Surface shape simulation calculation optimization method for multi-robot collaborative machining scene

Abstract

The present application relates to the technical field of optical processing surface shape simulation, and particularly relates to a surface shape simulation calculation optimization method for a multi-robot collaborative processing scene, the present application plans polishing areas and polishing tracks for each robot according to the surface shape sampling size of a workpiece to be processed and the number and position of the robots used for processing, and the dwell points in the polishing tracks of each robot; the dwell points of each robot are matched with the surface shape data of the workpiece to be processed to determine the surface shape data corresponding to the dwell points of each robot; and finally, the final dwell time distribution of each robot during processing is calculated according to the surface shape data corresponding to the dwell points of each robot and the removal function of the workpiece to be processed. The simulation calculation method of surface shape matching effectively eliminates the secondary frequency stacking problem during multi-robot processing, and a smooth dwell time distribution can be obtained.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical machining surface shape simulation, and particularly relates to a surface shape simulation calculation optimization method for a multi-robot collaborative machining scene. BACKGROUND

[0002] At present, in the manufacturing of large and super-large mirrors, the single-robot machining method will lead to a long machining cycle due to the restriction of the number of machining tools, and this method has no significant difference from numerical control machine tools. Therefore, the multi-robot collaborative machining method is used in the manufacturing of super-large mirrors, and theoretically, the machining efficiency of the mirror can be doubled by using a reasonable trajectory planning and a multi-robot collaborative machining strategy. However, the commonly used trajectory planning schemes are grating type, spiral line and circular ring type trajectory planning, and these trajectory planning methods have certain limitations in the multi-robot collaborative machining scene.

[0003] The application patent application with the patent name of "surface shape tool mark error prediction method based on continuous tool function" and the patent publication number of CN116679622A and the publication date of October 3, 2023 discloses that the error caused by "aliasing" can be eliminated by matching the machining trajectory and the sampling density of the surface to be machined. However, in the scene of multi-robot collaborative machining, this method cannot simultaneously adapt to the planning strategy of different direction trajectory intervals in different machining areas.

[0004] The application patent application with the patent name of "fast solution method for polishing residence time of large-aperture optical element" and the patent publication number of CN117473802A and the publication date of March 19, 2024 discloses a method for reducing the sampling of the overall surface shape. This method cannot be applied to the trajectory planning scheme of more than two different direction trajectory intervals, that is, this method can only completely eliminate the one-dimensional direction "aliasing" error. In the face of the trajectory planning scheme with different resolutions on the same surface, a new secondary "aliasing" error is introduced, which will cause the residence time result of the simulation machining to be not smooth enough. Therefore, the actual machining guided by this method will have a great influence on the surface machining precision. SUMMARY

[0005] Therefore, the application provides a surface shape simulation calculation optimization method for a multi-robot collaborative machining scene. The simulation calculation method of "surface shape" matching solves the two-dimensional "aliasing" problem caused by the inconsistent resolution in different directions in the trajectory planning scheme adopted in different machining areas in the multi-robot collaborative simulation machining, which cannot be solved by the method of "matching the sampling density of the machining trajectory and the surface to be machined" and the like. The smoothness of the algorithm is improved, and a smooth residence time calculation method is provided for the multi-robot collaborative machining simulation calculation.

[0006] To achieve the above object, the technical scheme of the present application is implemented as follows:

[0007] A surface shape simulation calculation optimization method for a multi-robot collaborative machining scene, specifically comprising the following steps:

[0008] S1: measuring the surface shape of the workpiece to be machined by an interferometer to obtain the discretized surface shape data on the workpiece to be machined;

[0009] S2: establishing a removal function model according to the polishing tool, and then obtaining the theoretical removal function of the workpiece to be machined;

[0010] S3: planning the polishing trajectory of each robot arm and the dwell point in the polishing trajectory of each robot arm according to the surface shape sampling size of the workpiece to be machined and the number and position of the not less than two robot arms used for machining;

[0011] S4: matching the dwell points of all robot arms with the surface shape data in the corresponding polishing area to determine the non-overlapping frequency distribution of the corresponding polishing area of all robot arms;

[0012] S5: calculating the initial dwell time distribution of all robot arms in the collaborative machining scene, and updating and iterating the initial dwell time distribution based on the non-overlapping frequency distribution to obtain the final dwell time distribution of all robot arms in the collaborative machining scene.

[0013] Further, in step S2, a flat rotary polishing head is selected as the polishing tool, and a removal function model is established by the following formula:

[0014]

[0015] wherein, represents the removal function on the workpiece to be machined, r represents the radius of the flat rotary polishing head, e represents the offset generated by the flat rotary polishing head during machining, represents the machining distance of the flat rotary polishing head, K represents a constant term in the removal function model, and P represents a pressure term in the removal function model.

[0016] Further, in step S4, for the dwell point coordinates of each robot arm, the corresponding surface shape data is wherein represents the number of points of the discretized surface points on the workpiece to be machined, M represents the maximum value of the number of surface points, represents the number of points of the dwell point of each robot arm, and N represents the maximum value of the number of dwell points.

[0017] Further, step S5 specifically comprises the following steps:

[0018] S51: Calculate the dwell time distribution of each robot when it is machining in the respective polishing track by the following formula:

[0019]

[0020] wherein, , , ; represents the dwell time distribution of each robot at the jth dwell point, represents the distribution of the removal function on the workpiece to be machined;

[0021] S52: Set the optimization objective as:

[0022]

[0023] ;

[0024] wherein, , , ;

[0025] wherein, represents the optimization objective function, represents the initial regularization factor, represents the lower bound constraint condition for solving the dwell time distribution, and the above formula is the solution of the minimum value of the optimization objective function in the case of to obtain the initial dwell time distribution;

[0026] S53: Iteratively update the initial dwell time distribution according to the following formula:

[0027] ;

[0028] wherein, represents the dwell time distribution at the kth iteration, represents the number of iterations, represents the optimization objective function corresponding to the dwell time distribution at the kth iteration, represents the regularization factor at the k+1th iteration; represents the iteration step size at the kth iteration, which is obtained by the following formula:

[0029] ;

[0030] wherein, k>1, represents the partial derivative of the optimization objective function corresponding to the dwell time distribution at the k-1th iteration, i.e.:

[0031] ​

[0032] wherein, denotes the set condition of the residence time distribution at the kth iteration, i.e.

[0033] S54: update the regularization factor by the following formula:

[0034]

[0035] S55: repeat steps S53-S54 until the updated residence time distribution satisfies the following formula:

[0036]

[0037] wherein, denotes the convergence condition of iteration, denotes the 2-norm calculation;

[0038] The residence time distribution obtained at this time is the final residence time distribution.

[0039] Compared with the prior art, the present application can achieve the following beneficial effects:

[0040] The surface shape simulation calculation optimization method for the multi-robot collaborative machining scene of the present application can effectively eliminate the secondary "stacking frequency" problem caused by the inconsistent direction and size of the trajectory interval of different regions of the same surface shape due to the use of different trajectory planning schemes for different regions to improve machining precision and efficiency in the multi-robot collaborative machining and simulation calculation scene. In the same machining region of a mirror workpiece, the method can still obtain a residence time distribution with good smoothness even when different resolution trajectory scenes are used in different machining regions. BRIEF DESCRIPTION OF DRAWINGS

[0041] The accompanying drawings, which form a part of the present application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the present application and serve to explain the principles of the present application. In the drawings:

[0042] Figure 1 The flowchart of the surface shape simulation calculation optimization method for the multi-robot collaborative machining scene according to the present application;

[0043] Figure 2 The geometric diagram of the flat rotary grinding head during machining according to the present application; ​​​​

[0044] Figure 3 A schematic diagram of a removal function model of a flat rotating grinding head according to an embodiment of the present application;

[0045] Figure 4 A schematic diagram of a surface shape point on a workpiece to be processed, a polishing trajectory of each mechanical arm and a dwell point thereof according to an embodiment of the present application;

[0046] Figure 5 A schematic diagram of a result after matching a surface shape point on a workpiece to be processed and a polishing trajectory of each mechanical arm and a dwell point thereof according to an embodiment of the present application;

[0047] Figure 6 A schematic diagram of a polishing trajectory of each mechanical arm and a dwell point thereof according to an embodiment of the present application;

[0048] Figure 7 A simulation result diagram without any optimization operation;

[0049] Figure 8 A simulation result diagram of an optimization operation according to a prior method;

[0050] Figure 9 A simulation result diagram of an optimization operation of a surface shape simulation calculation optimization method for a multi-mechanical arm cooperative processing scene according to the present application. DETAILED DESCRIPTION

[0051] In order to make the objectives, technical solutions and advantages of the present application more clear, the present application will be further described in detail below with reference to the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and do not constitute a limitation on the present application.

[0052] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0053] In the description of the present application, it should be understood that the terms "center", "longitudinal", "transverse", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation of the present application. In addition, the terms "first", "second" and the like are only for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined with "first", "second" and the like can be explicitly or implicitly included one or more. In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more.

[0054] In the description of the present application, it should be noted that unless otherwise specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, or it can be connected inside two elements. For those skilled in the art, the specific meaning of the above terms in the present application can be understood through specific circumstances.

[0055] The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments.

[0056] As Figures 1 to 6 shown, the surface shape simulation calculation optimization method for multi-robot collaborative machining scene described in the embodiments of the present application specifically includes the following steps:

[0057] S1: Measure the surface shape of the workpiece to be machined by an interferometer to obtain the discretized surface shape data on the workpiece to be machined.

[0058] S2: Establish a removal function model according to the polishing tool, and then obtain the theoretical removal function of the workpiece to be machined.

[0059] In the embodiments of the present application, a flat rotary grinding head is preferably used as a polishing tool, and in combination with the reference paper "Residence Time Algorithm Research on Combined Machining Technology of Large Aperture Aspheric Mirror" from the Graduate School of the Chinese Academy of Sciences (Changchun Institute of Optics, Fine Mechanics and Physics), when the flat rotary grinding head is used as a polishing tool and machined as shown in Figure 2 , the removal function model is obtained as:

[0060] ;

[0061] wherein r represents the radius of the flat rotating grinding head, e represents the offset generated by the flat rotating grinding head during the machining process, represents the machining distance of the flat rotating grinding head, i.e. the machining distance between any point on the edge of the machining circle generated by the flat rotating grinding head during the machining and the machining center point of the flat rotating grinding head.

[0062] Figure 2 wherein point O represents the machining center point of the flat rotating grinding head, and point A represents any point on the edge of the machining circle generated by the flat rotating grinding head, and at this time represents the machining angle of the flat rotating grinding head during the machining when the flat rotating grinding head rotates around the machining center point O. Since the material removal at point A during the machining of the flat rotating grinding head varies with the machining distance between point A and the machining center point O , the action angle of the flat rotating grinding head on point A within one cycle of rotation is . Since the polishing speed of the flat rotating grinding head is constant, the material removal is the angle integral of the action of the flat rotating grinding head on the workpiece to be machined, i.e.

[0063] ;

[0064] wherein represents the removal function on the workpiece to be machined, K represents the constant term in the removal function model, and P represents the pressure term in the removal function model;

[0065] The removal function model is established by combining the above two equations:

[0066] .

[0067] The removal function model of the flat rotating grinding head is shown in Figure 3 . Figure 3 wherein the longitudinal direction is z, and the other two are x and y, the color bar on the right represents the removal function, i.e. the removal amount distribution per unit time, z is the depth of removal, and x and y represent the action range of the removal function. If magnetorheological polishing is used, an experimental piece with the same physical properties as the workpiece to be machined, such as material and size, should be selected, and the machining environment of the two should also be consistent, and the removal amount per unit time is measured as the removal function.

[0068] S3: planning the polishing trajectory of each mechanical arm and the dwell point in the polishing trajectory of each mechanical arm according to the surface shape sampling size of the workpiece to be machined and the number and position of the mechanical arms used for machining.

[0069] In the embodiment of the present application, preferably, two mechanical arms are arranged to process the workpiece to be processed, and the two mechanical arms are placed opposite to each other, and the processing area of the entire workpiece to be processed is divided into two parts. The polishing track and the dwell point of each mechanical arm are planned as shown in Figure 4 In Figure 4 , the black dots represent the surface points on the workpiece to be processed, each surface point has its surface data; “Area 1” and “Area 2” represent the processing areas of the two mechanical arms, respectively; the black broken lines in “Area 1” and “Area 2” represent the polishing tracks corresponding to each mechanical arm; the hollow circles on the polishing track represent the dwell points on the polishing track.

[0070] S4: Matching the dwell points of all the mechanical arms with the surface data in the corresponding polishing area to determine that the corresponding polishing area of all the mechanical arms has no overlapping frequency distribution.

[0071] In step S4, the matching process is as shown in Figure 5 For the coordinates of the dwell points of each mechanical arm , there is corresponding surface data as , wherein represents the number of discrete surface points on the workpiece to be processed, M represents the maximum value of the number of surface points, represents the number of dwell points of each mechanical arm, and N represents the maximum value of the number of dwell points. Figure 6 Fig. 4 shows the polishing tracks of each mechanical arm when processing a workpiece to be processed with a diameter of about 100 mm, wherein x and y represent the two-dimensional rectangular coordinates of the surface of the workpiece, and the upper horizontal black broken line and the lower vertical broken line represent the polishing tracks of the two mechanical arms planned respectively.

[0072] S5: Calculating the initial dwell time distribution of all the mechanical arms in the scenario of cooperative processing, and performing an update iteration based on the non-overlapping frequency distribution on the initial dwell time distribution to obtain the final dwell time distribution of all the mechanical arms in the scenario of cooperative processing.

[0073] Step S5 specifically includes the following steps:

[0074] S51: The dwell time distribution of each mechanical arm when processing in the corresponding polishing track is calculated by the following formula:

[0075]

[0076] wherein, , , ; represents the dwell time distribution of each mechanical arm at the jth dwell point, represents the distribution of the removal function on the workpiece to be processed;

[0077] S52: Set the optimization objective as:

[0078]

[0079] ;

[0080] wherein, , , ;

[0081] wherein, represents the optimization objective function, represents the initial regularization factor, represents the lower bound constraint condition for solving the residence time distribution, the above formula is the solution of the minimum value of the optimization objective function in the case of , to obtain the initial residence time distribution ;

[0082] S53: Iterates the initial residence time distribution according to the following formula:

[0083] ;

[0084] wherein, represents the residence time distribution at the kth iteration, represents the number of iterations, represents the gradient of the optimization objective function corresponding to the residence time distribution at the kth iteration, represents the regularization factor at the k+1th iteration; represents the iteration step length at the kth iteration, which is obtained by the following formula:

[0085] ;

[0086] wherein, k>1, represents the partial derivative of the optimization objective function corresponding to the residence time distribution at the k-1th iteration, that is:

[0087] ;

[0088] wherein, represents the set condition of the residence time distribution at the kth iteration, that is ;

[0089] S54: Update the regularization factor by the following formula:

[0090] ;

[0091] S55: repeating steps S53-S54 until the updated dwell time distribution meets the following formula:

[0092] ;

[0093] wherein, represents the 2-norm calculation, represents the convergence condition of iteration, in the embodiment of the present application, the convergence condition of iteration is preferably set to 10 -8 The dwell time distribution obtained at this time is the final dwell time distribution.

[0094] To clearly show the surface shape simulation calculation optimization method provided by the embodiment of the present application for the multi-robot collaborative machining scene, the following operations are performed: no optimization operation is performed (the results are shown in Figure 7 ), the comparative optimization operation is performed according to the invention patent application with the Chinese patent publication number CN116679622A and the publication date of September 1, 2023, and the patent name of "Surface shape tool mark error prediction method based on continuous tool function" (the optimization results are shown in Figure 8 ), and the optimization operation of the surface shape simulation calculation optimization method provided by the present application for the multi-robot collaborative machining scene (the optimization results are shown in Figure 9 ). Among them, Figure 7 It can be seen from the comparative optimization operation without any optimization operation that the surface shape of the machined element will have a large area of frequency stacking according to the simulation calculation results using this calculation scheme as a guide; Figure 8 The comparative optimization operation can only achieve single region optimization, but the other region still has frequency stacking; and the method provided by the present application can obviously see that the machining simulation results of the upper and lower half regions are very smooth. This scheme can be theoretically applied to n robot collaborative machining n≥2, so that it is concluded that the embodiment of the present application adjusts the surface shape distribution of different regions to match the resolution of the track, and can well solve the influence of multi-region frequency stacking in multi-robot collaborative machining, and obtain a smooth dwell time distribution. Compared with the existing method, the present application can well solve the influence of multi-region frequency stacking in multi-robot collaborative machining, and obtain a smooth dwell time distribution. Compared with other schemes, the present scheme can be applied to the multi-robot collaborative machining scene, and the machining efficiency is greatly improved.

[0095] It should be understood that the various forms of flow shown above can be used to reorder, add or delete steps. For example, the steps recorded in the present disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions of the present disclosure can be achieved, which is not limited herein.

[0096] The above detailed description does not limit the scope of the application. Various modifications, combinations, sub-combinations and alternatives can be made to the detailed description. Any modification, equivalent replacement and improvement etc. made within the spirit and principle of the application shall be included in the scope of the application.

Claims

1. A surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios, characterized by: The specific steps include: S1: measuring the surface shape of the workpiece to be processed by an interferometer to obtain discretized surface shape data of the workpiece to be processed; S2: establishing a removal function model according to the polishing tool, thereby obtaining a theoretical removal function of the workpiece to be processed; S3: planning a polishing area and a polishing trajectory for each robotic arm according to the surface sampling size of the workpiece to be processed and the number and positions of at least two robotic arms used for processing, and planning a dwell point in the polishing trajectory of each robotic arm; S4: matching the dwell points of all the robotic arms with the surface shape data in the corresponding polishing areas to ensure that the corresponding polishing areas of all the robotic arms have no overlapping frequency distribution; S5: Calculate the initial dwell time distribution of all robotic arms in the collaborative processing scenario, and perform an iterative update on the initial dwell time distribution based on the non-overlapping frequency distribution to obtain the final dwell time distribution of all robotic arms in the collaborative processing scenario; Step S5 includes: S51: The dwell time distribution of each robot arm during processing in its respective polishing track is calculated by the following formula: in, , , ; represents the residence time distribution of each robot at the jth residence point, represents the distribution of the removal function on the workpiece to be processed.

2. The surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios according to claim 1 is characterized by: In step S2, a flat rotating grinding head is selected as the polishing tool, and the removal function model is established by the following formula: in, represents the removal function on the workpiece to be processed, r represents the grinding head radius of the flat rotating grinding head, e represents the offset generated by the flat rotating grinding head during the processing, represents the machining distance of the flat rotating grinding head, K represents the constant term in the removal function model, and P represents the pressure term in the removal function model.

3. The surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios according to claim 2 is characterized by: In step S4, the coordinates of the station point of each robot arm are The corresponding surface data is ,in represents the number of discretized surface points on the workpiece to be processed, M represents the maximum number of surface points, represents the number of dwell points of each robot arm, and N represents the maximum number of dwell points.

4. The surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios according to claim 3 is characterized by: The step S5 further comprises the following steps: S52: Set the optimization goal as: ； in, , , ; in, represents the optimization objective function, represents the initial regularization factor, Indicates the solution of the lower limit constraint of the residence time distribution. The above formula is Under the condition of , the minimum value of the optimization objective function is solved to obtain the initial residence time distribution ; S53: Iterating the initial residence time distribution according to the following formula: ； in, represents the residence time distribution at the kth iteration, represents the number of iterations, represents the regularization factor at k+1 iterations; represents the optimization objective function corresponding to the residence time distribution at the kth iteration; It represents the iteration step size at the kth iteration, which is obtained by the following formula: ； Where k>1, represents the partial derivative of the optimization objective function corresponding to the residence time distribution at the k-1th iteration, that is: ； in, represents the collective condition of the residence time distribution at the kth iteration, that is, ； S54: Update the regularization factor using the following formula: ； S55: Repeat steps S53 to S54 until the updated dwell time distribution satisfies the following formula: ； in, represents the convergence condition of the iteration, Indicates 2-norm calculation; The residence time distribution obtained at this time is the final residence time distribution.

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