Surface shape simulation calculation optimization method oriented to multi-mechanical-arm collaborative processing scene

Abstract

The invention relates to the technical field of optical machining surface shape simulation, in particular to a surface shape simulation calculation optimization method for a multi-mechanical-arm cooperative machining scene, and the method comprises the steps: planning a polishing region and a polishing track belonging to each mechanical arm according to the surface shape sampling size of a workpiece to be machined and the number and position of the mechanical arms for machining; and a residence point in the polishing track of each mechanical arm; the residence point of each mechanical arm is matched with the surface shape data of the workpiece to be machined, and the surface shape data corresponding to the residence point of each mechanical arm is determined; and finally, according to the surface shape data corresponding to the residence point of each mechanical arm and the removal function of the workpiece to be machined, final residence time distribution of each mechanical arm during machining is obtained through calculation. According to the method, a surface shape matching simulation calculation method is utilized, the secondary frequency superposition problem occurring during multi-mechanical-arm machining is effectively eliminated, and meanwhile residence time distribution with good smoothness can be obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of optical processing surface simulation, and in particular relates to a surface simulation calculation optimization method for a multi-robot collaborative processing scenario. Background Art

[0002] At present, the manufacturing of large-size and extra-large-size reflectors still uses a single robot arm processing method, which will result in a long processing cycle due to the limitation of the number of processing tools. This method is not significantly different from CNC machine tools. Therefore, the use of multi-robot collaborative processing methods for the manufacture of extra-large-size reflectors has entered the field of vision of scientific researchers. In theory, the use of multi-robot collaborative processing strategies through reasonable trajectory planning can double the processing efficiency of reflectors. However, the most commonly used trajectory planning schemes are grating, spiral, and circular trajectory planning. These trajectory planning methods have certain limitations in the multi-robot collaborative processing scenario.

[0003] The Chinese patent publication number is CN116679622A, the publication date is October 3, 2023, and the patent name is "Surface tool mark error prediction method based on continuous tool function". The invention patent application discloses that the error effect caused by "overlapping frequency" can be eliminated by matching the sampling density of the processing trajectory and the surface shape to be processed. However, in the scenario of multi-manipulator collaborative processing, this method cannot simultaneously adapt to the planning strategy of using different direction trajectory intervals in different processing areas; The Chinese patent publication number is CN117473802A, and the publication date is March 19, 2024. The invention patent application named "Fast Solution Method for Polishing Dwell Time of Large-Aperture Optical Components" discloses a method for downsampling the overall surface shape. This method cannot be applied to trajectory planning schemes with more than two segments of trajectory intervals in different directions, that is, this method can only completely eliminate the "overlapping frequency" error in one-dimensional direction. When facing trajectory planning schemes with different resolutions on the same surface shape, new secondary "overlapping frequency" errors will be introduced. The newly introduced secondary "overlapping frequency" will cause the dwell time results of the simulated processing to be not smooth enough. Using this as a reference to guide actual processing will have a great impact on the surface processing accuracy. Summary of the invention

[0004] In view of this, the present invention aims to provide a surface simulation calculation optimization method for multi-robot collaborative processing scenarios. By utilizing the "surface shape" matching simulation calculation method, the two-dimensional "overlapping frequency" problem caused by inconsistent resolutions in different directions in trajectory planning schemes adopted in different processing areas in multi-robot collaborative processing, which could not be solved by previous methods such as "matching the processing trajectory and the sampling density of the surface shape to be processed", is solved. The smoothness of the algorithm is improved, and a smooth residence time calculation method is provided for multi-robot collaborative processing simulation calculations.

[0005] To achieve the above object, the technical solution created by the present invention is implemented as follows: A surface shape simulation calculation optimization method for a multi-manipulator collaborative processing scenario specifically includes the following steps: 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: Establish a removal function model based on the polishing tool, and then obtain the theoretical removal function of the workpiece to be processed; S3: planning the polishing trajectory of each robotic arm according to the surface sampling size of the workpiece to be processed and the number and position of at least two robotic arms used for processing, and planning the dwelling points in the polishing trajectory of each robotic arm; S4: matching the station points of all the robot arms with the surface shape data in the corresponding polishing areas to determine that the corresponding polishing areas of all the robot arms have no overlapping frequency distribution; S5: Calculate the initial residence time distribution of all robot arms in the scenario of collaborative processing, and iterate the initial residence time distribution based on the non-overlapping frequency distribution to obtain the final residence time distribution of all robot arms in the scenario of collaborative processing.

[0006] Further, in step S2, a flat rotating grinding head is selected as a polishing tool, and a removal function model is established by the following formula:

[0007] 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 processing distance of the horizontal rotating grinding head, K represents the constant term in the removal function model, and P represents the pressure term in the removal function model.

[0008] Furthermore, in step S4, for the station point coordinates of each robot arm 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, Indicates the number of dwell points of each robot arm, and N indicates the maximum number of dwell points.

[0009] Furthermore, step S5 specifically includes the following steps: S51: The dwell time distribution of each robot arm during processing in its respective polishing track is calculated by the following formula:

[0010] 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 machined; S52: Set the optimization goal as:

[0011] ; in, , , ; in, represents the optimization objective function, represents the initial regularization factor, Represents the lower limit constraint condition for solving 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: Iterate 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 optimization objective function corresponding to the residence time distribution at the kth iteration, represents the regularization factor at k+1 iterations; It represents the iteration step size at the kth iteration, which is obtained by the following formula: ; Where k>1, It 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 by the following formula: ; S55: Repeat steps S53 to S54 until the updated residence 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.

[0012] Compared with the prior art, the invention can achieve the following beneficial effects: The surface shape simulation calculation optimization method for multi-robot collaborative processing scenarios created by the present invention aims at the problem that existing methods cannot eliminate the secondary "overlapping frequency" problem caused by inconsistent trajectory spacing directions and sizes in different areas of the same surface shape due to the use of different trajectory planning schemes for different areas in the multi-robot collaborative processing and its simulation calculation scenarios in order to improve processing accuracy and efficiency. A surface shape simulation calculation optimization method for multi-robot collaborative processing is proposed. This method not only effectively eliminates the secondary "overlapping frequency" problem, but also can obtain a residence time distribution with good smoothness in the scenario where trajectories with different resolutions are used in different processing areas of the same reflector workpiece. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings: Figure 1 A schematic diagram of the flow of a surface shape simulation calculation optimization method for a multi-manipulator collaborative processing scenario described in an embodiment of the present invention; Figure 2 A geometric diagram of the flat rotating grinding head during processing according to an embodiment of the present invention; Figure 3 A schematic diagram of a removal function model of a flat rotating grinding head according to an embodiment of the present invention; Figure 4 A schematic diagram of the surface points on the workpiece to be processed, the polishing trajectory of each robot arm and its residence point according to an embodiment of the present invention; Figure 5 A schematic diagram of the result after matching the surface points on the workpiece to be processed with the polishing trajectory and the dwelling points of each robot arm according to the embodiment of the present invention; Figure 6 A schematic diagram of the polishing trajectory and the dwelling point of each robot arm described in the embodiment of the present invention; Figure 7 This is the simulation result diagram without any optimization operation; Figure 8 A diagram showing simulation results of an optimization operation performed according to an existing method; Fig. 9A simulation result diagram of the optimization operation of the surface simulation calculation optimization method for a multi-robot collaborative processing scenario provided according to the present invention as described in an embodiment of the present invention. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0015] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0016] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0017] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0018] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0019] like Figure 1 to Figure 6 As shown, the surface shape simulation calculation optimization method for a multi-manipulator collaborative processing scenario described in an embodiment of the present invention specifically includes the following steps: S1: Measure the surface shape of the workpiece to be processed by an interferometer to obtain discrete surface shape data on the workpiece to be processed.

[0020] S2: Establish a removal function model based on the polishing tool, and then obtain the theoretical removal function of the workpiece to be processed.

[0021] In the embodiment of the present invention, a flat rotating grinding head is preferably used as a polishing tool, and combined with the reference paper "Research on the dwell time algorithm of large-aperture aspheric reflector combined processing technology" from the Graduate School of the Chinese Academy of Sciences (Changchun Institute of Optics, Fine Mechanics and Physics), a flat rotating grinding head is used as a polishing tool and the following is performed. Figure 2 When the processing is shown, the removal function model is: ; Among them, r represents the radius of the flat rotating grinding head, e represents the offset of the flat rotating grinding head during the machining process, It indicates the processing distance of the flat rotating grinding head, that is, the processing distance between any point on the edge of the processing circle generated by the flat rotating grinding head during processing and the processing center point of the flat rotating grinding head.

[0022] Figure 2 Point O in the middle represents the machining center point of the horizontal rotating grinding head, and point A represents any point on the edge of the machining circle generated by the horizontal rotating grinding head. It indicates the machining angle when the horizontal rotating grinding head rotates around the machining center point O. Since the material removal at point A during machining by the horizontal rotating grinding head increases with the machining distance from point A to the machining center point O, Since the machining traces produced during the machining process are rotationally symmetrical, the angle of action of the horizontally rotating grinding head on point A during one rotation cycle is Since the polishing speed of the horizontal rotating grinding head is constant, the material removal is the integral of the angle between the horizontal rotating grinding head and the workpiece to be processed, that is: ; in, represents the removal function on the workpiece to be processed, K represents the constant term in the removal function model, and P represents the pressure term in the removal function model; Combine the above two equations to establish the removal function model: .

[0023] The removal function model of the horizontal rotating grinding head is as follows: Figure 3 shown. Figure 3 The vertical axis in the middle is z, and the other two are x and y. The color bar on the right represents the removal function, that is, the distribution of the amount of removal per unit time. z is the depth of removal, and x and y represent the range of the removal function. If magnetorheological polishing is used, a test piece with the same physical properties as the workpiece to be processed, such as material and size, should be selected, and the processing environment of the two should also be the same, and the removal amount per unit time should be measured as the removal function.

[0024] S3: planning the polishing trajectory of each robotic arm according to the surface sampling size of the workpiece to be processed and the number and position of at least two robotic arms used for processing, and planning the dwelling points in the polishing trajectory of each robotic arm.

[0025] In the embodiment of the present invention, two robotic arms are preferably arranged to process the workpiece to be processed, and the two robotic arms are placed opposite to each other. In this case, the processing area of ​​the entire workpiece to be processed is divided into two parts. The polishing trajectory and the dwell point of each robotic arm are planned as follows: Figure 4 As shown. Figure 4 The black dots in the middle represent the surface points on the workpiece to be processed, and each surface point has its surface data; "Area 1" and "Area 2" represent the processing areas of the two robotic arms respectively; the black broken lines in "Area 1" and "Area 2" represent the polishing tracks corresponding to each robotic arm; the hollow dots on the polishing tracks represent the dwell points on the polishing tracks.

[0026] S4: Matching the station points of all the robot arms with the surface shape data in the corresponding polishing areas to determine that the corresponding polishing areas of all the robot arms have no overlapping frequency distribution.

[0027] In step S4, the matching process is as follows Figure 5 As shown, for the station point coordinates of each robot Each of them has its corresponding face shape data: ,in represents the number of discretized surface points on the workpiece to be processed, M represents the maximum number of surface points, Indicates the number of dwell points of each robot arm, and N indicates the maximum number of dwell points. Figure 6 The figure shows the polishing trajectory of each robot arm when processing a workpiece with a diameter of about 100 mm. In the figure, x and y represent the two-dimensional rectangular coordinates of the workpiece surface, and the upper horizontal black broken line and the lower vertical broken line represent the polishing trajectories of the two robot arms after planning.

[0028] S5: Calculate the initial residence time distribution of all the robot arms in the scenario of collaborative processing, and iterate the initial residence time distribution based on the non-overlapping frequency distribution to obtain the final residence time distribution of all the robot arms in the scenario of collaborative processing.

[0029] Step S5 specifically includes the following steps: S51: The dwell time distribution of each robot arm during processing in its respective polishing track is calculated by the following formula:

[0030] 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 machined; S52: Set the optimization goal as:

[0031] ; in, , , ; in, represents the optimization objective function, represents the initial regularization factor, Represents the lower limit constraint condition for solving 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: Iterate 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 gradient of the optimization objective function corresponding to the residence time distribution at the kth iteration, represents the regularization factor at k+1 iterations; It represents the iteration step size at the kth iteration, which is obtained by the following formula: ; Where k>1, It 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 by the following formula: ; S55: Repeat steps S53 to S54 until the updated residence time distribution satisfies the following formula: ; in, represents the 2-norm calculation, represents the convergence condition of the iteration. In the embodiment of the present invention, it is preferred to set the convergence condition of the iteration For 10 -8 The residence time distribution obtained at this time is is the final residence time distribution.

[0032] In order to clearly demonstrate the surface shape simulation calculation optimization method for multi-robot collaborative processing scenarios provided by the embodiment of the present invention, the following examples are performed without any optimization operation (the results are shown in FIG. Figure 7 As shown), the comparative optimization operation was performed according to the invention patent application with Chinese patent publication number CN116679622A, publication date September 1, 2023, and patent name "Surface shape tool mark error prediction method based on continuous tool function" (the optimization results are shown in Figure 8 As shown), and the optimization operation of the surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios provided by the present invention (the optimization results are shown in Fig. 9 ). Among them, Figure 7 Without any optimization operation, it can be seen that using this calculation scheme as a guide, the surface shape of the processed components will produce large-area overlapping frequency according to the simulation calculation results; Figure 8 The comparative optimization operation can only achieve the optimization of a single area, but there is still overlap in another area; while the method provided by the present invention can obviously show that the processing simulation results of the upper and lower half-areas are very smooth. This scheme can theoretically be applied to n robotic arms for joint processing n≥2, thereby concluding that the embodiment of the present invention adjusts the surface distribution of different areas to match the resolution of the trajectory respectively, and can solve the influence of multi-area overlap in multi-robotic arm collaborative processing, and obtain a smooth residence time distribution. Compared with the existing method, the present invention can solve the influence of multi-area overlap in multi-robotic arm collaborative processing, and obtain a smooth residence time distribution. Compared with other schemes, this scheme can be applicable to multi-robotic arm collaborative processing scenarios, and greatly improves processing efficiency.

[0033] 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 the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0034] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

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 on the workpiece to be processed; S2: establishing a removal function model according to the polishing tool, and then obtaining a theoretical removal function of the workpiece to be processed; S3: planning the polishing area and polishing trajectory of each robotic arm according to the surface sampling size of the workpiece to be processed and the number and position of at least two robotic arms used for processing, and planning the dwelling point in the polishing trajectory of each robotic arm; S4: matching the station points of all the robot arms with the surface shape data in the corresponding polishing areas to determine that the corresponding polishing areas of all the robot arms have no overlapping frequency distribution; S5: Calculate the initial residence time distribution of all the robot arms in the scenario of collaborative processing, and iterate the initial residence time distribution based on the non-overlapping frequency distribution to obtain the final residence time distribution of all the robot arms in the scenario of collaborative processing.

2. The surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios according to claim 1 is characterized in that: In the 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 in that: 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 dwelling points of each robot arm, and N represents the maximum number of dwelling points.

4. The surface shape simulation calculation optimization method for multi-manipulator collaborative processing scenarios according to claim 3 is characterized in that: The step S5 specifically comprises the following steps: 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 removal functions on the workpiece to be processed; S52: Set the optimization goal as: ； in, , , ; in, represents the optimization objective function, represents the initial regularization factor, It means solving 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, It 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 by the following formula: ； S55: Repeat steps S53 to S54 until the updated residence 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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