Sand belt orthogonal polishing system and polishing method for double-robot cooperation

Abstract

The application relates to the technical field of optical processing, in particular to a double-robot cooperative abrasive belt orthogonal polishing system and a polishing method. The polishing method first calibrates the removal functions of a first abrasive belt polishing assembly carried by a first robot and a second abrasive belt polishing assembly carried by a second robot, the abrasive belt linear velocity direction of the first abrasive belt polishing assembly and the abrasive belt linear velocity direction of the second abrasive belt polishing assembly are mutually orthogonal, the first abrasive belt polishing assembly is used for removing materials, and the second abrasive belt polishing assembly is used for smoothing textures; a multi-target optimization functional is constructed according to an established convolution superposition model, optimal residence time and feeding speed are solved, a control file is generated, and the first robot is used for first processing and the second robot is used for lag processing. The double-robot orthogonal posture physical complementary cooperative processing mode is adopted, the decoupling of material removal efficiency and optical element surface texture quality is realized, the medium frequency error is effectively inhibited, and the overall processing efficiency of a large-aperture optical element is improved.

Description

Technical Field

[0001] This invention belongs to the field of optical processing technology, and in particular relates to a dual-robot collaborative belt orthogonal polishing system and polishing method. Background Technology

[0002] As modern optical systems develop towards larger apertures, higher precision, and lighter weights, high-end optical equipment such as inertial confinement fusion high-power laser systems (e.g., the US NIF and China's Shenguang series), ground-based maximum telescopes, and high-resolution Earth observation satellites are placing near-physical limits on the surface processing quality requirements of optical components. These precision optical systems not only demand extremely high accuracy in the low-frequency surface shape of optical components but also impose stringent constraints on the comprehensive control of surface shape errors across the entire frequency range. Among these constraints, the ability to suppress mid-spatial frequency (MSF) error has become a key factor limiting the imaging and operational performance of optical components.

[0003] Traditional full-aperture polishing techniques are no longer sufficient to meet the high-precision machining requirements of complex optical components such as aspherical and freeform surfaces. Against this backdrop, computer-controlled surface forming technology has gradually become the mainstream technology for precision optical processing, with robotic grinding and polishing technology being the most widely used. Compared with traditional processes, robotic belt polishing has significant advantages such as high material removal efficiency, controllable processing thermal effects, and strong adaptability to complex curved surfaces, and is now widely used in the grinding and rough polishing processes of large-aperture optical components.

[0004] At present, the belt polishing of large-diameter optical components generally adopts a single posture following processing mode. In this mode, when the robot holds the belt polishing tool and completes the full-diameter scanning processing along the preset trajectory such as the grating scanning path or the spiral path, the control system always keeps the direction of the belt linear velocity parallel to the direction of the tool feed speed on the workpiece surface.

[0005] This machining method, where the feed and rotation speed are in the same direction, causes the cutting texture direction to highly coincide with the scanning path direction, resulting in highly directional grating-track tool marks easily remaining on the workpiece surface. These directional textures manifest as high-energy peaks at specific frequencies in the spatial frequency domain, ultimately forming severe micro-fiber scattering (MSF). To eliminate directional tool marks and MSF, existing machining processes require one or more precision smoothing processes, such as small-head polishing or magnetorheological polishing, after belt polishing. This not only significantly increases equipment investment and the overall machining cycle, but also results in low processing efficiency for small-head smoothing processes and easily introduces edge effects and other machining errors, affecting the overall surface accuracy of the component.

[0006] In summary, existing belt polishing technology for large-aperture optical components has the following three major drawbacks: First, MSF (Mean Slippage) is difficult to eliminate from its underlying mechanism. The traditional single parallel feed mode results in uniform machining texture and directional accumulation of errors. Even with optimization of process parameters such as path spacing and scanning speed, it is impossible to eliminate the periodic ripples distributed along the machining path from a physical mechanism perspective, thus limiting the MSF suppression effect.

[0007] Second, the overall processing efficiency is low. To reduce directional texture residue and MSF, existing processes typically optimize processing quality by reducing feed rate and increasing path overlap, directly sacrificing material removal efficiency. At the same time, the subsequent additional precision smoothing process further lengthens the overall manufacturing cycle, making it difficult to meet the needs of batch and high-efficiency processing.

[0008] Third, the adaptability to complex curved surfaces is insufficient. The removal function of the belt polishing slender type has poor curvature matching with the aspherical and free-form surfaces with large curvature. During the processing, uneven local contact pressure distribution on the workpiece surface is prone to occur, which seriously affects the surface convergence accuracy of the component and makes it difficult to adapt to the high-precision processing requirements of complex curved surface optical components. Summary of the Invention

[0009] In view of this, the present invention aims to provide a dual-robot collaborative belt orthogonal polishing system and polishing method to decouple material removal efficiency from surface texture quality, effectively suppress mid-frequency errors, eliminate the need for subsequent independent smoothing processes, and significantly shorten the manufacturing cycle of large-aperture optical components.

[0010] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A dual-robot collaborative belt polishing system includes: a first robot, a second robot, a first belt polishing assembly, a second belt polishing assembly, and a workpiece stage; the first robot and the second robot are respectively disposed on opposite sides of the workpiece stage, the first belt polishing assembly is fixedly mounted on the end effector of the first robot, the second belt polishing assembly is fixedly mounted on the end effector of the second robot, and an optical element to be processed is fixedly clamped on the workpiece stage; The orthogonal polishing system also includes a central collaborative control module, which controls the first robot and the second robot to polish the optical element using a pre-designed continuous processing trajectory shared by the first and second robots, a pre-planned end posture of the first and second robots at each processing trajectory point, and a set feed rate of the first and second robots at each processing trajectory point. During the polishing process, the linear velocity direction of the first abrasive belt polishing component is controlled to be orthogonal to the linear velocity direction of the second abrasive belt polishing component.

[0011] Furthermore, the central collaborative control module includes a removal function calibration unit, a removal function matrix establishment unit, a convolution superposition model establishment unit, a multi-objective optimization functional construction unit, a feed rate calculation unit, and a feed rate setting unit; The removal function calibration unit is used to calibrate a first removal function corresponding to the first abrasive belt polishing component and a second removal function corresponding to the second abrasive belt polishing component, wherein the abrasive belt linear velocity direction of the first abrasive belt polishing component and the abrasive belt linear velocity direction of the second abrasive belt polishing component are orthogonal to each other. The removal function matrix establishment unit is used to establish a first removal function matrix corresponding to a first removal function and a second removal function matrix corresponding to a second removal function. The convolution stacking model building unit is used to combine the first removal function matrix and the second removal function matrix to build a convolution stacking model. Multi-objective optimization functional building unit, used to construct multi-objective optimization functionals based on convolution stacking models; The feed rate calculation unit is used to iteratively solve the multi-objective optimization functional using the trust region reflection algorithm to obtain the optimal dwell time sequence of the first robot and the second robot at each processing trajectory point; then, based on the optimal dwell time sequence, the feed rate of the first robot and the second robot at each processing trajectory point is calculated respectively. The feed rate setting unit is used to set the feed rate of the first robot and the second robot at each machining trajectory point based on the feed rate calculation unit calculated by the feed rate calculation unit, and the corresponding limit speed threshold.

[0012] Furthermore, both the first and second robots are six-degree-of-freedom robotic arms.

[0013] A dual-robot collaborative belt orthogonal polishing method, based on the aforementioned belt orthogonal polishing system, includes the following steps: S1: Calibrate the coordinate transformation relationship of the first robot coordinate system, the second robot coordinate system, the first belt polishing component coordinate system, and the second belt polishing component coordinate system relative to the same workpiece coordinate system, and obtain the belt linear velocity direction of the first belt polishing component and the second belt polishing component in the workpiece coordinate system; S2: Select a substrate of the same material as the optical element and perform point polishing on it. The first belt polishing assembly is used to remove material, and the second belt polishing assembly is used to smooth the texture. Control the belt linear velocity directions of the first and second belt polishing assemblies to be orthogonal. Calibrate the first removal function corresponding to the first belt polishing assembly and the second removal function corresponding to the second belt polishing assembly, and establish the first removal function matrix corresponding to the first removal function. and the second removal function matrix corresponding to the second removal function ; S3: Obtain the original wavefront data of the optical element surface, map the original wavefront data onto the workpiece coordinate system, and obtain the surface shape error distribution matrix to be corrected. , as the target removal amount of optical elements; S4: Design a continuous machining trajectory shared by the first robot and the second robot in the workpiece coordinate system. Based on the continuous machining trajectory, plan the end posture of the first robot and the second robot at each machining trajectory point so that the linear velocity direction of the first sand belt polishing component is always perpendicular to the feed direction, and the linear velocity direction of the second sand belt polishing component is always parallel to the feed direction. S5: Combine with the first removal function matrix Second removal function matrix A convolutional superposition model is established, and a multi-objective optimization functional is constructed based on the convolutional superposition model. The optimal dwell time series of the first robot and the second robot are solved. The feed rate of the first robot and the second robot at each processing trajectory point is calculated according to the optimal dwell time series. S6: The continuous machining trajectory, the end poses of the first and second robots, and the feed speeds of the first and second robots at each machining trajectory point are converted into motion / attitude control files for the first and second robots. The first robot starts first, and the second robot starts after a preset time, completing the dual-robot collaborative belt orthogonal polishing machining.

[0014] Furthermore, step S2 includes the following steps: S21: Control the first and second abrasive belt polishing components to perform point polishing on the workpiece to be plated sequentially using the same polishing parameters, thereby obtaining a first removal function corresponding to the first abrasive belt polishing component and a second removal function corresponding to the second abrasive belt polishing component; wherein, the abrasive belt linear velocity direction of the first abrasive belt polishing component and the abrasive belt linear velocity direction of the second abrasive belt polishing component are orthogonal to each other; S22: Normalize the first removal function and the second removal function respectively to obtain the first removal function matrix corresponding to the first removal function. and the second removal function matrix corresponding to the second removal function .

[0015] Furthermore, step S4 includes the following steps: S41: Design a continuous machining trajectory shared by the first and second robots in the workpiece coordinate system, and discretize the continuous machining trajectory into several machining trajectory points. ,in, , N This represents the total number of processing trajectory points; S42: Calculate each machining trajectory point Unit tangential feed vector at the location The calculation formula is as follows: ; Among them, the trajectory endpoints of the processing trajectory points adopt one-sided difference, and the non-trajectory endpoints adopt center difference; S43: Set machining trajectory points The unit outward normal feed vector at the location is Assume the contact direction of the first abrasive belt polishing component is along Direction, the direction of the linear velocity of the abrasive belt in the first abrasive belt polishing assembly. Let it be the feed vector perpendicular to the unit tangential direction in the tangential plane. The direction, satisfy Then, the target pose rotation matrix corresponding to the first robot. for Rotate the target attitude matrix After performing quaternion transformation, the end-effector quaternion of the first robot is obtained. ; S44: Let the direction of the abrasive belt linear velocity of the second abrasive belt polishing component be... Unit tangential feed vector The direction corresponds to the target pose rotation matrix of the second robot. for Rotate the target attitude matrix After performing quaternion transformation, the end-effector quaternion of the second robot is obtained. .

[0016] Furthermore, step S5 includes the following steps: S51: Combining the first removal function matrix Second removal function matrix Establish a convolution stacking model, which is as follows: ; in, This is the matrix representing the total amount of optical elements removed, predicted by a convolutional stacking model based on a preset dwell time. and These are the dwell time vectors for the first robot and the second robot, respectively. S52: Construct a multi-objective optimization functional based on a convolution stacking model. The multi-objective optimization functional is: ; in, Let be the objective functional value to be minimized; These are the weighting coefficients for balancing the surface accuracy term and the intermediate frequency suppression term; It is a two-dimensional discrete Fourier transform operator used to map residuals to the frequency domain; Weights for a bandpass filter designed for the step frequency of a continuous machining trajectory; S53: The trust region reflection algorithm is used to iteratively solve the multi-objective optimization functional to obtain the value at the processing trajectory point. Optimal dwell time sequence of the first robot at the location Optimal dwell time series of the second robot ; S54: Based on the optimal dwell time sequences of the first and second robots, calculate the time at each machining trajectory point. The feed rate of the first robot Feed rate of the second robot The calculation formula is as follows: ; ; in, For adjacent machining trajectory points on a continuous machining trajectory and The arc length between; If the feed speed of the first robot Not greater than its limit speed threshold Then the feed speed of the first robot is set to ;like Then the feed speed of the first robot is set to At the same time, reduce the belt speed of the first robot at that processing trajectory point. Or reduce cylinder pressure To ensure that the amount of material removed remains constant; If the feed speed of the second robot Not greater than its limit speed threshold Then the feed speed of the second robot is set to ;like Then the feed speed of the second robot is set to At the same time, reduce the belt speed of the second robot at this processing trajectory point. Or reduce cylinder pressure This ensures that the amount of material removed remains constant.

[0017] Furthermore, after step S6, step S7 is also included: detecting the residual surface error of the processed optical element, calculating the root mean square error of the residual surface error, and if the root mean square error is less than a preset threshold, then the polishing process of the optical element is completed; if the root mean square error is greater than or equal to the preset threshold, then the residual surface error is used as the new target removal amount of the optical element, and steps S5 and S6 are repeated until the root mean square error of the residual surface error is less than the preset threshold.

[0018] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention employs a collaborative processing mode with two robots sharing the same processing trajectory and orthogonal posture physical complementarity. By utilizing the "long integral path" characteristic of the parallel feed mode, it suppresses and smooths the periodic textures generated by the orthogonal feed mode, achieving decoupling between material removal efficiency and surface texture quality of optical components. This effectively suppresses mid-frequency errors, eliminates the need for subsequent independent smoothing processes, and improves the overall processing efficiency of large-diameter optical components. Simultaneously, this dual-mode removal function solves the problem of uneven removal caused by curvature mismatch in the high-curvature edge regions of optical components, achieving highly deterministic manufacturing from planar to freeform surfaces. Attached Figure Description

[0019] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic diagram of the structure of the dual-robot collaborative belt orthogonal polishing system described in the embodiment of the present invention; Figure 2 A schematic flowchart of the dual-robot collaborative belt orthogonal polishing method described in the embodiments of the present invention; Figure 3 This is a schematic diagram of the dual-mode removal function described in an embodiment of the present invention.

[0020] Explanation of reference numerals in the attached figures: 1. First robot; 2. Second robot; 3. First belt polishing assembly; 4. Second belt polishing assembly; 5. Workpiece stage; 6. End effector; 7. Optical element; 8. Central collaborative control module. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0023] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0024] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0025] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0026] like Figure 1 As shown, this embodiment of the invention provides a dual-robot collaborative belt orthogonal polishing system, including: a first robot 1, a second robot 2, a first belt polishing assembly 3, a second belt polishing assembly 4, and a workpiece stage 5; the first robot 1 and the second robot 2 are respectively disposed on both sides of the workpiece stage 5, the first belt polishing assembly 3 is fixedly installed on the end effector 6 of the first robot 1, the second belt polishing assembly 4 is fixedly installed on the end effector 6 of the second robot 2, and an optical element 7 to be processed is fixedly clamped on the workpiece stage 5; The belt orthogonal polishing system also includes a central collaborative control module 8, which controls the first robot 1 and the second robot 2 to polish the optical element 7 using a pre-designed continuous processing trajectory shared by the first robot 1 and the second robot 2, a pre-planned end posture of the first robot 1 and the second robot 2 at each processing trajectory point, and a set feed speed of the first robot 1 and the second robot 2 at each processing trajectory point. During the polishing process, the belt linear velocity direction of the first belt polishing component 3 is controlled to be orthogonal to the belt linear velocity direction of the second belt polishing component 4.

[0027] In some embodiments, the central collaborative control module 8 includes a removal function calibration unit, a removal function matrix establishment unit, a convolution superposition model establishment unit, a multi-objective optimization functional construction unit, a feed rate calculation unit, and a feed rate setting unit. The removal function calibration unit is used to calibrate the first removal function corresponding to the first abrasive belt polishing component 3 and the second removal function corresponding to the second abrasive belt polishing component 4, wherein the abrasive belt linear velocity direction of the first abrasive belt polishing component 3 and the abrasive belt linear velocity direction of the second abrasive belt polishing component 4 are orthogonal to each other. The removal function matrix establishment unit is used to establish a first removal function matrix corresponding to a first removal function and a second removal function matrix corresponding to a second removal function. The convolution stacking model building unit is used to combine the first removal function matrix and the second removal function matrix to build a convolution stacking model. Multi-objective optimization functional building unit, used to construct multi-objective optimization functionals based on convolution stacking models; The feed rate calculation unit is used to iteratively solve the multi-objective optimization functional using the trust region reflection algorithm to obtain the optimal dwell time sequence of the first robot 1 and the second robot 2 at each processing trajectory point; then, based on the optimal dwell time sequence, the feed rate of the first robot 1 and the second robot 2 at each processing trajectory point is calculated respectively. The feed rate setting unit is used to set the feed rates of the first robot 1 and the second robot 2 at each machining trajectory point based on the feed rate calculation unit calculated by the feed rate calculation unit and their corresponding limit speed thresholds.

[0028] The specific method for setting the feed rate of the first robot 1 and the second robot 2 at each machining trajectory point is as follows: If the feed speed of the first robot 1 Not greater than its limit speed threshold Then the feed speed of the first robot 1 is set to ;like Then the feed speed of the first robot 1 is set to At the same time, reduce the belt speed of the first robot 1 at the processing trajectory point. Or reduce cylinder pressure To ensure that the amount of material removed remains constant; If the feed speed of the second robot 2 Not greater than its limit speed threshold Then the feed speed of the second robot 2 is set to ;like Then the feed speed of the second robot 2 is set to At the same time, reduce the belt speed of the second robot 2 at this processing trajectory point. Or reduce cylinder pressure This ensures that the amount of material removed remains constant.

[0029] In some embodiments, both the first robot 1 and the second robot 2 are six-degree-of-freedom robotic arms. It should be noted that the collaborative machining motion execution mechanism composed of the first robot 1 and the second robot 2 can also be replaced by a five-axis gantry machine tool or a hybrid robot, as long as it has multiple degrees of freedom and can adjust the posture of the end polishing tool; in addition, the number of robots is not limited to two, and can be extended to a collaborative machining system with more than two robots, for example, using multiple robots to perform orthogonal high-efficiency removal and parallel smoothing texture respectively.

[0030] In some embodiments, both the first belt polishing assembly 3 and the second belt polishing assembly 4 include a servo motor, a drive wheel driven by the servo motor, a pneumatic tensioning wheel, an elastic contact wheel that contacts the optical element 7, and a sanding belt tensioned between the drive wheel, the pneumatic tensioning wheel, and the elastic contact wheel; the servo motor drives the sanding belt to circulate via the drive wheel, and the elastic contact wheel presses the working section of the sanding belt against the surface of the optical element 7; the abrasive surface of the working section of the sanding belt is actually removed; the linear velocity of the sanding belt... The surface linear velocity of the working section of the abrasive belt along its running direction is independently driven by a servo motor via a drive wheel. The elastic contact wheels are made of rubber materials of different hardness, which determines the size of the Hertz contact area and the pressure distribution characteristics.

[0031] In some embodiments, the first belt polishing assembly 3 and the second belt polishing assembly 4 may each be independently selected from one of the following: a cylindrical grinding wheel, a computer-controlled small grinding head, an airbag polishing head, a magnetorheological polishing head, or a roller polishing brush.

[0032] like Figure 2 As shown, combined with Figure 1 The present invention also provides a dual-robot collaborative belt orthogonal polishing method, which is implemented based on the aforementioned dual-robot collaborative belt orthogonal polishing system.

[0033] The removal mechanism of this polishing method is based on the classical Preston equation, whose differential form is: (1); in, The depth of material removal per unit time; This is a process factor, related to the material and abrasive of optical element 7; This is the normal pressure at the point of contact. The relative velocity modulus of the first belt polishing assembly 3 or the second belt polishing assembly 4 and the optical element 7 at that point.

[0034] According to the principles of kinematics, the relative velocity of the contact point between the first belt polishing component 3 or the second belt polishing component 4 and the optical element 7 is... It is the linear velocity of the sanding belt. With feed rate vector sum: (2); In equation (1), the relative velocity modulus determines the material removal efficiency. ,satisfy This invention utilizes a cooperative processing mode based on orthogonal attitude physical complementarity, and its velocity synthesis calculation is as follows: Orthogonal feed mode: When the angle between the linear velocity direction of the first belt polishing component 3 and its feed direction is... When the angle is 90°, that is, the direction of the abrasive belt linear velocity is perpendicular to the feed direction, according to the vector composition rule, the relative velocity modulus of the orthogonal feed mode is... for: (3); At this point, the relative speed in the orthogonal feed mode The direction is approximately perpendicular to the feed path direction (due to) (The composite angle is close to 90°). The first abrasive belt polishing component 3 completes the polishing process in the transverse direction, with a wider polishing sweep width and higher material removal efficiency.

[0035] Parallel feed mode: When the angle between the linear velocity direction of the second belt polishing component 4 and the feed direction is... When the angle is 0°, the abrasive belt linear velocity direction is parallel to the feed direction. It is usually set to the opposite direction to obtain the maximum relative velocity. The relative velocity modulus of the parallel feed mode is... for: (4); At this point, the relative speed in the parallel feed mode The direction coincides with the feed path direction, removing texture distribution along the path and providing strong smoothing and brightening capabilities.

[0036] Since the elastic contact wheel is an elastic body, its contact with optical element 7 (assuming it is rigid) is a surface contact. According to Hertzian contact theory, the contact area is usually elliptical, and the normal pressure inside it is... It is distributed in an ellipsoidal shape: (5); in, For the contact center pressure, and These are the semi-axis lengths of the contact ellipse in the feed direction (X-direction of the workpiece coordinate system) and its perpendicular direction (Y-direction of the workpiece coordinate system), respectively. Contact center pressure. With applied normal polishing force The relationship is: (6); Contact ellipse semi-axis length , The size is determined by the normal polishing force The equivalent radius of curvature at the contact point between the optical element 7 and the first belt polishing assembly 3 or the second belt polishing assembly 4 and the material properties of both (elastic modulus) Poisson's ratio The relationship between the two parties, who jointly decide the matter, can be represented as follows: (7); in, and The shape factor, For the equivalent elastic modulus, , These are the Poisson's ratios of the two contact bodies between the elastic contact wheel and the optical element 7, respectively, of the first belt polishing assembly 3 and the second belt polishing assembly 4. , These are the elastic moduli (i.e., Young's modulus) of the two contact bodies, the elastic contact wheel and the optical element 7, corresponding to the first abrasive belt polishing assembly 3 and the second abrasive belt polishing assembly 4, respectively.

[0037] normal pressure With relative velocity modulus Substituting into the Preston equation and integrating over the contact region yields the analytical model of the removal function. The core of this invention lies in fundamentally altering the spatial form of the removal function by changing the tool feed attitude.

[0038] Define the Hertzian contact ellipse parameters of the elastic contact wheel in the first belt polishing assembly 3 or the second belt polishing assembly 4 under static conditions: (Contact half-major axis): Half of the width of the sand belt.

[0039] (Contact half-short shaft): half of the deformation length corresponding to the elastic contact wheel being pressed in.

[0040] (Contact center pressure): The maximum Hertzian pressure at the center of the contact area.

[0041] The instantaneous removal rate model is based on the Preston equation, which describes the instantaneous removal rate at a single point. for: (8); Substituting equation (5) into equation (8), the instantaneous removal rate Converted to: (9).

[0042] In actual processing, the focus is on the unit removal function generated per unit time by the movement of the first belt polishing component 3 or the second belt polishing component 4 along the processing path. Its cross-sectional profile is the integral of the instantaneous removal rate along the direction of movement. In this invention, due to the use of mutually orthogonal feed postures, the integration paths are different, resulting in two distinctly different removal function forms: Orthogonal feed mode ( Cross-sectional profile model for: (10); Parallel feed mode ( Cross-sectional profile model for: (11).

[0043] Because the effective width is determined by the contact semi-minor axis The decision was made because the long integral path resulted in a large amount of center removal. It exhibits a "narrow and steep" parabolic distribution.

[0044] As can be seen from the cross-sectional profile models of equations (10) and (11), the "volume (i.e., removal rate)" and "bottom area (i.e., resolution)" of the removal function are directly controlled by the process parameters of the first belt polishing assembly 3 or the second belt polishing assembly 4. The present invention uses the central collaborative control module 8 to modulate the following process parameters in real time: 1. Removal rate (volume) modulation, peak removal rate of the removal function. The formula for adjusting the linear velocity and modulus of the sanding belt and normal polishing force During the rough polishing stage, the linear velocity and modulus of the abrasive belt are increased simultaneously. (Directly increase the relative speed modulus of the parallel feed mode) Relative velocity modulus of orthogonal feed mode ) and normal polishing force To achieve the maximum removal rate.

[0045] 2. Remove bandwidth (bottom area) modulation and adjust the normal polishing force according to Hertzian contact theory. Contact semi-major shaft (Bandwidth in orthogonal mode) and normal polishing force The cube root relationship is as follows: (12); When the first belt polishing component 3 or the second belt polishing component 4 processes to the edge of the optical element 7 or its equivalent radius of curvature In areas of rapid change, to prevent "edge collapse," the belt orthogonal polishing system reduces the normal polishing force in real time. This directly leads to contact with the semi-major shaft. The size of the spot is reduced, which narrows the removal function in the orthogonal feed mode, realizing "variable spot size" processing and ensuring the consistency of the removal of the optical element 7 across the entire aperture.

[0046] The dual-robot collaborative belt orthogonal polishing method of this invention includes the following steps: S1: Calibrate the coordinate transformation relationship of the first robot 1 coordinate system, the second robot 2 coordinate system, the first sanding belt polishing component 3 coordinate system, and the second sanding belt polishing component 4 coordinate system relative to the same workpiece coordinate system, and obtain the sanding belt linear velocity direction of the first sanding belt polishing component 3 and the second sanding belt polishing component 4 in the workpiece coordinate system.

[0047] The transformation matrices of the coordinate systems of the first robot 1 and the second robot 2 relative to the workpiece coordinate system are measured using a laser tracker. The transformation matrices of the first belt polishing assembly 3 and the second belt polishing assembly 4 relative to the center of the end effector 6 of their respective robots are then calibrated. The coordinate systems of the first robot 1, the second robot 2, the first belt polishing assembly 3, and the second belt polishing assembly 4 are all unified to the same workpiece coordinate system, and the belt linear velocity of the first belt polishing assembly 3 and the second belt polishing assembly 4 is obtained. The direction in the workpiece coordinate system.

[0048] S2: Select a substrate of the same material as optical element 7 and perform point polishing on it. The first belt polishing assembly 3 is used to remove material, and the second belt polishing assembly 4 is used to smooth the texture. Control the belt linear velocity directions of the first belt polishing assembly 3 and the second belt polishing assembly 4 to be orthogonal. Calibrate the first removal function corresponding to the first belt polishing assembly 3 and the second removal function corresponding to the second belt polishing assembly 4, and establish the first removal function matrix corresponding to the first removal function. and the second removal function matrix corresponding to the second removal function Step S2 includes the following steps: S21: Control the first belt polishing assembly 3 and the second belt polishing assembly 4 to perform point polishing on the workpiece to be plated sequentially using the same polishing parameters, and use an interferometer to measure its removal profile to obtain the first removal function corresponding to the first belt polishing assembly 3. and the second removal function corresponding to the second abrasive belt polishing component 4 The abrasive belt linear velocity direction of the first abrasive belt polishing component 3 is orthogonal to the abrasive belt linear velocity direction of the second abrasive belt polishing component 4.

[0049] First removal function The cross-section along the feed direction exhibits a "wide and shallow" characteristic, with its effective bandwidth determined by the width of the abrasive belt. Second removal function. It exhibits a "narrow and deep" characteristic in the cross-section along the feed direction, and its effective bandwidth is determined by the indentation length of the contact wheel in the belt polishing assembly.

[0050] The dual-mode removal function, consisting of the first removal function and the second removal function, is as follows: Figure 3 As shown in the figure, R1 represents the first removal function and R2 represents the second removal function.

[0051] S22: For the first removal function Second removal function Normalization is performed separately to obtain the first removal function matrix corresponding to the first removal function. and the second removal function matrix corresponding to the second removal function .

[0052] S3: Obtain the original wavefront data of the surface of optical element 7, map the original wavefront data onto the workpiece coordinate system, and obtain the surface shape error distribution matrix to be corrected. The target removal amount for optical element 7.

[0053] A laser interferometer or a high-precision profilometer is used to perform full-aperture measurements on the surface of optical element 7 to obtain the original wavefront data of the surface of optical element 7. Rigid body displacement terms such as tilt and defocus are removed through wavefront fitting, and the original wavefront data is mapped onto the mesh nodes of the workpiece coordinate system using an interpolation algorithm to obtain the surface shape error distribution matrix to be corrected. The target removal amount for optical element 7.

[0054] S4: Design a continuous machining trajectory shared by the first robot 1 and the second robot 2 in the workpiece coordinate system. Based on the continuous machining trajectory, plan the end postures of the first robot 1 and the second robot 2 at each machining trajectory point, ensuring that the linear velocity direction of the abrasive belt of the first abrasive belt polishing component 3 is always perpendicular to the feed direction, and the linear velocity direction of the abrasive belt of the second abrasive belt polishing component 4 is always parallel to the feed direction. The continuous machining trajectory is a continuous grating machining trajectory, such as... Figure 3 As shown in the figure, Tra represents the continuous grating processing trajectory. Step S4 includes the following steps: S41: Design a continuous machining trajectory shared by the first robot 1 and the second robot 2 in the workpiece coordinate system, and discretize the continuous machining trajectory into several machining trajectory points. ,in, , N This represents the total number of processing trajectory points.

[0055] S42: Calculate each machining trajectory point Unit tangential feed vector at the location The calculation formula is as follows: (13); Among them, the trajectory endpoints of the processing trajectory points adopt one-sided difference, while the non-trajectory endpoints adopt center difference.

[0056] S43: Set machining trajectory points The unit outward normal feed vector at the location is Assume the contact direction of the first abrasive belt polishing component 3 is along Direction, the direction of the linear velocity of the abrasive belt in the first abrasive belt polishing component 3. Let it be the feed vector perpendicular to the unit tangential direction in the tangential plane. The direction, satisfy Then, the target posture rotation matrix corresponding to the first robot 1. for Rotate the target attitude matrix After performing quaternion transformation, the end-effector quaternion of the first robot 1 is obtained. .

[0057] S44: Let the direction of the abrasive belt linear velocity of the second abrasive belt polishing component 4 be... Unit tangential feed vector The direction corresponds to the target posture rotation matrix of the second robot 2. for Rotate the target attitude matrix After performing quaternion transformation, the end-effector quaternion of the second robot 2 is obtained. .

[0058] In some embodiments, the quaternion transformation processing method can be the classic transformation method of finding quaternions from rotation matrices, namely the Shepperd method.

[0059] S5: Combine with the first removal function matrix Second removal function matrix A convolutional superposition model is established, and a multi-objective optimization functional is constructed based on the convolutional superposition model to solve the optimal dwell time sequence of the first robot 1 and the second robot 2. The feed rate of the first robot 1 and the second robot 2 at each processing trajectory point is calculated according to the optimal dwell time sequence.

[0060] The present invention utilizes a collaborative removal strategy in which a first robot 1 and a second robot 2 perform orthogonal postures on the same continuous processing trajectory. The physical process of material removal no longer follows a simple linear superposition, but is based on a spatiotemporal coupled convolutional model.

[0061] Step S5 includes the following steps: S51: Combining the first removal function matrix Second removal function matrix Establish a convolution stacking model and convert the total removal matrix Defined as the linear superposition of the two convolution processes, the convolution superposition model is: (14); in, This is the matrix representing the total removal amount of optical element 7 predicted by a convolutional stacking model based on a preset dwell time. and These are the dwell time vectors of the first robot 1 and the second robot 2 at the same processing trajectory point, respectively.

[0062] S52: Construct a multi-objective optimization functional based on a convolution stacking model. The multi-objective optimization functional is: (15); in, Let be the objective functional value to be minimized; These are the weighting coefficients for balancing the surface accuracy term and the intermediate frequency suppression term; It is a two-dimensional discrete Fourier transform operator used to map residuals to the frequency domain; Weights for a bandpass filter designed for the step frequency of a continuous machining trajectory; first term For spatial domain residuals, ensure that the surface shape accuracy meets the standards; the second item This is a frequency domain suppression term, which forces the algorithm to automatically increase the dwell time vector of the second robot 2 in the regions where raster textures are generated. Perform smoothing.

[0063] It should be noted that, and All are material removal depth distribution matrices on the surface of optical element 7: It is the target removal amount (i.e., the optimized input target) obtained from the measured surface shape error. This is the total amount of data that will actually be removed (i.e., the optimized, controllable output) predicted by a convolutional stacking model based on the planned preset dwell time. Subsequent multi-objective optimization then drives... Approaching The smaller the residual between the two, the better the surface convergence.

[0064] S53: The trust region reflection algorithm is used to iteratively solve the multi-objective optimization functional. Under the premise of satisfying the non-negativity constraint of the dwell time, the value at the processing trajectory point is obtained. The optimal dwell time sequence of the first robot 1 at location 1 Optimal dwell time series of the second robot 2 ; S54: Based on the optimal dwell time sequence of the first robot 1 and the second robot 2, calculate the dwell time at each machining trajectory point. The feed rate of the first robot 1 Feed rate of the second robot 2 The calculation formula is as follows: (16); (17); in, For adjacent machining trajectory points on a continuous machining trajectory and The arc length between (i.e., the machining trajectory points) (corresponding path element length). , These are the machining trajectory points of the first robot 1 and the second robot 2 obtained from the optimization solution. The optimal residence time series at a given location, i.e., the residence time vector. , The Each component. Because the first and second removal functions have different forms and need to be independently proportioned to achieve mid-frequency selective smoothing, the optimal dwell times of the first robot 1 and the second robot 2 at the same processing trajectory point are generally not equal (i.e., ...). Therefore, the feed speeds of the first robot 1 and the second robot 2 at the same processing trajectory point are generally different; the first robot 1 and the second robot 2 only share the same continuous processing trajectory and end-effector posture planning, and the second robot 2 runs behind the first robot 1 by a preset time to avoid collision.

[0065] Based on the calculated feed rates obtained from equations (16) and (17), the specific settings for the feed rates of the first robot 1 and the second robot 2 at each machining trajectory point are as follows: If the feed speed of the first robot 1 Not greater than its limit speed threshold Then the feed speed of the first robot 1 is set to ;like Then the feed speed of the first robot 1 is set to At the same time, reduce the belt speed of the first robot 1 at the processing trajectory point. Or reduce cylinder pressure To ensure that the amount of material removed remains constant; If the feed speed of the second robot 2 Not greater than its limit speed threshold Then the feed speed of the second robot 2 is set to ;like Then the feed speed of the second robot 2 is set to At the same time, reduce the belt speed of the second robot 2 at this processing trajectory point. Or reduce cylinder pressure This ensures that the amount of material removed remains constant.

[0066] S6: The continuous processing trajectory, the end poses of the first robot 1 and the second robot 2, and the feed speeds of the first robot 1 and the second robot 2 at each processing trajectory point are converted into motion / attitude control files for the first robot 1 and the second robot 2. The first robot 1 starts first, and the second robot 2 starts after a preset time, thus completing the dual-robot collaborative belt orthogonal polishing process.

[0067] Using the central collaborative control module 8 to synchronously issue the corresponding instructions of the control file, the dual-robot collaborative belt orthogonal polishing system is started. The first robot 1, equipped with the first belt polishing component 3, performs an orthogonal infeed posture, which is the first to start as the main material removal process, responsible for removing most of the surface shape error material. The second robot 2, equipped with the second belt polishing component 4, performs a parallel infeed posture, which is the smoothing texture process. The second robot 2 starts after the first robot 1 by a preset time. The preset time is obtained based on the preset safe distance between the second robot 2 and the first robot 1 in space, so as to complete the dual-robot collaborative belt orthogonal polishing process.

[0068] The dual-robot collaborative belt orthogonal polishing method provided in this embodiment further includes step S7 after step S6: detecting the residual surface shape error of the processed optical element 7, calculating the root mean square error (RMS) of the residual surface shape error, and completing the polishing process of the optical element 7 if the RMS is less than a preset threshold; if the RMS is greater than or equal to the preset threshold, the residual surface shape error is used as the new target removal amount of the optical element 7, and steps S5 and S6 are repeated until the RMS of the residual surface shape error is less than the preset threshold.

[0069] In some embodiments, during the polishing process, the Euclidean distance between the center of the first belt polishing component 3 and the center of the second belt polishing component 4 is calculated in real time. The calculation formula is: (18); in, , These are the real-time coordinates of the center of the first belt polishing component 3 and the center of the second belt polishing component 4 in the workpiece coordinate system. The belt orthogonal polishing system is immediately stopped when the Euclidean distance is less than a preset safety distance threshold.

[0070] In some embodiments, the relative attitude angle of the dual-robot cooperative belt orthogonal polishing method provided in this embodiment can be arbitrarily set or adjusted, that is, it is not limited to strict orthogonality. ) and parallel ( ( ), or any combination of angles that can form complementary shapes of the removed functions.

[0071] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0072] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A dual-robot collaborative belt orthogonal polishing system, comprising: A first robot, a second robot, a first belt polishing assembly, a second belt polishing assembly, and a workpiece table; the first robot and the second robot are respectively disposed on both sides of the workpiece table, the first belt polishing assembly is fixedly installed on the end effector of the first robot, the second belt polishing assembly is fixedly installed on the end effector of the second robot, and an optical element to be processed is fixedly clamped on the workpiece table; The system is characterized in that the orthogonal polishing system further includes a central collaborative control module, which controls the first robot and the second robot to polish the optical element using a pre-designed continuous processing trajectory shared by the first robot and the second robot, a pre-planned end posture of the first robot and the second robot at each processing trajectory point, and a set feed speed of the first robot and the second robot at each processing trajectory point. During the polishing process, the system controls the abrasive belt linear velocity direction of the first abrasive belt polishing component to be orthogonal to the abrasive belt linear velocity direction of the second abrasive belt polishing component.

2. The dual-robot collaborative belt orthogonal polishing system according to claim 1, characterized in that, The central collaborative control module includes a removal function calibration unit, a removal function matrix establishment unit, a convolution superposition model establishment unit, a multi-objective optimization functional construction unit, a feed rate calculation unit, and a feed rate setting unit. The removal function calibration unit is used to calibrate a first removal function corresponding to the first abrasive belt polishing component and a second removal function corresponding to the second abrasive belt polishing component, wherein the abrasive belt linear velocity direction of the first abrasive belt polishing component and the abrasive belt linear velocity direction of the second abrasive belt polishing component are orthogonal to each other. The removal function matrix establishment unit is used to establish a first removal function matrix corresponding to the first removal function and a second removal function matrix corresponding to the second removal function; The convolution stacking model building unit is used to combine the first removal function matrix and the second removal function matrix to build a convolution stacking model. The multi-objective optimization functional construction unit is used to construct a multi-objective optimization functional based on the convolution stacking model. The feed rate calculation unit is used to iteratively solve the multi-objective optimization functional using the trust region reflection algorithm to obtain the optimal dwell time sequence of the first robot and the second robot at each processing trajectory point; and then calculates the feed rate of the first robot and the second robot at each processing trajectory point according to the optimal dwell time sequence. The feed rate setting unit is used to set the feed rate of the first robot and the second robot at each processing trajectory point based on the feed rate of the first robot and the second robot at each processing trajectory point calculated by the feed rate calculation unit, and the corresponding limit speed threshold.

3. The dual-robot collaborative belt orthogonal polishing system according to claim 1, characterized in that, Both the first robot and the second robot are six-degree-of-freedom robotic arms.

4. A dual-robot collaborative belt orthogonal polishing method, implemented based on the belt orthogonal polishing system described in any one of claims 1 to 3, characterized in that, Includes the following steps: S1: Calibrate the coordinate transformation relationship of the first robot coordinate system, the second robot coordinate system, the first belt polishing component coordinate system, and the second belt polishing component coordinate system relative to the same workpiece coordinate system, and obtain the belt linear velocity direction of the first belt polishing component and the second belt polishing component in the workpiece coordinate system; S2: Select a substrate of the same material as the optical element and perform point polishing on it. The first belt polishing assembly is used to remove material, and the second belt polishing assembly is used to smooth the texture. Control the belt linear velocity directions of the first and second belt polishing assemblies to be orthogonal. Calibrate the first removal function corresponding to the first belt polishing assembly and the second removal function corresponding to the second belt polishing assembly, and establish a first removal function matrix corresponding to the first removal function. and the second removal function matrix corresponding to the second removal function ; S3: Obtain the original wavefront data of the optical element surface, map the original wavefront data onto the workpiece coordinate system, and obtain the surface shape error distribution matrix to be corrected. , as the target removal amount of the optical element; S4: Design a continuous machining trajectory shared by the first robot and the second robot in the workpiece coordinate system, and plan the end posture of the first robot and the second robot at each machining trajectory point based on the continuous machining trajectory, so that the abrasive belt linear velocity direction of the first abrasive belt polishing component is always perpendicular to the feed direction, and the abrasive belt linear velocity direction of the second abrasive belt polishing component is always parallel to the feed direction. S5: Combine the first removal function matrix and the second removal function matrix A convolutional superposition model is established, and a multi-objective optimization functional is constructed based on the convolutional superposition model. The optimal dwell time sequence of the first robot and the second robot is solved, and the feed rate of the first robot and the second robot at each processing trajectory point is calculated according to the optimal dwell time sequence. S6: The continuous processing trajectory, the end poses of the first robot and the second robot, and the feed speed of the first robot and the second robot at each processing trajectory point are converted into motion / attitude control files for the first robot and the second robot. The first robot starts first, and the second robot starts after a preset time delay, thus completing the dual-robot collaborative belt orthogonal polishing process.

5. The dual-robot collaborative belt orthogonal polishing method according to claim 4, characterized in that, Step S2 includes the following steps: S21: Control the first and second abrasive belt polishing components to perform point polishing on the slated workpieces sequentially using the same polishing parameters, thereby obtaining a first removal function corresponding to the first abrasive belt polishing component and a second removal function corresponding to the second abrasive belt polishing component; wherein, the abrasive belt linear velocity direction of the first abrasive belt polishing component and the abrasive belt linear velocity direction of the second abrasive belt polishing component are orthogonal to each other; S22: Normalize the first removal function and the second removal function respectively to obtain the first removal function matrix corresponding to the first removal function. and the second removal function matrix corresponding to the second removal function .

6. The dual-robot collaborative belt orthogonal polishing method according to claim 4, characterized in that, Step S4 includes the following steps: S41: Design a continuous machining trajectory shared by the first robot and the second robot in the workpiece coordinate system, and discretize the continuous machining trajectory into several machining trajectory points. ,in, , N The total number of the processing trajectory points; S42: Calculate each machining trajectory point Unit tangential feed vector at the location The calculation formula is as follows: ； Among them, the trajectory endpoints of the processing trajectory points adopt one-sided difference, and the non-trajectory endpoints adopt center difference; S43: Set machining trajectory points The unit outward normal feed vector at the location is Assume the contact direction of the first abrasive belt polishing assembly is along Direction, the direction of the linear velocity of the abrasive belt in the first abrasive belt polishing assembly. Let it be the feed vector perpendicular to the unit tangential direction in the tangential plane. The direction, satisfy Then, the target pose rotation matrix corresponding to the first robot for Rotate the target attitude matrix After performing quaternion transformation, the end-effector quaternion of the first robot is obtained. ; S44: Let the direction of the abrasive belt linear velocity of the second abrasive belt polishing assembly be... Unit tangential feed vector The direction corresponds to the target pose rotation matrix of the second robot. for Rotate the target attitude matrix After performing quaternion transformation, the end-effector quaternion of the second robot is obtained. .

7. The dual-robot cooperative belt orthogonal polishing method according to claim 4, characterized in that, Step S5 includes the following steps: S51: Combining the first removal function matrix Second removal function matrix Establish a convolution stacking model, wherein the convolution stacking model is as follows: ； in, This is the total removal matrix of the optical element predicted by the convolutional stacking model according to a preset dwell time. and These are the dwell time vectors for the first robot and the second robot, respectively; S52: Construct a multi-objective optimization functional based on the convolution stacking model, wherein the multi-objective optimization functional is: ； in, Let be the objective functional value to be minimized; These are the weighting coefficients for balancing the surface accuracy term and the intermediate frequency suppression term; It is a two-dimensional discrete Fourier transform operator used to map residuals to the frequency domain; Weights for the bandpass filter designed for the step frequency of the continuous machining trajectory; S53: The trust region reflection algorithm is used to iteratively solve the multi-objective optimization functional to obtain the value at the processing trajectory point. The optimal dwell time sequence of the first robot at the location And the optimal dwell time sequence of the second robot ; S54: Based on the optimal dwell time sequence of the first robot and the second robot, calculate the time at each processing trajectory point. The feed speed of the first robot The feed speed of the second robot The calculation formula is as follows: ； ； in, Adjacent machining trajectory points on the continuous machining trajectory and The arc length between; If the feed speed of the first robot Not greater than its limit speed threshold The feed speed of the first robot is then set to... ;like The feed speed of the first robot is then set to... At the same time, reduce the belt speed of the first robot at that processing trajectory point. Or reduce cylinder pressure To ensure that the amount of material removed remains constant; If the feed speed of the second robot Not greater than its limit speed threshold The feed speed of the second robot is then set to... ;like The feed speed of the second robot is then set to... At the same time, reduce the belt speed of the second robot at that processing trajectory point. Or reduce cylinder pressure This ensures that the amount of material removed remains constant.

8. The dual-robot collaborative belt orthogonal polishing method according to claim 4, characterized in that, After step S6, step S7 is also included: detecting the residual surface shape error of the processed optical element, calculating the root mean square error of the residual surface shape error, and if the root mean square error is less than a preset threshold, then the polishing process of the optical element is completed. If the root mean square error is greater than or equal to the preset threshold, then the residual surface error is used as the new target removal amount of the optical element, and steps S5 and S6 are repeated until the root mean square error of the residual surface error is less than the preset threshold.

Images