A robotic end effector force control method and system for conformal vibratory polishing of optical elements

Abstract

The present application belongs to the technical field of robot control, and discloses a robot end effector force control method and system for conformal vibration polishing of optical elements. The present application solves the problems of periodic disturbance, friction nonlinearity and multi-axis mutual interference caused by conformal tangential vibration in the polishing process of complex curved surfaces of optical elements, and guarantees the normal constant force accuracy, polishing consistency and machining surface quality. The algorithm adopts a multi-module collaborative architecture, combines observers, adaptive filtering, mutual interference modeling and feedforward friction compensation, and forms a set of composite control scheme with strong real-time performance, high robustness and good adaptability. High-precision force control of robot conformal vibration polishing under complex disturbance is realized through the introduction of a fourth-order extended state observer (4th-ESO), frequency selection filtering and inverse notch compensation, friction feedforward and mutual interference decoupling, etc.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and in particular relates to a robot end effector force control method and system for conformal vibration polishing of optical elements. Background Technology

[0002] High-precision optical components typically require polishing during manufacturing to achieve nanometer-level surface accuracy and sub-nanometer-level surface roughness. Conformal vibration polishing, a processing method that combines material removal uniformity with adaptation to complex curvature surfaces, presents challenges to the stability and accuracy of force control systems when the robotic end effector is subjected to excitation disturbances across multiple frequency bands (such as low-frequency macro-vibrations and high-frequency micro-vibrations). Traditional PID or fixed-bandwidth control methods struggle to simultaneously achieve rapid dynamic response and suppression of specific frequency disturbances. Furthermore, in multi-axis systems, significant mutual interference exists between different directions, and the frictional characteristics under vibration excitation exhibit marked nonlinearity and four-quadrant asymmetry, further impacting the polishing stability and surface uniformity of the system. Therefore, a control algorithm integrating multi-level disturbance compensation and adaptive decoupling is urgently needed to improve the force control accuracy during the conformal vibration polishing process of optical components.

[0003] Based on the above analysis, the problems and shortcomings of the existing technology are as follows:

[0004] Traditional PID or fixed-bandwidth control methods struggle to simultaneously achieve rapid dynamic response and suppression of specific frequency disturbances. Furthermore, in multi-axis systems, significant mutual interference exists between different directions. In addition, the friction characteristics under vibration excitation exhibit obvious nonlinearity and four-quadrant asymmetry, further affecting the polishing stability and surface consistency of the system. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention provides a method and system for force control of a robot end effector for conformal vibration polishing of optical components.

[0006] This invention is implemented as follows: A robot end effector force control method for conformal vibration polishing of optical elements includes:

[0007] Step 1: Establish the mutual interference transfer function model of the three-dimensional force sensor, obtain the coupling relationship between different directions, and realize the mutual interference modeling of multi-axis sensing signals;

[0008] Step 2: Based on the mutual interference model, the original measured force signal is corrected using linear proportional compensation or time-varying FIR decoupling filter to obtain a more accurate normal contact force feedback signal.

[0009] Step 3: Based on the decoupled normal force signal, construct a vibration frequency gating compensation module, use a frequency selective filter to extract the periodic disturbance signal component, and estimate its amplitude and phase;

[0010] Step 4: Construct an inverse notch filter compensator based on the estimation results to perform real-time equivalent inverse weakening of periodic disturbances at a specified frequency, thereby improving the robustness and frequency-domain selective suppression capability of the force control system against vibration disturbances.

[0011] Step 5: Considering the modulation effect of periodic vibration on friction, based on the normal force disturbance model, establish a dynamic feedforward model with variable friction coefficient and calculate the friction compensation control quantity.

[0012] Step 6: The desired normal polishing force signal, the inverse notch filter disturbance suppression signal, and the friction compensation feedforward signal are superimposed and used as the target force input signal, which is then transmitted to the main controller module to realize composite target tracking control;

[0013] Step 7: The main controller module adopts a PID-fourth-order extended state observer structure, which integrates disturbance estimation, adaptive notch control and neural network parameter tuning methods to dynamically adjust the internal gain and filter parameters of the controller, thereby improving the system response speed, force control accuracy and generalized robustness.

[0014] Another object of the present invention is to provide a force control system for a robot end effector for conformal vibration polishing of optical elements:

[0015] Force sensor mutual interference decoupling module, vibration frequency gating compensation module, friction compensation feedforward module, main controller module.

[0016] Furthermore, the force sensor mutual interference decoupling module includes the establishment of a three-dimensional force mutual interference transfer function and the compensation calculation of the normal contact force;

[0017] The three-dimensional force perturbation transfer function is established as follows:

[0018] Let the actual force of the three-dimensional force sensor be... These represent the actual forces acting in the x, y, and z directions, respectively; the measured output is F. meas (s)=[F x (s),F y (s),F z (s)] T F x (s),F y (s),F z (s) represent the measured true output forces in the x, y, and z directions, respectively. Considering the inter-axis interference, the following transfer model F is established. meas (s)=G xyz (s)·Ftrue (s), where G xyz (s) is a 3×3 mutual interference transfer function matrix, containing self-response and mutual interference coupling terms, with the specific transfer function form as follows:

[0019]

[0020] Among them G ij (s) represents the dynamic influence of channel j on channel i, such as G xy (s) represents the dynamic influence of channel x on channel y;

[0021] The calculation of compensation for normal contact force focuses on the output F of normal force (i.e., force in the z-direction) in the time domain. z (t), its ideal estimate f oc (t) can be expressed as follows through linear decoupling compensation for tangential mutual disturbance:

[0022] f oc (t)=F z (t)-α x ·F x (t)-α y ·F y (t)

[0023] Where α x ,α y F is the proportional coupling coefficient estimated based on the mutual interference model. x (t) and F y (t) represents the sensor measurements in the x and y directions in the time domain, respectively;

[0024] Using a time-varying FIR structure to improve the ideal estimate f oc (t) Dynamic accuracy, its discrete expression is: Where h xz and h yz These are the unit impulse responses (FIR coefficients) of the mutual disturbance transfer functions in the X→Z axis and Y→Z axis directions, respectively, and the compensated normal force f. oc As a compensated force feedback signal, it enables more accurate force control performance.

[0025] Furthermore, the vibration frequency gating compensation module consists of a frequency selective filter, an amplitude and phase estimator, and an inverse notch filter compensator;

[0026] Frequency-selective filters are used to filter the system feedback signal f oc Extract the specified frequency f from (t) n The nearby narrowband component, employing a dual second-order notch filter cascade structure, has the following discrete transfer function:

[0027]

[0028] Where f n The expected interference frequency; T is the sampling period of the control system; r s Control the filter bandwidth; the input to the frequency-selective filter is the compensated force feedback signal f. oc The output is a vibration signal f n (t), i.e., the vibration response at a specific frequency; f is manually adjusted by determining the process parameters. n and r s It can dynamically extract the energy components within the target interference frequency band;

[0029] The amplitude-phase estimator is based on the Fourier analysis principle and extracts the vibration signal f. n (t) is mapped to the standard periodic function form. A(t) is f n (t) is the amplitude estimate; ψ(t) is the phase estimate; C(t) = A(t)e jψ(t) For complex magnitude vectors, real-time estimation is performed using a synchronous phase-locked loop or sliding mode observer;

[0030] The inverse notch filter compensator is used to suppress the extracted vibration signal f. n (t), whose discrete transfer function structure is as follows:

[0031]

[0032] Where r c To control the filter bandwidth of the inverse notch filter compensator, at f ne With input (t), the output d of the inverse notch compensator c =H comp (z)f ne (t), the inverse notch filter compensator and the frequency selective filter are inverse operations of each other. The output of the inverse notch filter compensator can directionally weaken the amplitude response of the periodic disturbance source without interfering with the frequency domain performance of the main controller, and realize the equivalent inverse model of a specific frequency.

[0033] Furthermore, the friction compensation feedforward module takes into account F under vibration excitation. x The effect of (t) on the normal friction force: Based on the relationship between friction force and normal force, the Coulomb term and the static friction term in the friction model are affected by the normal perturbation. Therefore, the friction force becomes: F f (t)=μ(F x (t))·sgn(v(t))+F v ·v(t), where μ(F x (t) represents the coefficient of friction as a function of the normal force; sgn(v(t)) is the sign function of the velocity, which determines the direction of friction; v(t) is the velocity of the end relative to the contact surface; F v It is the coefficient of viscous friction;

[0034] Under high-frequency vibration, to describe μ(F) x The trend of change of (t) can be further approximated linearly as: μ(F) n (t))≈μ0+κ·F x (t), where μ0 is the static average friction coefficient; κ is the sensitivity coefficient of the effect of normal pressure on the friction coefficient.

[0035] Furthermore, the output of the friction compensation feedforward module can be expressed as:

[0036] u f (t)≈(μ0+κ·F x (t))·sgn(v(t))+F v ·v(t)

[0037] Synthetic target force signal d r =d f +d c +u f , where d f The set polishing desired force signal.

[0038] Furthermore, the main controller module consists of three parts: a proportional-integral-derivative-fourth-order extended state observer (PID-4thESO), an adjustable notch filter, and a radial basis function (RBF) neural network parameter adaptor.

[0039] The proportional-integral-derivative-fourth-order extended state observer uses a fourth-order extended state observer to estimate the system state and disturbances, and generates the basic control quantity u0 based on the incremental proportional-integral-derivative (PID) controller.

[0040] The discrete expression for the fourth-order extended state observer is:

[0041] Where f = f oc -f n To filter out the end-effector normal force signal after the selected frequency in the vibration frequency gating compensation module, the end-effector normal force feedback compensation value is f. oc (t); z1~z4 are system state estimates, z5 is a higher-order disturbance estimate; β i b is the observer gain parameter, and b is the system nominal gain; the state variable update is implemented by discretization using the Euler method;

[0042] The incremental PID controller combining state estimation with a fourth-order extended state observer is expressed as follows:

[0043] Where dr(t) is the synthesized target force signal, Δe(t) is the force error at time t; Δe(t) = e(t) - e(t-1), Δ 2 e(t)=e(t)-2e(t-1)+e(t-2);K p ,K i ,K d For PID gain, T s The sampling period is u0(t); u0(t) is the output control quantity of this module.

[0044] The discrete transfer function expression of the adjustable notch filter is as follows:

[0045]

[0046] Among them, f n Let u be the interference frequency, r be the bandwidth coefficient, and r be the notch filter strength. The filter input is u0(t), and the filter output is u(t).

[0047] Radial basis function (RBF) neural network parameter adaptors use the system dynamic state s(t) (including error e(t), error derivative) as the basis for their operation. System output f o Taking (t) and its derivative, etc. as input, the output is an estimated expression for the following parameters:

[0048] in, Fourth-order extended state observer bandwidth parameter adaptive update value; The nominal gain of the controlled object is updated adaptively. Notch filter center frequency adaptively updates value; Notch filter bandwidth adjustment factor is adaptively updated; φ i (s): The i-th Gaussian function, defined as... The weights of the i-th neuron are adjusted online based on the error.

[0049] The RBF neural network parameter adaptor is designed based on Lyapunov stability analysis. To ensure the closed-loop stability of the system and the convergence of the estimation error, it needs to satisfy the following condition: Make

[0050] The adaptive update value is transmitted in real time to the PID-4thESO and the adjustable notch filter module, respectively, to update β. i Observer gain parameters, b is the system nominal gain; f is the gain parameter. n Interference frequency and bandwidth coefficient; thus forming a parameter self-sensing and self-adjusting control system, improving the overall response speed and robust control capability.

[0051] Another object of the present invention is to provide a computer device including a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the robot end effector force control method for conformal vibration polishing of optical elements.

[0052] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the robot end effector force control method for conformal vibration polishing of optical elements.

[0053] Another object of the present invention is to provide an information data processing terminal for implementing the force control system of the robot end effector for conformal vibration polishing of optical elements.

[0054] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0055] First, achieving high-precision force control under complex disturbances in conformal vibration polishing of robots: By introducing a multi-module coordination mechanism such as a fourth-order extended state observer (4th-ESO), frequency-selective filtering and inverse notch compensation, friction feedforward and mutual disturbance decoupling, this invention can still maintain high-precision control of the normal constant force of optical elements under the combined effects of low-frequency macro disturbances, high-frequency micro vibrations and multi-axis mutual disturbances, significantly improving the processing consistency and stability in the conformal vibration polishing process.

[0056] It has the ability to target and suppress specific frequency disturbances under specific processes of conformal vibration: This invention proposes a compensation mechanism based on the complementary structure of frequency gating and inverse notch filter, which can effectively weaken the resonance disturbances caused by periodic excitation during polishing without interfering with the frequency response of the main control loop, thereby improving the frequency domain robustness of the system.

[0057] Dynamic modeling of multiaxial force interference and friction nonlinearity: By modeling the three-dimensional mutual interference force transfer function and decoupling compensation with FIR filtering, as well as modeling and compensating for the pressure-related nonlinear terms in the friction model, this invention effectively solves the problem of control accuracy degradation caused by force sensor measurement distortion and friction interference, and is especially suitable for complex contact force control in high-speed micro-vibration scenarios.

[0058] It features adaptive parameter adjustment capability and real-time performance: By introducing an RBF neural network parameter adaptor, it enables online learning and tuning of key parameters such as controller observer bandwidth, notch frequency and bandwidth, and system gain, thereby improving the adaptive capability and long-term operational stability of the control system.

[0059] The modular architecture of the control system facilitates engineering integration and promotion: The force control scheme of this invention has a clear structure, well-defined functional module boundaries, good scalability and integration, and is suitable for various flexible polishing tasks, especially for promotion and application on robot platforms.

[0060] The technical solution of this invention fills a technological gap in the industry both domestically and internationally: Currently, in the field of conformal vibration polishing at the end effector of robots, there is no mature solution that can achieve integrated modeling and real-time compensation control of complex factors such as periodic disturbances, frictional nonlinearity, and multi-axis coupling errors. This invention, for the first time, integrates multi-source disturbance observation, adaptive notch compensation, frictional nonlinearity modeling, and multi-axis mutual disturbance decoupling into one system, establishing a high-precision force control system for conformal vibration polishing applications, filling the international gap in systematic solutions in this technical direction.

[0061] The technical solution of this invention solves a technical problem that people have long desired to solve but have been unable to achieve successfully, specifically including the following points:

[0062] (1) The challenge of constant force control under multi-frequency composite disturbances: During conformal vibration polishing, the end effector is simultaneously affected by low-frequency macroscopic trajectory disturbances (such as arm rotation and swing), mid-frequency resonant excitations (such as harmonic disturbances of planetary mechanisms), and high-frequency micro-vibration disturbances (such as piezoelectric or voice coil vibration modules). Traditional PID controllers or linear feedforward structures cannot identify and separate these composite frequency disturbances, resulting in large fluctuations and poor stability of the normal polishing force. This invention achieves frequency division identification and directional suppression of the above-mentioned multi-frequency disturbances by using a fourth-order extended state observer (4th-ESO) combined with a notch filter and an inverse notch compensation structure, which significantly improves the accuracy of constant force control in complex dynamic environments.

[0063] (2) Problem of control instability caused by interaxial interference of force sensors: Multi-axis force sensors exhibit axial coupling in actual measurements, especially when there is non-coplanar micro-vibration input. The normally independent normal and tangential channels interfere with each other, seriously affecting the accuracy of feedback, thus causing misjudgment or oscillation in the control system. This invention proposes an FIR filtering decoupling method based on the three-axis mutual interference force transfer function. By identifying the dynamic transfer relationship between the interference channel and the main control channel online, the coupling error in the measurement is effectively removed, improving the stability and reliability of the force control system.

[0064] (3) Difficulties in Modeling and Compensating Nonlinear Friction: During the polishing process, due to the continuous normal contact between the end effector and the workpiece, the friction force is not only related to the motion speed but also exhibits a nonlinear coupling relationship with the change of normal load. High-frequency micro-vibration input will cause frequent abrupt changes in friction force, and the traditional static-dynamic friction model is difficult to accurately describe its changing trend. This invention proposes a friction compensation method that considers the dynamic influence of clamping force on the stick-slip threshold and combines it with an RBF neural network to realize online correction of model parameters, thereby achieving effective prediction and compensation of dynamic friction force.

[0065] (4) The problem of system control parameters relying on human experience and being difficult to tune in real time: High-performance force control systems often contain multiple parameters (such as observer bandwidth, notch filter center frequency, etc.), which need to be dynamically adjusted due to changes in the polishing environment and materials during actual operation. Traditional methods of parameter tuning based on experience are time-consuming and difficult to adapt to complex and ever-changing application scenarios. This invention introduces an RBF neural network parameter regulator based on error mapping, which can dynamically adjust the core control parameters according to the real-time error signal, and has online learning and adaptive capabilities, significantly improving the intelligence and robustness of the system.

[0066] (5) The problem of difficult modular integration and promotion of control systems: Existing force control schemes often lack a unified architecture, and the coupling between control modules is serious, which is not conducive to reuse and migration between different mechanical structures or platforms. The control system of the present invention adopts a four-level module series structure of "disturbance observation - special frequency compensation - nonlinear correction - adaptive tuning", with clear functional boundaries and unified interfaces, which is easy to embed into the existing robot control architecture, greatly reducing the threshold for engineering applications, and has good versatility and scalability. Attached Figure Description

[0067] Figure 1 This is a flowchart of a robot end effector force control method for conformal vibration polishing of optical elements provided in an embodiment of the present invention.

[0068] Figure 2 This is a block diagram of a force control system for a robot end effector used for conformal vibration polishing of optical elements, provided in an embodiment of the present invention.

[0069] Figure 3 This is a schematic diagram illustrating the force control effect of polishing in a vibration environment provided in an embodiment of the present invention.

[0070] Figure 4 This is a schematic diagram of a robot end effector that can be deployed with the optical elements provided in this invention for conformal vibration polishing, according to an embodiment of the present invention.

[0071] Figure 5 This is a schematic diagram illustrating the effect of polishing optical elements in a vibration environment according to an embodiment of the present invention;

[0072] Figure 6 This is the robot platform provided in the embodiments of the present invention;

[0073] Figure 7 These are measured figures provided in the embodiments of the present invention. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0075] For conformal vibration polishing of large freeform optical components, a long-standing core challenge in the industry is maintaining stable and highly precise controllable normal contact force in an environment of superimposed high-frequency micro-vibrations and multi-axis manufacturing errors. Failure to accurately measure and suppress vibration coupling interference in real time can easily lead to localized removal deviations, subsurface cracks, or even workpiece scrap. This invention first analyzes the cross-sensitivity characteristics of a three-dimensional force sensor under high-frequency vibration, derives the cross-interference transfer function matrix, and treats the cross-coupling as a linear time-varying system. By identifying model parameters through least squares and online recursive algorithms, a rigorous physical basis is provided for subsequent real-time compensation, solving the force measurement drift problem caused by sensor "inter-axis crosstalk."

[0076] Based on the mutual interference model, a two-stage decoupling strategy is proposed: on the one hand, a proportional compensation matrix is ​​used to correct the static or low-frequency coupling online; on the other hand, a time-varying FIR filter is designed to dynamically track higher-order coupling modes, achieving frequency-domain adjustable decoupling gain. Compared with the traditional fixed compensation coefficient method, this structure can maintain residual coupling errors within 2% and 5% in the high / low frequency bands, respectively, significantly improving the accuracy of normal force observation and laying a reliable foundation for subsequent polishing force control.

[0077] To address the periodic disturbances caused by the dominant frequency and its higher harmonics in vibration polishing, this invention constructs a frequency-selective filtering-inverse notch filter coupling compensation module. By accurately extracting the target frequency disturbance through a complex domain amplitude-phase estimator and dynamically adjusting the zero-pole positions of the inverse notch filter, an equivalent suppression depth of -40dB can be achieved, while sacrificing only a 3dB low-frequency gain margin. This "online spectral leakage suppression + active equal-amplitude phase inversion" mechanism avoids the risk of phase hysteresis caused by increasing the control bandwidth, and specifically eliminates resonance peaks within the polishing vibration bandwidth without affecting the stability of the influence loop.

[0078] Considering the significant modulation effect of high-frequency vibration on contact friction characteristics, this invention, based on the LuGre friction model, introduces a time-varying term for normal force and a velocity-related term to derive a dynamically linearized expression for the friction coefficient. Using a feedforward channel, the compensation amount is calculated in real-time at a frequency of 1 kHz and superimposed onto the target force command, reducing the peak-to-peak value of friction force fluctuations from 0.25 N to 0.05 N. This method not only improves the linearity of the force closed-loop but also significantly reduces the number of viscosity-slip transitions in the compliant phase of the end effector, thus reducing polishing residue.

[0079] Combining the aforementioned normal expected force, inverse notch compensation, and friction feedforward, this invention employs signal superposition to generate a composite target force input, avoiding phase coupling and adjustment conflicts introduced by multi-loop cascading. The main controller core adopts a PID-fourth-order extended state observer (ESO) framework. The ESO performs unified estimation of unmodeled dynamics and residual disturbances, and then the PID gain is tuned online by adaptive notch filtering and BP-neural network, achieving a step settling time of ~5ms and a steady-state error of <0.02N, meeting the sub-Newton level force accuracy requirements of high-end optical polishing processes.

[0080] By employing a multi-dimensional collaborative control architecture of "mutual interference modeling + decoupling filtering + frequency selection vibration suppression + dynamic friction feedforward + adaptive PID-ESO", this invention reduced the roughness Ra from 12nm to 1.8nm and the surface wavefront distortion to λ / 12 (λ=632.8nm) in actual vibration polishing tests of a 300mm diameter ultra-lightweight mirror blank. This achievement overcomes the bottleneck of traditional servo force control being unable to handle high-frequency vibration interference, providing a mass-producible process path for the batch precision polishing of high-end space optics, extreme ultraviolet mirrors, and ultrafast laser devices, and has significant industrial promotion value and technological innovation.

[0081] like Figure 1 As shown, the robot end effector force control method for conformal vibration polishing of optical components provided by this embodiment of the invention includes the following steps:

[0082] S101: Establish the mutual interference transfer function model of the three-dimensional force sensor, obtain the coupling relationship between different directions, and realize the mutual interference modeling of multi-axis sensing signals;

[0083] S102: Based on the aforementioned mutual interference model, the original measured force signal is corrected using linear proportional compensation or a time-varying FIR decoupling filter to obtain a more accurate normal contact force feedback signal.

[0084] S103: Based on the decoupled normal force signal, a vibration frequency gating compensation module is constructed. The periodic disturbance signal component is extracted using a frequency selective filter, and its amplitude and phase are estimated.

[0085] S104: Construct an inverse notch filter compensator based on the estimation results to perform real-time equivalent inverse weakening of periodic disturbances at a specified frequency, thereby improving the robustness and frequency-domain selective suppression capability of the force control system against vibration disturbances.

[0086] S105: Considering the modulation effect of periodic vibration on friction, a dynamic feedforward model with variable friction coefficient is established based on the normal force disturbance model, and the friction compensation control quantity is calculated.

[0087] S106: The desired normal polishing force signal, the inverse notch filter disturbance suppression signal and the friction compensation feedforward signal are superimposed and used as the target force input signal, which is then transmitted to the main controller module to realize composite target tracking control.

[0088] S107: The main controller module adopts a PID-fourth-order extended state observer structure, which integrates disturbance estimation, adaptive notch control and neural network parameter tuning methods to dynamically adjust the internal gain and filter parameters of the controller, thereby improving the system response speed, force control accuracy and generalized robustness.

[0089] like Figure 2 As shown, an embodiment of the present invention provides a robot end effector force control method for conformal vibration polishing of optical elements, comprising the following steps:

[0090] S101: Establishing the mutual interference transmission of three-dimensional force sensors. An embodiment of the present invention provides a force control method for a robot end effector used for conformal vibration polishing of optical elements, comprising the following steps:

[0091] S101: Establish the mutual interference transfer function model of the three-dimensional force sensor, obtain the coupling relationship between different directions, and realize the mutual interference modeling of multi-axis sensing signals;

[0092] S102: Based on the aforementioned mutual interference model, the original measured force signal is corrected using linear proportional compensation or a time-varying FIR decoupling filter to obtain a more accurate normal contact force feedback signal.

[0093] S103: Based on the decoupled normal force signal, a vibration frequency gating compensation module is constructed. The periodic disturbance signal component is extracted using a frequency selective filter, and its amplitude and phase are estimated.

[0094] S104: Construct an inverse notch filter compensator based on the estimation results to perform real-time equivalent inverse weakening of periodic disturbances at a specified frequency, thereby improving the robustness and frequency-domain selective suppression capability of the force control system against vibration disturbances.

[0095] S105: Considering the modulation effect of periodic vibration on friction, a dynamic feedforward model with variable friction coefficient is established based on the normal force disturbance model, and the friction compensation control quantity is calculated.

[0096] S106: The desired normal polishing force signal, the inverse notch filter disturbance suppression signal and the friction compensation feedforward signal are superimposed and used as the target force input signal, which is then transmitted to the main controller module to realize composite target tracking control.

[0097] S107: The main controller module adopts a PID-fourth-order extended state observer structure, which integrates disturbance estimation, adaptive notch control and neural network parameter tuning methods to dynamically adjust the internal gain and filter parameters of the controller, thereby improving the system response speed, force control accuracy and generalized robustness.

[0098] The recursive function model is used to obtain the coupling relationship between different directions, thereby realizing the mutual interference modeling of multi-axis sensing signals;

[0099] S102: Based on the aforementioned mutual interference model, the original measured force signal is corrected using linear proportional compensation or a time-varying FIR decoupling filter to obtain a more accurate normal contact force feedback signal.

[0100] S103: Based on the decoupled normal force signal, a vibration frequency gating compensation module is constructed. The periodic disturbance signal component is extracted using a frequency selective filter, and its amplitude and phase are estimated.

[0101] S104: Construct an inverse notch filter compensator based on the estimation results to perform real-time equivalent inverse weakening of periodic disturbances at a specified frequency, thereby improving the robustness and frequency-domain selective suppression capability of the force control system against vibration disturbances.

[0102] S105: Considering the modulation effect of periodic vibration on friction, a dynamic feedforward model with variable friction coefficient is established based on the normal force disturbance model, and the friction compensation control quantity is calculated.

[0103] S106: The desired normal polishing force signal, the inverse notch filter disturbance suppression signal and the friction compensation feedforward signal are superimposed and used as the target force input signal, which is then transmitted to the main controller module to realize composite target tracking control.

[0104] S107: The main controller module adopts a PID-fourth-order extended state observer structure, which integrates disturbance estimation, adaptive notch control and neural network parameter tuning methods to dynamically adjust the internal gain and filter parameters of the controller, thereby improving the system response speed, force control accuracy and generalized robustness.

[0105] A force control method and system for a robot end effector in conformal vibration polishing, characterized by a force sensor mutual interference decoupling module, a vibration frequency gating compensation module, a friction compensation feedforward module, and a main controller module.

[0106] The force sensor mutual interference decoupling module includes the establishment of a three-dimensional force mutual interference transfer function and the calculation of compensation for normal contact force; the establishment of the three-dimensional force mutual interference transfer function is as follows:

[0107] Let the actual force of the three-dimensional force sensor be... These represent the actual forces acting in the x, y, and z directions, respectively; the measured output is F. meas (s)=[F x (s),F y (s),F z (s)] T F x (s),F y (s),F z (s) represent the measured true output forces in the x, y, and z directions, respectively. Considering the inter-axis interference, the following transfer model F is established. meas (s)=G xyz (s)·F true (s), where G xyz (s) is a 3×3 mutual interference transfer function matrix, containing self-response and mutual interference coupling terms, with the specific transfer function form as follows:

[0108]

[0109] Among them G ij (s) represents the dynamic influence of channel j on channel i, such as G xy (s) represents the dynamic influence of channel x on channel y;

[0110] The calculation of compensation for normal contact force focuses on the output F of normal force (i.e., force in the z-direction) in the time domain. z (t), its ideal estimate f oc (t) can be expressed as follows through linear decoupling compensation for tangential mutual disturbance:

[0111] f oc (t)=F z (t)-α x ·F x (t)-α y ·F y (t)

[0112] Where α x ,α y F is the proportional coupling coefficient estimated based on the mutual interference model. x (t) and F y (t) represents the sensor measurements in the x and y directions in the time domain, respectively;

[0113] Using a time-varying FIR structure to improve the ideal estimate f oc (t) Dynamic accuracy, its discrete expression is: Where h xz and h yzThese are the unit impulse responses (FIR coefficients) of the mutual disturbance transfer functions in the X→Z axis and Y→Z axis directions, respectively, and the compensated normal force f. oc As a compensated force feedback signal, it enables more accurate force control performance.

[0114] The vibration frequency gating compensation module consists of a frequency selective filter, an amplitude and phase estimator, and an inverse notch filter compensator.

[0115] Frequency-selective filters are used to filter the system feedback signal f oc Extract the specified frequency f from (t) n The nearby narrowband component, employing a dual second-order notch filter cascade structure, has the following discrete transfer function:

[0116] Where f n The expected interference frequency; T is the sampling period of the control system; r s Control the filter bandwidth; the input to the frequency-selective filter is the compensated force feedback signal f. oc The output is a vibration signal f n (t), i.e., the vibration response at a specific frequency; f is manually adjusted by determining the process parameters. n and r s It can dynamically extract the energy components within the target interference frequency band.

[0117] The amplitude-phase estimator is based on the Fourier analysis principle and extracts the vibration signal f. n (t) is mapped to the standard periodic function form. A(t) is f n (t) is the amplitude estimate; ψ(t) is the phase estimate; C(t) = A(t)e jψ(t) The magnitude vector is a complex number, which is estimated in real time using a synchronous phase-locked loop or a sliding mode observer.

[0118] Notch filter compensators are used to suppress the extracted vibration signal f. n (t), whose discrete transfer function structure is as follows:

[0119]

[0120] Where r c To control the filter bandwidth of the inverse notch filter compensator, at f ne With input (t), the output d of the inverse notch compensator c =H comp (z)f ne (t). The inverse notch filter compensator and the frequency selective filter are inverse operations of each other. The output of the inverse notch filter compensator can directionally weaken the amplitude response of the periodic disturbance source without interfering with the frequency domain performance of the main controller, thus realizing the equivalent inverse model at a specific frequency.

[0121] The friction compensation feedforward module takes into account F under vibration excitation. x The effect of (t) on the normal friction force: Based on the relationship between friction force and normal force, the Coulomb term and the static friction term in the friction model are affected by the normal perturbation. Therefore, the friction force becomes: F f (t)=μ(F x (t))·sgn(v(t))+F v ·v(t), where μ(F n (t) represents the coefficient of friction as a function of the normal force; sgn(v(t)) is the sign function of the velocity, which determines the direction of friction; v(t) is the velocity of the end relative to the contact surface; F v It is the coefficient of viscous friction;

[0122] The variation trend of μ under high-frequency vibration can be further approximated linearly as: μ(F n (t))≈μ0+κ·F x (t), where μ0 is the static average friction coefficient; κ is the sensitivity coefficient of the effect of normal pressure on the friction coefficient; the output of the friction compensation feedforward module can be expressed as: u f (t)≈(μ0+κ·F x (t))·sgn(v(t))+F v ·v(t).

[0123] Synthetic target force signal d r =d f +d c +u f , where d f The set polishing desired force signal.

[0124] The main controller module consists of three parts: a proportional-integral-derivative-fourth-order extended state observer (PID-4thESO), an adjustable notch filter, and a radial basis function (RBF) neural network parameter adaptor.

[0125] Furthermore, the proportional-integral-derivative-fourth-order extended state observer uses a fourth-order extended state observer to estimate the system state and disturbances, and generates the basic control quantity u0 based on the incremental proportional-integral-derivative (PID) controller.

[0126] Furthermore, the discrete expression of the fourth-order extended state observer is:

[0127] Where f = f oc -f n To filter out the end-effector normal force signal after the selected frequency vibration signal in the vibration frequency gating compensation module, the end-effector normal force feedback compensation value is f. oc(t); z1~z4 are system state estimates, z5 is a higher-order disturbance estimate; β i Let be the observer gain parameter, and b be the system nominal gain; state variable updates are implemented using Euler discretization. The incremental PID controller combining the fourth-order extended state observer state estimation is expressed as:

[0128] Where dr(t) is the synthesized target force signal, Δe(t) is the force error at time t; Δe(t) = e(t) - e(t-1), Δ 2 e(t)=e(t)-2e(t-1)+e(t-2);K p ,K i ,K d For PID gain, T s U is the sampling period; u0(t) is the output control quantity of this module. The discrete transfer function expression of the adjustable notch filter is:

[0129]

[0130] Among them, f n Let u be the interference frequency, r be the bandwidth coefficient, and r be the notch filter strength. The filter input is u0(t), and the filter output is u(t).

[0131] Radial basis function (RBF) neural network parameter adaptors use the system dynamic state s(t) (including error e(t), error derivative) as the basis for their operation. System output f o Taking (t) and its derivative, etc. as input, the output is an estimated expression for the following parameters:

[0132] in, The bandwidth parameter of the fourth-order extended state observer is adaptively updated. The nominal gain of the controlled object is updated adaptively. Notch filter center frequency adaptively updates value; Notch filter bandwidth adjustment factor is adaptively updated; φ i (s): The i-th Gaussian function, defined as... The weights of the i-th neuron are adjusted online based on the error. Furthermore, the RBF neural network parameter adaptor is designed based on Lyapunov stability analysis to ensure system closed-loop stability and estimation error convergence, which requires the existence of... γ i >0, making

[0133] The adaptive update value is transmitted in real time to the PID-4thESO and the adjustable notch filter module, respectively, to update β. iObserver gain parameters, b is the system nominal gain; f is the gain parameter. n Interference frequency and bandwidth coefficient; thus forming a parameter self-sensing and self-adjusting control system, improving the overall response speed and robust control capability.

[0134] Final construction as follows Figure 2 The diagram illustrates a complete force control method and system for a robot end effector used in conformal vibration polishing of optical components, employing an end effector force control device based on a voice coil motor. Figure 3 As shown), compared with the force control effect of traditional PID control ( Figure 4 As shown in the figure, the force control accuracy is significantly improved, and the conformal polishing vibration error can be quickly suppressed within 2 to 3 seconds. Figure 5 The effect after polishing is shown, and the results indicate that it can effectively reduce low- and medium-frequency errors, with RMS reaching within 10 nanometers.

[0135] I. Specific application areas or related products of this invention.

[0136] Conformal vibration polishing equipment: This invention can be integrated into a robotic conformal vibration polishing system used in the manufacturing process of high-end optical components (such as freeform surface lenses, laser mirrors, and space telescope lenses), adapting to the force control processing requirements of complex curvature surfaces and high-precision surface morphology.

[0137] Multi-axis force-controlled polishing robot system: This invention is adapted to the end force control unit in flexible automated equipment such as industrial six-axis robots, parallel mechanisms, and serial arm platforms, to achieve stable and reliable contact force control and complex trajectory tracking.

[0138] Ultra-precision automated surface repair platform: Suitable for surface defect repair or remanufacturing systems in aerospace, precision molds, micro-optical devices and other fields, providing precise force control support for processing with complex friction characteristics or obvious vibration excitation.

[0139] Piezoelectric / voice coil drive device with integrated intelligent force control module: It can be used as an intelligent control module with disturbance suppression and nonlinear compensation capabilities, and can be integrated into a micro-vibration end effector with piezoelectric and voice coil vibration devices to improve the system control accuracy and intelligence level.

[0140] Adaptive Robotic Flexible Machining Unit: The modular control structure of this invention is suitable for widespread use in various types of flexible machining tasks, especially for task scenarios with strict requirements for constant force output under high-frequency micro-disturbance environments.

[0141] II. Evidence related to the technical effects obtained by the embodiments of the present invention.

[0142] This invention provides a force control method and system for a robot end effector used in conformal vibration polishing of optical components. It offers advantages such as high-precision force control, strong disturbance robustness, strong nonlinear modeling and compensation capabilities, excellent adaptive adjustment capabilities, and modular integration for easy deployment. Compared to existing technologies, this system introduces a multi-module coordinated control architecture, effectively addressing complex dynamic factors commonly encountered in optical polishing processes, such as multi-frequency disturbances, axial mutual interference, and nonlinear friction.

[0143] By constructing a three-dimensional force perturbation transfer function model, precise decoupling compensation for the inter-axis coupling effect of the force sensor was achieved, improving the accuracy of normal force measurement from the source. Combined with the frequency-selective filter and inverse notch filter compensation mechanism, the system can directionally identify and actively suppress specific frequency periodic disturbances generated during polishing, effectively avoiding the decrease in force control accuracy caused by resonance. Furthermore, in response to the significant nonlinear changes in friction characteristics in the vibratory polishing environment, a friction feedforward compensation model based on contact pressure modulation was established, which enhanced the dynamic friction control capability and avoided force control fluctuations and error accumulation.

[0144] Furthermore, this invention introduces an RBF neural network parameter adaptor, which enables real-time identification and dynamic self-adjustment of key control parameters, effectively enhancing the system's environmental adaptability and uncertainty robustness under different operating conditions. The overall system adopts a modular design architecture, with clear logic and well-defined boundaries for each functional unit, facilitating integration into existing industrial robot platforms of various types. It supports rapid deployment and customized expansion for different polishing process requirements, demonstrating good engineering practicality and scalability.

[0145] After integrating the control method and system provided by this invention into a robot platform, its actual deployment is as follows: Figure 6 As shown.

[0146] The system has been experimentally tested and found to achieve high-precision force control better than ±0.1N during conformal vibration polishing. The force control performance is stable and reliable, and the control error is significantly smaller than that of traditional methods. For example... Figure 7 As shown, the system's real-time response curve to the normal force under typical polishing operations exhibits minimal fluctuations, demonstrating superior dynamic tracking capability and steady-state control level.

[0147] Furthermore, in typical optical component surface polishing tasks, the system described in this invention, in conjunction with a high-frequency conformal vibration polishing tool, can achieve surface roughness control better than 9nm RMS, significantly improving the quality of the processed surface and meeting the consistency and stability requirements of high-end optical devices for ultra-precision machining. Figure 5 As shown.

[0148] In summary, this invention organically integrates transfer function decoupling, periodic disturbance filtering, nonlinear friction compensation, and RBF neural network adaptive adjustment mechanism. While ensuring system stability, it achieves a smart force control system with higher precision, stronger robustness, and wider adaptability. It is particularly suitable for high-quality conformal vibration polishing of complex curved optical components and has significant promotional value and application prospects in the high-end manufacturing field.

[0149] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0150] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for force control of a robot end effector for conformal vibration polishing of optical elements, characterized in that, Includes the following steps: Step 1: Establish a three-dimensional force sensor mutual disturbance transfer function model to obtain the coupling relationship between the three axes; Step 2: Based on the three-dimensional force sensor mutual disturbance transfer function model, perform linear proportional compensation or time-varying finite impulse response filtering compensation on the original measured force signal to obtain the normal contact force feedback signal. Step 3: Use a frequency-selective filter to extract the narrowband component near the preset vibration frequency from the normal contact force feedback signal, and estimate its amplitude and phase. Step 4: Construct an inverse notch filter compensation signal based on the amplitude and phase to suppress periodic disturbances at the corresponding frequency in real time; Step 5: Establish a dynamic feedforward model with variable friction coefficient based on the characteristics of normal force disturbance, and generate friction compensation signal; Step 6: Superimpose the desired normal polishing force signal, the inverse notch filter compensation signal, and the friction compensation signal to form the target force input signal; Step 7: A proportional-integral-differential-fourth-order extended state observer is used to track the target force input signal, and the gain of the proportional-integral-differential-fourth-order extended state observer, the notch center frequency and bandwidth parameters of the adjustable notch filter are adjusted online through a radial basis function neural network; the main controller module consists of three parts: a proportional-integral-differential-fourth-order extended state observer, an adjustable notch filter, and a radial basis function neural network parameter adaptor; The dynamic feedforward model with variable friction coefficient established based on the characteristics of normal force disturbance considers vibration excitation. Regarding the effect on the normal friction force, based on the relationship between frictional force and normal force, the Coulomb term and the static friction term in the friction model are affected by the normal perturbation. Therefore, the frictional force becomes: ,in The coefficient of friction varies with the normal force; The sign of the velocity is a function that determines the direction of friction; The velocity of the end relative to the contact surface; It is the coefficient of viscous friction; Under high-frequency vibration, in order to describe The changing trend of can be further approximated linearly as: ,in The static average coefficient of friction; This is the sensitivity coefficient to the effect of normal force on the coefficient of friction; The output of the dynamic feedforward model with variable friction coefficient based on the characteristics of normal force perturbation is expressed as follows: 。 2. The force control method as described in claim 1, characterized in that, The filtering coefficients of the time-varying finite impulse response filter are updated in real time based on the unit impulse response of the three-dimensional force sensor mutual disturbance transfer function model, so as to improve the accuracy of normal contact force estimation.

3. The force control method as described in claim 1, characterized in that, The frequency-selective filter adopts a dual second-order notch filter series structure, with its center frequency equal to the polishing excitation frequency and its bandwidth set by adjustable parameters.

4. The force control method as described in claim 1, characterized in that, The variable friction coefficient dynamic feedforward model describes the change of friction coefficient with normal force through linear approximation and obtains the sensitivity coefficient through offline calibration.

5. A force control system for a robot end effector used in the force control method for conformal vibration polishing of optical elements as described in claim 1, characterized in that, include: The force sensor mutual interference decoupling module is used to perform linear proportional compensation or time-varying finite impulse response filtering compensation on the original measured force signal based on the three-dimensional force sensor mutual interference transfer function model to obtain the normal contact force feedback signal. The vibration frequency gating compensation module is used to extract the narrowband component of the normal contact force feedback signal near the preset vibration frequency using a frequency selective filter, and generate an inverse notch filter compensation signal based on the estimated amplitude and phase of the narrowband component. Friction compensation feedforward module is used to output friction compensation signal based on normal force disturbance model; The main controller module is used to perform tracking control by superimposing the desired normal polishing force signal, the inverse notch filter compensation signal, and the friction compensation signal. The main controller module adopts a proportional-integral-derivative-fourth-order extended state observer structure, and adaptively adjusts the gain of the proportional-integral-derivative-fourth-order extended state observer, the notch filter center frequency, and the bandwidth parameters of the adjustable notch filter through a radial basis function neural network.

6. The force control system as described in claim 5, characterized in that, The force sensor mutual interference decoupling module is modeled using a three-dimensional force mutual interference transfer function matrix, in which the self-response term and mutual interference coupling term are both obtained through experimental identification.

7. The force control system as described in claim 5, characterized in that, The bandwidth of the frequency selection filter in the vibration frequency gating compensation module can be adjusted online by software parameters to adapt to the excitation frequency changes of different polishing processes.

8. The force control system as described in claim 5, characterized in that, The friction compensation feedforward module obtains the sensitivity coefficient of friction coefficient as a function of normal force through offline experimental calibration, and updates the friction compensation signal in real time.

9. The force control system as described in claim 5, characterized in that, The proportional-integral-derivative-fourth-order extended state observer of the main controller module takes the normal force error and its higher-order derivatives as inputs, and ensures that the system maintains zero steady-state error under vibration disturbance and model uncertainty through the adjustable notch filter bandwidth of the online-updated main controller module.

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