A high-precision polishing method for a cylindrical aspherical optical element based on a mechanical arm

Abstract

The application discloses a kind of high-precision polishing method of cylindrical aspherical optical element based on mechanical arm, comprising the following steps:1) for the high-precision coordinate system space error compensation of cylindrical asphere processed by mechanical arm: obtain dynamic processing information by real-time acquisition of multiple sensors, and automatically adjust processing pose according to the dynamic processing information to keep processing state consistency, finally obtain the cylindrical aspherical element of set precision;2) for the further error compensation of cylindrical asphere processed after compensation coordinate system based on profilometer and three-coordinate measurement: for the reference inconsistency problem caused by profilometer measurement principle, the model is established based on the reference of three-coordinate measuring instrument and profilometer combination;Wherein high-precision measurement analysis calculation model is proposed based on profilometer measurement result, for compensating high-precision surface precision;The deviation of space coordinate system is calculated by the deviation of compensation position in the initial compensation based on profilometer, and closed-loop compensation is completed.

Description

Technical Field

[0001] This invention belongs to the field of precision and ultra-precision machining of robotic arms, specifically relating to a high-precision polishing method for cylindrical aspherical optical elements based on robotic arms. Background Technology

[0002] Polishing optical components using robotic arms is a very important and valuable research process, especially for long cylindrical and aspherical surfaces. There is no unified evaluation standard for the surface accuracy of these surfaces, and maintaining a certain level of precision and consistency during processing compensation is very challenging.

[0003] Due to the inherent precision limitations of the robotic arm and the high precision requirements of optical components, this process remains technically challenging. Currently, this field suffers from drawbacks such as low machining accuracy, cumbersome robotic arm control, high cost, low machining efficiency, and difficulties in process planning and compensation. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by providing a high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm.

[0005] The present invention is achieved using the following technical solution:

[0006] A high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm includes the following steps:

[0007] 1) Spatial error compensation for high-precision coordinate system of cylindrical and aspherical surfaces for robotic arm machining

[0008] Dynamic processing information is acquired in real time by multiple sensors, and the processing posture is automatically adjusted according to the dynamic processing information to maintain the consistency of the processing state, and finally a cylindrical non-spherical component with a set accuracy is obtained.

[0009] 2) Further error compensation based on profilometer and coordinate measuring machine for cylindrical and aspherical surfaces machined using a compensated coordinate system.

[0010] To address the issue of inconsistent benchmarks caused by the profilometer's measurement principle, a model is established based on a benchmark combining a coordinate measuring machine and a profilometer. A high-precision measurement analysis and calculation model is proposed based on the profilometer's measurement results to compensate for high-precision surface accuracy. The deviation of the calculation space coordinate system is fed back by the deviation of the compensation position in the initial compensation of the profilometer, thus completing closed-loop compensation.

[0011] A further improvement of this invention is that, in step 1), the spatial error compensation for the high-precision coordinate system of the cylindrical aspherical surface processed by the robotic arm includes the following:

[0012] 101) In order to reduce the machining error caused by position error, posture error and repeatability error of the robotic arm, a three-dimensional force sensor, accelerometer and rotary encoder are used to record and feed back the motion state of the robotic arm, so as to design a control system to achieve high-precision end control;

[0013] 102) The evaluation method for polishing accuracy of cylindrical aspherical surfaces is divided into two parts: generatrix direction and cylindrical direction. The generatrix direction refers to the direction perpendicular to the central axis of the cylindrical surface, and the cylindrical direction refers to the direction along the central axis of the cylindrical surface. Specifically, it includes: the generatrix surface accuracy PV value, the generatrix surface quality roughness, and the consistency between the cylindrical direction roughness and the generatrix. Among them, the generatrix surface accuracy PV value and the generatrix surface quality roughness are used to evaluate the polishing accuracy of the aspherical generatrix, that is, the polishing accuracy in the two-dimensional direction of the generatrix. This parameter affects the focusing ability, imaging distortion, and astigmatism effect of the aspherical surface. The cylindrical direction roughness and the consistency between the generatrix are used to evaluate the polishing accuracy in the cylindrical direction. The generatrix consistency refers to the consistency of the surface accuracy of different generatrixes along the cylindrical axis and the consistency of the surface morphology feature positions along the generatrix direction. This parameter affects the transmittance, reflectance, or absorptivity of optical elements.

[0014] 103) A high-precision multi-process robotic arm coordinate system establishment method, namely an error-progressive tool setting method from coarse coordinate system establishment to fine coordinate system establishment, includes three steps: First, the robotic arm end effector is used to coarsely establish the workpiece coordinate system. Due to the low positioning accuracy of the robotic arm, there is an error of 20-30 micrometers in this step, including deviations in three directions and three positions. Second, a dial indicator is used to accurately measure the deviations in the three directions, controlling the error to the micrometer level. Finally, a laser tracker is used to calibrate the relative position between the robotic arm end effector and the workpiece, thereby obtaining the three position deviations. Through the three-step progressive calibration, a high-precision workpiece coordinate system is obtained.

[0015] A further improvement of the present invention is that, in step 1), 101), a three-dimensional force sensor is set at the end of the robotic arm to collect the magnitude of the polishing force.

[0016] A further improvement of the present invention is that, in step 1), 101), an accelerometer is installed at the end of the robotic arm to collect the end-effector velocity.

[0017] A further improvement of the present invention is that, in step 1), 101), a rotary encoder is installed on the shaft joint to collect the rotation information of the robotic arm shaft, i.e., the attitude information.

[0018] A further improvement of this invention is that, after the multi-sensor acquisition method, a feedback control system is designed based on the data, namely an adaptive control method, which makes real-time adjustments based on the dynamic multi-fusion data of the system to achieve ideal end-effector motion accuracy; wherein the input signals are force feedback signals, angle feedback signals and speed feedback signals, and force control algorithms and PID controllers are used for specific control implementation, specifically, the spatial position of the robotic arm is adjusted according to the existing pose of the robotic arm and the parameters of the polishing head to ensure constant polishing pressure.

[0019] A further improvement of this invention is that, in step 1), step 103), the step of coarsely establishing the workpiece coordinate system at the end of the robotic arm is as follows: the center position of the spherical polishing head at the end of the robotic arm is replaced by the tool tip, and the three endpoints of the upper surface of the cylindrical non-spherical surface are recorded to construct the coordinate system; the step of measuring the directional deviation with a dial indicator is as follows: a dial indicator is installed at the end of the robotic arm using a magnetic base, and the dial indicator is used to measure the x, y, and z directions of movement between the robotic arm and the clamping tool table, respectively, to obtain the movement distance and the dial indicator reading, thereby calculating the deflection angles in the three directions; the relative position between the end of the robotic arm tool and the workpiece is measured using a laser tracker to obtain the three position offsets;

[0020] The offset of the coordinate point cloud is calculated based on the measurement offset results. Let the angular deviations measured along the x, y, and z axes be α, β, and γ, respectively, that is:

[0021]

[0022] In the formula, Δh x Δh y Δh z Let dx, dy, and dz be the differences in per mille, respectively, and dx, dy, and dz be the distances traveled by the robotic arm along the x, y, and z axes, respectively; then the rotation matrix R xyz for:

[0023]

[0024] The compensated point cloud coordinates are:

[0025]

[0026] A further improvement of this invention is that, in step 2), the error compensation method for polishing cylindrical aspherical surfaces by a robotic arm based on a profilometer and coordinate measuring machine includes the following:

[0027] 201) A method for high-precision compensation machining of a robotic arm by combining a profilometer and a coordinate measuring machine; specifically, the profilometer measures the surface error data of the aspherical cylindrical surface in the direction of the generatrix to guide the compensation machining, and the coordinate measuring machine measures the highest point of the aspherical cylindrical surface to calibrate the consistency of the profilometer's measurement datum, that is, the generatrix datum position of the profilometer is offset according to the position of the highest point measured by the coordinate measuring machine, so as to calculate the positional relationship of the generatrix feature points;

[0028] 202. High-precision spatial error feedback compensation model for cylindrical aspherical surfaces based on a profilometer; specifically, feedback compensation calculation is performed based on the positional deviation of the first compensation by the profilometer; assuming the initial point cloud coordinates are (x0, y0, z0), and the actual machining position point cloud coordinates after force control compensation are (x, y, z), and the offset along the vertical direction has no significant error impact on the polishing process, let the offset errors on the y and z axes be Δy and Δz, and the tilt angle of the robotic arm pose at this point be k. Then, based on the known pose of the robotic arm, the coordinates of the two theoretical points and the actual point of the profilometer, and the aspherical surface formula, the process parameter d is obtained. According to the trigonometric relationship, we can obtain:

[0029]

[0030] In the formula, d1 and d2 are the process parameters for the two compensation positions, k1 and k2 are the tilt angles of the robotic arm for the two compensation positions, and we have:

[0031]

[0032] 203) The error compensation calculation method based on the single busbar measurement data of the profilometer is as follows: Feature value extraction is performed, including maximum and minimum points; the difference between the maximum and minimum points and the material removal rate of the polishing head are calculated for high-precision compensation polishing; the second derivative of the profilometer measurement data is calculated using the finite difference method, and a compensation polishing method of removing superposition is adopted at the maximum point where the second derivative is large, i.e., multi-path compensation polishing is performed at the maximum point; the number of paths n is also related to the second derivative, thus ensuring the smoothness index of the optical element; the threshold f″(x0) of the second derivative is related to the contact removal area a of the polishing head, the target compensation error Δy0, and the smoothness requirements of the material, and the superposition compensation range Δx at the maximum point is related to the magnitude of the second derivative, i.e.

[0033]

[0034] Where n≥1, Δx≥0, the total length of single-point compensation d=n*Δx; k1, k2, k3 are parameter influence coefficients, which are obtained by quantitative experiments.

[0035] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0036] This invention provides a high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm. It belongs to the theory of machining error in robotic arm polishing and proposes a high-precision spatial error model and compensation method. By combining multiple sensors and multiple error compensation methods for different coordinate systems, and finally combining the measurement data of a profilometer, a certain machining accuracy is achieved.

[0037] The above technologies improve the error compensation accuracy and efficiency of robotic arm polishing. The repeatability of the robotic arm is 20μm, and submicron-level surface accuracy can be achieved through high-precision polishing methods. Attached Figure Description

[0038] Figure 1 This is a high-precision spatial error compensation model for cylindrical aspherical surfaces based on a robotic arm in this embodiment of the invention;

[0039] Figure 2 This is a high-precision spatial error compensation model for cylindrical aspherical surfaces based on a robotic arm, as described in this embodiment of the invention; wherein... Figure 2 (a) Steps for roughly establishing the coordinate system for the robotic arm. Figure 2 (b) Steps for establishing a coordinate system for a dial indicator;

[0040] Figure 3 This is a feedback error compensation model based on a profilometer in an embodiment of the present invention; wherein... Figure 3 (a) is the compensation model for measurement results of a single busbar. Figure 3 (b) A compensation model that takes into account the inclination angle of the polishing tool;

[0041] Figure 4 This is an error compensation model for the polishing of cylindrical and aspherical surfaces by a robotic arm based on a profilometer and coordinate measuring machine in an embodiment of the present invention.

[0042] Figure 5 Measurements before and after a single cycle;

[0043] Figure 6 This is a diagram of the surface profile of a cylindrical aspherical surface, where... Figure 6 (a) before fine polishing, Figure 6 (b) after fine polishing. Detailed Implementation

[0044] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0045] This invention provides a high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm, comprising the following steps:

[0046] 1) A method for compensating spatial errors in a high-precision coordinate system for cylindrical and aspherical surfaces processed by robotic arms.

[0047] A method for evaluating the machining accuracy of cylindrical aspherical surfaces is proposed. A novel method for establishing the coordinate system of a high-precision multi-process robotic arm is also proposed, namely, an error-progressive tool setting method from coarse coordinate system to fine coordinate system, combined with point cloud offset calculation based on measurement results. A method combining sensor fusion and adaptive control is proposed to improve the polishing motion accuracy of the robotic arm. Machining information is acquired in real time by multiple sensors, and the machining posture is automatically adjusted according to the dynamic information to maintain the consistency of the machining state, ultimately obtaining cylindrical aspherical components with a certain accuracy.

[0048] 2) For cylindrical aspherical surfaces processed by the compensation coordinate system, a further error compensation method based on profilometer and coordinate measuring machine is proposed.

[0049] After the components achieve a certain level of accuracy through coordinate system compensation, measurement feedback-based error compensation is used to further improve accuracy. Addressing the issue of inconsistent benchmarks caused by the profilometer's measurement principle, a benchmark establishment model combining a coordinate measuring machine (CMM) and a profilometer is proposed. A high-precision spatial error feedback compensation model for cylindrical and aspherical surfaces based on the profilometer is also proposed. The deviation of the spatial coordinate system is calculated based on the deviation of the compensation position during the initial compensation by the profilometer, completing closed-loop compensation. A high-precision measurement analysis and calculation model is proposed based on the profilometer measurement results to compensate for high-precision surface accuracy. Finally, an optimization method for the machining process is guided by the error compensation principle.

[0050] Step 1) Propose a high-precision spatial error compensation method for cylindrical aspherical surfaces based on a robotic arm, including the following:

[0051] 101) A method for evaluating the polishing accuracy of cylindrical aspherical surfaces is proposed. It is mainly divided into two parts: the generatrix direction and the cylindrical direction. The generatrix direction refers to the direction perpendicular to the central axis of the cylindrical surface, while the cylindrical direction refers to the direction along the central axis of the cylindrical surface. Specifically, it includes: the PV value of the generatrix surface profile accuracy, the surface roughness of the generatrix surface quality, and the surface profile consistency in the cylindrical direction. Among these, the PV value and roughness generatrix parameter of the cylindrical aspherical surface are used to evaluate the polishing accuracy of the aspherical generatrix, i.e., the polishing accuracy in the two-dimensional direction of the generatrix. This parameter mainly affects the focusing ability, imaging distortion, and astigmatism effect of the aspherical surface. The cylindrical direction roughness and generatrix consistency are used to evaluate the polishing accuracy in the cylindrical direction. Generatrix consistency refers to the consistency of the surface profile accuracy and the consistency of the surface morphology feature positions along the generatrix direction for different generatrixes along the cylindrical axis. This parameter mainly affects the transmittance, reflectance, or absorptivity of optical elements.

[0052] 102) A novel high-precision multi-process robotic arm coordinate system establishment method is proposed, namely, an error-progressive tool setting method from coarse coordinate system establishment to fine coordinate system establishment. Due to the low motion accuracy of robotic arms, a high-precision coordinate system establishment method is proposed, mainly including three steps: First, a coarse workpiece coordinate system is established using the robotic arm end effector. This step has a relatively large error of 20-30 micrometers due to the low positioning accuracy of the robotic arm, mainly due to deviations in three directions and three positions. Second, a dial indicator is used to accurately measure the deviations in the three directions, controlling the error to the micrometer level. Finally, a laser tracker is used to calibrate the relative position between the robotic arm end effector and the workpiece, thereby obtaining the three position deviations. Through these three progressive calibration steps, a high-precision workpiece coordinate system is obtained. See attached details. Figure 1 As shown.

[0053] Specifically, the steps for establishing the workpiece coordinate system at the end of the robotic arm are as follows: replace the center position of the spherical polishing head at the end of the robotic arm with the tool tip, and record the three endpoints of the cylindrical and aspherical surfaces to construct the coordinate system; the steps for measuring the directional deviation with a dial indicator are as follows: install a dial indicator on a magnetic base at the end of the robotic arm, and perform dial indicator measurements in the x, y, and z directions of movement between the robotic arm and the clamping tool table to obtain the movement distance and dial indicator readings, thereby calculating the deflection angles in the three directions; use a laser tracker to measure the relative position between the end of the robotic arm tool and the workpiece to obtain the three position offsets.

[0054] Furthermore, the offset of the coordinate point cloud is calculated based on the measurement offset results. Let the angular deviations measured along the x, y, and z axes be α, β, and γ, respectively, that is:

[0055]

[0056] In the formula, Δh x Δh y Δh zLet denoted as the difference in per mille, and dx, dy, and dz be the distances traveled by the robotic arm along the x, y, and z axes, respectively. Then the rotation matrix R... xyz for:

[0057]

[0058] The compensated point cloud coordinates are:

[0059]

[0060] 103) A method combining sensor fusion and adaptive control is proposed to improve the polishing motion accuracy of the robotic arm. After high-precision compensation, in order to reduce the processing error caused by position error, posture error and repeatability error of the robotic arm, a three-dimensional force sensor, accelerometer and rotary encoder are proposed to record and feed back the motion state of the robotic arm, so as to design a control system to achieve high-precision end control.

[0061] Specifically, a three-dimensional force sensor is installed at the end of the robotic arm to collect the magnitude of the polishing force; an accelerometer is also installed at the end of the robotic arm to collect the end-effector velocity; and a rotary encoder is installed on the axis joint to collect the robotic arm's axis rotation information, i.e., attitude information. In summary, by using multiple different types of sensors, i.e., a sensor fusion method, the data is integrated to obtain the actual motion posture of the robotic arm.

[0062] Specifically, after designing a multi-sensor acquisition method, a feedback control system, i.e., an adaptive control method, is designed based on the data. This system makes real-time adjustments based on the dynamic multi-fusion data to achieve the ideal end-effector motion accuracy. The input signals include force feedback, angle feedback, and velocity feedback signals, and force control algorithms and PID controllers are used for specific control implementation.

[0063] Step 2) Proposes an error compensation method for polishing cylindrical aspherical surfaces using a robotic arm based on a profilometer and coordinate measuring machine, including the following:

[0064] (201) A method for high-precision compensation machining of robotic arms is proposed, combining a profilometer and a coordinate measuring machine (CMM). Specifically, the profilometer can measure the surface error data along the generatrix direction of a cylindrical aspherical surface to guide compensation machining. However, due to the measurement principle of the profilometer, the measurement reference positions of different generatrixes of the cylindrical aspherical surface will be different. Therefore, it is proposed to use a CMM to measure the highest point of the cylindrical aspherical surface to calibrate the consistency of the profilometer's measurement reference. That is, the generatrix reference position of the profilometer is offset according to the position of the highest point measured by the CMM, thereby calculating the positional relationship of the generatrix feature points.

[0065] 202) A high-precision spatial error feedback compensation model for cylindrical aspherical surfaces based on a profilometer is proposed. Specifically, the implementation method of positive error control was provided above. Feedback compensation calculation is then performed based on the positional deviation compensated by the profilometer in its first compensation. This model is shown in the attached figure. Figure 2 As shown. This model primarily considers the impact of offset on the compensation position. Based on a structural design combining an end-effector 3D force sensor with robotic arm pose control for polishing force, this model solves the problem of complex contact states caused by tool head position offset in actual machining. Let the initial point cloud coordinates be (x0, y0, z0), and the actual machining position point cloud coordinates after force control compensation be (x, y, z). Since the offset along the vertical direction has no significant error impact on polishing, let the offset errors on the y and z axes be Δy and Δz, and the robotic arm pose tilt angle at this point be k. Then, based on the known robotic arm pose, the coordinates of the two theoretical points and the actual point of the profilometer, and the aspherical formula, the process parameter d in the figure is obtained. According to the trigonometric relationship, we can obtain:

[0066]

[0067] In the formula, d1 and d2 are the process parameters for the two compensation positions, as shown in the attached figure. Figure 2 As shown, k1 and k2 are the tilt angles of the robotic arm at the two compensation positions, and we have:

[0068]

[0069] 203) Specifically, the error compensation calculation method based on the single busbar measurement data of the profilometer is as follows: Feature value extraction is performed, including maximum and minimum points; the difference between the maximum and minimum points and the material removal rate of the polishing head are calculated for high-precision compensation polishing. It is proposed to use the difference method to calculate the second derivative of the profilometer measurement data, and to adopt a compensation polishing method that removes superposition at the maximum point position where the second derivative is large. (See Appendix 2) Figure 4 As shown, multi-path compensation polishing is performed within a certain range of this maximum point. The number of paths, n, is also related to the second derivative, thus ensuring the smoothness of the optical element. The threshold f″(x0) of the second derivative is related to parameters such as the contact removal area a of the polishing head, the target compensation error Δy0, and the smoothness requirements of the material. The superimposed compensation range Δx at this maximum point is related to the magnitude of the second derivative.

[0070]

[0071] Where n≥1, Δx≥0, and the total length of single-point compensation d=n*Δx. k1, k2, and k3 are parameter influence coefficients. Since the polishing process is more complex than these influence coefficients, it is proposed to use quantitative experiments to obtain the influence coefficients.

[0072] The polishing object 1 is a cylindrical aspherical surface made of K9 glass. The upper surface S1 of the cylinder is a complex curved surface—a cylindrical aspherical surface—with a total vertical length of 200mm and an effective area requirement of 100mm. The generatrix direction is aspherical, and the equation is:

[0073]

[0074] The aspherical parameters are shown in the table below, with the effective area length on both sides centered at the origin being 16mm:

[0075] R 8.364 K -1.004811 A4 0.000153225 A6 -1.40E-06 A8 4.24E-08 A10 -3.02E-10 A12 -6.84E-13 A14 -1.10E-15

[0076] The measurement and polishing effect of one cycle is shown in the figure below, achieving quantitative removal at several maxima. Due to the large amount of data, only a two-dimensional curve is displayed. Figure 5 As shown.

[0077] After the error-compensated polishing process described above, the surface inspection image of the test piece changed from the image after fine grinding to the image after fine polishing. Figure 6 As shown.

[0078] The final cylindrical aspherical surface achieved a surface profile accuracy of 2.187 micrometers and a PWR value of 0.174 micrometers with a PV value of over 30 micrometers from the precision-ground part. The surface profile accuracy achieved in the example demonstrates the superiority of this invention.

[0079] Although the present invention has been described in detail above with general descriptions and specific embodiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

Claims

1. A high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm, characterized in that, Includes the following steps: 1) Spatial error compensation for high-precision coordinate system of cylindrical and aspherical surfaces for robotic arm machining Dynamic machining information is acquired in real time through multiple sensors, and the machining posture is automatically adjusted based on this information to maintain consistency in the machining process, ultimately resulting in a cylindrical aspherical component with a set precision. Specifically, this includes the following: 101) In order to reduce the machining error caused by position error, posture error and repeatability error of the robotic arm, a three-dimensional force sensor, accelerometer and rotary encoder are used to record and feed back the motion state of the robotic arm, so as to design a control system to achieve high-precision end control; 102) The evaluation method for polishing accuracy of cylindrical aspherical surfaces is divided into two parts: generatrix direction and cylindrical direction. The generatrix direction refers to the direction perpendicular to the central axis of the cylindrical surface, and the cylindrical direction refers to the direction along the central axis of the cylindrical surface. Specifically, it includes: the generatrix surface accuracy PV value, the generatrix surface quality roughness, and the consistency between the cylindrical direction roughness and the generatrix. Among them, the generatrix surface accuracy PV value and the generatrix surface quality roughness are used to evaluate the polishing accuracy of the aspherical generatrix, that is, the polishing accuracy in the two-dimensional direction of the generatrix. This parameter affects the focusing ability, imaging distortion, and astigmatism effect of the aspherical surface. The cylindrical direction roughness and the consistency between the generatrix are used to evaluate the polishing accuracy in the cylindrical direction. The generatrix consistency refers to the consistency of the surface accuracy of different generatrixes along the cylindrical axis and the consistency of the surface morphology feature positions along the generatrix direction. This parameter affects the transmittance, reflectance, or absorptivity of optical elements. 103) A high-precision multi-process robotic arm coordinate system establishment method, namely an error-progressive tool setting method from coarse coordinate system establishment to fine coordinate system establishment, includes three steps: First, the robotic arm end effector is used to coarsely establish the workpiece coordinate system. Due to the low positioning accuracy of the robotic arm, there is an error of 20-30 micrometers in this step, including deviations in three directions and three positions. Second, a dial indicator is used to accurately measure the deviations in the three directions, controlling the error to the micrometer level. Finally, a laser tracker is used to calibrate the relative position between the robotic arm end effector and the workpiece, thereby obtaining the three position deviations. Through the three-step progressive calibration, a high-precision workpiece coordinate system is obtained. 2) Further error compensation based on profilometer and coordinate measuring machine for cylindrical and aspherical surfaces processed using a compensated coordinate system. To address the issue of inconsistent benchmarks caused by the profilometer's measurement principle, a model is established based on a benchmark combining a coordinate measuring machine and a profilometer. Among these, a high-precision measurement analysis and calculation model is proposed based on the profilometer's measurement results to compensate for high-precision surface accuracy. By using the deviation of the compensation position in the initial compensation of the profilometer to feed back the deviation of the computational spatial coordinate system, closed-loop compensation is completed.

2. The high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm according to claim 1, characterized in that, In step 1), 101), a three-dimensional force sensor is placed at the end of the robotic arm to collect the magnitude of the polishing force.

3. The high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm according to claim 2, characterized in that, In step 1), 101), an accelerometer is installed at the end of the robotic arm to collect the end-effector velocity.

4. The high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm according to claim 3, characterized in that, In step 1), 101), a rotary encoder is installed on the shaft joint to collect the rotation information of the robotic arm shaft, i.e., the attitude information.

5. The high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm according to claim 4, characterized in that, Following the multi-sensor acquisition method, a feedback control system, i.e., an adaptive control method, is designed based on the data. The system makes real-time adjustments based on the dynamic multi-fusion data to achieve the ideal end-effector motion accuracy. The input signals include force feedback signals, angle feedback signals, and speed feedback signals. Force control algorithms and PID controllers are used for specific control implementation. Specifically, based on the existing pose of the robotic arm and the parameters of the polishing head, the spatial position of the robotic arm is adjusted to ensure constant polishing pressure.

6. The high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm according to claim 1, characterized in that, In step 1), step 103), the steps for establishing the workpiece coordinate system at the end of the robotic arm are as follows: replace the center position of the spherical polishing head at the end of the robotic arm with the tool tip, and record the three endpoints of the upper surface of the cylindrical and aspherical surfaces to construct the coordinate system; the steps for measuring the directional deviation with a dial indicator are as follows: install a dial indicator on the end of the robotic arm using a magnetic base, and perform dial indicator measurements in the x, y, and z directions of movement between the robotic arm and the clamping tool table to obtain the movement distance and dial indicator readings, thereby calculating the deflection angles in the three directions; use a laser tracker to measure the relative position between the end of the robotic arm tool and the workpiece to obtain the three position offsets; The offset of the coordinate point cloud is calculated based on the measurement offset results. Let the angular deviations measured along the x, y, and z axes be α, β, and γ, respectively, that is: In the formula, These are the differences in per mille. Let x, y, and z represent the distances traveled by the robotic arm along the x, y, and z axes, respectively; then the rotation matrix... for: The compensated point cloud coordinates are: 。 7. The high-precision polishing method for cylindrical aspherical optical elements based on a robotic arm according to claim 1, characterized in that, In step 2), the error compensation method for polishing cylindrical aspherical surfaces by a robotic arm based on a profilometer and coordinate measuring machine includes the following: 201) A method for high-precision compensation machining of a robotic arm by combining a profilometer and a coordinate measuring machine; specifically, the profilometer measures the surface error data of the cylindrical aspherical surface in the direction of the generatrix to guide the compensation machining, and the coordinate measuring machine measures the highest point of the cylindrical aspherical surface to calibrate the consistency of the profilometer's measurement datum, that is, the generatrix datum position of the profilometer is offset according to the position of the highest point measured by the coordinate measuring machine, so as to calculate the positional relationship of the generatrix feature points; 202. High-precision spatial error feedback compensation model for cylindrical aspherical surfaces based on a profilometer; specifically, feedback compensation calculation is performed based on the positional deviation of the first compensation by the profilometer; assuming the initial point cloud coordinates are (x0, y0, z0), and the actual machining position point cloud coordinates after force control compensation are (x, y, z), and the offset along the vertical direction has no significant error impact on the polishing process, let the offset errors on the y and z axes be Δy and Δz, and the tilt angle of the robot arm pose at this point be k. Then, based on the known pose of the robot arm, the coordinates of the two theoretical points and the actual point of the profilometer, and the aspherical surface formula, the process parameter d is obtained. According to the trigonometric relationship, we can obtain: In the formula These are the process parameters for the two compensation positions. Let be the tilt angles of the robotic arm at the two compensation positions, and we have: 203) The error compensation calculation method based on the measurement data of a single busbar of the profilometer is as follows: extract feature values, including maximum and minimum points; calculate the difference between the maximum and minimum points and the material removal rate of the polishing head to perform high-precision compensation polishing; The second derivative of the profilometer measurement data is calculated using the finite difference method. At the maxima of the second derivative, a compensation polishing method that removes superposition is employed, i.e., multi-path compensation polishing is performed at these maxima. The number of paths, n, is also related to the second derivative, thus ensuring the smoothness of the optical components. The threshold value of the second derivative is... Contact removal area 'a' with polishing head, target compensation error magnitude And related to the smoothness requirements of the material, the maximum point removes the superimposed compensation range. It is related to the magnitude of the second derivative, that is in 1, 0, the total length of single-point compensation is d=n* ; , , The influence coefficient of the parameter is obtained through quantitative experiments.

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