Double-vector cooperative compensation method and system for multi-degree-of-freedom motion error of computer rotating shaft

Abstract

The invention provides a double-vector cooperative compensation method and system for a multi-degree-of-freedom motion error of a computer rotating shaft, and the method comprises the following steps: synchronously collecting a translation vector and a rotation vector of the rotating shaft through a sensor, and unifying the data of the translation vector and the rotation vector to the same time-space reference; constructing a coupling error model of translation and rotation vectors, and integrating data of the translation and rotation vectors into a unified six-degree-of-freedom error amount; in combination with a feedforward-feedback mechanism, translation and rotation vector compensation weights are dynamically distributed in a time domain, and a real-time adjustment compensation amount is generated through rolling time domain optimization. The method does not need to depend on a complex parameter identification process of a traditional rotating shaft physical model, six-degree-of-freedom error cooperative compensation can be achieved only through sensor data synchronization and a dynamic optimization algorithm, the method is suitable for computer rotating shafts of different loads and motion scenes, and the motion precision and reliability of equipment are remarkably improved.

Description

Technical Field

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

[0002] With the rapid development of portable electronic devices and high-density storage technologies, the computer rotating shaft, as the core moving component of precision devices such as laptop computers and optical drive reading and writing mechanisms, its multi-degree-of-freedom motion accuracy directly affects the reliability and functional performance of the devices. During the compound motion of high-speed telescoping and multi-axis rotation in traditional rotating shaft systems, the six-degree-of-freedom pose errors (including axial displacement deviation and rotational attitude deviation) caused by factors such as mechanical clearance, load disturbance, and drive non-linearity have become the key bottleneck restricting the improvement of device accuracy.

[0003] In the prior art, the compensation methods for the motion errors of the rotating shaft are mostly limited to single-degree-of-freedom or static coupling models, and there are the following problems:

[0004] The acquisition of translation and rotation vectors often uses independent sensors, without achieving unified spatio-temporal reference, resulting in distorted coupling error modeling;

[0005] Traditional feedforward or PID feedback control uses fixed weight allocation and cannot adapt to the error characteristics that dynamically change during the motion stage of the rotating shaft. Summary of the Invention

[0006] Aiming at the deficiencies of 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 rotating shaft to solve the problems raised in the above background art.

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

[0008] Synchronously collect the translation vector and rotation vector of the rotating shaft through sensors, and unify the data of the translation vector and rotation vector to the same spatio-temporal reference;

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

[0010] Combined with the feedforward-feedback mechanism, dynamically allocate the compensation weights of the translation and rotation vectors in the time domain, and generate real-time adjustment compensation amounts through rolling horizon optimization;

[0011] Based on the compensation parameters generated by MPC collaborative optimization, the translation and rotation compensation amounts are separated by 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] Based on the sensor, the translation vector and rotation vector are measured respectively, and the hardware synchronization and coordinate system calibration are completed;

[0014] Among them, hardware synchronization uses the IEEE 1588 PTP protocol to achieve sensor clock synchronization, and the coordinate system calibration establishes a global coordinate system with the center of mass of the rotating 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 construction of the coupled error model of the translation and rotation vectors and integration of the data of the translation and rotation vectors into a unified six-degree-of-freedom error specifically includes:

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

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

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

[0019] Among them, the definition formula of the coupling error term is:

[0020] , ;

[0021] in, The coupling error term of the shift vector, represents the coupling error term of the rotating vector, K1 and K2 are the cross-interference coefficients calibrated experimentally, 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] Among them, represents the Kalman filter state vector, F represents the state transition matrix, H represents the observation matrix, and represent process noise and observation noise.

[0025] As a further preference, 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 for the interpolated gyroscope rotation vector is:

[0027] ;

[0028] Among them, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the clock residual 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] where τ represents the time offset.

[0032] As a further preference, the step of combining the feedforward-feedback mechanism to dynamically allocate the compensation weights of the translation and rotation vectors in the time domain and generate a real-time adjusted compensation amount through rolling horizon optimization specifically includes:

[0033] Establish a discrete state space model of the six-degree-of-freedom system, define the system state variables as translation position, translation velocity, rotation attitude angle, and rotation angular velocity, set the double vector compensation amount as the control input, divide the prediction time window and the control time window, and generate an initial prediction sequence of the feedforward compensation amount based on the reference trajectory;

[0034] Calculate the feedforward compensation amount according to the reference trajectory and the system disturbance model, and generate a feedback compensation correction amount based on the deviation between the real-time measured system state and the predicted state;

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

[0036] Among them, the objective function is:

[0037] ;

[0038] Among them, J represents the total cost function of rolling horizon optimization, represents the translational tracking error, represents the rotational tracking error, represents the change rate of the control variable, represents the prediction horizon step number, represents the control horizon step number, represents the time-varying weight matrix of the translational error, represents the time-varying weight matrix of the selection error;

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

[0040] Extract the optimal control variable at the current moment , and output the double-vector compensation command to the actuator;

[0041] Based on the updated system state measurement values, roll and update the prediction horizon window, repeat the optimization process to achieve closed-loop dynamic adjustment, fuse the feedforward prediction compensation amount and the feedback correction amount, and output the global six-degree-of-freedom optimized real-time adjustment compensation amount.

[0042] As a further preference, the compensation parameters generated by MPC collaborative optimization, separating the translational and rotational compensation amounts through a motion decoupling algorithm, and performing feedforward-feedback composite control with a high-frequency closed-loop of 10 kHz, dynamically distributing the axial force and torque, and suppressing the pose error of the rotating shaft, the process includes:

[0043] Based on the global compensation parameters generated by MPC collaborative optimization, use the Lie group-Lie algebra decoupling algorithm to map the compensation amount to the local coordinate system of the rotating shaft, separate the axial translational force and the radial deviation correction force, as well as the torsional torque and the tilt correction torque, and eliminate the coupling interference between degrees of freedom;

[0044] Synchronize the actual pose data of the rotating shaft with a control period of 10 kHz in microseconds, calculate the position and angle deviations, combine the acceleration feedforward compensation of the reference trajectory and the robust feedback correction, and drive the linear motor and the torque motor to output the dynamically distributed force / torque, realizing high-precision closed-loop suppression of the axial telescopic error and the rotational attitude deviation of the rotating shaft.

[0045] As a further preference, a double-vector collaborative compensation system for multi-degree-of-freedom motion errors of a computer rotating shaft, used to implement the double-vector collaborative compensation method for multi-degree-of-freedom motion errors of the above-mentioned computer rotating shaft, includes:

[0046] A space-time calibration module, used to unify the data of the collected translation vector and rotation vector of the rotating shaft to the same space-time reference;

[0047] A model construction module, which constructs a coupling error model of the translation and rotation vectors, and integrates the data of the translation and rotation vectors into a unified six-degree-of-freedom error quantity;

[0048] A collaborative optimization module, by combining a feedforward-feedback mechanism, dynamically allocates the compensation weights of the translation and rotation vectors in the time domain, and generates a real-time adjustment compensation amount through rolling horizon optimization;

[0049] An error compensation module, based on the compensation parameters generated by MPC collaborative optimization, separates the translation and rotation compensation amounts through a motion decoupling algorithm, and executes a feedforward-feedback composite control with a high frequency of 10 kHz in a closed loop, dynamically allocates the axial force and torque, and suppresses the pose error of the rotating shaft.

[0050] As a further preference, the construction of the coupling error model of the translation and rotation vectors and the integration of the data of the translation and rotation vectors into a unified six-degree-of-freedom error quantity specifically includes:

[0051] Receiving the translation vector and rotation vector data unified to the same space-time reference, verifying the data integrity and removing outliers, and ensuring strict alignment of timestamps through dynamic delay compensation;

[0052] Performing interpolation synchronization and dynamic delay compensation for the difference in sensor sampling rates;

[0053] Performing numerical differentiation on the translation vector to calculate the global linear velocity, differentiating the rotation vector to obtain the angular acceleration, constructing a double-vector coupling error model, defining a coupling error term based on the double-vector coupling model, and generating a state equation and an observation equation through filter fusion;

[0054] Among them, the definition formula of the coupling error term is:

[0055] , ;

[0056] Among them, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are both cross-interference coefficients calibrated by experiments, 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] Among them, represents the Kalman filter state vector, F represents the state transition matrix, H represents the observation matrix, and represent the process noise and the observation noise.

[0060] As a further preference, 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 for the interpolated gyroscope rotation vector is:

[0062] ;

[0063] Among them, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the clock residual 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] where τ represents the time offset.

[0067] As a further preference, the step of combining the feedforward-feedback mechanism to dynamically allocate the translation and rotation vector compensation weights in the time domain and generate real-time adjusted compensation amounts through rolling horizon optimization specifically includes:

[0068] Establish a discrete state space model of the six-degree-of-freedom system, define the system state variables as the translation position, translation velocity, rotation attitude angle, and rotation angular velocity, and set the dual vector compensation amount as the control input. Divide the prediction time domain window and the control time domain window, and generate an initial prediction sequence of the feedforward compensation amount based on the reference trajectory;

[0069] Calculate the feedforward compensation amount according to the reference trajectory and the system disturbance model, and generate a feedback compensation correction amount based on the deviation between the real-time measured system state and the predicted state;

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

[0071] Among them, the objective function is:

[0072] ;

[0073] Among them, J represents the total cost function of rolling horizon optimization, represents the translational tracking error, represents the rotational tracking error, represents the rate of change of the control variable, represents the prediction horizon steps, represents the control horizon steps, represents the time-varying weight matrix of the translational error, represents the time-varying weight matrix of the selection error;

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

[0075] Extract the optimal control variable at the current moment , and output a dual-vector compensation command to the actuator;

[0076] Based on the updated system state measurement values, roll and update the prediction horizon window, repeat the optimization process to achieve closed-loop dynamic adjustment, fuse the feedforward prediction compensation amount and the feedback correction amount, and output the global six-degree-of-freedom optimized real-time adjustment compensation amount.

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

[0078] Dynamic coupling error modeling and real-time suppression: Based on the dual-vector coupling model and the Kalman filtering algorithm, the cross-interference error between the translational and rotational vectors is corrected in real time, significantly reducing the comprehensive error of position and attitude, and achieving high-robustness error compensation without relying on complex physical modeling;

[0079] Adaptive time-domain optimization and collaborative control: Adopt model predictive control combined with a feedforward-feedback mechanism, dynamically allocate the translational and rotational error weights according to the rotating shaft motion stage, preferentially suppress oscillations during high-speed telescoping, and balance the tracking accuracy during precision pose adjustment (such as the positioning of the optical drive laser head), with a compensation response speed reaching the millisecond level, adapting to the requirements of complex working conditions;

[0080] High-frequency decoupling and precise execution: Separate the global compensation amount into local axial forces and torques through the Lie group-Lie algebra decoupling algorithm, drive the linear motor and torque motor with a 10 kHz high-frequency closed-loop control, directly eliminate the coupling interference between degrees of freedom, and achieve smaller axial position errors and rotational attitude deviations of the rotating shaft, meeting the stringent requirements of high-density storage devices for nanoscale positioning;

[0081] The present invention does not rely on the complex parameter identification process of the traditional rotating shaft physical model. It can achieve six-degree-of-freedom error collaborative compensation only through sensor data synchronization and dynamic optimization algorithms, and is applicable to computer rotating shafts with different loads and motion scenarios, significantly improving the motion accuracy and reliability of the device. At the same time, this method is not limited to specific rotating shaft types and can be extended to the suppression of multi-degree-of-freedom errors in other precision electromechanical systems, with strong versatility and broad application prospects. Brief Description of the Drawings

[0082] Figure 1 It is a flowchart of the dual-vector collaborative compensation method for multi-degree-of-freedom motion errors of the computer rotating shaft of the present invention;

[0083] Figure 2 It is a block diagram of the dual-vector collaborative compensation system for multi-degree-of-freedom motion errors of the computer rotating shaft of the present invention. Detailed Embodiment

[0084] The following details the embodiments of the present invention. The examples of the embodiments are shown in the drawings, where the same or similar reference numerals represent the same or similar elements or elements with the same or similar functions throughout. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as a limitation of the present invention.

[0085] The following disclosure provides many different embodiments or examples for implementing different structures of the present invention. To simplify the disclosure of the present invention, the components and settings of specific examples are described below. Of course, they are only examples and are not intended to limit the present invention. In addition, the present invention may repeat reference numerals and / or reference letters in different examples. This repetition is for the purpose of simplification and clarity and does not 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 of ordinary skill in the art can be aware of the application of other processes and / or the use of other materials.

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

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

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

[0089] The translation vector and the rotation vector are measured separately by sensors, and hardware synchronization and coordinate system calibration are completed;

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

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

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

[0093] Specifically, receive the translation vector and rotation vector data unified to the same space-time reference, verify the data integrity and eliminate outliers, and ensure strict alignment of timestamps through dynamic delay compensation;

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

[0095] Among them, 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 for the interpolated gyroscope rotation vector is:

[0097] ;

[0098] Among them, represents the interpolated gyroscope rotation vector, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the clock residual 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 clock residual error is:

[0100] ;

[0101] Among them, τ represents the time offset;

[0102] Perform numerical differentiation on the translation vector to calculate the global linear velocity, differentiate the rotation vector to obtain the angular acceleration, construct a double-vector coupling error model, define the coupling error term based on the double-vector coupling model, and generate the state equation and the observation equation through filtering and fusion;

[0103] Among them, the definition formula of the coupling error term is:

[0104] , ;

[0105] Among them, the coupling error term of the translation vector, represents the coupling error term of the rotation vector, and K1 and K2 are both cross-interference coefficients calibrated by experiments, 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] Among them, represents the Kalman filter state vector, F represents the state transition matrix, H represents the observation matrix, and represent the process noise and the 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 filtering parameters, the state vector is dynamically estimated through the prediction-update loop. In the prediction stage, the state is calculated according to the motion model. In the update stage, the sensor observation values are fused and the deviation is corrected by using the coupling error, while suppressing the influence of the process noise and the sensor noise;

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

[0112] S3: Combining the feedforward-feedback mechanism, dynamically allocate the compensation weights of the translation and rotation vectors in the time domain, and generate a real-time adjustment compensation amount through rolling horizon optimization;

[0113] Establish a discrete state space model of the six-degree-of-freedom system, define the system state variables as the translation position, translation velocity, rotation attitude angle and rotation angular velocity, and set the dual-vector compensation amount as the control input. Divide the prediction time domain window and the control time domain window, and generate an initial prediction sequence of the feedforward compensation amount based on the reference trajectory;

[0114] Calculate the feedforward compensation amount according to the reference trajectory and the system disturbance model, which is used to offset the predicted dynamic error caused by the inertial coupling effect. Generate the feedback compensation correction amount 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 translational vector and rotational vector data volume, and the predicted state is specifically the estimated value of the system state at future times deduced within the prediction time domain;

[0116] Define the time-varying weight function and , dynamically adjust the optimization priorities of the translational error and the rotational 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] Among them, J represents the total cost function of the rolling time domain optimization, represents the translational tracking error, represents the rotational tracking error, represents the control variable change rate, represents the number of steps in the prediction time domain, represents the number of steps in the control time domain, represents the time-varying weight matrix of the translational error, represents the time-varying weight matrix of the selection error;

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

[0121] Extract the optimal control amount at the current moment , and output the dual-vector compensation command to the actuator;

[0122] Based on the updated system state measurement value, roll and update the prediction time domain window, repeat the optimization process to achieve closed-loop dynamic adjustment, fuse the feedforward prediction compensation amount and the feedback correction amount, and output the global six-degree-of-freedom optimized real-time adjustment compensation amount.

[0123] In this embodiment, the time-varying weight functions and are dynamically adjusted according to the system acceleration stage and the steady state stage. The weight of the rotational error is reduced in the acceleration stage to suppress oscillation, and the translational and rotational weights are evenly distributed in the steady state stage; the dual-vector compensation command includes the force vector in the translational direction and the torque vector in the rotational direction, and the two achieve six-degree-of-freedom collaborative compensation through dynamic weight distribution.

[0124] S4: Based on the compensation parameters generated by MPC collaborative optimization, the translational and rotational compensation amounts are separated through a motion decoupling algorithm, and a feedforward-feedback composite control is executed with a high-frequency closed-loop of 10 kHz to dynamically allocate the axial force and torque, suppressing the pose error of the rotating shaft.

[0125] Specifically, based on the global compensation parameters generated by MPC collaborative optimization, the Lie group-Lie algebra decoupling algorithm is used to map the compensation amounts to the local coordinate system of the rotating shaft, separating the axial translational force and the radial deviation correction force, as well as the torsional torque and the tilt correction torque, to eliminate the coupling interference between degrees of freedom; Subsequently, the actual pose data of the rotating shaft is synchronized with a control period of 10 kHz in microseconds, the position and angle deviations are calculated, and combined with the acceleration feedforward compensation (canceling inertial lag) and robust feedback correction (such as sliding mode control) of the reference trajectory, the linear motor and the torque motor are driven to output the dynamically allocated force / torque, realizing the high-precision closed-loop suppression of the axial telescopic error and the rotational attitude deviation of the rotating shaft.

[0126] As Figure 2 shown, this embodiment also provides a dual-vector collaborative compensation system for the multi-degree-of-freedom motion error of a computer rotating shaft, which is used to implement the dual-vector collaborative compensation method for the multi-degree-of-freedom motion error of the computer rotating shaft, including:

[0127] A space-time calibration module, which is used to unify the data of the translational vector and the rotational vector of the rotating shaft collected to the same space-time reference;

[0128] A model construction module, which constructs a coupling error model of the translational and rotational vectors and integrates the data of the translational and rotational vectors into a unified six-degree-of-freedom error quantity;

[0129] A collaborative optimization module, which dynamically allocates the compensation weights of the translational and rotational vectors in the time domain by combining the feedforward-feedback mechanism, and generates real-time adjusted compensation amounts through rolling horizon optimization;

[0130] An error compensation module, based on the compensation parameters generated by MPC collaborative optimization, separates the translational and rotational compensation amounts through a motion decoupling algorithm, and executes a feedforward-feedback composite control with a high-frequency closed-loop of 10 kHz to dynamically allocate the axial force and torque, suppressing the pose error of the rotating shaft.

[0131] Among them, constructing a coupling error model of the translational and rotational vectors and integrating the data of the translational and rotational vectors into a unified six-degree-of-freedom error quantity specifically includes:

[0132] Receiving the data of the translational vector and the rotational vector unified to the same space-time reference, verifying the data integrity and removing outliers, and ensuring strict alignment of timestamps through dynamic delay compensation;

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

[0134] Numerically differentiate the translation vector to calculate the global linear velocity, differentiate the rotation vector to obtain the angular acceleration, construct a dual-vector coupling error model, define the coupling error term based on the dual-vector coupling model, and generate the state equation and observation equation through filter fusion;

[0135] Among them, the definition formula of the coupling error term is:

[0136] , ;

[0137] Among them, represents the coupling error term of the translation vector, represents the coupling error term of the rotation vector, K1 and K2 are both 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] Among them, represents the Kalman filter state vector, F represents the state transition matrix, H represents the observation matrix, and represent the process noise and observation noise.

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

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

[0143] ;

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

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

[0146] ;

[0147] Among them, τ represents the time offset.

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

[0149] Establish a discrete state-space model of the six-degree-of-freedom system, define the system state variables as the translation position, translation velocity, rotation attitude angle, and rotation angular velocity, set the dual-vector compensation amount as the control input, divide the prediction horizon window and the control horizon window, and generate the initial prediction sequence of the feedforward compensation amount based on the reference trajectory;

[0150] Calculate the feedforward compensation amount according to the reference trajectory and the system disturbance model, and generate the feedback compensation correction amount based on the deviation between the real-time measured system state and the predicted state;

[0151] Define the time-varying weight function and , dynamically adjust the optimization priorities of the translation error and the rotation error according to the system motion stage, and construct the receding horizon optimization objective function;

[0152] Among them, the objective function is:

[0153] ;

[0154] Among them, J represents the total cost function of the receding horizon optimization, represents the translation tracking error, represents the rotation tracking error, represents the change rate of the control quantity, represents the number of steps in the prediction horizon, represents the number of steps in the control horizon, represents the time-varying weight matrix of the translation error, represents the time-varying weight matrix of the selection error;

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

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

[0157] Based on the updated system state measurement value, roll and update the prediction horizon window, repeat the optimization process to achieve closed-loop dynamic adjustment, fuse the feedforward prediction compensation amount and the feedback correction amount, and output the global six-degree-of-freedom optimized real-time adjustment compensation amount.

[0158] Although embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present 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 hinge, characterized in that The following steps are involved: The translation vector and rotation vector of the rotating shaft are synchronously collected by the sensor, and the data of the translation vector and the rotation vector are unified to the same time and space reference; Construct a coupled error model of translation and rotation vectors, and integrate the data of translation and rotation vectors into a unified six-degree-of-freedom error; 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; Based on the compensation parameters generated by MPC collaborative optimization, the motion decoupling algorithm is used to separate the translation and rotation compensation amounts, and the feedforward-feedback compound control is performed in a 10kHz 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 error of a computer hinge according to claim 1, wherein 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: Based on the sensor, the translation vector and rotation vector are measured respectively, and the hardware synchronization and coordinate system calibration are completed; Among them, hardware synchronization uses the IEEE 1588 PTP protocol to achieve sensor clock synchronization, and the coordinate system calibration establishes a global coordinate system with the center of mass of the rotating shaft as the origin, and solves the rigid transformation of the sensor local coordinate system through the calibration point set.

3. A dual-vector collaborative compensation method for multi-degree-of-freedom motion error of a computer hinge, according to claim 1, wherein The construction of the coupled error model of the translation and rotation vectors and integration of the data of the translation and rotation vectors 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 alignment of timestamps through dynamic delay compensation; Interpolation synchronization and dynamic delay compensation for sensor sampling rate differences; The global linear velocity is calculated by numerically differentiating the translation vector, the angular acceleration is obtained by differentiating the rotation vector, a dual-vector coupling error model is constructed, the coupling error term is defined based on the dual-vector coupling model, and the state equation and observation equation are generated through filtering fusion; Among them, the definition formula of the coupling error term is: ， ； Among them, the coupling error term of the translation vector, represents the coupling error term of the rotation vector, and K1 and K2 are both 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 as follows: ; The observation equation is as follows: ; Among them, represents the Kalman filter state vector, F represents the state transition matrix, H represents the observation matrix, and represent process noise and observation noise.

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

5. A dual-vector collaborative compensation method for multi-degree-of-freedom motion error of a computer hinge, according to claim 1, characterized in that The steps of dynamically allocating translation and rotation vector compensation weights in the time domain in combination with the feedforward-feedback mechanism and generating real-time adjustment compensation amounts through rolling time domain optimization specifically include: A discrete state space model of the six-degree-of-freedom system is established, and the system state variables are defined as translation position, translation velocity, rotation attitude angle, and rotation angular velocity. The dual vector compensation is set as the control input, and the prediction time domain window and the control time domain window are divided. The initial prediction sequence of the 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 priorities of the translational error and the rotational error according to the system motion stage, and construct a receding horizon optimization objective function; Among them, the objective function is: ； Among them, \(J\) represents the total cost function of rolling horizon optimization, represents the translational tracking error, represents the rotational tracking error, represents the rate of change of the control variable, represents the prediction horizon step number, represents the control horizon step number, represents the time-varying weight matrix of the translational error, represents the time-varying weight matrix of the selection error; Add actuator saturation constraints and state variable safety boundaries as inequality constraints, and use a numerical optimization solver to online solve the constrained optimization problem to obtain the optimal control sequence ; Extract the optimal control quantity at the current moment , and output a dual-vector compensation instruction 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. The feedforward prediction compensation and feedback correction are integrated to output the global six-degree-of-freedom optimization real-time adjustment compensation.

6. A dual-vector collaborative compensation method for multi-degree-of-freedom motion error of a computer hinge, characterized in that, The compensation parameters generated based on MPC collaborative optimization are separated from the translation and rotation compensation amounts by a motion decoupling algorithm, and a feedforward-feedback compound control is performed in a 10 kHz high-frequency closed loop to dynamically distribute the axial force and torque to suppress the position error of the rotating shaft. The process includes: Based on the global compensation parameters generated by MPC collaborative optimization, the Lie group-Lie algebra decoupling algorithm is used to map the compensation amount to the local coordinate system of the rotating shaft, separate the axial translation force and radial correction force, as well as the torsional moment and tilt correction moment, and eliminate the coupling interference between degrees of freedom. The actual position and posture data of the rotating axis are synchronized with a control cycle of 10 kHz microseconds, and the position and angle deviations are calculated. Combined with the 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 axial telescopic error and rotational posture deviation of the rotating axis.

7. A dual-vector collaborative compensation system for multi-degree-of-freedom motion error of a computer hinge, which is used to implement the dual-vector collaborative compensation method for multi-degree-of-freedom motion error of a computer hinge according to any one of claims 1-6, characterized in that, include: A time-space calibration module is used to unify the collected data of the axis translation vector and rotation vector to the same time-space reference; A model building module builds a coupled error model of translation and rotation vectors and integrates the data of translation and rotation vectors into a unified six-degree-of-freedom error quantity; The collaborative optimization module dynamically allocates translation and rotation vector compensation weights in the time domain by combining the feedforward-feedback mechanism, and generates real-time adjustment compensation through rolling time domain optimization; The error compensation module, based on the compensation parameters generated by MPC collaborative optimization, separates the translation and rotation compensation through the motion decoupling algorithm, performs feedforward-feedback compound control in a 10 kHz high-frequency closed loop, dynamically distributes axial force and torque, and suppresses the position error of the rotating shaft.

8. A dual-vector collaborative compensation system for multi-degree-of-freedom motion error of a computer hinge, according to claim 7, characterized in that The construction of the coupled error model of the translation and rotation vectors and integration of the data of the translation and rotation vectors 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 alignment of timestamps through dynamic delay compensation; Interpolation synchronization and dynamic delay compensation for sensor sampling rate differences; The global linear velocity is calculated by numerically differentiating the translation vector, the angular acceleration is obtained by differentiating the rotation vector, a dual-vector coupling error model is constructed, the coupling error term is defined based on the dual-vector coupling model, and the state equation and observation equation are generated through filtering fusion; Among them, the definition formula of the coupling error term is: ， ； Among them, the coupling error term of the translation vector, represents the coupling error term of the rotation vector, and K1 and K2 are both cross-interference coefficients calibrated experimentally, represents the angular velocity vector, represents the linear velocity vector in the global coordinate system, represents the angular acceleration vector; The state equation is as follows: ; The observation equation is as follows: ; wherein, represents the Kalman filter state vector, F represents the state transition matrix, H represents the observation matrix, and represent the process noise and the observation noise.

9. A dual-vector collaborative compensation system for multi-degree-of-freedom motion error of a computer hinge, according to claim 8, wherein The interpolation synchronization includes performing cubic spline interpolation on the low sampling rate data to generate a sequence synchronized with the laser displacement sensor; The calculation formula of the interpolated gyroscope rotation vector is: ； Among them, represents the gyroscope rotation vector after interpolation, represents the cubic spline interpolation coefficient, represents the cubic B-spline basis function, represents the clock residual 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 clock residual error is: ； 𝜏where τ represents the time offset.

10. A dual-vector collaborative compensation system for multi-degree-of-freedom motion error of a computer hinge, characterized in that, The steps of dynamically allocating translation and rotation vector compensation weights in the time domain in combination with the feedforward-feedback mechanism and generating real-time adjustment compensation amounts through rolling time domain optimization specifically include: A discrete state space model of the six-degree-of-freedom system is established, and the system state variables are defined as translation position, translation velocity, rotation attitude angle, and rotation angular velocity. The dual vector compensation is set as the control input, and the prediction time domain window and the control time domain window are divided. The initial prediction sequence of the feedforward compensation is generated based on the reference trajectory. Calculate the feedforward compensation amount according to the reference trajectory and the system disturbance model, and generate a feedback compensation correction amount 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 priorities of translational error and rotational error according to the system motion stage, and construct a receding horizon optimization objective function; Among them, the objective function is: ； where \(J\) represents the total cost function of rolling horizon optimization, represents the translational tracking error, represents the rotational tracking error, represents the rate of change of the control input, represents the prediction horizon steps, represents the control horizon steps, represents the time-varying weight matrix of the translational error, represents the time-varying weight matrix of the selection error; Add actuator saturation constraints and state variable safety boundaries as inequality constraints, and use a numerical optimization solver to online solve the constrained optimization problem to obtain the optimal control sequence ; Extract the optimal control quantity at the current moment , and output a dual-vector compensation instruction to the actuator; Based on the updated system state measurement value, roll-update the prediction time domain window, repeat the optimization process to achieve closed-loop dynamic adjustment, fuse the feedforward prediction compensation amount and the feedback correction amount, and output the global six-degree-of-freedom optimized real-time adjustment compensation amount.

Images