Curved surface assembly constraint-based robot operating margin calculation method

Abstract

Disclosed in the present invention is a curved surface assembly constraint-based robot operating margin calculation method, comprising: obtaining assembled aircraft fuselage point clouds X and assembly-pending skin point clouds Y; extracting assembly-pending boundary sequence point clouds E on the basis of the assembled aircraft fuselage point clouds X; performing minimum margin matching on the assembly-pending boundary sequence point clouds E and the assembly-pending skin point clouds Y, searching for the nearest-neighbor matched pair, establishing an error optimization equation of a minimum margin variance constraint; establishing a skin micro-deformation equation on the basis of the fuselage point clouds X, and jointly optimizing a differentiable point cloud matching equation under a local deformation upper limit constraint; using a gradient equation of the differentiable matching equation and a Hessian matrix to calculate a rotation matrix and a translation vector of the next optimization direction; and calculating an optimized error, if the optimized error is less than a preset error threshold or the number of iterations is greater than a preset total number of iterations, outputting a result to obtain a currently matched boundary, and supplying said boundary to a milling operation robot to remove a machining margin to obtain a final assembly curved surface. The present invention improves assembly procedures, achieves efficient calculation, and has extremely high availability.

Description

A method for calculating robot working allowance based on surface assembly constraints

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on December 22, 2023, the application number of which is 2023117763555, and the name of the invention is “A method for calculating robot operating allowance based on surface assembly constraints”, all or part of which is incorporated by reference into this application. Technical Field

[0002] The present invention relates to the technical field of industrial applications, and in particular to a method for calculating robot operating allowance based on curved surface assembly constraints. Background Art

[0003] High-precision and high-reliability assembly of fuselage skins ensures the ability of aircraft to withstand the extremely harsh conditions of high altitude, low temperature and low pressure, and determines the aerodynamic performance during flight. However, the traditional manual positioning combined with semi-mechanical riveting assembly method has poor consistency, low efficiency, and difficulty in ensuring accuracy.

[0004] As a key technology in the industrial automation production process, machine vision technology has also made great strides with the technological breakthroughs in 3D image acquisition hardware equipment. It obtains the 3D point cloud of the aircraft skin to be assembled as a spatial shape representation, constructs a skin spatial transformation model, and combines the target assembly boundary to replace manual boundary matching and calibrate the assembly pose. In the aerospace intelligent manufacturing system, assembly estimation methods based on 3D visual images have always been a key technology that needs to be mastered. Traditional boundary point cloud matching usually uses the ICP (Iterative Closest Point) point set matching method, which uses the minimum distance error of the nearest neighbor point pairs between 3D point clouds as the optimization target to shorten the gap between the two surfaces as much as possible. This algorithm is simple and efficient, laying a good framework foundation for point set matching.

[0005] In addition, the current rigid modeling cannot effectively incorporate the tiny deformations of the skin into the optimization process. At the same time, non-rigid assembly will cause large-scale deformation of the skin, destroying the rigidity of the skin surface, making it difficult to obtain a highly feasible assembly solution. Therefore, solving the visual estimation assembly of large, complex, and irregularly curved skins is a major problem that needs to be solved urgently.

[0006] Summary of the Invention

[0007] In order to solve the above technical problems, the present invention provides a method for calculating robot working allowance based on surface assembly constraints.

[0008] The technical solution adopted by the present invention to solve the technical problem is:

[0009] A method for calculating robot working allowance based on surface assembly constraints, the method comprising the following steps:

[0010] S100: Using a 3D scanner to obtain 3D point cloud coordinates of the assembled aircraft fuselage and the skin to be assembled, obtaining the assembled aircraft fuselage point cloud X and the skin to be assembled point cloud Y;

[0011] S200: Extracting a boundary sequence point cloud E to be assembled based on the assembled aircraft fuselage point cloud X; wherein the boundary sequence point cloud E to be assembled is composed of the edges of the empty areas on the fuselage outer surface; the skin to be assembled is milled to remove the excess, thereby completing the assembly of the fuselage outer surface;

[0012] S300: Perform minimum margin matching on the boundary sequence point cloud E to be assembled and the skin point cloud Y to be assembled, search for nearest neighbor matching pairs, and establish an optimization error equation with minimum margin variance constraint; establish a skin micro-deformation equation based on the fuselage point cloud X, and jointly optimize the differentiable point cloud matching equation under the local deformation upper limit constraint;

[0013] S400: Calculate the rotation matrix and translation vector of the next optimization direction using the gradient equation of the differentiable matching equation and the Hesser matrix;

[0014] S500: Calculate the optimized error. If it is less than the preset error threshold or the number of iterations is greater than the preset total number of iterations, output the result to obtain the current matched boundary, which is provided to the milling robot to remove the machining allowance and obtain the final assembly surface F. Otherwise, return to S300 and calculate the number of iterations.

[0015] Preferably, S200 includes:

[0016] S210: Calculate the curvature of the body point cloud X point by point, and filter the point cloud according to the curvature of each point cloud in the point cloud X to obtain the candidate assembly edge point set X e ;

[0017] S220: For the candidate assembly edge point set X e Perform triangulation to obtain a triangular mesh S consisting of three points j and the triangular mesh S j The corresponding normal vector N j ;

[0018] S230: After obtaining the normal vectors of all triangles, obtain the normal vector angles q{N j ,N j+1}>a2's triangular mesh S j ,S j+1 The adjacent points of the boundary sequence point cloud E to be assembled, where a2 = e -4 .

[0019] Preferably, S210 specifically includes:

[0020] Get point x i The neighbor point set X' in the point cloud X = {x n |||x n –x i ||≤rn}, construct the matrix M:

[0021] Among them, m is the number of point clouds of the neighboring point set X', point x i ∈X, rn is the point x i The neighborhood radius of the neighboring point set, x n is a point in the neighborhood, and all points within the neighborhood radius rn constitute the set of neighboring points X i ; Use the singular value decomposition algorithm to decompose the matrix M = UDV T , D is a diagonal matrix, U and V are both unitary matrices, and the diagonal element eigenvalues ​​of D after sorting are λ1>λ2>λ3, and the minimum value λ3 is the point cloud curvature; the point set with λ3>a1 is selected as the candidate assembly edge point set X e , a1 is the threshold of curvature screening, points with curvature greater than a1 are considered candidates, otherwise they are considered to be low curvature points and are not counted as edge candidates.

[0022] Preferably, S220 specifically includes:

[0023] For the candidate assembly edge point set X e Perform point cloud uniformization downsampling with the goal of density unification to reduce the density within the point cloud unit space and obtain a low-density edge point set X ed ;

[0024] Filter each X ed Point within radius d e If the number of point sets within the spherical range is less than N, they are set as outliers and the triangular facets of the current edge point are deleted. The remaining edge point sets are combined into triangular neighboring facets.

[0025] The triangular mesh S composed of three points j = {x1, x2, x3} and the triangle mesh S j The corresponding normal vector N j =sign{(x1-c)·[(x2-x1)×(x3-x1)]}*(x2-x1)×(x3-x1), where × represents the vector cross multiplication operation and · represents the vector dot multiplication operation. The sign{} function is defined as a sign function. When the internal vector dot product is greater than 0, the direction of the triangle normal vector remains unchanged, otherwise it is reversed.

[0026] Preferably, S300 includes:

[0027] S310: Establishing a Kd-tree for the skin point cloud Y to be assembled, searching for the nearest neighbor points of the boundary sequence point cloud E to be assembled in the skin point cloud Y to be assembled, and establishing one-to-one matching point pairs;

[0028] S320: Establishing a margin distance metric for the points of the skin point cloud Y to be assembled;

[0029] S330: Establishing the optimization error equation Where i is the candidate assembly edge point set X e In the index, j is the index of the skin point cloud Y to be assembled;

[0030] S340: The nearest neighbor point Y of the to-be-assembled boundary sequence point cloud E in the to-be-assembled skin point cloud Y j Establish the skin micro-deformation equation;

[0031] S350: Establishing deformation constraints of other non-neighboring point sets;

[0032] S360: Taylor expansion to obtain differentiable point cloud matching equations.

[0033] Preferably, S310 specifically includes:

[0034] Establish a Kd-tree for the skin point cloud Y to be assembled, and for all points E in the boundary sequence point cloud E to be assembled i ∈E Search for the nearest neighbor point Y j ∈Y, forming a matching point pair E i →Y j ,Y j =min j {||Y j -E i || 2}, current error

[0035] S320 specifically:

[0036] Get S200 to extract the skin point cloud Y to be assembled and the candidate assembly edge point set X e The outer boundary E y , calculate the matching pair E point by point i →Y j Point Y where the backbone points are concentrated j ∈Y margin error This defines the minimum matching equation of the residual variance Where n is the number of point sets in the boundary sequence point cloud E to be assembled, and k is the index number;

[0037] S330 specifically:

[0038] Establishing the optimization error equation Among them, the differentiable transformation parameters are expressed as Where R∈R 3x3 ,t∈R 1 ,0 dim Represents a vector of all 0s with a base element dimension of dim, 1 dim The vector of all 1s with 1 as the basis element dimension dim, t is the differentiable translation parameter, R = [δ x ,δ y ,δ z ] T , δ x ,δ y ,δ z The three rotation transformation basis vectors are .

[0039] Preferably, S340 specifically includes:

[0040] Based on the optimized error parameter representation ξ established in S330, the nearest neighbor point Y of the boundary E in the assembly skin point cloud Y is considered. j Establish the skin micro-deformation equation:

[0041] Among them, n i Defined as the mean of the normal vectors of all adjacent triangles at the current point, t i is the differentiable translation parameter of the current deformation point on the normal vector, R j is the rotation matrix of the current point;

[0042] S350 is specifically:

[0043] Establish deformation constraints for other non-neighbor point sets, and search for neighbor backbone point sets N(j) for all non-neighbor point sets to perform known deformation smoothing constraints:

[0044] S360: Taylor expansion to obtain differentiable point cloud matching equations,

[0045] Preferably, S400 specifically includes:

[0046] For S360 Solve the first-order gradient equation f'(ξ)| ξ＝0 =J f”(ξ)| ξ＝0 =H, where J is the gradient matrix and H is the Heiser matrix;

[0047] Solve the current optimal parameter ξ=min f(ξ) as the current optimization direction, and get the closed-form solution ξ=- H -1 J,ξ={ΔR,Δt}, where ΔR is the rotation matrix and Δt is the translation vector.

[0048] Preferably, S500 is specifically as follows:

[0049] Set a preset error threshold a3, and substitute the current optimal solution ξ = -H -1 J into

[0050] When f(ξ) < a3 or the iteration does not converge after the number of iterations is greater than the total number of preset iterations, terminate the optimization and output the final optimal solution, transform the point cloud E of the待 assembled boundary sequence, and use its adjacent boundary on the assembly surface skin Y as the final milling boundary to remove the surplus and obtain the final assembly surface F.

[0051] The above method for calculating the robot operation allowance based on surface assembly constraints obtains the three-dimensional point cloud representations of the assembled aircraft fuselage and the待 assembled skin, calculates the edge of the待 assembled fuselage gap and the shape surface of the assembled skin, and models the traditional riveting positioning problem as a point cloud matching problem under a systematic constraint system. It can break away from the existing manual riveting point alignment mode and solve a series of problems such as poor consistency, poor assembly consistency, low efficiency, and difficulty in ensuring accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] FIG. 1 is a flowchart of a method for calculating the robot operation allowance based on surface assembly constraints in an embodiment of the present invention;

[0053] FIG. 2 is a flowchart of a method for calculating the robot operation allowance based on surface assembly constraints in another embodiment of the present invention;

[0054] FIG. 3 is a schematic diagram of the allowance milling operation process in an embodiment of the present invention, where (a) represents the boundary extraction for riveting assembly, and (b) represents the allowance removal operation based on the assembly boundary. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0055] In order to enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0056] In one embodiment, as shown in FIGS. 1 and 2, a method for calculating the robot operation allowance based on surface assembly constraints includes the following steps:

[0057] S100: Use a three-dimensional scanner to obtain the three-dimensional point cloud coordinates of the assembled aircraft fuselage and the待 assembled skin, and obtain the point cloud X of the assembled aircraft fuselage and the point cloud Y of the待 assembled skin.

[0058] Specifically, in this example, the three-dimensional point cloud coordinates of adjacent view scenes are obtained through a 3D depth scanning sensor, and the coordinates of the point cloud X of the assembled aircraft fuselage and the point cloud Y of the待 assembled skin are obtained.

[0059] S200: Extracting a boundary sequence point cloud E to be assembled based on the assembled aircraft fuselage point cloud X; wherein the boundary sequence point cloud E to be assembled is composed of the edges of the empty areas on the fuselage outer surface; removing the excess of the skin to be assembled by milling, thereby achieving assembly of the fuselage outer surface.

[0060] In one embodiment, S200 includes:

[0061] S210: Calculate the curvature of the body point cloud X point by point, and filter the point cloud according to the curvature of each point cloud in the point cloud X to obtain the candidate assembly edge point set X e ;

[0062] S220: For the candidate assembly edge point set X e Perform triangulation to obtain a triangular mesh S consisting of three points j and the triangular mesh S j The corresponding normal vector N j ;

[0063] S230: After obtaining the normal vectors of all triangles, obtain the normal vector angles q{N j ,N j+1}>a2's triangular mesh S j ,S j+1 The adjacent points of the boundary sequence point cloud E to be assembled, where a2 = e -4 .

[0064] In one embodiment, S210 specifically includes:

[0065] Get point x i The neighbor point set X' in the point cloud X = {x n |||x n –x i ||≤rn}, construct the matrix M:

[0066] Among them, m is the number of point clouds of the neighboring point set X', point x i ∈X, rn is the point x i The neighborhood radius of the neighboring point set, x n is a point in the neighborhood, and all points within the neighborhood radius rn constitute the set of neighboring points X i ; Use the singular value decomposition algorithm to decompose the matrix M = UDV T , D is a diagonal matrix, U and V are both unitary matrices, and the diagonal element eigenvalues ​​of D after sorting are λ1>λ2>λ3, and the minimum value λ3 is the point cloud curvature; the point set with λ3>a1 is selected as the candidate assembly edge point set X e, a1 is the threshold for curvature screening. Points with curvature greater than a1 are considered candidates, otherwise they are considered to be low curvature points and are not counted as edge candidates.

[0067] Specifically, in this example, rn = 0.1m, a1 = e -4 .

[0068] In one embodiment, S220 specifically includes:

[0069] For the candidate assembly edge point set X e Perform point cloud uniformization downsampling with the goal of density unification to reduce the density within the point cloud unit space and obtain a low-density edge point set X ed ;

[0070] Filter each X ed Point within radius d e If the number of point sets within the spherical range is less than N, they are set as outliers and the triangular facets of the current edge point are deleted. The remaining edge point sets are combined into triangular neighboring facets.

[0071] The triangular mesh S composed of three points j = {x1, x2, x3} and the triangle mesh S j The corresponding normal vector N j =sign{(x1-c)·[(x2-x1)×(x3-x1)]}*(x2-x1)×(x3-x1), where × represents the vector cross multiplication operation and · represents the vector dot multiplication operation. The sign{} function is defined as a sign function. When the internal vector dot product is greater than 0, the direction of the triangle normal vector remains unchanged, otherwise it is reversed.

[0072] Specifically, reduce the density of the point cloud unit space to D, D = 10 / mm 3 .

[0073] S300: Perform minimum margin matching on the boundary sequence point cloud E to be assembled and the skin point cloud Y to be assembled, search for nearest neighbor matching pairs, and establish an optimization error equation with minimum margin variance constraint; establish the skin micro-deformation equation based on the fuselage point cloud X, and jointly optimize the differentiable point cloud matching equation under the local deformation upper limit constraint.

[0074] In one embodiment, S300 includes:

[0075] S310: Establishing a Kd-tree for the skin point cloud Y to be assembled, searching for the nearest neighbor points of the boundary sequence point cloud E to be assembled in the skin point cloud Y to be assembled, and establishing one-to-one matching point pairs;

[0076] S320: Establishing a margin distance metric for the points of the skin point cloud Y to be assembled;

[0077] S330: Establishing the optimization error equation Where i is the candidate assembly edge point set X e In the index, j is the index of the skin point cloud Y to be assembled;

[0078] S340: The nearest neighbor point Y of the to-be-assembled boundary sequence point cloud E in the to-be-assembled skin point cloud Y j Establish the skin micro-deformation equation;

[0079] S350: Establishing deformation constraints of other non-neighboring point sets;

[0080] S360: Taylor expansion to obtain differentiable point cloud matching equations.

[0081] In one embodiment, S310 specifically includes:

[0082] Establish a Kd-tree for the skin point cloud Y to be assembled, and for all points E in the boundary sequence point cloud E to be assembled i ∈E Search for the nearest neighbor point Y j ∈Y, forming a matching point pair E i →Y j ,Y j =min j {||Y j -E i || 2}, current error

[0083] S320 specifically:

[0084] Get S200 to extract the skin point cloud Y to be assembled and the candidate assembly edge point set X e The outer boundary E y , calculate the matching pair E point by point i →Y j Point Y where the backbone points are concentrated j ∈Y margin error This defines the minimum matching equation of the residual variance Where n is the number of point sets in the boundary sequence point cloud E to be assembled, and k is the index number;

[0085] S330 specifically:

[0086] Establishing the optimization error equation Among them, the differentiable transformation parameters are expressed as Where R∈R 3x3 ,t∈R 1 ,0 dim Represents a vector of all 0s with a base element dimension of dim, 1 dimThe vector of all 1s with 1 as the basis element dimension dim, t is the differentiable translation parameter, R = [δ x ,δ y ,δ z ] T , δ x ,δ y ,δ z The three rotation transformation basis vectors are .

[0087] In one embodiment, S340 specifically includes:

[0088] Based on the optimized error parameter representation ξ established in S330, the nearest neighbor point Y of the boundary E in the assembly skin point cloud Y is considered. j Establish the skin micro-deformation equation:

[0089] Among them, n i Defined as the mean of the normal vectors of all adjacent triangles at the current point, t i is the differentiable translation parameter of the current deformation point on the normal vector, R j is the rotation matrix of the current point;

[0090] S350 is specifically:

[0091] Establish deformation constraints for other non-neighbor point sets, and search for neighbor backbone point sets N(j) for all non-neighbor point sets to perform known deformation smoothing constraints:

[0092] S360: Taylor expansion to obtain differentiable point cloud matching equations,

[0093] S400: Calculate the rotation matrix and translation vector of the next optimization direction using the gradient equation of the differentiable matching equation and the Hesser matrix.

[0094] In one embodiment, S400 specifically includes:

[0095] For S360 Solve the first-order gradient equation f'(ξ)| ξ＝0 =J f”(ξ)| ξ＝0 =H, where J is the gradient matrix and H is the Heiser matrix;

[0096] Solve the current optimal parameter ξ=minf(ξ) as the current optimization direction, and get the closed-form solution ξ=-H -1 J,ξ={ΔR,Δt}, where ΔR is the rotation matrix and Δt is the translation vector.

[0097] S500: Calculate the optimized error. If it is less than the preset error threshold or the number of iterations is greater than the total number of preset iterations, output the result, obtain the currently matched boundary, supply it to the milling operation robot to remove the machining allowance, and obtain the final assembled surface F. Otherwise, return to S300 and calculate the number of iterations.

[0098] In one embodiment, S500 is specifically as follows:

[0099] Set the preset error threshold a3, and substitute the current optimized solution ξ = -H -1 J into

[0100] When f(ξ) < a3 or the number of iterations is greater than the total number of preset iterations and still does not converge, terminate the optimization and output the final optimized solution, transform the point cloud E of the boundary sequence to be assembled, and use its adjacent boundary on the assembly surface skin Y as the final milling boundary to cut off the allowance and obtain the final assembled surface F.

[0101] Specifically, a3 = e -3 .

[0102] The schematic diagram of the surplus milling operation process is shown in Figure 3. The first step: extract the boundary Xe to be assembled; the second step: the main method of this application realizes assembly matching; the third step: after the corresponding S500 loop termination condition, when the error is less than e, output the estimated boundary (dashed part), as shown in Figure 3(a), and finally supply it to the milling operation robot to remove the machining allowance (that is, the robot performs milling operations along the coordinates of the dashed points), as shown in Figure 3(b).

[0103] The above-mentioned robot operation allowance calculation method based on surface assembly constraints is divided into two parts.其一, 通过提取装配边界点云,利用点云高曲率特征筛选潜在可能存在边界点的区域,建立该区域的点云三角网格,通过三角网格的平面方程表示获取准确的点云法向量,取法向量变化大的邻接三角网格的点作为装配边界点云;其二,提取待装配蒙皮上表面点云,与装配边界点集合进行点与法向量匹配,在匹配平滑度、位置约束以及余量平均的约束下,优化待装配蒙皮上的铣边边界。因此,本发明提出了一种全新的蒙皮装配估计方法体系,通过目标约束匹配最优的铣边边界,极大地改善了装配工序,并且能够应用于大尺寸高精度的飞机蒙皮装配,计算高效高精,具有极高的可用性。

[0104] For the Chinese part in item that was not fully translated in the previous response, here is the complete translation:其一, By extracting the point cloud of the assembly boundary, using the high-curvature feature of the point cloud to screen the areas where boundary points may potentially exist, establishing the triangular mesh of the point cloud in this area, obtaining the accurate point cloud normal vector through the plane equation representation of the triangular mesh, and taking the points of the adjacent triangular meshes with large changes in the normal vector as the point cloud of the assembly boundary;其二, Extract the point cloud of the upper surface of the skin to be assembled, perform point and normal vector matching with the set of assembly boundary points, and optimize the milling edge boundary on the skin to be assembled under the constraints of matching smoothness, position constraints, and allowance averaging. Therefore, the present invention proposes a brand-new method system for skin assembly estimation. By matching the optimal milling edge boundary through target constraints, it greatly improves the assembly process and can be applied to the assembly of large-size and high-precision aircraft skins, with high calculation efficiency and accuracy and extremely high usability.The technical effect achieved by this invention is as follows: By acquiring a 3D point cloud representation of the assembled aircraft fuselage and the skin to be assembled, this method calculates the gap edges of the assembled fuselage and the shape and surface of the assembled skin, thereby modeling the traditional riveting positioning problem as a systematic point cloud matching problem within a constrained system. This method breaks away from the existing manual riveting point alignment model and solves a series of problems associated with it, such as poor consistency, poor assembly consistency, low efficiency, and difficulty in ensuring accuracy.

[0105] This model consists of a skin deformation model and an assembly constraint model. The skin deformation model extracts the assembly boundary point cloud and uses the high curvature characteristics of the point cloud to identify areas with potential boundary points. A triangulated mesh of the point cloud in this area is constructed, and accurate point cloud normals are obtained from the plane equation representation of the triangulated mesh. This serves as the boundary point cloud for assembly calculations. The assembly deformation model is then constructed by matching the point cloud of the assembled skin's upper surface with the set of assembly boundary points. The assembly constraint model consists of matching smoothness, position constraints, and margin averaging constraints. Based on the established assembly deformation model, the milling boundary parameters of the assembled skin are optimized, significantly improving the robustness of the algorithm. The algorithm can be applied to large-scale automated skin assembly, achieving efficient, high-precision assembly results and high usability. By introducing a point cloud-based estimation model, the system is freed from the constraints of manual intervention, enabling high-precision, large-scale assembly. The proposed novel deformation model significantly improves the theoretical feasibility of the algorithm, enabling the algorithm to perform milling on large, complex, and anisotropically curved aerospace skins, improving assembly accuracy and robustness, and reducing the failure rate of the method.

[0106] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A method for calculating robot working allowance based on surface assembly constraints, characterized in that: The method includes the following steps: S100: Use a 3D scanner to obtain the 3D point cloud coordinates of the assembled aircraft fuselage and the skin to be assembled, and obtain the assembled aircraft fuselage point cloud X and the skin to be assembled point cloud Y; S200: Extract the boundary sequence point cloud E to be assembled based on the assembled aircraft fuselage point cloud X; among them, the boundary sequence point cloud E to be assembled is composed of the edges of the empty areas on the outer surface of the fuselage; the skin to be assembled removes the surplus by milling to achieve the assembly of the outer surface of the fuselage; S300: Perform minimum margin matching on the boundary sequence point cloud E to be assembled and the skin point cloud Y to be assembled, search for the nearest neighbor matching pairs, and establish an optimization error equation with minimum margin variance constraints; establish a skin micro-deformation equation based on the fuselage point cloud X, and jointly optimize the differentiable point cloud matching equation under the local deformation upper limit constraint; S400: Calculate the rotation matrix and translation vector of the next optimization direction using the gradient equation and Hessian matrix of the differentiable matching equation; S500: Calculate the optimized error. If it is less than the preset error threshold or the number of iterations is greater than the total number of preset iterations, output the result, obtain the currently matched boundary, supply it to the milling robot to remove the machining allowance, and obtain the final assembled surface F. Otherwise, return to S300 and calculate the number of iterations.

2. The method according to claim 1, characterized in that S200 includes: S210: Calculate the curvature of the body point cloud X point by point, and filter the point cloud according to the curvature of each point cloud in the point cloud X to obtain a candidate assembly edge point set X e ; S220: For the candidate assembly edge point set X e Perform triangulation to obtain a triangular mesh S consisting of three points j And the triangular mesh S j The corresponding normal vector N j ; S230: After obtaining the normal vectors of all triangular facets, obtain the normal vector angles q{N j ,N j+1 }>a2's triangular mesh S j ,S j+1 The adjacent points are the point cloud of the boundary sequence to be assembled E, where a2 = e -4 .

3. The method according to claim 2, characterized in that Specifically, S210: Get point x i The neighbor point set X' in the point cloud X = {x n |||x n –x i ||≤rn}, construct the matrix M: Among them, m is the number of point clouds of the neighboring point set X', point x i ∈X, rn is a point x i The neighborhood radius of the neighboring point set, x n is a point in the neighborhood, and all points within the neighborhood radius rn constitute the set of neighboring points X i ; Use the singular value decomposition algorithm to decompose the matrix M = UDV T , D is a diagonal matrix, U and V are both unitary matrices, and the eigenvalues ​​of the diagonal elements in the sorted D are λ1>λ2>λ3, and the minimum value λ3 is the point cloud curvature; the point set with λ3>a1 is selected as the candidate assembly edge point set X e , a1 is the threshold for curvature screening. Points with curvature greater than a1 are considered candidates, otherwise they are considered to be low curvature points and are not counted as edge candidates.

4. The method according to claim 3, characterized in that Specifically, S220: For the candidate assembly edge point set X e Perform point cloud uniformization downsampling with the goal of density unification, reduce the density in the point cloud unit space, and obtain a low-density edge point set X ed ; Filter each X ed Points within radius d e If the number of point sets within the spherical range is less than N, set them as outliers and delete the triangular facets of the current edge points, and combine the remaining edge point sets with triangular neighbor facets; The triangular mesh S composed of three points j = {x1, x2, x3} and the triangle mesh S j The corresponding normal vector N j =sign{(x1-c)·[(x2-x1)×(x3-x1)]}*(x2-x1)×(x3-x1), where × represents the vector cross multiplication operation, · represents the vector dot multiplication operation, and the sign{} function is defined as a sign function. When the internal vector dot product is greater than 0, the direction of the triangle normal vector remains unchanged, otherwise it is reversed.

5. The method according to claim 4, characterized in that S300 includes: S310: Establish a Kd-tree for the skin point cloud Y to be assembled, search for the nearest neighbor points of the boundary sequence point cloud E to be assembled in the skin point cloud Y to be assembled, and establish one-to-one corresponding matching pairs; S320: Establish a margin distance metric for the points of the skin point cloud Y to be assembled; S330: Establishing the optimization error equation Where i is the candidate assembly edge point set X e In, j is the index of the skin point cloud Y to be assembled; S340: The nearest neighbor point Y of the to-be-assembled boundary sequence point cloud E in the to-be-assembled skin point cloud Y j Establish the skin micro-deformation equation; S350: Establish deformation constraints for other non-neighbor point sets; S360: Obtain the differentiable point cloud matching equation by Taylor expansion.

6. The method according to claim 5, characterized in that Specifically, S310: For the skin point cloud Y to be assembled, a Kd-tree is established, and for all points E in the boundary sequence point cloud E to be assembled i ∈E Search for the nearest neighbor point Y j ∈Y, forming a matching point pair E i →Y j ,Y j =min j {||Y j -E i || 2 }, current error Specifically, S320: Get S200 to extract the skin point cloud Y to be assembled and the candidate assembly edge point set X e The outer boundary E y , calculate the matching pair E point by point i →Y j Point Y in the backbone point concentration j ∈Y margin error This defines the residual variance minimum matching equation Where n is the number of point sets of the boundary sequence point cloud E to be assembled, and k is the index number; Specifically, S330: Establishing the optimization error equation Among them, the differentiable transformation parameters are expressed as Where R∈R 3x3 ,t∈R 1 ,0 dim represents a vector of all 0s with a base element dimension of dim, 1 dim The vector with all 1s as the basis element and dim as the dimension is 1, t is the differentiable translation parameter, R = [δ x ,δ y ,δ z ] T , δ x ,δ y ,δ z The three rotation transformation bases are Vector.

7. The method according to claim 6, characterized in that Specifically, S340: Based on the optimized error parameter representation ξ established in S330, the nearest neighbor point Y of the boundary E in the assembly skin point cloud Y is j Establish the skin micro deformation equation: Among them, n i Defined as the mean of the normal vectors of all adjacent triangles at the current point, t i is the differentiable translation parameter of the current deformation point on the normal vector, R j is the rotation matrix of the current point; Specifically, S350: Establish deformation constraints for other non-neighbor point sets, and search for neighbor backbone point sets N(j) for all non-neighbor point sets to perform known deformation smoothing constraints: S360: Taylor expansion to obtain differentiable point cloud matching equations, 8. The method according to claim 7, characterized in that Specifically, S400: For S360 Solve the first-order gradient equation f'(ξ)| ξ＝0 =J f”(ξ)| ξ＝0 =H, where J is the gradient matrix and H is the Hessian matrix; Solve the current optimal parameter ξ=min f(ξ) as the current optimization direction, and get the closed-form solution ξ=-H -1 J, ξ = {ΔR, Δt}, where ΔR is the rotation matrix and Δt is the translation vector.

9. The method according to claim 8, characterized in that Specifically, S500: Set the preset error threshold a3, and set the current optimization solution ξ=-H -1 J Substitution When f(ξ) < a3 or the number of iterations is greater than the total number of preset iterations and still does not converge, terminate the optimization and output the final optimized solution, transform the boundary sequence point cloud E to be assembled, and use its neighboring boundary on the assembled surface skin Y as the final milling boundary to cut off the surplus and obtain the final assembled surface F.

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