Laser reflection system machining and calibration method based on geometric constraints to solve machining allowance

Abstract

The present invention relates to a laser reflection system processing and calibration method based on constraint solution of machining allowance, and in particular to a laser reflection system processing and calibration method based on geometric constraint solution of machining allowance, which solves the problems that the prior art uses manual experience to grind and adjust the position of the base, the results are difficult to quantify and control, the grinding is repetitive, and the base has the risk of being scrapped. The method includes the following steps: Step 1: pre-assemble and determine whether the spot constraint is met; if so, complete the calibration; if not, execute Step 2; Step 2: construct a world coordinate system; Step 3: initialize parameters; Step 4: construct an example based on geometric constraints to solve the machining allowance of the four corner points on the bottom surface of the base and the mathematical optimization model of the installation position of three of the corner points after machining; Step 5: solve the optimal solution based on the machining process; Step 6: process the base and then install it in the corresponding position. The present invention is suitable for the calibration of laser reflection systems.

Description

Technical Field

[0001] The invention relates to a laser reflection system processing and assembly calibration method based on constraint solution of processing allowance, and in particular to a laser reflection system processing and assembly calibration method based on geometric constraint solution of processing allowance. Background Art

[0002] Laser systems usually have complex and long optical paths. The optical paths of some special multi-pass amplified laser systems exceed 100 meters. The laser passes through (refracts) or is reflected by each optical component on the optical path in turn. Therefore, the accuracy of the propagation direction of the laser after passing through each optical component is extremely important for the laser system. Once the propagation direction error of the laser after passing through one of the optical components is too large, the final laser system parameters are likely to fail to meet the design indicators, or even fail to emit light; reflective components are more sensitive, because the change in the emission angle is twice the change in the angle of the reflection surface. Once a reflective component deviates from the reflected optical path, after subsequent reflections by more reflective components, the deviation of the optical path will increase rapidly at an exponential level. Therefore, the processing accuracy and installation accuracy of the reflective components are crucial to the entire laser system.

[0003] Reflective components in laser systems are generally placed on optical adjustment frames or optical mirror frames, where optical mirror frames are divided into adjustable mirror frames that can be adjusted in multiple directions and fixed mirror frames that cannot be adjusted. Optical adjustment frames and adjustable mirror frames can achieve fine and precise adjustment of the laser light path. They are easy and quick to use and are suitable for laser experiments. They can quickly adjust the light spot to the target point of the light spot. However, the stability of optical adjustment frames and adjustable mirror frames is not good. In actual use, the light spot has high-frequency jitter, and due to the stress release of the adjustable structural material and other external factors, it will be slightly deformed, so that the light spot will drift, which is unacceptable for a laser system that needs to work stably for a long time. The fixed mirror frame cannot be adjusted in angle, which can well maintain the stability of the light path reflection, but it cannot directly achieve the reflection of multiple precise angles of the laser system. To adjust the angle, different gaskets need to be replaced, and it mainly relies on manual assembly and adjustment. Although the operation is simple, the accuracy is insufficient; there are also manual grinding solutions proposed, but the grinding force and grinding allowance are difficult to control.

[0004] The core components of high-energy lasers include many parts such as multi-pass pumps, which have multiple reflection structures. Due to the requirements of processing accuracy and assembly accuracy, many installation surfaces and positioning references with high stability and high reliability need to be set up during actual installation and calibration. These all require extremely high-precision grinding and calibration to ensure the installation position and angle attitude of the optical components.

[0005] See also Figure 1Taking the reflective component 3 as a reflective prism as an example, a reflective model of a group of reflective prisms in a laser reflective system is considered. The reflective surface 31 of the reflective prism generally has excellent surface accuracy, but due to the influence of the processing technology, the shape and position tolerance between its mounting surface and the reflective surface 31 is generally large, and it cannot be processed again. Therefore, the reflective prism is usually bonded to an independently designed base 2, and the base 2 is usually preferably a metal base. The reflective prism is mounted on the fixed plate 1 through the base 2. After the incident light 5 of the laser is reflected by the reflective surface 31 of the reflective prism, its reflected light 6 passes through the light spot target point on the reflected light receiving surface 4. , at the light spot target point When the reflected light 6 does not pass through the target point of the light spot, When Figure 1 As shown, a light spot 7 before adjustment is formed on the reflected light receiving surface 4. At this time, the base 2 of the reflecting prism needs to be polished and the position adjusted so that the incident light 5 of the laser is reflected by the reflecting surface 31 of the reflecting prism after the base 2 is polished and the position is adjusted, and the reflected light 6 passes through the light spot target point , which is hereinafter referred to as the spot constraint. For the grinding and position adjustment of the base 2, the prior art generally performs grinding and position adjustment through manual experience, but the results are difficult to quantify and control, the grinding is repetitive, the base 2 has the risk of being scrapped, and it is difficult to ensure that the laser meets the spot constraint after being reflected by the reflective prism after the base 2 is ground and the position is adjusted.

[0006] In summary, there is an urgent need to develop a processing and calibration method that can quantitatively and controllably process and adjust the position of the base of the reflective component in the laser reflection system, so that the laser can meet the spot constraint after being reflected by the reflective component. Summary of the invention

[0007] The purpose of the present invention is to solve the technical problems that in the prior art, when the base of the reflective component in the laser reflection system is ground and the position is adjusted through manual experience, the results are difficult to quantify and control, the grinding is repetitive, and the base has the risk of being scrapped. A laser reflection system processing and assembly method based on geometric constraint solution of processing allowance is provided.

[0008] In order to solve the above technical problems, the technical solution adopted by the present invention is:

[0009] A laser reflection system processing and assembly method based on geometric constraint solution of processing allowance, the laser reflection system includes a fixing plate, a base, a reflection component, a light source and a reflected light receiving surface; a rectangular boss is provided on the upper surface of the fixing plate; the reflecting element is fixedly connected to the base and is installed on the boss through the base, the bottom surface of the base is coplanar with the upper surface of the boss, and the reflecting surface of the reflecting element is located above the fixing plate for receiving the light source The incident light emitted is reflected to the light spot target point on the reflected light receiving surface ; Its special feature is that it includes the following steps:

[0010] Step 1: Pre-assemble the laser reflection system and determine whether it meets the spot constraint. The spot constraint refers to the light source. The incident light must pass through the light spot target point after being reflected by the reflective component. If yes, then complete the processing and calibration; if no, proceed to step 2;

[0011] Step 2: According to the world coordinate system The axis is perpendicular to the upper surface of the boss. axis, The axes are parallel to the directions of the two adjacent sides of the rectangle on the upper surface of the boss, and the world coordinate system is constructed;

[0012] Step 3: Initialize parameters;

[0013] Step 3.1: Obtain the basic parameters of the laser reflection system pre-assembled in step 1. The basic parameters are the basic parameters of the world coordinate system constructed in step 2, including: light source , the four corner points on the upper surface of the boss, and any point set on the reflection surface 、Light spot target point And the installation positions of the four corner points on the bottom of the base 、 、 、 The position coordinates of the incident light ray are also included. and the normal to the reflecting surface The coordinates of

[0014] Step 3.2: Calculate the plane according to the basic parameters obtained in step 3.1 The unit normal vector of

[0015] Step 4: In order to meet the light spot constraint, the installation position needs to be 、 、 、 The four corner points of the corresponding base bottom surface are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and set the installation location 、 、 After the three corner points of the corresponding base bottom surface are processed, the corresponding corner points need to be installed on the top surface of the boss at the following positions: , , , , , , are all greater than or equal to 0; then assume that the bottom surface of the processed base is a plane, and assume that the light source The incident light emitted is a straight line, and the reflection of the reflecting surface is assumed to conform to the law of mirror reflection. On this basis, according to the initialization parameters in step 3, an example solution is constructed based on geometric constraints. , , , , , as well as A mathematical optimization model, which is an under-constrained mathematical optimization model;

[0016] Step 5: Based on the processing technology, for the mathematical optimization model constructed in step 4, a model enhancement optimization solution is formulated to obtain the optimal solution, and the , , , , , as well as The corresponding optimal solutions respectively;

[0017] Step 6: Remove the pre-assembled base in step 1 together with the reflective components fixed thereto from the fixing plate, and clamp the base with the bottom surface facing upward on the workbench of the five-axis CNC machine tool; then, according to the solution obtained in step 5, , , , The corresponding optimal solutions are respectively, using a five-axis CNC machine tool to process the bottom surface of the base by a plane interception method, and after the processing is completed, it is removed; finally, according to the solution obtained in step 5 , as well as According to the corresponding optimal solutions, the removed base and the reflective components fixed thereto are installed at the corresponding positions on the upper surface of the boss to complete the processing and calibration.

[0018] Furthermore, in order to simplify the calculation, when constructing the world coordinate system in step 2, the world coordinate system axis, The shafts are all located inside the upper surface of the boss;

[0019] The plane calculated in step 3.2 The unit normal vector is denoted by , .

[0020] Furthermore, the light source obtained in step 3.1 The position coordinates are marked , the four corner points on the upper surface of the boss , , , The position coordinates of , , , , any point set on the reflection surface The position coordinates are marked , spot target point The position coordinates are marked , installation positions of the four corner points on the bottom of the base , , , The position coordinates of , , , , the incident direction of the incident light Coordinate marking of , the normal to the reflecting surface Coordinate marking of ;

[0021] The step 4 is specifically as follows:

[0022] Step 4.1: Construct the first set of constraint equations, specifically:

[0023] In order to meet the light spot constraint, the installation position needs to be , , , The four corner points of the corresponding base bottom surface are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and the processed position is defined as , , , , , , , are all greater than or equal to 0; then based on the processing technology requirements, assuming that the bottom surface of the base after processing is a plane, the , , , The constraint condition that the two sides are in the same plane must be satisfied, and this constraint condition is defined as the first constraint condition; then according to the set , , , and the initialization parameters in step 3, solve the plane The normal vector , and construct the first constraint equation group corresponding to the first constraint condition, and solve the plane The normal vector The values ​​of each coordinate in include the machining allowance to be calculated. , , , The first set of constraint equations constructed is a function containing the machining allowance to be determined. , , , The mathematical equation of

[0024] Step 4.2: Construct the second set of constraint equations, specifically:

[0025] In order to meet the light spot constraint, the installation position , , After the three corner points of the corresponding base bottom surface are processed, the corresponding corner points need to be installed on the top surface of the boss at the following positions: , , ; Then, according to the calibration, the bottom surface of the base before and after processing is coplanar with the upper surface of the boss, and the triangle With triangle are congruent triangles, then , , Need to meet , , Both are on the upper surface of the boss and are consistent with the plane calculated in step 3.2 The unit normal vector vertical, and , and as well as and The lengths of the constraints are equal, and this constraint is defined as the second constraint; then according to the set , , , the value set in step 4.1 , , , , and the initialization parameters in step 3, construct the second constraint equation group corresponding to the second constraint condition, the second constraint equation group is a set of equations including the machining allowance to be determined , , , and the location to be requested , , Mathematical equations for the coordinates in ;

[0026] Step 4.3: Construct the third constraint equation, specifically:

[0027] Step 4.3.1: The normal of the reflecting surface obtained in step 3.1 The planes obtained in step 4.1 are respectively The normal vector On and plane Internal projection, It is expressed as:

[0028] ;

[0029] In the expression: , , All include the required machining allowance , , , Function of

[0030] At the same time, The planes obtained in step 4.1 are respectively The normal vector On and plane Internal projection, It is expressed as:

[0031] ;

[0032] In the expression: , , All include the required machining allowance , , , Function of

[0033] Step 4.3.2: Place the base as described in step 4.1. , , , After processing, follow the steps set in step 4.2. , , After installation, the normal direction of the reflective surface of the reflective component connected to it is set to , as described in step 3.1 The position to move to is set to , the target point of the light spot described in step 3.1 The symmetric point relative to the reflective surface of the reflective component is set as ; then according to , And plane The relative position of , And plane The relative positions of In order to meet the light spot constraint, the installation position After the corresponding corner points of the bottom surface of the base are processed, their corresponding corner points need to be at the installation position on the upper surface of the boss, as well as in step 4.3.1. The expression and The expression of and ; Solve the obtained and The values ​​of each coordinate in include the machining allowance to be calculated. , , , and the location to be requested , , Function of each coordinate in ;

[0034] Step 4.3.3: According to the light spot target point obtained in step 3.1 Location coordinates , and the solution obtained in step 4.3.2 and , solve the value set in step 4.3.2 , the solution obtained is The values ​​of each coordinate in include the machining allowance to be calculated. , , , and the location to be requested , , Function of each coordinate in ;

[0035] Step 4.3.4: Assume the light source The incident light emitted is a straight line, and the reflection of the reflecting surface is assumed to conform to the law of mirror reflection. On this basis, in order to meet the light spot constraint, the light source The incident light emitted must pass through the solution obtained in step 4.3.3. , construct a third constraint equation corresponding to the spot constraint;

[0036] Step 4.4: Construct the fourth constraint inequality equation system, specifically:

[0037] As described in step 4.3.2 The position coordinates are set to , according to the bottom surface of the processed base needs to be assembled on the upper surface of the boss, then , , , All must satisfy the conditions obtained in step 3.1 , , as well as The constraint condition within the enclosed quadrilateral is defined as the fourth constraint condition; then the bottom surface of the processed base is set to be a parallelogram, and based on this, the above , the solution obtained is The value of each coordinate in contains the position to be sought , , The function of each coordinate in; finally, according to the solution obtained The value of the coordinate in the middle, constructs the fourth constraint inequality equation group corresponding to the fourth constraint condition, and the fourth constraint inequality equation group is a set of equations containing the position to be determined , , The mathematical inequalities of the coordinates in the equations; the first constraint equation group, the second constraint equation group, the third constraint equation group and the fourth constraint inequality equation group together constitute the mathematical optimization model to complete the construction of the mathematical optimization model.

[0038] Furthermore, the first set of constraint equations constructed in step 4.1 is:

[0039] .

[0040] Furthermore, the second constraint equation set constructed in step 4.2 is:

[0041] .

[0042] Furthermore, the third constraint equation constructed in step 4.3.4 is:

[0043] .

[0044] Further, the The values ​​of the coordinates in are:

[0045] ;

[0046] The fourth constrained inequality equation set constructed is:

[0047] .

[0048] Furthermore, in order to obtain the optimal solution and make subsequent process implementation easier, the step 5 is specifically as follows:

[0049] Step 5.1: constructing a variety of objective functions and additional constraint strategies for the mathematical optimization model constructed in step 4 according to different processing technology strategies;

[0050] Step 5.2: Perform different additive combinations on two or more of the multiple objective functions and additional constraint strategies constructed in step 5.1, and solve the multiple combined strategy solutions obtained by the combination, and obtain multiple optimization solutions by adding different solution conditions;

[0051] Step 5.3: Sort the various optimization solutions obtained in step 5.2 in order from easy to difficult according to the degree of difficulty in process implementation, and the optimization solution ranked last must be able to obtain the optimal solution; then, in order, start with the optimization solution that is easiest to implement in process, and use the optimization solutions in turn to solve the above , , , , , as well as During the solution process, each time an optimization solution is completed, it is determined in real time whether the optimal solution is obtained; if not, the next optimization solution is used for solution; if so, the solution is completed.

[0052] Furthermore, the multiple objective functions and additional constraint strategies constructed in step 5.1 include three types, specifically:

[0053] Strategy 1: ;

[0054] Strategy 2: ;

[0055] Strategy 3:

[0056] ;

[0057] The multiple optimization solutions obtained in step 5.2 include three types, specifically:

[0058] The first optimization solution: Add strategies 1, 2, and 3 described in step 5.1 and Solve under the conditions of ;

[0059] The second optimization solution: Add strategies 1, 2, and 3 described in step 5.1 and , choose the smallest possible machining allowance Solve under the conditions of ;

[0060] The third optimization solution: Add strategy 1 and strategy 3 described in step 5.1 and solve under the following conditions:

[0061] ;

[0062] In step 5.3, the three optimization solutions obtained in step 5.2 are arranged in order from easy to difficult according to the difficulty of implementation in the process: the first optimization solution, the second optimization solution, and the third optimization solution.

[0063] Furthermore, in order to more conveniently obtain the optimal solution, in step 5, solve the , , , , , as well as When the corresponding optimal solutions are obtained, mathematical optimization solvers are used.

[0064] The beneficial effects of the present invention are:

[0065] (1) In the laser reflection system processing and calibration method for solving the processing allowance based on geometric constraints of the present invention, an example is constructed based on geometric constraints to solve the , , , , , as well as The mathematical optimization model is used to solve , , , , , as well as Compared with the method of grinding and adjusting the position of the base of the reflective component in the laser reflection system by manual experience, it has the advantages of completing the calculation in one go, accurate calculation, high calculation precision, quantification and control of the result, and the spot constraint can be satisfied; and in the present invention, the processing allowance is calculated , , , Finally, a five-axis CNC machine tool is used to complete the processing and remove the excess in one go, without the need for repeated processing, and thus there is no risk of the base being scrapped; therefore, the present invention solves the technical problems in the prior art of grinding and adjusting the position of the base of the reflective component in the laser reflection system through manual experience, in which the results are difficult to quantify and control, the grinding is repetitive, and the base has the risk of being scrapped.

[0066] (2) In the laser reflection system processing and calibration method for solving the processing allowance based on geometric constraints of the present invention, the example solution based on geometric constraints is constructed. , , , , , as well as The mathematical optimization model is a solution for solving an example. It constructs a mathematical optimization model based on geometric constraint solving by sorting out the geometric elements and constraints of the problem. The mathematical optimization model directly expresses the geometric constraints in the problem as mathematical equations and inequality equations, without using geometric constraint modeling software, which makes the establishment of the model highly flexible, versatile and portable; at the same time, the present invention takes into account the process factors, and can flexibly add constraints, which not only meets the light spot constraints, but also reduces the difficulty of processing and calibration, and improves the accuracy of processing; furthermore, the mathematical optimization model constructed in the present invention is a pure mathematical model, and its solution can be completed using a general mathematical optimization solver. These mathematical optimization solvers have more solution methods and stronger solution performance than dedicated geometric constraint solvers, and have richer solution strategies and methods, and the solution is more flexible, convenient and efficient.

[0067] (3) The method of geometric constraint solving is divided into general solution and example solution according to the universality of the solution method. General solution refers to the use of a general geometric constraint solving tool to represent all geometric constraints, and then use a geometric constraint solver to solve them. This solution method has the following disadvantages: first, the representation of geometric constraints is relatively complex, and the problem to be solved by the present invention involves constraints such as distance, symmetry, and rigid body invariance, and there are many constraints; second, since the problem to be solved by the present invention is an under-constrained problem, how to find a feasible solution suitable for process processing and how to design corresponding solution constraints are additional work; in addition, the solution after modeling depends on the solution performance of the software, which is difficult to control manually; while the mathematical optimization model of the example solution constructed in the present invention is used for solution, there is no need to use a geometric constraint solver for solution, and the solution can be completed using a general mathematical optimization solver, so the above-mentioned problems caused by the general solution can be avoided.

[0068] (4) In the laser reflection system processing and calibration method based on geometric constraint solution of processing allowance, the present invention calculates , , , Finally, a five-axis CNC machine tool is used for processing. The positioning accuracy and repeatability of the five-axis CNC machine tool are less than 6″. Combined with the popular on-machine measurement function, it can intelligently perform extremely high-precision processing and calibration, which can meet the requirements of high angle accuracy and high stability in laser experiments.

[0069] (5) Due to the use of the laser reflection system processing and calibration method based on geometric constraint-based processing allowance solution, the processing allowance required for the base and the installation position of the base after processing can be quickly, conveniently and accurately calculated in order to meet the light spot constraint. Therefore, when the angle needs to be adjusted in the laser experiment, the method of the present invention can be used to quickly, conveniently and accurately recalculate the processing allowance required for the base and the installation position of the base after processing in order to meet the light spot constraint. Therefore, the method of the present invention can take into account the application requirements of angle adjustment and light path reflection stability in laser experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 It is a schematic diagram of the reflection model structure of a group of reflection prisms in the laser reflection system mentioned in the background technology;

[0071] Figure 2 Parameters involved in solving the machining allowance in an embodiment of the present invention are first-view schematic diagrams of distribution positions on the laser reflection system preassembled in step 1;

[0072] Figure 3 Parameters involved in solving the machining allowance in an embodiment of the present invention are schematically shown from a second viewing angle of the distribution position of the laser reflection system preassembled in step 1;

[0073] Figure 4 Parameters involved in solving the machining allowance in the embodiment of the present invention, in step 6, the base is processed and installed on the laser reflection system at the corresponding position on the upper surface of the boss according to the position coordinates obtained by the solution, and the distribution position is shown from the first perspective;

[0074] Figure 5 Parameters involved in solving the machining allowance in the embodiment of the present invention, in step 6, the base is processed and installed on the laser reflection system at the corresponding position on the upper surface of the boss according to the position coordinates obtained by the solution. A second viewing angle diagram of the distribution position;

[0075] Figure 6 is a flow chart of step 5.3 in an embodiment of the present invention.

[0076] The descriptions of the numbers in the figure are as follows:

[0077] 1-fixed plate; 2-base; 3-reflecting element; 31-reflecting surface; 4-reflected light receiving surface; 5-incident light; 6-reflected light; 7-light spot before adjustment. DETAILED DESCRIPTION

[0078] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] See also Figure 2 The present invention discloses a laser reflection system processing and assembly method based on geometric constraint solution of processing allowance. The laser reflection system includes a fixing plate 1, a base 2, a reflection component 3, a light source and a reflected light receiving surface 4; a rectangular parallelepiped boss is provided on the upper surface of the fixing plate 1; the reflecting element 3 is fixedly connected to the base 2 and is mounted on the above-mentioned boss through the base 2, the bottom surface of the base 2 is coplanar with the upper surface of the boss, and the reflecting surface 31 of the reflecting element 3 is located above the fixing plate 1 for receiving the light source The incident light 5 is emitted and reflected to the light spot target point on the reflected light receiving surface 4 In order to facilitate processing, the base 2 is usually made of metal, and a stainless steel base is selected in this embodiment.

[0080] The laser reflection system processing and calibration method for solving processing allowance based on geometric constraints of the present invention comprises the following steps:

[0081] Step 1: See Figure 2 and Figure 3 , pre-assemble the laser reflection system and determine whether it meets the spot constraint. The spot constraint refers to the light source The incident light 5 emitted needs to pass through the light spot target point after being reflected by the reflective element 3 If yes, then complete the processing and calibration; if no, proceed to step 2;

[0082] Step 2: According to the world coordinate system The axis is perpendicular to the upper surface of the boss. axis, The axes are parallel to the directions of the two adjacent sides of the rectangle on the upper surface of the boss to construct the world coordinate system; see Figure 2 and Figure 3 In this embodiment, when constructing the world coordinate system, the world coordinate system axis, The axes are all located on the upper surface of the boss, that is, the world coordinate system The plane is coplanar with the upper surface of the boss; in this embodiment, the origin of the world coordinate system is located at the corner point A on the upper surface of the boss; in the present invention, unless otherwise specified, all coordinates are coordinates in the world coordinate system;

[0083] Step 3: Initialize parameters;

[0084] Step 3.1: See Figure 2 and Figure 3 , obtain the basic parameters of the laser reflection system pre-assembled in step 1, which are the basic parameters in the world coordinate system constructed in step 2, including: light source , the four corner points on the upper surface of the boss, and any point set on the reflection surface 、Light spot target point And the installation positions of the four corner points on the bottom surface of base 2 , , , The position coordinates of the incident light ray are also included. and the normal to the reflecting surface The coordinates of

[0085] In this embodiment, the light source obtained The position coordinates are marked , the four corner points on the upper surface of the boss , , , The position coordinates of , , , , any point set on the reflection surface The position coordinates are marked , spot target point The position coordinates are marked , installation positions of the four corner points on the bottom surface of base 2 , , , The position coordinates of , , , , the incident direction of the incident light Coordinate marking of , the normal to the reflecting surface Coordinate marking of ;

[0086] Step 3.2: Calculate the plane according to the basic parameters obtained in step 3.1 The unit normal vector of the plane The unit normal vector is denoted by , due to the plane Coplanar with the upper surface of the boss and in the world coordinate system In the plane, so the plane The unit normal vector ;

[0087] Step 4: In order to meet the light spot constraint, the installation position needs to be , , , The four corner points of the bottom surface of the corresponding base 2 are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and set the installation location , , After the three corner points of the bottom surface of the corresponding base 2 are processed, the positions of the corresponding corner points to be installed on the surface of the boss are set as , , , the above , , , are all greater than or equal to 0; then based on the processing technology requirements, it is assumed that the bottom surface of the processed base 2 is a plane and the light source The incident light 5 emitted is a straight line, and the reflection of the reflection surface 31 is assumed to conform to the law of mirror reflection. On this basis, according to the initialization parameters in step 3, an example solution is constructed based on geometric constraints. , , , , , as well as A mathematical optimization model, which is an under-constrained mathematical optimization model;

[0088] The above step 4 is specifically as follows:

[0089] Step 4.1: Construct the first set of constraint equations, specifically:

[0090] See also Figure 2 and Figure 3 In order to meet the light spot constraint, the installation position needs to be , , , The four corner points of the bottom surface of the corresponding base 2 are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and the processed position is defined as , , , , the above , , , are all greater than or equal to 0; then based on the processing technology requirements, assuming that the bottom surface of the processed base 2 is a plane, then , , , The constraint condition that the two sides are in the same plane must be satisfied, and this constraint condition is defined as the first constraint condition. , , , and the initialization parameters in step 3, solve the plane The normal vector , and construct the first constraint equation group corresponding to the above first constraint condition; in this embodiment, solve the plane The normal vector The specific process of constructing the first constraint equation group corresponding to the above first constraint condition is as follows:

[0091] In order to meet the light spot constraint, the installation position needs to be , , , The four corner points of the bottom surface of the corresponding base 2 are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and the processed position is defined as , , , , combined with the installation positions of the four corner points on the bottom surface of the base 2 obtained in step 3.1 above , , , Location coordinates , , , ,but , , , The corresponding position coordinates are , , , ,and then , , then, the plane The normal vector Solve by the following formula:

[0092] ;

[0093] Similarly, , , then, the plane The normal vector of is solved by the following formula:

[0094] ;

[0095] because , , , The first constraint condition of being in the same plane must be satisfied. The normal vector of the plane The normal vectors of are collinear, then the first constraint equation group corresponding to the first constraint condition constructed based on this is as follows:

[0096] ;

[0097] The plane obtained by the above solution The normal vector The values ​​of each coordinate in include the machining allowance to be calculated. , , , The first set of constraint equations constructed is the function of , , , The mathematical equation of

[0098] Step 4.2: Construct the second set of constraint equations, specifically:

[0099] See also Figure 2 , Figure 3 , Figure 4 as well as Figure 5 , in order to meet the light spot constraint, the installation position , , After the three corner points of the bottom surface of the corresponding base 2 are processed, the positions of the corresponding corner points to be installed on the surface of the boss are set as , , ; Then according to the calibration, the bottom surface of the base 2 before and after processing is coplanar with the upper surface of the boss, and the triangle With triangle are congruent triangles, then the above , , Need to meet , , Both are on the upper surface of the boss and are consistent with the plane calculated in step 3.2 The unit normal vector vertical, and , and as well as and The lengths of the constraints are equal, and this constraint is defined as the second constraint; then according to the set , , , set in step 4.1 , , , , and the initialization parameters in step 3, construct the second constraint equation group corresponding to the above second constraint condition; in this embodiment, according to the above second constraint condition, the second constraint equation group constructed is shown as follows:

[0100] ;

[0101] The second constraint equation group mentioned above includes the machining allowance to be determined , , , and the location to be requested , , Mathematical equations for the coordinates in ;

[0102] Step 4.3: Construct the third constraint equation, specifically:

[0103] Step 4.3.1: The normal of the reflecting surface obtained in step 3.1 Add the planes obtained in step 4.1 to the The normal vector On and plane Internal projection; In this embodiment, the normal of the reflecting surface obtained in step 3.1 To the plane obtained in step 4.1 The normal vector The projection onto is:

[0104] ;

[0105] The normal direction of the reflecting surface obtained in step 3.1 Towards plane The projection inside is shown on the right side of the equation below:

[0106] ;

[0107] By solving the above two equations simultaneously, we can get It is expressed as:

[0108] ;

[0109] In the expression: , , All include the required machining allowance , , , A function of and As shown below:

[0110] ;

[0111] Likewise, Add the planes obtained in step 4.1 to the The normal vector On and plane Internal projection, Do the above decomposition and convert It is expressed as:

[0112] ;

[0113] In the expression: , , All include the required machining allowance , , , The function of , , As shown below:

[0114] ;

[0115] Step 4.3.2: See Figure 4 and Figure 5 , set base 2 to the position set in step 4.1 , , , After processing, follow the settings in step 4.2 , , After installation, the normal direction of the reflective surface of the reflective component connected to it is set to , the above point in step 3.1 The position to move to is set to , the target point of the light spot in step 3.1 The symmetric point relative to the reflective surface of the reflective component is set as ; then according to , And plane The relative position of , And plane The relative positions of In order to meet the light spot constraint, the installation position After the corresponding corner points of the bottom surface of the base 2 are processed, their corresponding corner points need to be at the installation position on the upper surface of the boss, as well as in step 4.3.1. The expression and The expression of and In this embodiment, the solution obtained is As shown below:

[0116] ;

[0117] The solution obtained As shown below:

[0118] ;

[0119] The solution obtained and The values ​​of each coordinate in include the machining allowance to be calculated. , , , and the location to be requested , , Function of each coordinate in;

[0120] Step 4.3.3: According to the light spot target point obtained in step 3.1 Location coordinates , and the solution obtained in step 4.3.2 and , solve the above set in step 4.3.2 ; In this embodiment, solve the set in step 4.3.2 The specific process is:

[0121] Light spot target point For the above symmetrical points on the reflective surface of the reflective component Satisfy the following formula:

[0122] ;

[0123] Then obtain , , As shown below:

[0124] ;

[0125] The solution obtained The values ​​of each coordinate in include the machining allowance to be calculated. , , , and the location to be requested , , Function of each coordinate in;

[0126] Step 4.3.4: Assume the light source The incident light 5 emitted is a straight line, and the reflection of the reflection surface 31 is assumed to conform to the law of mirror reflection. On this basis, according to the light spot constraint, the light source The incident light 5 emitted needs to be solved in step 4.3.3 , construct the third constraint equation corresponding to the spot constraint; in this embodiment, the constructed third constraint equation is:

[0127] ;

[0128] From the derivation process of the above construction, it can be seen that the constructed third constraint equation is essentially a constraint that contains the machining allowance to be determined. , , , and the location to be requested , , Mathematical equations for the coordinates in ;

[0129] Step 4.4: Construct the fourth constraint inequality equation system, specifically:

[0130] Repeat step 4.3.2 above The position coordinates are set to , according to the bottom surface of the processed base 2 needs to be assembled on the upper surface of the boss, then , , , All must satisfy the conditions obtained in step 3.1 , , as well as The constraint condition within the enclosed quadrilateral is defined as the fourth constraint condition; then the bottom surface of the processed base 2 is set to be a parallelogram, and based on this, the solution is , and the solution is The values ​​of the coordinates in are:

[0131] ;

[0132] The above solution obtains The value of each coordinate in contains the position to be sought , , The function of each coordinate in; finally, according to the solution The value of the mid-coordinate is used to construct the fourth constraint inequality equation group corresponding to the fourth constraint condition. The constructed fourth constraint inequality equation group is:

[0133] ;

[0134] The fourth constraint inequality equation system mentioned above is the one containing the position to be determined , , The mathematical inequalities of the coordinates in the equations; the first constraint equation group, the second constraint equation group, the third constraint equation group and the fourth constraint inequality equation group together constitute a mathematical optimization model to complete the construction of the mathematical optimization model;

[0135] Step 5: Based on the processing technology, for the mathematical optimization model constructed in step 4, formulate a model enhancement optimization solution that can solve the optimal solution, and solve it accordingly , , , , , as well as The corresponding optimal solutions respectively;

[0136] The above step 5 is specifically as follows:

[0137] Step 5.1: According to different processing strategies, construct various objective functions and additional constraint strategies for the mathematical optimization model constructed in step 4;

[0138] In this embodiment, two types of decision variables are involved, one is the processing allowance , , , , the other is , , , Relative to , , , The translation amount of the former affects the latter; since the problem to be solved in the mathematical optimization model of the present invention is an under-constrained problem, and the feasible solution is a set, different constraints can be added to obtain a better feasible solution. Here, for a better standard, there are different setting methods according to different processing technology strategies. The following introduces three commonly used processing technology strategies:

[0139] Processing strategy 1: Minimum processing allowance;

[0140] Since the position parameters obtained during the parameter initialization are measured based on the pre-assembled laser reflection system, there are natural errors in the initialization parameters, which has a serious impact on the calculation of the machining allowance and installation position in the mathematical optimization model. Therefore, when the measurement accuracy is poor, in order to retain a larger solution space for secondary processing, the machining allowance should be as small as possible. Therefore, according to the processing technology strategy 1, the objective function and additional constraint strategy for the mathematical optimization model constructed in step 4 are:

[0141] Strategy 1: ;

[0142] Processing strategy 2: average machining allowance;

[0143] From the perspective of mechanical processing, when the machining allowances of the four corner points are equal, it is easier to use a five-axis CNC machine tool to position the bottom surface of the base, and the machining effect is less affected by the positioning accuracy of the machine tool. Therefore, according to the second machining process strategy, the objective function and additional constraint strategy for the mathematical optimization model constructed in step 4 are:

[0144] Strategy 2: ;

[0145] Processing strategy three: minimum translation;

[0146] After processing, the translation amounts of the installation positions of the four corner points on the bottom surface of the base are , , , , when the translation amount is larger, the error of the base installation after processing is larger, the installation accuracy requirement is higher, and the installation process requirement is stricter; on the contrary, the smaller the translation amount is, the easier it is to control the installation error, the easier it is to implement in terms of process, and the stronger the operability. Therefore, according to the processing technology strategy three, the objective function and additional constraint strategy of the mathematical optimization model constructed in step 4 are:

[0147] Strategy 3:

[0148] ;

[0149] Step 5.2: Perform different additive combinations of two or more of the multiple objective functions and additional constraint strategies constructed in step 5.1, and solve the multiple combined strategy solutions obtained by the combination, and obtain multiple optimization solutions by adding different solution conditions;

[0150] Combining the initialization parameters and the many variables, constraints, and processing strategies mentioned above, the optimal solution of the constructed mathematical optimization model is solved. According to mathematical optimization theory, this problem is a quadratic programming model. In this embodiment, the above-mentioned multiple optimization solutions include three types, specifically:

[0151] The first optimization solution: Add the above strategies 1, 2 and 3 in step 5.1 and Solve under the condition of ; if the optimal solution cannot be solved at this time, the second optimization solution can be used;

[0152] The second optimization solution: Add the above strategies 1, 2 and 3 in step 5.1 and , choose the smallest possible machining allowance Solve under the condition of ; if the optimal solution cannot be solved at this time, the third optimization solution can be used;

[0153] The third optimization solution: Add and combine the above strategies 1 and 3 in step 5.1 and solve under the following conditions:

[0154] ;

[0155] Since the third optimization solution does not add solution conditions to the mathematical optimization model, the third optimization solution can definitely solve the optimal solution of the mathematical optimization model;

[0156] Step 5.3: The multiple optimization solutions obtained in step 5.2 are sorted in order from easy to difficult according to the difficulty of realizing the process, and the optimization solution ranked last must be able to obtain the optimal solution; in this embodiment, the three optimization solutions obtained in step 5.2 are sorted in order from easy to difficult according to the difficulty of realizing the process: the first optimization solution, the second optimization solution, and the third optimization solution; see Figure 6 Then, sort by the optimization solution that is easiest to implement in terms of process, and use the above optimization solutions to solve the problems. , , , , , as well as During the solution process, each time an optimization solution is solved, it is determined in real time whether the optimal solution is obtained; if not, the next optimization solution is used for solution; if so, the solution is completed; in this embodiment, the solution , , , , , as well as When the corresponding optimal solutions are obtained, mathematical optimization solvers are used;

[0157] Step 6: Remove the base 2 pre-assembled in step 1 together with the reflective element 3 fixed thereto from the fixing plate 1, and clamp the base 2 with the bottom surface facing upward on the workbench of the five-axis CNC machine tool; then, according to the solution obtained in step 5 , , , The corresponding optimal solutions are respectively: a five-axis CNC machine tool is used to process the bottom surface of the base 2 by a plane interception method. After the processing is completed, it is removed; finally, according to the solution obtained in step 5 , as well as According to the corresponding optimal solutions, the removed base 2 together with the reflective element 3 fixed thereto are installed at the corresponding position on the upper surface of the boss to complete the processing and calibration.

[0158] In the laser reflection system processing and calibration method for solving the processing allowance based on geometric constraints of the present invention, the example solution based on geometric constraints is constructed. , , , , , as well as The mathematical optimization model is a solution for solving an example. It constructs a mathematical optimization model based on geometric constraint solving by sorting out the geometric elements and constraints of the problem. The mathematical optimization model directly expresses the geometric constraints in the problem as mathematical equations and inequality equations, without using geometric constraint modeling software, which makes the establishment of the model highly flexible, versatile and portable; at the same time, the present invention takes into account the processing technology factors, and can flexibly add constraints, which not only satisfies the light spot constraints, but also reduces the difficulty of processing and calibration, and improves the accuracy of processing; furthermore, the mathematical optimization model constructed in the present invention is a pure mathematical model, and its solution can be completed using a general mathematical optimization solver. These mathematical optimization solvers have more solving methods and stronger solving performance than dedicated geometric constraint solvers, and have richer solving strategies and methods, and the solution is more flexible, convenient and efficient. The present invention is suitable for the calibration of laser reflection systems.

Claims

1. A method for processing and calibrating a laser reflection system based on solving processing allowances based on geometric constraints, the laser reflection system comprising a fixing plate (1), a base (2), a reflection component (3), a light source and a reflected light receiving surface (4); the upper surface of the fixing plate (1) is provided with a rectangular parallelepiped boss; the reflective component (3) is fixedly connected to the base (2) and is mounted on the boss via the base (2); the bottom surface of the base (2) and the upper surface of the boss are coplanar; the reflective surface (31) of the reflective component (3) is located above the fixing plate (1) and is used to receive the light source The incident light (5) is emitted and reflected to the light spot target point on the reflected light receiving surface (4) ; It is characterized in that, The following steps are involved: Step 1: Pre-assemble the laser reflection system and determine whether it meets the spot constraint. The spot constraint refers to the light source. The incident light (5) emitted by the reflective element (3) needs to pass through the light spot target point If yes, then complete the processing and calibration; if no, proceed to step 2; Step 2: According to the world coordinate system The axis is perpendicular to the upper surface of the boss. axis, The axes are parallel to the directions of the two adjacent sides of the rectangle on the upper surface of the boss, and the world coordinate system is constructed; Step 3: Initialize parameters; Step 3.1: Obtain the basic parameters of the laser reflection system pre-assembled in step 1. The basic parameters are the basic parameters of the world coordinate system constructed in step 2, including: light source , the four corner points on the upper surface of the boss, and any point set on the reflection surface 、Light spot target point And the installation positions of the four corner points on the bottom surface of the base (2) , , , The position coordinates of the incident light ray are also included. and the normal to the reflecting surface The coordinates of Step 3.2: Calculate the plane according to the basic parameters obtained in step 3.1 The unit normal vector of Step 4: In order to meet the light spot constraint, the installation position needs to be , , , The four corner points of the bottom surface of the corresponding base (2) are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and set the installation location , , After the three corner points of the bottom surface of the corresponding base (2) are processed, the positions of the corresponding corner points to be installed on the surface of the boss are set as , , , , , , are all greater than or equal to 0; then assume that the bottom surface of the processed base (2) is a plane, and assume that the light source The incident light (5) is a straight line, and the reflection of the reflection surface (31) is assumed to conform to the law of mirror reflection. On this basis, according to the initialization parameters in step 3, an example solution is constructed based on geometric constraints. , , , , , as well as A mathematical optimization model, which is an under-constrained mathematical optimization model; Step 5: Based on the processing technology, for the mathematical optimization model constructed in step 4, a model enhancement optimization solution is formulated to obtain the optimal solution, and the , , , , , as well as The corresponding optimal solutions respectively; Step 6: Remove the base (2) pre-assembled in step 1 together with the reflective element (3) fixed thereto from the fixing plate (1), and clamp the base (2) with the bottom surface facing upward on the workbench of the five-axis CNC machine tool; then, according to the solution obtained in step 5, , , , The optimal solutions corresponding to each of them are respectively to use a five-axis CNC machine tool to process the bottom surface of the base (2) by a plane interception method, and after the processing is completed, remove it; finally, according to the solution obtained in step 5 , as well as According to the corresponding optimal solutions, the removed base (2) together with the reflective component (3) fixed thereto are installed at the corresponding position on the upper surface of the boss to complete the processing and calibration.

2. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 1, characterized in that: When constructing the world coordinate system in step 2, the world coordinate system axis, The shafts are all located inside the upper surface of the boss; The plane calculated in step 3.2 The unit normal vector is denoted by , .

3. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 2, characterized in that: The light source obtained in step 3.1 The position coordinates are marked , the four corner points on the upper surface of the boss , , , The position coordinates of , , , , any point set on the reflection surface The position coordinates are marked , spot target point The position coordinates are marked , the installation positions of the four corner points on the bottom of the base (2) , , , The position coordinates of , , , , the incident direction of the incident light Coordinate marking of , the normal to the reflecting surface Coordinate marking of ; The step 4 is specifically as follows: Step 4.1: Construct the first set of constraint equations, specifically: In order to meet the light spot constraint, the installation position needs to be , , , The four corner points of the bottom surface of the corresponding base (2) are respectively along the world coordinate system constructed in step 2 The machining allowance for axial machining is set as , , , , and the processed position is defined as , , , , , , , are all greater than or equal to 0; then based on the processing technology requirements, assuming that the bottom surface of the processed base (2) is a plane, then the , , , The constraint condition that the two sides are in the same plane must be satisfied, and this constraint condition is defined as the first constraint condition; then according to the set , , , and the initialization parameters in step 3, solve the plane The normal vector , and construct the first constraint equation group corresponding to the first constraint condition, and solve the plane The normal vector The values ​​of each coordinate in the table include the machining allowance to be determined. , , , The first set of constraint equations constructed is a function containing the machining allowance to be determined. , , , The mathematical equation of Step 4.2: Construct the second set of constraint equations, specifically: In order to meet the light spot constraint, the installation position , , After the three corner points of the bottom surface of the corresponding base (2) are processed, the positions of the corresponding corner points to be installed on the surface of the boss are set as , , ; Then, according to the calibration, the bottom surface of the base (2) before and after processing is coplanar with the upper surface of the boss, and the triangle With triangle are congruent triangles, then , , Need to meet , , Both are on the upper surface of the boss and are consistent with the plane calculated in step 3.2 The unit normal vector vertical, and , and as well as and The lengths of the constraints are equal, and this constraint is defined as the second constraint; then according to the set , , , the value set in step 4.1 , , , , and the initialization parameters in step 3, construct the second constraint equation group corresponding to the second constraint condition, the second constraint equation group is a set of equations including the machining allowance to be determined , , , and the location to be requested , , Mathematical equations for the coordinates in ; Step 4.3: Construct the third constraint equation, specifically: Step 4.3.1: The normal of the reflecting surface obtained in step 3.1 The planes obtained in step 4.1 are respectively The normal vector On and plane Internal projection, It is expressed as: ； In the expression: , , All include the required machining allowance , , , Function of At the same time, The planes obtained in step 4.1 are respectively The normal vector On and plane Internal projection, It is expressed as: ； In the expression: , , All include the required machining allowance , , , Function of Step 4.3.2: Place the base (2) as described in step 4.

1. , , , After processing, follow the steps set in step 4.

2. , , After installation, the normal direction of the reflective surface of the reflective component connected to it is set to , as described in step 3.1 The position to move to is set to , the target point of the light spot described in step 3.1 The symmetric point relative to the reflective surface of the reflective component is set as ; then according to , And plane The relative position of , And plane The relative positions of In order to meet the light spot constraint, the installation position After the bottom corners of the corresponding base (2) are processed, their corresponding corners must be located at the installation position on the upper surface of the boss and at the position in step 4.3.

1. The expression and The expression of and ; Solve the obtained and The values ​​of each coordinate in the table include the machining allowance to be determined. , , , and the location to be requested , , Function of each coordinate in; Step 4.3.3: According to the light spot target point obtained in step 3.1 Location coordinates , and the solution obtained in step 4.3.2 and , solve the value set in step 4.3.2 , the solution obtained is The values ​​of each coordinate in the table include the machining allowance to be determined. , , , and the location to be requested , , Function of each coordinate in ; Step 4.3.4: Assume the light source The incident light (5) emitted is a straight line, and the reflection of the reflection surface (31) is assumed to conform to the law of mirror reflection. On this basis, in order to meet the light spot constraint, the light source The incident light (5) emitted must pass through the solution obtained in step 4.3.

3. , construct a third constraint equation corresponding to the spot constraint; Step 4.4: Construct the fourth constraint inequality equation system, specifically: As described in step 4.3.2 The position coordinates are set to , according to the bottom surface of the processed base (2) needs to be assembled on the top surface of the boss, then , , , All must satisfy the conditions obtained in step 3.1 , , as well as The constraint condition within the enclosed quadrilateral is defined as the fourth constraint condition; then the bottom surface of the processed base (2) is set to be a parallelogram, and based on this, the solution is obtained. , the solution obtained is The value of each coordinate in contains the position to be sought , , The function of each coordinate in; finally, according to the solution obtained The value of the coordinate in the middle, constructs the fourth constraint inequality equation group corresponding to the fourth constraint condition, and the fourth constraint inequality equation group is a set of equations containing the position to be determined , , The mathematical inequalities of the coordinates in the equations; the first constraint equation group, the second constraint equation group, the third constraint equation group and the fourth constraint inequality equation group together constitute the mathematical optimization model to complete the construction of the mathematical optimization model.

4. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 3 is characterized in that: The first set of constraint equations constructed in step 4.1 is: 。 5. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 3, characterized in that: The second set of constraint equations constructed in step 4.2 is: 。 6. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 3, characterized in that: The third constraint equation constructed in step 4.3.4 is: 。 7. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 3 is characterized by: The solution obtained in step 4.4 is The values ​​of the coordinates in are: ； The fourth constrained inequality equation set constructed is: 。 8. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 3 is characterized by: The step 5 is specifically as follows: Step 5.1: constructing a variety of objective functions and additional constraint strategies for the mathematical optimization model constructed in step 4 according to different processing technology strategies; Step 5.2: Perform different additive combinations on two or more of the multiple objective functions and additional constraint strategies constructed in step 5.1, and solve the multiple combined strategy solutions obtained by the combination, and obtain multiple optimization solutions by adding different solution conditions; Step 5.3: Sort the various optimization solutions obtained in step 5.2 in order from easy to difficult according to the degree of difficulty in process implementation, and the optimization solution ranked last must be able to obtain the optimal solution; then, in order, start with the optimization solution that is easiest to implement in process, and use the optimization solutions in turn to solve the above , , , , , as well as During the solution process, each time an optimization solution is completed, it is determined in real time whether the optimal solution is obtained; if not, the next optimization solution is used for solution; if so, the solution is completed.

9. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to claim 8, characterized in that: The multiple objective functions and additional constraint strategies constructed in step 5.1 include three types, specifically: Strategy 1: ; Strategy 2: ; Strategy 3: ； The multiple optimization solutions obtained in step 5.2 include three types, specifically: The first optimization solution: Add strategies 1, 2, and 3 described in step 5.1 and Solve under the conditions of ; The second optimization solution: Add strategies 1, 2, and 3 described in step 5.1 and , choose the smallest possible machining allowance Solve under the conditions of ; The third optimization solution: Add strategy 1 and strategy 3 described in step 5.1 and solve under the following conditions: ； In step 5.3, the three optimization solutions obtained in step 5.2 are arranged in order from easy to difficult according to the difficulty of implementation in the process: the first optimization solution, the second optimization solution, and the third optimization solution.

10. The laser reflection system processing and calibration method based on geometric constraint solution of processing allowance according to any one of claims 1 to 9, characterized in that: In step 5, solve the , , , , , as well as When the corresponding optimal solutions are obtained, mathematical optimization solvers are used.

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