A prediction control method for silicon-based flexible robot digital twin driving

Abstract

The application discloses a silicon-based flexible robot digital twinborn driving prediction control method and relates to the technical field of digital twinborn simulation. The application discloses a silicon-based flexible robot digital twinborn driving prediction control method and relates to a kind of digital twinborn simulation technical field, by being directed to physical silicon-based flexible robot Construction one-to-one mapping digital twinborn virtual model, and carry out static and dynamic parameter pair mark, ensure that virtual model and physical entity are highly consistent, provide reliable foundation for subsequent work, then carry out global frequency sweep simulation and resonance frequency distribution extraction, accurately obtain global resonance frequency distribution, eliminate simulation pseudo-peak interference, then construct the prediction control model with spectrum constraint, combine the discrete state space prediction model with the composite optimization objective containing spectrum constraint, consider various performance requirements, then generate resonance-free driving waveform by rolling optimization solution, block resonance excitation from excitation source end, finally carry out physical driving execution and twinborn model closed loop iteration correction, adapt to the parameter drift caused by material creep and working condition change.

Description

Technical Field

[0001] This invention relates to the field of digital twin simulation technology, specifically a predictive control method for driving a silicon-based flexible robot digital twin. Background Technology

[0002] Silicon-based flexible materials, due to their unique low Young's modulus, large deformation range, good biocompatibility, and structural compliance, have shown broad application prospects in precision work equipment such as micro-flexible manipulators, flexible micro-actuators, and biomimetic flexible drive joints. However, the inherent low damping coefficient of silicon-based materials makes it easy to excite structural resonance when the drive signal frequency matches the inherent modal frequency of the structure, leading to unexpected large deformations. This resonance phenomenon, superimposed on the conventional dynamic response, further causes overshoot in the deformation output, deviating from the predetermined target positioning value. At the same time, the low damping characteristics also lead to slow dissipation of vibration energy, resulting in a longer convergence period for deformation positioning, making it difficult to meet the high requirements of precision work in terms of steady-state accuracy.

[0003] Existing technical solutions for vibration and overshoot suppression in silicon-based flexible robots mostly employ feedback-based post-correction methods. These solutions collect the deviation between the actual output and the target trajectory using sensors, and then use algorithms such as PID and sliding mode control to correct the driving quantity. However, this traditional approach has many inherent limitations. First, the control action lags significantly behind the occurrence of resonance and overshoot, making it impossible to promptly block the excitation at the excitation source. It can only remedy the problem after it occurs, failing to address the root cause. Second, it lacks pre-identification of the full-range resonant frequency under all operating conditions, hindering control... The algorithm lacks prior information on the vulnerable frequency bands of the structure in the frequency domain, which makes it unable to effectively deal with resonance problems when faced with complex and ever-changing working conditions. Furthermore, the optimization objective only focuses on time-domain tracking and control smoothness, without setting frequency domain constraints on the driving waveform, and cannot actively filter out resonance excitation components, so resonance problems may still exist. Finally, single-point calibration and fixed parameter models cannot adapt to modal drift under large deformation and variable load. Under large-scale deformation and load changes, the control robustness is insufficient, making it difficult to ensure that silicon-based flexible robots can achieve high-precision deformation positioning under various working conditions. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a predictive control method for digital twin-driven silicon-based flexible robots. This method constructs a one-to-one mapping digital twin virtual model of the physical silicon-based flexible robot and performs static and dynamic parameter calibration to ensure a high degree of consistency between the virtual model and the physical entity, providing a reliable foundation for subsequent work. Next, it conducts full-domain frequency sweep simulation and resonant frequency distribution extraction to accurately obtain the full-domain resonant frequency distribution and eliminate simulation spurious peak interference. Then, it constructs a predictive control model with spectral constraints, combining the discrete state-space predictive model with a composite optimization objective containing spectral constraints to accommodate various performance requirements. Subsequently, it generates a resonant-free driving waveform through rolling optimization, blocking resonant excitation from the excitation source. Finally, it performs physical drive execution and closed-loop iterative correction of the twin model to adapt to parameter drift caused by material creep and changes in operating conditions, ensuring the accuracy of the digital twin model and the effectiveness of resonant constraints, forming a complete technology chain to meet the control requirements of silicon-based flexible precision work equipment.

[0005] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a predictive control method for digital twin actuation of a silicon-based flexible robot, the method comprising the following specific steps: S1: Construct a digital twin virtual model integrating geometry, materials mechanics, drive-structure coupled dynamics, boundary and disturbance, synchronously map the structure, materials, drive and boundary parameters of the physical silicon-based flexible robot to the virtual model and complete the static and dynamic response benchmarking to ensure that the virtual model is consistent with the dynamic characteristics of the physical entity; S2: Conduct full-condition, full-point frequency sweep excitation simulation in the benchmarked digital twin model. By collecting the dynamic response of multiple measurement points and performing peak identification and pseudo-peak removal, the full-domain resonant frequency distribution is obtained by fusing multi-condition data, and the resonant frequency forbidden set and resonant frequency band interval are determined. S3: Based on the dynamic parameters identified by the twin model, a discrete state-space prediction model is established. In the rolling optimization framework of model predictive control, a composite objective function including time-domain tracking error, control quantity smoothing penalty, and resonant frequency band spectrum constraint is constructed, and a hard constraint on the resonant frequency band spectrum amplitude is set. S4: Using the current actual state of the system as the initial condition, solve the composite optimization objective in the prediction time domain under the premise of satisfying the spectrum, driving amplitude and deformation output constraints, and output the smooth driving waveform without resonance frequency band excitation components after filtering out the resonant frequency band. S5: Apply the non-resonant smooth drive waveform to the physical silicon-based flexible robot, collect the actual deformation and vibration data and send them back to the digital twin to correct the model parameters and resonance distribution online, and execute the above steps in a fixed control cycle to achieve closed-loop non-resonant drive and high-precision positioning control.

[0006] Further, in S1, the specific steps for static and dynamic response benchmarking are as follows: By applying graded static driving loads within the rated driving range to the physical silicon-based flexible robot, the actual static deformation of key monitoring nodes of the flexible body is collected using a laser displacement sensor. This measured data is then compared point-by-point with the simulated deformation of the digital twin virtual model under the same static load input and boundary constraint conditions. The static deformation deviation value of each measuring point is calculated. For deviations exceeding a preset threshold, the material elastic modulus, Poisson's ratio, and local geometric dimensions of the flexible body in the virtual model are corrected first. After correction, the static simulation and measured comparison are repeated until the static deformation deviation of all measuring points is controlled within the allowable range. Based on this, the static deformation of the physical silicon-based flexible robot is further compared point-by-point with the measured data. The prototype is subjected to a fixed-frequency sinusoidal dynamic excitation and a low-amplitude sweep excitation covering the working frequency band. Vibration acceleration, dynamic deformation amplitude and phase data of each measuring point are collected synchronously through a high-frequency response accelerometer and a dynamic displacement sensor. The dynamic response simulation results of the virtual model under the same excitation conditions are compared. The overlap of the time domain response waveform and the matching degree of the frequency domain characteristic curve are verified. For the dynamic response deviation, the material damping coefficient, the coupling stiffness coefficient between the driving unit and the flexible body and the equivalent stiffness dynamic parameters of the boundary constraint in the model are corrected step by step. After each round of parameter correction, the static and dynamic benchmark verification are reproduced synchronously. The iteration cycle continues until the consistency between the static and dynamic response data of the virtual model and the measured data of the physical entity meets the preset technical indicators.

[0007] Furthermore, in S2, within the digital twin virtual model after completing precise static and dynamic alignment, a sweep frequency range consistent with the actual operating frequency band of the silicon-based flexible robot is defined. Continuous frequency-modulated excitation signals are generated according to a set uniform frequency step size. Equal amplitude excitation is applied sequentially to all working conditions, including no load, standard load, variable load, small deformation, and rated large deformation. The signal is input to the virtual drive node at each frequency point. Dynamic deformation amplitude, vibration acceleration, and time-domain response data of the monitoring positions at the end, middle, and root of the flexible body are collected simultaneously. Peak retrieval and feature extraction are performed on the amplitude-frequency response curves of each measuring point. The frequencies where the response amplitude increases abruptly are marked as candidate resonant frequencies. Combined with the signal-to-noise ratio threshold, the noise of numerical simulation and the pseudo-peak interference caused by grid discretization error are screened out. Then, the effective resonant frequency data under multiple working conditions are integrated, classified, and merged with adjacent frequency intervals. Finally, a global resonant frequency distribution dataset covering all structural measuring points and all working conditions is formed, and the set of resonant forbidden frequencies that cannot be used for excitation and the corresponding narrowband resonant intervals are identified.

[0008] Furthermore, in S2, the specific technical solution for peak retrieval and feature extraction of the amplitude-frequency response curves at each measurement point is as follows: First, the amplitude-frequency response curves at each measurement point are processed by moving average smoothing and denoising to reduce the interference of curve fluctuations caused by numerical simulation noise and grid discretization error. Then, peak retrieval is carried out point by point along the frequency axis. Taking the current frequency point as the center, the response amplitudes of the adjacent set number of frequency points are compared. When the amplitude of the point is higher than the adjacent points on both sides and exceeds the set multiple of the reference response amplitude, it is marked as a candidate peak point. The frequency value and response amplitude corresponding to the peak are recorded simultaneously. For each candidate peak point, feature parameters such as the half-power bandwidth of the amplitude-frequency curve near the frequency and the amplitude attenuation rate on both sides of the peak are further extracted. Combined with the preset signal-to-noise ratio threshold and the sudden increase characteristics of the resonant response amplitude, false peaks caused by simulation interference are screened out, and finally the effective resonant peak and corresponding frequency information of each measurement point are determined.

[0009] Furthermore, in S3, based on the dynamic parameters of the silicon-based flexible robot system obtained through static and dynamic benchmarking and frequency sweeping identification using the digital twin model, the driving input, the intermediate deformation state of the flexible body, and the end-effector deformation output positioning are selected as core variables to build a discrete state-space prediction model. Combined with the dynamic response requirements of the actual operation of the silicon-based flexible robot, a matching prediction time domain and control time domain are defined. Based on the aforementioned state-space model, the future... Intra-step flexible body deformation output trajectory and The rolling deduction of the trend of the driving variable changes within the step; on this basis, in the rolling optimization framework of model predictive control, a composite optimization objective function is constructed that integrates the time-domain tracking error term, the control increment smoothing penalty term, and the resonant frequency band driving waveform spectrum constraint term. At the same time, a hard constraint on the amplitude of the driving spectrum component in the resonant frequency band is set, and the prior frequency domain information of the global resonant frequency distribution is transformed into a quantitative constraint condition that can be directly used in the optimization calculation. By combining soft penalty and hard constraint, the overall optimization objective actively suppresses the excitation component falling into the resonant frequency band while taking into account the deformation trajectory tracking accuracy and the stability of the driving signal, so as to ensure that the driving waveform is free from resonance interference.

[0010] Furthermore, in S3, the spatial prediction model is: ,in for The system state vector at any time includes the state variables of deformation and vibration velocity at key measuring points of the flexible body; The system state matrix is ​​obtained from the mechanical parameters of silicon-based materials and the structural parameters of flexible bodies. The input matrix represents the influence coefficients of the driving signal on the system state; for Constant-time driving input volume for The positioning amount is output based on the deformation of the flexible body's end. The output matrix is ​​used to map the system state vector into observable deformation output quantities.

[0011] Furthermore, in S3, a composite optimization objective function is constructed that integrates the time-domain tracking error term, the control increment smoothing penalty term, and the resonant frequency band drive waveform spectrum constraint term. The function formula is as follows: ,in, for The deformation trajectory of the flexible target at any given moment. For model predictions Output amount of deformation at any time This is a tracking error weighting matrix used to adjust the weights for deformation trajectory tracking accuracy. for Constantly driving the input increment, This is a smoothing weighting matrix for the control input, used to suppress sudden changes in the driving signal; These are the spectral constraint weighting coefficients, used to adjust the priority of resonance suppression; To identify the global resonant frequency-forbidden set, For the drive signal at frequency The spectral energy at the location; simultaneously, setting hard amplitude constraints for the driving spectral components within the resonant frequency band. ,in For the drive signal at frequency Spectral amplitude at that location, This is the upper limit of the preset resonant frequency band spectrum amplitude.

[0012] Furthermore, in S4, the system state of the silicon-based flexible robot, measured by sensors at the current moment, including end deformation, vibration acceleration, and real-time output of the drive unit, is used as the initial input condition for rolling optimization. This is substituted into the constructed discrete state-space prediction model and the composite optimization objective function. Rolling optimization is initiated within a preset prediction time domain. During the solution process, the upper limit of the drive input amplitude, the maximum deformation limit of the flexible body, and the hard constraint boundary conditions of the resonant frequency band spectrum amplitude are simultaneously incorporated. A quadratic programming algorithm is used for iterative optimization to minimize the combined objectives of time-domain deformation tracking error, sudden changes in drive signal increment, and energy penalty of the resonant frequency band spectrum. The optimal drive input sequence within the future control time domain is obtained. Frequency domain characteristic analysis and verification are performed on this sequence. After confirming that the amplitude of all excitation components falling into the resonant forbidden frequency set and corresponding frequency bands is lower than a preset allowable threshold, a smooth, non-resonant drive waveform that can be directly loaded onto the physical drive unit is output, ensuring that the drive signal does not excite structural resonance after acting on the silicon-based flexible body.

[0013] Furthermore, in S4, the specific steps of iterative optimization using the quadratic programming algorithm are as follows: The composite optimization objective function is transformed into a standard mathematical form adapted to the quadratic programming algorithm. The initial driving input sequence obtained after substituting the current system state is used as the initial feasible solution for iteration. Simultaneously, the upper and lower limits of the driving input amplitude and the maximum deformation limit of the flexible body are transformed into linear inequality constraints. The hard constraint of the resonant frequency band spectrum amplitude is transformed into linear constraint conditions based on the Fourier transform of the driving signal, and these are embedded into the quadratic programming solution framework. Iterative optimization is carried out using the feasible direction method. In each iteration, the gradient direction of the objective function is calculated, and feasible search directions that satisfy all boundary requirements are selected based on the constraint conditions. The steps are adjusted according to a preset step size. The system drives the input sequence parameters, updates the candidate input sequences for future control time, and simultaneously verifies the changes in the objective function value corresponding to the candidate sequence. If the current objective function value does not reach the preset convergence threshold, or if the candidate sequence still has unmet constraints, the search direction and step size are corrected based on the results of the previous iteration. The gradient calculation, direction selection, parameter adjustment, and constraint verification process are repeated. After each iteration, the dual verification of the objective function value and constraint satisfaction is reproduced simultaneously. When the objective function value converges to the preset minimum threshold and the candidate driving input sequence fully satisfies all boundary constraints and spectral constraints, the iteration process is terminated. This candidate sequence is the optimal driving input sequence for future control time.

[0014] Furthermore, in step S5, the solved harmonic-free smooth drive waveform is loaded into the physical drive unit of the silicon-based flexible robot through the drive control module, driving the flexible body to complete the preset deformation positioning action. At the same time, the actual deformation and vibration acceleration time-domain response data of the flexible body end actuator and deformation-sensitive area are collected in real time through laser displacement sensor and high-frequency acceleration sensor, and the data is synchronously transmitted back to the digital twin virtual model. Based on the deviation analysis between the measured data and the simulation data under the same excitation and boundary conditions of the virtual model, the material damping coefficient, the coupling stiffness coefficient between the drive unit and the flexible body and the equivalent stiffness parameters of the boundary constraints in the model are corrected online. This compensates for the creep effect caused by long-term operation of silicon-based materials and the modal frequency drift caused by load switching and deformation range changes. The global resonant frequency distribution dataset and the resonant frequency restriction library are updated synchronously and iteratively. According to the preset fixed control cycle, the complete process of global frequency sweep simulation, predictive control optimization model iteration, rolling optimization solution, physical drive loading and data transmission correction is repeatedly executed to continuously ensure the accuracy of the digital twin model and the effectiveness of resonant constraints, and realize the stable closed-loop control of the silicon-based flexible robot with harmonic-free drive and high-precision deformation positioning.

[0015] Compared with existing technologies, this predictive control method for digital twin-driven silicon-based flexible robots has the following advantages: This invention employs a combined static and dynamic twin model calibration method to ensure a high degree of consistency between the static and dynamic responses of the virtual model and the physical entity, laying a reliable foundation for resonance identification and control optimization. It utilizes a full-condition frequency sweep combined with a refined peak extraction algorithm to accurately obtain the global resonant frequency distribution, effectively eliminating simulation spurious peak interference and greatly improving the accuracy of frequency domain constraints. By combining a discrete state-space prediction model with a composite optimization objective containing spectral constraints, it simultaneously considers time-domain tracking performance, drive smoothness, and resonance suppression requirements, ensuring the feasibility and accuracy of the optimal solution through quadratic programming iterative optimization. Finally, it actively filters out resonant frequencies from the excitation source. The segment component blocks the resonance excitation conditions at the source, unlike traditional feedback post-correction, completely eliminating control lag and significantly reducing the probability of resonance and deformation overshoot; the resonance-free smooth drive can effectively reduce the vibration amplitude of flexible bodies, accelerate vibration decay, and simultaneously improve positioning convergence speed and steady-state accuracy; the twin model and resonance distribution are corrected online through measured data, adapting to parameter drift caused by material creep and changes in working conditions, and the robustness under all working conditions is better than that of traditional fixed parameter controllers. The whole forms a complete technology chain, and the control mechanism and implementation path have outstanding non-obviousness and creativity, which is suitable for the control needs of silicon-based flexible precision operation equipment.

[0016] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0018] Figure 1 A flowchart of a predictive control method for digital twin-driven silicon-based flexible robot; Figure 2 A flowchart of step S2 in a predictive control method for digital twin-driven silicon-based flexible robot; Figure 3 This is a flowchart of step S3 of a predictive control method for digital twin-driven silicon-based flexible robot. Detailed Implementation

[0019] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structures, features and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0020] This invention provides a predictive control method for digital twin-driven silicon-based flexible robots. It constructs a one-to-one mapping digital twin virtual model of the physical silicon-based flexible robot and performs static and dynamic parameter calibration to ensure a high degree of consistency between the virtual model and the physical entity, providing a reliable foundation for subsequent work. Next, it conducts full-domain frequency sweep simulation and resonant frequency distribution extraction to accurately obtain the full-domain resonant frequency distribution and eliminate simulation spurious peak interference. Then, it constructs a predictive control model with spectral constraints, combining the discrete state-space predictive model with a composite optimization objective containing spectral constraints to accommodate various performance requirements. Subsequently, it generates a resonant-free driving waveform through rolling optimization to block resonant excitation from the excitation source. Finally, it performs physical drive execution and closed-loop iterative correction of the twin model to adapt to parameter drift caused by material creep and changes in operating conditions, ensuring the accuracy of the digital twin model and the effectiveness of resonant constraints, forming a complete technology chain to meet the control requirements of silicon-based flexible precision work equipment.

[0021] This embodiment uses a silicon-based flexible electrostatically driven micro-gripper as the controlled object, such as... Figure 1As shown, 3D modeling technology is used to recreate the complete structure of the physical gripper, focusing on replicating the key morphological features of the flexible gripper arm. Then, a mechanical constitutive model of PDMS-doped silicon-based material is imported, and a multi-physics coupled dynamic model is built by combining the electrostatically driven electric field-deformation coupling principle. Finite element meshing technology is used to refine the mesh in deformation-sensitive areas such as the gripper arm, ensuring the model can accurately capture the mechanical response characteristics of the flexible body. Simultaneously, boundary constraint and load perturbation models are integrated to recreate the installation and fixing conditions and external load effects in actual operation. In the static deformation calibration stage, graded static drive loads within the rated drive range are applied to the physical silicon-based flexible robot. Laser displacement sensors are used to collect the actual static deformation of key monitoring nodes of the flexible body. This measured data is compared point-by-point with the simulated deformation of the digital twin virtual model under the same static load input and boundary constraint conditions. The static deformation deviation value of each measuring point is calculated. For deviations exceeding a preset threshold, the material elastic modulus, Poisson's ratio, and local deformation of the flexible body in the virtual model are corrected first. After correcting the static parameters of geometric dimensions, static simulation and actual measurement are carried out again until the static deformation deviation of all measurement points is controlled within the allowable range. This technical solution can effectively eliminate the static characteristic deviation of the virtual model and ensure the accuracy of static deformation simulation. In the dynamic excitation response calibration stage, a fixed frequency sinusoidal dynamic excitation and a frequency sweep excitation covering the working frequency band are applied to the physical prototype. The time domain response waveform and frequency domain characteristic data of each measurement point are collected simultaneously. The simulation results of the virtual model under the same conditions are compared. The overlap of time domain waveforms and the matching degree of amplitude-frequency and phase-frequency characteristic curves are checked. For dynamic response deviation, the material damping coefficient, the coupling stiffness coefficient of the drive and flexible body and the equivalent stiffness parameters of boundary constraints are corrected step by step. After each round of correction, the static and dynamic calibration verification is reproduced simultaneously. The iteration cycle continues until the consistency between the static and dynamic response data of the virtual model and the measured data of the physical entity meets the preset technical indicators. This dynamic calibration technology can accurately compensate for the dynamic characteristic deviation of the virtual model and finally realize the accurate reproduction of the static and dynamic response of the physical entity by the virtual model, laying a solid foundation for subsequent resonance identification and control optimization.

[0022] After completing the modeling and benchmarking, full-domain frequency sweep simulation and resonant frequency distribution extraction were performed. A frequency sweep range consistent with the working frequency band of the physical prototype was defined in the virtual model. Continuous frequency-variable amplitude excitation signals were generated at uniform frequency steps, sequentially covering all working conditions including no-load, variable load, small deformation, and large deformation, ensuring coverage of all scenarios in the actual operation of the gripper. The excitation signal was input to the virtual drive node at each frequency point, and dynamic deformation amplitude and vibration acceleration data at each measuring point were collected simultaneously to ensure data comprehensiveness. In the signal processing stage, a moving average smoothing and denoising technique was used to filter the collected amplitude-frequency response curves, effectively reducing the interference of simulation noise and mesh discretization errors, making the amplitude-frequency characteristic curve smoother and the peak characteristics more prominent. In the peak retrieval stage, the amplitude-frequency response curves at each measuring point were first processed by moving average smoothing and denoising to reduce the interference of numerical simulation noise and mesh discretization errors, and then peak retrieval was performed point by point along the frequency axis, comparing the current frequency point with other peaks. The response amplitudes of adjacent frequency points are set. When the amplitude of a point is higher than that of the two adjacent points and exceeds the set multiple of the reference response amplitude, it is marked as a candidate peak point. The frequency value and response amplitude corresponding to the peak are recorded simultaneously. For each candidate peak point, characteristic parameters such as the half-power bandwidth of the amplitude-frequency curve near the frequency and the amplitude attenuation rate on both sides of the peak are further extracted. Combined with the preset signal-to-noise ratio threshold and the sudden increase characteristics of the resonant response amplitude, spurious peaks caused by simulation interference are screened out. Finally, the effective resonant peak value and corresponding frequency information of each measurement point are determined. Finally, the effective resonant frequency data under multiple operating conditions are integrated and classified, and adjacent frequency intervals are merged to form a full-domain resonant frequency distribution dataset covering all measurement points and all operating conditions. The resonant frequency forbidden set and the corresponding narrowband resonant interval are clearly defined. This technical solution can comprehensively and accurately capture the resonant characteristics of the clamp under different operating conditions, providing a reliable frequency domain constraint basis for the spectral constraints of subsequent predictive control, and effectively avoiding control failure problems caused by the omission of resonant frequencies.

[0023] Subsequently, a predictive control model with spectral constraints is constructed, such as... Figure 2 As shown, based on the dynamic parameters identified by the virtual model, the driving input, the intermediate deformation state of the flexible body, and the end deformation output positioning are selected as core variables to build a discrete state-space prediction model. The discretization period of the model is kept consistent with the subsequent control period to ensure that the model derivation is synchronized with the actual control rhythm. The model expression is as follows: ,in for The system state vector at any given time includes core state variables such as deformation and vibration velocity at key measurement points of the flexible body. The system state matrix is ​​calculated from the identified material mechanical parameters and structural parameters, and can accurately reflect the evolution law of the system state. The input matrix represents the impact of the driving input on the system state, ensuring the accuracy of the correlation between the driving signal and the system response; for The constant-time input is the electrostatic driving voltage, and the output is the deformation at the end of the flexible body. The output matrix is ​​used to map the system state vector to an observable output signal, ensuring consistency between the model output and actual measured parameters. After defining the prediction and control time domains, this model can accurately predict the deformation output trajectory and driving force trends within the preset time domain, providing a reliable predictive basis for subsequent optimization solutions. Based on this, a composite optimization objective function is constructed, expressed as: ,in for The deformation trajectory of the flexible target at any given moment. For model predictions Output amount of deformation at any time This is a tracking error weighting matrix used to adjust the weights for deformation trajectory tracking accuracy. for Constantly driving the input increment, This is a smoothing weighting matrix for the control input, used to suppress sudden changes in the driving signal; These are the spectral constraint weighting coefficients, used to adjust the priority of resonance suppression; To identify the global resonant frequency-forbidden set, For the drive signal at frequency The spectral energy at the location; simultaneously, setting hard amplitude constraints for the driving spectral components within the resonant frequency band. ,in For the drive signal at frequency Spectral amplitude at that location, To predetermine the upper limit of the spectral amplitude in the resonant frequency band, this function integrates a time-domain tracking error term, a control quantity smoothing penalty term, and a resonant frequency band drive waveform spectral constraint term. The tracking error weighting matrix prioritizes trajectory tracking accuracy, effectively improving the accuracy of the gripper's deformation positioning. The control quantity smoothing weighting matrix suppresses sudden changes in the drive signal, preventing additional vibration interference caused by these changes. The spectral constraint weighting coefficients balance resonance suppression and trajectory tracking performance, ensuring precise tracking of the target trajectory while strictly suppressing resonant excitation. Furthermore, hard constraints on spectral amplitude are set for the resonant forbidden frequency set and corresponding frequency bands, limiting the spectral amplitude within the resonant frequency band to not exceeding the predetermined upper limit, thus blocking resonant excitation at its source. The drive input amplitude constraint and the maximum deformation constraint of the flexible body are transformed into linear constraints, ensuring that both the drive signal and deformation action remain within safe limits. The predictive control model constructed by this technical solution achieves the dual objectives of accurate time-domain tracking and frequency-domain resonance suppression, providing core technical support for the subsequent generation of resonant-free drive waveforms.

[0024] like Figure 3 As shown, the system state of the silicon-based flexible robot, measured by sensors at the current moment, including end-effector deformation, vibration acceleration, and real-time output of the drive unit, is used as the initial input conditions for rolling optimization. These are precisely substituted into the constructed discrete state-space prediction model and the composite optimization objective function. Rolling optimization is then initiated within a preset prediction time domain. During the solution process, the upper limit of the drive input amplitude, the maximum deformation limit of the flexible body, and the hard constraint boundary conditions of the resonant frequency band spectrum amplitude are simultaneously incorporated. A quadratic programming algorithm is used for iterative optimization to minimize the combined objective of time-domain deformation tracking error, sudden changes in drive signal increment, and energy penalty of the resonant frequency band spectrum. The optimal drive input sequence within the future control time domain is obtained. The core technical advantage of this method is its ability to efficiently search for the optimal solution while satisfying all constraints. The specific process is as follows: In each iteration, the gradient of the objective function is calculated first to accurately locate the descent direction of the function; combined with linear constraints such as drive amplitude, deformation range, and spectrum amplitude, feasible search directions that satisfy all boundary requirements are selected, avoiding errors during the iteration process. If the current constraint is violated, the driving input sequence parameters are adjusted according to the preset step size, and the driving input candidate sequence in the future control time domain is updated. The objective function value change and constraint satisfaction of the candidate sequence are checked simultaneously to ensure the correctness of the iteration direction. If the objective function value does not reach the convergence threshold or there are constraint-unsatisfied terms in the candidate sequence, the search direction and step size are adaptively corrected based on the previous iteration result. The gradient calculation, direction screening, parameter adjustment and double verification process are repeated until the objective function converges and all constraint conditions are met. The iteration is terminated and the optimal driving input sequence is output. The frequency domain characteristics of the sequence are checked to confirm that the spectral amplitude in the resonant frequency band meets the constraint requirements. After effectively avoiding the risk of resonant excitation, the digital driving sequence is transformed into a continuous and smooth analog driving waveform through digital-to-analog conversion and linear interpolation smoothing. This technical solution can ensure that the output driving waveform has both optimal trajectory tracking performance and stability, and is completely free of resonant interference, which can effectively suppress the vibration and overshoot problems in the operation of the gripper.

[0025] The optimized, resonant-free smooth drive waveform is loaded into the electrostatic drive unit of the physical micro-gripper via the drive control module, driving the gripping arm to complete the target gripping deformation action. This drive method can effectively reduce the vibration amplitude during the gripper's operation, reduce deformation overshoot, improve deformation convergence speed, and ensure precise and stable gripping action. Simultaneously, laser displacement and acceleration sensors collect end-effector deformation and vibration acceleration data in real time, and the measured data is packaged and transmitted back to the digital twin system according to a fixed control cycle, realizing real-time data interaction between the physical state and the virtual system. Based on the measured data and simulation data under the same excitation and constraints of the virtual model, deviation analysis is performed. When the deviation exceeds the standard, the material damping coefficient, the coupling stiffness coefficient between the drive and the flexible body, and the equivalent stiffness parameters of the boundary constraints of the virtual model are corrected online. This correction technology can effectively compensate for the creep effect generated by the long-term operation of silicon-based materials and the load. Modal frequency drift caused by switching and deformation range changes is addressed to ensure that the virtual model always maintains a high degree of matching with the physical entity. The global resonant frequency distribution dataset is updated synchronously and iteratively, and newly added resonant frequencies are merged while those that have not been reproduced are removed. This continuously ensures the real-time effectiveness of the resonant frequency domain constraint library and avoids control failures caused by resonant frequency drift. The complete process of global frequency sweep simulation, predictive control model iteration, rolling optimization solution, physical drive loading, and data feedback correction is repeated cyclically according to a fixed control cycle. Regular full-condition frequency sweep re-checks are conducted to further verify the model accuracy and resonant constraint effect. This closed-loop correction technology can realize the dynamic adaptive adjustment of the control system, effectively resist the influence of external interference and internal parameter drift, and ensure that the gripper maintains excellent control performance during long-term operation and complex working condition switching, continuously achieving resonant-free, high-precision, and fast-converging flexible gripping operations.

[0026] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A predictive control method for digital twin actuation of a silicon-based flexible robot, characterized in that, The method includes the following specific steps: S1: Construct a digital twin virtual model integrating geometry, materials mechanics, drive-structure coupled dynamics, boundary and disturbance, synchronously map the structure, materials, drive and boundary parameters of the physical silicon-based flexible robot to the virtual model and complete the static and dynamic response benchmarking to ensure that the virtual model is consistent with the dynamic characteristics of the physical entity; S2: Conduct full-condition, full-point frequency sweep excitation simulation in the benchmarked digital twin model. By collecting the dynamic response of multiple measurement points and performing peak identification and pseudo-peak removal, the full-domain resonant frequency distribution is obtained by fusing multi-condition data, and the resonant frequency forbidden set and resonant frequency band interval are determined. S3: Based on the dynamic parameters identified by the twin model, a discrete state-space prediction model is established. In the rolling optimization framework of model predictive control, a composite objective function including time-domain tracking error, control quantity smoothing penalty, and resonant frequency band spectrum constraint is constructed, and a hard constraint on the resonant frequency band spectrum amplitude is set. S4: Using the current actual state of the system as the initial condition, solve the composite optimization objective in the prediction time domain under the premise of satisfying the spectrum, driving amplitude and deformation output constraints, and output the smooth driving waveform without resonance frequency band excitation components after filtering out the resonant frequency band. S5: Apply the non-resonant smooth drive waveform to the physical silicon-based flexible robot, collect the actual deformation and vibration data and send them back to the digital twin to correct the model parameters and resonance distribution online, and execute the above steps in a fixed control cycle to achieve closed-loop non-resonant drive and high-precision positioning control.

2. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 1, characterized in that, In step S1, the specific steps for static and dynamic response benchmarking are as follows: A graded static driving load within the rated driving range is applied to the physical silicon-based flexible robot. A laser displacement sensor is used to collect the actual static deformation of key monitoring nodes of the flexible body. This measured data is then compared point-by-point with the simulated deformation of the digital twin virtual model under the same static load input and boundary constraints. The static deformation deviation value of each measuring point is calculated. If the deviation exceeds a preset threshold, the material elastic modulus, Poisson's ratio, and local geometric dimensions of the flexible body in the virtual model are corrected first. After correction, the static simulation and measured comparison are repeated until the static deformation deviation of all measuring points is controlled within the allowable range. Based on this, a graded static driving load within the rated driving range is applied to the physical prototype. A fixed-frequency sinusoidal dynamic excitation and a low-amplitude sweep excitation covering the working frequency band are applied. Vibration acceleration, dynamic deformation amplitude, and phase data at each measuring point are collected synchronously through a high-frequency response accelerometer and a dynamic displacement sensor. The dynamic response simulation results of the virtual model under the same excitation conditions are compared. The overlap of the time-domain response waveform and the matching degree of the frequency-domain characteristic curve are verified. For dynamic response deviations, the material damping coefficient, the coupling stiffness coefficient between the driving unit and the flexible body, and the equivalent stiffness dynamic parameters of the boundary constraints in the model are corrected step by step. After each round of parameter correction, the static and dynamic benchmark verification are reproduced synchronously. The iteration cycle continues until the consistency between the static and dynamic response data of the virtual model and the measured data of the physical entity meets the preset technical indicators.

3. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 1, characterized in that, In step S2, within the digital twin virtual model after completing precise static and dynamic alignment, a sweep frequency range consistent with the actual operating frequency band of the silicon-based flexible robot is defined. Continuous frequency-modulated excitation signals are generated according to a set uniform frequency step size. Equal amplitude excitation is applied sequentially to all working conditions, including no load, standard load, variable load, small deformation, and rated large deformation. The signal is input to the virtual drive node at each frequency point. Dynamic deformation amplitude, vibration acceleration, and time-domain response data of the monitoring positions at the end, middle, and root of the flexible body are collected simultaneously. Peak retrieval and feature extraction are performed on the amplitude-frequency response curves of each measuring point. The frequencies where the response amplitude increases abruptly are marked as candidate resonant frequencies. Combined with the signal-to-noise ratio threshold, the noise of numerical simulation and the pseudo-peak interference caused by grid discretization error are screened out. Then, the effective resonant frequency data under multiple working conditions are integrated, classified, and merged with adjacent frequency intervals. Finally, a global resonant frequency distribution dataset covering all structural measuring points and all working conditions is formed, and the set of resonant forbidden frequencies that cannot be used for excitation and the corresponding narrowband resonant intervals are identified.

4. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 3, characterized in that, In S2, the specific technical solution for peak retrieval and feature extraction of the amplitude-frequency response curves at each measurement point is as follows: First, the amplitude-frequency response curves at each measurement point are smoothed and denoised using a moving average method to reduce the interference of curve fluctuations caused by numerical simulation noise and grid discretization errors. Then, peak retrieval is carried out point by point along the frequency axis. Taking the current frequency point as the center, the response amplitudes of the adjacent set number of frequency points are compared. When the amplitude of the current point is higher than the adjacent points on both sides and exceeds the set multiple of the reference response amplitude, it is marked as a candidate peak point. The frequency value and response amplitude corresponding to the peak are recorded simultaneously. For each candidate peak point, feature parameters such as the half-power bandwidth of the amplitude-frequency curve near the frequency and the amplitude attenuation rate on both sides of the peak are further extracted. Combined with the preset signal-to-noise ratio threshold and the sudden increase characteristics of the resonant response amplitude, false peaks caused by simulation interference are screened out, and finally the effective resonant peak and corresponding frequency information of each measurement point are determined.

5. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 1, characterized in that, In step S3, based on the dynamic parameters of the silicon-based flexible robot system obtained through static and dynamic benchmarking and frequency sweeping identification using the digital twin model, the driving input, the intermediate deformation state of the flexible body, and the end-effector deformation output positioning are selected as core variables to build a discrete state-space prediction model. Combining this with the dynamic response requirements of the actual operation of the silicon-based flexible robot, a matching prediction time domain and control time domain are defined. Based on the aforementioned state-space model, the future... Intra-step flexible body deformation output trajectory and The rolling deduction of the trend of the driving variable changes within the step; on this basis, in the rolling optimization framework of model predictive control, a composite optimization objective function is constructed that integrates the time-domain tracking error term, the control increment smoothing penalty term, and the resonant frequency band driving waveform spectrum constraint term. At the same time, a hard constraint on the amplitude of the driving spectrum component in the resonant frequency band is set, and the prior frequency domain information of the global resonant frequency distribution is transformed into a quantitative constraint condition that can be directly used in the optimization calculation. By combining soft penalty and hard constraint, the overall optimization objective actively suppresses the excitation component falling into the resonant frequency band while taking into account the deformation trajectory tracking accuracy and the stability of the driving signal, so as to ensure that the driving waveform is free from resonance interference.

6. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 5, characterized in that, In S3, the spatial prediction model is: ,in for The system state vector at any time includes the state variables of deformation and vibration velocity at key measuring points of the flexible body; The system state matrix is ​​obtained from the mechanical parameters of silicon-based materials and the structural parameters of flexible bodies. The input matrix represents the influence coefficients of the driving signal on the system state; for Constant-time driving input volume for The positioning amount is output based on the deformation of the flexible body's end. The output matrix is ​​used to map the system state vector into observable deformation output quantities.

7. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 5, characterized in that, In step S3, a composite optimization objective function is constructed that integrates the time-domain tracking error term, the control increment smoothing penalty term, and the resonant frequency band drive waveform spectrum constraint term. The function formula is as follows: ,in, for The deformation trajectory of the flexible target at any given moment. For model predictions Output amount of deformation at any time This is a tracking error weighting matrix used to adjust the weights for deformation trajectory tracking accuracy. for Constantly driving the input increment, This is a smoothing weighting matrix for the control input, used to suppress sudden changes in the driving signal; These are the spectral constraint weighting coefficients, used to adjust the priority of resonance suppression; To identify the global resonant frequency-forbidden set, For the drive signal at frequency The spectral energy at the location; simultaneously, setting hard amplitude constraints for the driving spectral components within the resonant frequency band. ,in For the drive signal at frequency Spectral amplitude at that location, This is the upper limit of the preset resonant frequency band spectrum amplitude.

8. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 1, characterized in that, In step S4, the system state of the silicon-based flexible robot, measured by sensors at the current moment, including end deformation, vibration acceleration, and real-time output of the drive unit, is used as the initial input conditions for rolling optimization. These are substituted into the constructed discrete state-space prediction model and the composite optimization objective function. Rolling optimization is initiated within the preset prediction time domain. During the solution process, the upper limit of the drive input amplitude, the maximum deformation limit of the flexible body, and the hard constraint boundary conditions of the resonant frequency band spectrum amplitude are simultaneously incorporated. A quadratic programming algorithm is used for iterative optimization to minimize the comprehensive objective of time-domain deformation tracking error, sudden changes in drive signal increment, and energy penalty of the resonant frequency band spectrum. The optimal drive input sequence in the future control time domain is obtained by solving this problem. Frequency domain characteristic analysis and verification are performed on this sequence. After confirming that the amplitude of all excitation components falling into the resonant forbidden frequency set and the corresponding frequency band is lower than the preset allowable threshold, a smooth drive waveform without resonance that can be directly loaded onto the physical drive unit is output, ensuring that the drive signal does not excite structural resonance after acting on the silicon-based flexible body.

9. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 8, characterized in that, In S4, the specific steps of iterative optimization using the quadratic programming algorithm are as follows: the composite optimization objective function is transformed into a standard mathematical form adapted to the quadratic programming algorithm; the initial driving input sequence obtained after substituting the current system state is used as the feasible solution for the initial iteration; the upper and lower limits of the driving input amplitude and the maximum deformation limit of the flexible body are simultaneously transformed into linear inequality constraints; the hard constraint of the resonant frequency band spectrum amplitude is transformed into a linear constraint condition based on the Fourier transform of the driving signal, and the quadratic programming solution framework is embedded; iterative optimization is carried out using the feasible direction method; the gradient direction of the objective function is calculated in each iteration; feasible search directions that meet all boundary requirements are selected in combination with the constraint conditions; the driving input sequence parameters are adjusted according to the preset step size; the driving input candidate sequence in the future control time domain is updated; and the change of the objective function value corresponding to the candidate sequence is simultaneously verified. If the current objective function value does not reach the preset convergence threshold, or if there are still unmet constraints in the candidate sequence, the search direction and step size are corrected based on the results of the previous iteration, and the gradient calculation, direction filtering, parameter adjustment, and constraint verification process are repeated. After each iteration, the dual verification of the objective function value and the constraint satisfaction is reproduced simultaneously. When the iteration continues until the objective function value converges to the preset minimum threshold and the candidate driving input sequence fully satisfies all boundary constraints and spectral constraints, the iteration process terminates. This candidate sequence is the optimal driving input sequence in the future control time domain.

10. The predictive control method for digital twin actuation of a silicon-based flexible robot according to claim 1, characterized in that, In step S5, the solved harmonic-free smooth drive waveform is loaded into the physical drive unit of the silicon-based flexible robot through the drive control module, driving the flexible body to complete the preset deformation and positioning action. At the same time, the actual deformation and vibration acceleration time-domain response data of the flexible body end actuator and deformation-sensitive area are collected in real time through laser displacement sensor and high-frequency acceleration sensor, and the data is synchronously transmitted back to the digital twin virtual model. Based on the deviation analysis between the measured data and the simulation data under the same excitation and boundary conditions of the virtual model, the material damping coefficient, the coupling stiffness coefficient between the drive unit and the flexible body and the equivalent stiffness parameters of the boundary constraints in the model are corrected online. This compensates for the creep effect caused by long-term operation of silicon-based materials and the modal frequency drift caused by load switching and deformation range changes. The global resonant frequency distribution dataset and the resonant frequency restriction library are updated synchronously and iteratively. According to the preset fixed control cycle, the complete process of global frequency sweep simulation, predictive control optimization model iteration, rolling optimization solution, physical drive loading and data transmission correction is repeatedly executed to continuously ensure the accuracy of the digital twin model and the effectiveness of resonant constraints, and realize the stable closed-loop control of the silicon-based flexible robot with harmonic-free drive and high-precision deformation positioning.

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