is calculated based on the reference trajectory and the system disturbance model, and the feedback compensation correction is generated based on the deviation between the real-time measured system state and the predicted state; Define a time-varying weight function and , dynamically adjust the optimization priority of translation error and rotation error according to the system motion stage, and construct the rolling time domain optimization objective function; Among them, the objective function is: ； Where J represents the total cost function of the rolling horizon optimization, represents the translation tracking error, represents the rotation tracking error, Indicates the rate of change of the controlled quantity, Indicates the number of prediction time domain steps, represents the number of control time domain steps, represents the time-varying weight matrix of the translation error, A time-varying weight matrix representing the rotation error; Add actuator saturation constraints and state variable safety margins as inequality constraints, use numerical optimization solvers to solve the constrained optimization problem online, and obtain the optimal control sequence ; Extract the optimal control quantity at the current moment , output dual vector compensation instructions to the actuator; The prediction time domain window is updated based on the updated system state measurement value, and the optimization process is repeated to achieve closed-loop dynamic adjustment, integrating the feedforward prediction compensation and feedback correction, and outputting the global six-degree-of-freedom optimization real-time adjustment compensation.

6. The dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis according to claim 1, characterized in that: The real-time adjustment of the compensation amount is based on compensation parameters generated by MPC collaborative optimization. The compensation parameters are separated into translation and rotation compensation amounts through a motion decoupling algorithm. Feedforward-feedback composite control is performed in a 10 kHz high-frequency closed loop to dynamically distribute axial force and torque. The process of suppressing the position error of the rotating shaft includes the following: Based on the compensation parameters generated by MPC collaborative optimization, the Lie group-Lie algebra decoupling algorithm is used to map the compensation parameters to the local coordinate system of the rotating shaft, separating the axial translation force and radial correction force, as well as the torsional torque and tilt correction torque, to eliminate the coupling interference between the degrees of freedom. The actual position and posture data of the rotating shaft are synchronized with a 10 kHz microsecond control cycle to calculate the position and angle deviations. Combined with acceleration feedforward compensation and robust feedback correction of the reference trajectory, the linear motor and torque motor are driven to output dynamically distributed force / torque, achieving high-precision closed-loop suppression of the rotating shaft's axial telescopic error and rotational posture deviation.

7. A dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer axis, used to implement the dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of a computer axis as described in any one of claims 1 to 6, characterized in that: include: The spatiotemporal calibration module is used to unify the collected data of the axis translation vector and rotation vector to the same spatiotemporal reference; The model building module constructs the coupled error model of the translation vector and the rotation vector, and integrates the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error; The collaborative optimization module dynamically allocates translation and rotation compensation weights in the time domain by combining a feedforward-feedback mechanism, and generates real-time adjustment compensation through rolling time domain optimization. The error compensation module adjusts the compensation amount in real time based on the compensation parameters generated by MPC collaborative optimization. The compensation parameters separate the translation and rotation compensation amounts through the motion decoupling algorithm, and perform feedforward-feedback compound control in a 10 kHz high-frequency closed loop to dynamically distribute the axial force and torque and suppress the posture error of the rotating shaft.

8. The dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer axis according to claim 7, characterized in that: The construction of the coupled error model of the translation vector and the rotation vector, and integration of the data of the translation vector and the rotation vector into a unified six-degree-of-freedom error specifically includes: Receive translation and rotation vector data unified to the same spatiotemporal reference, verify data integrity and remove outliers, and ensure strict timestamp alignment through dynamic delay compensation; Perform interpolation synchronization and dynamic delay compensation for sensor sampling rate differences; The global linear velocity is calculated by numerically differentiating the translation vector, and the angular acceleration is obtained by differentiating the rotation vector. A dual-vector coupling error model is constructed, and the coupling error term is defined based on the dual-vector coupling model. The state equation and observation equation are generated through filtering and fusion. The coupling error term is defined as: ， ； in, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are experimentally calibrated cross-interference coefficients, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector; The state equation is: ; The observation equation is: ; in, represents the Kalman filter state vector, F represents the state transfer matrix, H represents the observation matrix, and represents process noise and observation noise, represents the observation vector.

9. The dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer axis according to claim 8, characterized in that: Interpolation synchronization includes performing cubic spline interpolation on low sampling rate data to generate a sequence synchronized with the laser displacement sensor; The calculation formula of the interpolated gyroscope rotation vector is: ； in, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the residual clock error between sensors, represents the discrete sampling time points of the translation vector, represents the discrete sampling time point of the rotation vector, and k represents the offset index of the neighborhood sampling point used in interpolation; The calculation formula for the clock residual error is: ； 𝜏where τ represents the time offset.

10. The dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer axis according to claim 9, characterized in that: The steps of dynamically allocating the translation vector and rotation vector compensation weights in the time domain by combining the feedforward-feedback mechanism and generating the real-time adjustment compensation amount by rolling time domain optimization specifically include: A discrete state-space model of the six-degree-of-freedom system is established, with the system state variables defined as translational position, translational velocity, rotational attitude angle, and rotational angular velocity. A dual-vector compensation is set as the control input, with the prediction time domain window and the control time domain window divided. An initial prediction sequence of feedforward compensation is generated based on the reference trajectory. The feedforward compensation is calculated based on the reference trajectory and the system disturbance model, and the feedback compensation correction is generated based on the deviation between the real-time measured system state and the predicted state; Define a time-varying weight function and , dynamically adjust the optimization priority of translation error and rotation error according to the system motion stage, and construct the rolling time domain optimization objective function; Among them, the objective function is: ； Where J represents the total cost function of the rolling horizon optimization, represents the translation tracking error, represents the rotation tracking error, Indicates the rate of change of the controlled quantity, Indicates the number of prediction time domain steps, represents the number of control time domain steps, represents the time-varying weight matrix of the translation error, A time-varying weight matrix representing the rotation error; Add actuator saturation constraints and state variable safety margins as inequality constraints, use numerical optimization solvers to solve the constrained optimization problem online, and obtain the optimal control sequence ; Extract the optimal control quantity at the current moment , output dual vector compensation instructions to the actuator; The prediction time domain window is updated based on the updated system state measurement value, and the optimization process is repeated to achieve closed-loop dynamic adjustment, integrating the feedforward prediction compensation and feedback correction, and outputting the global six-degree-of-freedom optimization real-time adjustment compensation.

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