A topology-aware spraying trajectory planning method for large-size multi-curvature spacecraft spraying

Abstract

The present application relates to a kind of topological perception spray trajectory planning methods for large size multi-curvature spacecraft spraying, comprising obtaining spacecraft surface point cloud data and constructing undirected topological graph and constructing the high-dimensional fusion feature vector of each vertex;Spacecraft surface point cloud data is segmented into several spray topological regions based on graph convolutional neural network;Global gravity direction vector is introduced to construct joint optimization objective function on each spray topological region and solve, construct global geodesic distance scalar field to generate smooth spray curve, construct the local spray trajectory of each spray topological region;Global path planning is carried out to spray topological region, and the global optimal region traversal sequence is obtained, and then global spray trajectory is obtained.The present application is suitable for spacecraft complex curved surface heat protection coating spraying scene, effectively eliminates the process defects of large curvature transition zone, significantly improves the thickness uniformity, quality consistency and process reliability of special coating manufacturing of spaceflight.

Description

Technical Field

[0001] This invention relates to the fields of advanced spacecraft manufacturing and offline programming control technology for industrial robots, and in particular to a topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft. Background Technology

[0002] With the rapid development of aerospace engineering, the service requirements of spacecraft (such as launch vehicle fairings and reentry capsules) under extreme aerodynamic heating environments are constantly increasing, placing extremely high demands on the thickness uniformity and morphological accuracy of thermal protection coatings on their large-scale, complex aerodynamic curved surfaces. Traditional robotic spraying trajectory planning mainly relies on ideal geometric slicing methods based on 3D CAD models (such as the intersecting plane method). While this method is feasible to some extent on conventional industrial parts or gently curved surfaces, it faces many insurmountable engineering bottlenecks in the actual manufacturing of special coatings for spacecraft.

[0003] Specifically, the aerodynamic shape of spacecraft typically includes numerous high-curvature transition regions and complex topological structures. Traditional planar slicing projection methods based on external Euclidean space are prone to causing projection distortion in three-dimensional space when dealing with high-curvature regions, leading to shrinkage or divergence in the spacing between adjacent spraying trajectories and severely compromising the spatial overlap uniformity of the coating. Secondly, aerospace special heat-resistant coatings typically have high viscosity and large thickness. Traditional purely geometrically driven trajectory planning methods completely ignore the fluid dynamics of the coating and fail to consider the nonlinear driving effect of gravity on the tangential component of complex curved surfaces, making it easy to induce severe coating sagging defects in high-curvature or high-angle regions. In addition, existing region segmentation and path splicing methods often lack a deep understanding of the inherent topological features of the surface and often use simple bounding boxes or mesh divisions, which makes it easy for the robot to experience sudden changes in spray gun attitude and ineffective redundant idling when spraying across regions. Therefore, there is an urgent need to propose an intelligent trajectory planning method that breaks free from the constraints of traditional pure geometric slicing and deeply integrates fluid physics properties with the intrinsic manifold geometry of curved surfaces, in order to meet the engineering requirements of high-quality heat-resistant coating spraying on large-size complex curved surfaces of spacecraft. Summary of the Invention

[0004] To address the shortcomings of existing technologies in the automated manufacturing of large-size, complex curved surface thermal protection coatings for spacecraft, such as local large curvature trajectory distortion, hydrodynamic sagging defects, and cross-regional attitude abrupt changes, this invention provides a topology-aware spraying trajectory planning method for large-size, multi-curvature spacecraft. This method aims to achieve collaborative optimization of the spraying trajectory from three levels: surface topology cognition, physical deposition modeling, and inherent geometric constraints of the surface. It utilizes high-dimensional topological feature adaptive perception via graph convolutional neural networks, discrete approximation of process parameters incorporating sagging penalty factors, geodesic distortion-free isometric mapping based on manifold equations, and global high-order dynamic smoothing stitching based on surface normal continuity. This enables high-precision trajectory generation and end-to-end control of the spraying robot on complex three-dimensional geometric surfaces.

[0005] To achieve the above-mentioned technical objectives, the present invention provides the following technical solution: a topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft, comprising the following steps:

[0006] The original three-dimensional point cloud data of the spacecraft surface is acquired, and the original three-dimensional point cloud data is preprocessed and spatially calibrated to obtain the spacecraft surface point cloud data in the base coordinate system of the spraying robot.

[0007] Calculate the unit normal vector, maximum principal curvature, and minimum principal curvature of each data point in the point cloud data of the spacecraft surface, and then obtain the surface shape index of each data point;

[0008] An undirected topological graph is constructed using all data points in the spacecraft surface point cloud data as vertices. The high-dimensional fused feature vectors of each vertex are constructed by combining the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature and surface shape index of each data point.

[0009] The undirected topological graph and the high-dimensional fused feature vectors of each vertex are fed into a pre-trained graph convolutional neural network to segment the point cloud data on the spacecraft surface into several sprayed topological regions.

[0010] The cumulative coating thickness of each data point within the spraying topology region is calculated, and then a sagging deformation penalty factor is constructed by combining the global gravity direction vector. A joint optimization objective function for the spray gun moving speed and spray overlap distance is constructed in each spraying topology region.

[0011] Under the constraints of process safety conditions, the joint optimization objective function is solved to obtain the optimal spray gun moving speed and the optimal spray overlap distance for each spraying topology region.

[0012] Each spraying topology region is reconstructed into a continuous three-dimensional curved manifold mesh and a global geodesic distance scalar field is constructed. Then, combined with the optimal spraying overlap distance, discrete isosurfaces are constructed in each spraying topology region to generate smooth spraying curves for each theoretical spraying trajectory axis and construct the local spraying trajectory for each spraying topology region.

[0013] Global path planning is performed on the topological region of the spraying to obtain the globally optimal region traversal sequence, thereby obtaining the global spraying trajectory and the expected pose matrix of the spraying robot's spray gun at each trajectory point.

[0014] Optionally, the step of acquiring the original three-dimensional point cloud data of the spacecraft surface, preprocessing and spatially calibrating the original three-dimensional point cloud data to obtain the spacecraft surface point cloud data in the base coordinate system of the painting robot includes:

[0015] Drive the three-dimensional measurement equipment to perform a global scan of the spacecraft surface and obtain raw three-dimensional point cloud data;

[0016] Voxel grid filtering is used to uniformly downsample the original 3D point cloud data to reduce data redundancy, and a statistical outlier removal algorithm is combined to remove noise points, thus obtaining preprocessed 3D point cloud data.

[0017] Solve for the rigid body transformation matrix between the coordinate system of the 3D measuring equipment and the base coordinate system of the spraying robot, and map the preprocessed 3D point cloud data to the base coordinate system of the spraying robot to obtain the point cloud data of the spacecraft surface.

[0018] Drive the three-dimensional measurement equipment to perform a global scan of the spacecraft surface and obtain raw three-dimensional point cloud data;

[0019] Voxel grid filtering is used to uniformly downsample the original 3D point cloud data to reduce data redundancy, and a statistical outlier removal algorithm is combined to remove noise points, thus obtaining preprocessed 3D point cloud data.

[0020] Solve for the rigid body transformation matrix between the coordinate system of the 3D measuring equipment and the base coordinate system of the spraying robot, and map the preprocessed 3D point cloud data to the base coordinate system of the spraying robot to obtain the point cloud data of the spacecraft surface.

[0021] Optionally, the calculation of the unit normal vector, maximum principal curvature, and minimum principal curvature of each data point in the spacecraft surface point cloud data, and thereby obtaining the surface shape index of each data point, includes:

[0022] The K-nearest neighbor algorithm is used to obtain the local spatial neighborhood point set of each data point in the point cloud data of the spacecraft surface;

[0023] Principal component analysis is performed on the local spatial neighborhood point set of each data point to obtain the unit normal vector of each data point and construct the local tangent plane of each data point.

[0024] The least squares method is used to fit the quadratic microsurface in the local tangent plane of each data point to construct the local curvature tensor of each data point.

[0025] Solve for the eigenvalues ​​and eigenvectors of the local curvature tensor, and analytically obtain the maximum and minimum principal curvatures of each data point;

[0026] Introducing positive numbers value range The surface shape index of each data point in the spacecraft surface point cloud data is calculated, and its mathematical representation is as follows:

[0027] ;

[0028] in, This indicates the first point cloud data on the spacecraft surface. The surface shape index for each data point; Pi; It is the arctangent function; , These represent the points in the spacecraft surface point cloud data, respectively. The maximum and minimum principal curvatures of the data points satisfy the constraints. .

[0029] Optionally, the step of constructing an undirected topological graph using all data points in the spacecraft surface point cloud data as vertices includes: generating an undirected edge if the Euclidean distance between two data points is less than a preset threshold, thereby forming an edge set of the undirected topological graph.

[0030] The process of constructing a high-dimensional fusion feature vector for each vertex by combining the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature, and surface shape index of each data point includes: concatenating and splicing the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature, and surface shape index of the data point to obtain the high-dimensional fusion feature vector of the vertex corresponding to the data point.

[0031] Optionally, the step of feeding the undirected topological graph and the high-dimensional fused feature vectors of each vertex into a pre-trained graph convolutional neural network to segment the spacecraft surface point cloud data into several sprayed topological regions includes:

[0032] By transposing and stacking the high-dimensional fused feature vectors of all vertices, we obtain the fused feature matrix. ;

[0033] The graph convolutional neural network includes an input layer, several graph convolutional hidden layers, and an output layer.

[0034] The graph convolutional hidden layer uses the following normalized approximation formula based on spectral graph theory to propagate the high-dimensional fused feature vectors of each vertex:

[0035] ;

[0036] in, The graph convolutional neural network represents the first... The input node feature matrix of the graph convolutional hidden layer, the initial graph convolutional hidden layer Set as ; The graph convolutional neural network represents the first... The output node feature matrix of the nth graph convolutional hidden layer, i.e., the nth... The input node feature matrix of the graph convolutional hidden layer; The self-loop adjacency matrix is ​​defined as follows: , The standard adjacency matrix of an undirected topological graph. It is the identity matrix; Let denote the self-circularity matrix, which is a diagonal matrix whose diagonal elements are scalars. The sum of the elements in the corresponding row; The graph convolutional neural network represents the first... The learnable parameter weight matrix of each graph convolutional hidden layer; Represents a nonlinear activation function;

[0037] The output layer outputs the probability distribution characteristics of the sprayed topology region to which each vertex belongs, that is, the probability distribution characteristics of the sprayed topology region to which each data point belongs, thereby dividing the spacecraft surface point cloud data into several sprayed topology regions.

[0038] Optionally, the cumulative coating thickness of each data point within the spraying topology region is calculated, and then a sagging deformation penalty factor is constructed by combining the global gravity direction vector. A joint optimization objective function regarding the spray gun moving speed and spray overlap distance is constructed for each spraying topology region, including:

[0039] Define the theoretical spraying trajectory axis and calculate the dynamic deposition amount of the spraying robot's spray gun:

[0040] ;

[0041] in, This represents the data points in the sprayed topology region. Indicates the overlap distance of the coating; The first part of the spray gun of the painting robot Dynamic deposition amount along the spray trajectory axis of the theoretical spraying method; This indicates the maximum deposition amount at the center axis of the spray gun on the painting robot. This represents an exponential function with the natural constant e as its base. The effective radius parameter characterizing the spray width; For data points To the The vertical Euclidean distance of the spraying trajectory axis in the theoretical spraying method; Represents the cosine function; Indicates the axis of the spray jet and the data points The angle between the unit normal vectors at that location;

[0042] Calculating the cumulative coating thickness at each data point within the spraying topology region based on the dynamic deposition amount of the spraying robot's spray gun. :

[0043] ;

[0044] in, This indicates the speed at which the spray gun of the painting robot moves; This represents the total number of theoretical spraying trajectory axes within the current spraying topology region;

[0045] A sagging deformation penalty factor is constructed based on the unit normal vector of data points and the cumulative coating thickness, combined with the global gravity direction vector. :

[0046] ;

[0047] in, The comprehensive physical property constants that characterize the fluid properties of the coating; For data points The unit normal vector; This represents the global gravity direction vector; Indicates the calculation of the modulus;

[0048] Construct information about the spray gun movement speed in each spraying topology region. Spraying overlap distance The joint optimization objective function is defined as follows:

[0049] ;

[0050] in, Indicates the first The joint optimization objective function for each sprayed topology region; The target process thickness for the coating; and These represent the thickness error terms. With the risk of slippage Weighting coefficients; Indicates the first One sprayed topological area; Indicates the first A spraying topology area Inner spraying topology area Do double integral, Indicates the first A spraying topology area Inner spraying topology area Do The double integral.

[0051] Optionally, under the constraints of process safety conditions, solving the joint optimization objective function to obtain the optimal spray gun moving speed and optimal spray overlap distance for each spraying topology region includes:

[0052] The joint optimization objective function is transformed into a weighted summation approximation of discrete data points within the spraying topology region, mathematically represented as follows:

[0053] ;

[0054] in, Representing data points The corresponding local infinitesimal approximation area;

[0055] Upper and lower limits are set for the spray gun movement speed and spray overlap distance. The process safety constraints are defined as follows:

[0056] ;

[0057] ;

[0058] in, , These represent the upper and lower limits of the spray gun's movement speed, respectively; , These represent the upper and lower limits of the coating overlap distance, respectively.

[0059] Under the constraints of process safety conditions, a sequential quadratic programming algorithm is used to minimize the joint optimization objective function after iterative solution by weighted summation approximation, and the optimal spray gun moving speed and optimal spray overlap distance of each spraying topology region are output.

[0060] Optionally, the step of reconstructing each spraying topology region into a continuous three-dimensional curved manifold mesh and constructing a global geodesic distance scalar field, and then constructing discrete isosurfaces in each spraying topology region in combination with the optimal spraying overlap distance, generating smooth spraying curves for each theoretical spraying trajectory axis, and constructing local spraying trajectories for each spraying topology region, includes:

[0061] A point cloud edge feature detection algorithm is used to extract the set of geometric boundary points of the outer contour of each sprayed topological region;

[0062] Using the set of geometric boundary points of the outer contour as the constraint boundary, the discrete data points in each spraying topological region are connected by Delaunay triangulation to make them have topological edge connectivity, thereby reconstructing a continuous three-dimensional curved surface manifold mesh.

[0063] A continuous geodesic distance scalar field is established on the continuous three-dimensional curved manifold mesh corresponding to each spraying topology region, and the geodesic distance scalar field of the points in the outer contour geometric boundary point set is initialized to 0;

[0064] Using the outer contour geometric boundary point set as the wavefront evolution reference, the fast travel method is used in each continuous three-dimensional manifold grid to solve the minimum value of all data points in the current spraying topology region reaching the outer contour geometric boundary point set along the surface of the continuous three-dimensional manifold grid, thereby constructing a global geodesic distance scalar field containing all data points in the current spraying topology region.

[0065] Based on the optimal spray overlap distance and the global geodesic distance scalar field, discrete isosurfaces are extracted from the current spray topology region, mathematically represented as follows:

[0066] ;

[0067] in, This represents the index of the theoretical spray trajectory axis within the current spray topology region; Indicates the first position within the current spraying topology region. The equidistant mapping trajectory curves of the spraying trajectory axis in the theory of topology divide the current spraying topology region into discrete isosurfaces; Indicates the first Data points in each sprayed topology region; Represents information about data points The global geodesic distance scalar field; Indicates the optimal spray overlap distance;

[0068] use The subuniform rational B-spline curves are used to perform spatial smoothing fitting on the equidistant mapped trajectory curves of each theoretical spray trajectory axis within the spray topology region, thereby generating all smooth spray curves within the spray topology region.

[0069] The smooth spraying curves corresponding to the theoretical spraying trajectory axes within a single spraying topology area are connected end to end in the order of the number of theoretical spraying trajectory axes to form a local spraying trajectory.

[0070] Optionally, the adoption The sub-uniform rational B-spline curves are used to perform spatial smoothing fitting on the equidistant mapped trajectory curves of each theoretical spray trajectory axis within the spraying topology region, generating all smooth spray curves within that spraying topology region, including:

[0071] Constructing parameterized curve equations for non-uniform rational B-splines in three-dimensional space:

[0072] ;

[0073] in, Indicates the first The non-uniform rational B-spline parameterized curve obtained by fitting the isochronous mapped trajectory curve; Denotes the normalized independent continuous parameter used to describe the parameterized curve of a non-uniform rational B-spline. ; indicates the control point index. This represents the total number of control points required for a smooth spatial fitting of the current equidistant mapped trajectory curve. Indicates the first A control point, wherein the control point is a spatial vertex used to control the spatial geometry of a non-uniform rational B-spline parameterized curve. For the first Weighting factors corresponding to each control point; For the first control points Subuniform rational B-spline basis functions;

[0074] Based on the cumulative chord length parameterization method for each data point on the discrete isometric mapping trajectory curve, a non-decreasing sequence of real numbers is constructed as the node vector. Combination number The values ​​of all B-spline basis functions were derived and calculated, including the initial zero-order basis function. Defined as:

[0075] ;

[0076] Higher-order basis functions The recursive calculation formula is:

[0077] ;

[0078] in, Represents the node vector The first in A fixed set of discrete node values ​​is used to define the local support interval of the basis function;

[0079] Set boundary protection constraints: when When a denominator of a subuniform rational B-spline basis function is zero during the solution process, the corresponding fractional term is defined as zero as a whole.

[0080] Construct a system of linear equations relating the data points, the basis function matrix, and the control points: ;in Let be the coordinate matrix composed of known data points on the equidistant mapped trajectory curve. This is the rational basis function matrix constructed by normalizing the basis functions. The matrix to be found is constructed from the control points; the control points are solved by inverse calculation using the least squares method. and their corresponding weighting factors This allows for the construction of a smooth spraying curve within the spraying topology region.

[0081] Optionally, the step of performing global path planning on the spraying topology region to obtain the globally optimal region traversal sequence, thereby obtaining the global spraying trajectory, and the expected pose matrix of the spraying robot's spray gun at each trajectory point, includes:

[0082] The starting and ending points of the local spraying trajectories of each spraying topology region are regarded as traversal nodes. A traveling salesman problem model is constructed. The cosine of the angle between the unit normal vectors at the starting and ending points of the local spraying trajectories of each spraying topology region and the spatial Euclidean distance are used as edge weights. The heuristic ant colony algorithm is used to solve the globally optimal region traversal sequence.

[0083] The global spraying trajectory is obtained by linking the local spraying trajectories of each spraying topology region based on the globally optimal region traversal sequence.

[0084] Calculate the unit normal vector for each trajectory point in the global spraying trajectory, and then calculate the expected pose matrix of the spray gun to ensure that the axis of the spray jet is always collinear with the normal vector of the trajectory point.

[0085] By employing the above technical solution, the present invention provides a topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft, which has at least the following beneficial effects:

[0086] (1) This invention proposes a high-dimensional topological feature adaptive perception mechanism based on graph convolutional neural networks. By introducing surface shape index and principal curvature with numerical stability protection to construct local geometric features, and using supervised pre-trained graph convolutional neural networks (GCN) for high-dimensional feature fusion and region classification, it gets rid of the traditional mechanical mesh division based on geometric boundaries. It can accurately identify complex topological structures such as large curvature transition areas and smooth surfaces of spacecraft, laying a solid foundation for intelligent and data-driven independent optimization of subsequent process parameters and smooth attitude transition.

[0087] (2) This invention constructs an adaptive optimization model for process parameters that integrates fluid dynamics and sagging penalty factors. In view of the physical characteristics of high viscosity and large thickness of aerospace special heat-resistant coatings, it innovatively introduces the coating sagging deformation caused by the tangential component of gravity into the joint optimization objective function. By solving the discrete point cloud using sequential quadratic programming (SQP), it adaptively matches the optimal spray gun moving speed and the optimal spray overlap distance for each spraying topology region. This fundamentally overcomes the coating sagging and accumulation defects in large curvature areas that are easily induced by traditional pure geometric trajectory planning, and significantly improves the overall thickness compliance rate and process reliability of the coating.

[0088] (3) This invention breaks through the distortion-free equidistant mapping technology of geodesics based on manifold equations, abandons the traditional planar slice projection method that relies on external Euclidean space, and directly generates strictly equidistant trajectory curves in three-dimensional intrinsic manifold space by numerically solving the surface geodesic constraint equations using the Fast Marching Method (FMM) on the sprayed topological region. This completely eliminates the problem of trajectory spacing shrinkage or divergence distortion caused by planar slice projection on large-size aerodynamic complex curved surfaces, and absolutely guarantees the spatial overlap uniformity of multiple coatings from the underlying geometric logic.

[0089] (4) This invention achieves high-order dynamic smoothing and global efficient splicing based on surface normal constraints. In solving the Traveling Salesman Problem (TSP) for cross-regional trajectory connections, it innovatively uses the cosine of the angle between the unit normal vectors at the start and end data points of the spraying topology region and the spatial Euclidean distance as the core edge weights of the heuristic ant colony algorithm, effectively avoiding sudden changes in the end posture of the spraying robot during cross-regional spraying; at the same time, it combines with The subuniform rational B-spline curves are used to continuously and spatially smooth the discrete equidistant mapped trajectory curves. This not only minimizes the space idle transition time, but also eliminates acceleration jumps during the joint execution process of the bottom spraying robot, which greatly improves the automation efficiency and motion execution quality of high-end surface treatment of spacecraft. Attached Figure Description

[0090] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0091] Figure 1 This is an overall flowchart of a topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft, according to the present invention. Detailed Implementation

[0092] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0093] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0094] Figure 1 This embodiment illustrates a specific implementation. It extracts high-dimensional fused feature vectors from point cloud data on the spacecraft surface and constructs an undirected topological graph. Based on a pre-trained graph convolutional neural network, it segments the sprayed topological region. A global gravity direction vector is introduced to construct and solve a joint optimization objective function within each sprayed topological region. Finally, a global geodesic distance scalar field is constructed and combined with... The subuniform rational B-spline curves extract the smooth spraying curves corresponding to the axes of each theoretical spraying trajectory, generate local spraying trajectories, and perform global path planning on the spraying topology region to generate global spraying trajectories. This effectively eliminates process defects in the large curvature transition zone and significantly improves the thickness uniformity, quality consistency, and process reliability of aerospace special coating manufacturing.

[0095] Please refer to Figure 1 This embodiment proposes a topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft. The method includes the following steps:

[0096] S1. Acquire the original three-dimensional point cloud data of the spacecraft surface, preprocess and spatially calibrate the original three-dimensional point cloud data to obtain the spacecraft surface point cloud data in the base coordinate system of the spraying robot.

[0097] As a preferred embodiment of step S1, the specific process includes:

[0098] S11. Drive the three-dimensional measurement equipment to perform a global scan of the large-sized complex curved surface of the spacecraft to obtain high-precision original three-dimensional point cloud data of the surface to be coated.

[0099] S12. Use voxel grid filtering to uniformly downsample the original 3D point cloud data to reduce data redundancy. Combine this with a statistical outlier removal algorithm to calculate the standard deviation distribution of the distance of each data point in its spatial neighborhood. Remove noise points caused by ambient light or metal surface reflection during the measurement process to obtain preprocessed 3D point cloud data.

[0100] S13. Extract the three-dimensional feature points of the preset calibration target in the spacecraft scanning scene, and use the singular value decomposition algorithm to solve the rigid body transformation matrix between the coordinate system of the three-dimensional measuring equipment and the base coordinate system of the spraying robot. The rigid body transformation matrix includes a global rotation matrix. With global translation vector In the initial stage of system deployment, the data was acquired offline through a global spatial calibration process. The preprocessed 3D point cloud data was then mapped to the base coordinate system of the painting robot to obtain the spacecraft surface point cloud data.

[0101] S2. Calculate the unit normal vector, maximum principal curvature, and minimum principal curvature of each data point in the point cloud data of the spacecraft surface, and then obtain the surface shape index of each data point.

[0102] As a preferred embodiment of step S2, the specific process includes:

[0103] S21 selects any data point from the spacecraft surface point cloud data. ( To index data points in the spacecraft surface point cloud data, and to improve computational efficiency, the K-nearest neighbor algorithm (Kd-Tree spatial index structure accelerates the search) is used. Local spatial neighborhood point set Among them, the number of domain points The point cloud density is typically set between 15 and 50.

[0104] S22, Data points The covariance matrix is ​​constructed from the local spatial neighborhood point set, and then principal component analysis (PCA) is performed. The eigenvector corresponding to the smallest eigenvalue of the covariance matrix is ​​taken, and normal consistency redirection is performed using the viewpoint direction to generate data points. unit normal vector to construct data points The local tangent plane.

[0105] S23, using data points Using the origin as the starting point, a quadratic microsurface is fitted using the least squares method within its local tangent plane, thus constructing data points smoothly. The local curvature tensor (i.e., the Weingarten mapping matrix).

[0106] S24. Solve for the eigenvalues ​​and eigenvectors of the local curvature tensor, and obtain the data points analytically. Maximum principal curvature Minimum principal curvature .

[0107] S25. While principal curvature can reflect the degree of local physical bending, it is difficult to intuitively distinguish the topological convexity / concaveness type of a surface (such as ridges, valleys, and saddles). To intuitively distinguish the topological convexity / concaveness type of a surface and ensure the absolute stability of engineering numerical calculations, the surface shape index of each data point in the spacecraft surface point cloud data is calculated, and its mathematical representation is as follows:

[0108] ;

[0109] in, This indicates the first point cloud data on the spacecraft surface. The surface shape index of each data point has a range distribution that continuously maps to... Within the range; Pi; It is the arctangent function; the maximum principal curvature Minimum principal curvature Strictly meet the constraints ; To prevent small positive numbers with a denominator of 0 (range of values) In this embodiment, it is set ).

[0110] In this step, the following is introduced It can effectively avoid large, flat areas on the spacecraft (when When the denominator approaches zero (i.e., at a local umbilicus), numerical divergence explosion occurs. The surface shape index maps the topological features of a local surface to a fixed interval, effectively enhancing the separability of complex aerodynamic features on spacecraft surfaces, such as flange edges and fairing spheres, in subsequent graph convolutional neural networks.

[0111] S3. Construct an undirected topological graph using all data points in the spacecraft surface point cloud data as vertices, and combine the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature and surface shape index of each data point to construct a high-dimensional fused feature vector for each vertex.

[0112] As a preferred embodiment of step S3, the specific process includes:

[0113] S31. Construct a vertex set from all data points in the spacecraft surface point cloud data. .

[0114] S32. If the Euclidean distance between any two data points (vertices) is less than a preset threshold, then an undirected edge is generated between the two points, forming the edge set of the undirected topological graph. The constructed undirected topological graph is denoted as . .

[0115] S33, For vertex set For any vertex in the array, obtain the position coordinate vector of its corresponding data point. Unit normal vector Maximum principal curvature Minimum principal curvature With surface shape index By concatenating and splicing the data, a high-dimensional fused feature vector of the corresponding vertex is obtained. The definition is as follows:

[0116] ;

[0117] in, Indicates the transpose operation; position coordinate vector This includes the x, y, and z coordinates of the data point in the base coordinate system of the painting robot. , , Defined as: Unit normal vector Includes three components along the x, y, and z axes. , , Defined as: .

[0118] S4. Input the undirected topological graph and the high-dimensional fused feature vectors of each vertex into a pre-trained graph convolutional neural network to segment the point cloud data on the spacecraft surface into several sprayed topological regions.

[0119] As a preferred embodiment of step S4, the specific process includes:

[0120] S41. Transpose and stack the high-dimensional fused feature vectors of all vertices to obtain the fused feature matrix. .

[0121] S42. A Graph Convolutional Neural Network (GCN) consists of an input layer, several graph convolutional hidden layers, and an output layer. The graph convolutional hidden layers propagate the high-dimensional fused feature vectors of each vertex using the following normalized approximation formula based on spectral graph theory:

[0122] ;

[0123] in, The graph convolutional neural network represents the first... The input node feature matrix of the graph convolutional hidden layer, the initial graph convolutional hidden layer Set as ; The graph convolutional neural network represents the first... The output node feature matrix of the nth graph convolutional hidden layer, i.e., the nth... The input node feature matrix of the graph convolutional hidden layer; The self-loop adjacency matrix is ​​defined as follows: , Undirected topological graph The standard adjacency matrix, It is the identity matrix; Let denote the self-circularity matrix, which is a diagonal matrix whose diagonal elements are scalars. The sum of the elements in the corresponding row; The graph convolutional neural network represents the first... The learnable parameter weight matrix of each graph convolutional hidden layer; This represents a non-linear activation function (the ReLU function is used in this embodiment).

[0124] The output layer outputs the probability distribution characteristics of the sprayed topology region to which each vertex (i.e. each data point) belongs through a fully connected layer and a Softmax activation function, thereby dividing the spacecraft surface point cloud data into several sprayed topology regions (including smooth aerodynamic surfaces, high curvature transition regions, and occlusion and narrow slit interference regions, etc.), providing high-precision region boundary prior data for subsequent adaptive parameter optimization and trajectory isometric mapping.

[0125] To ensure the network's feasibility, the graph convolutional neural network requires offline supervised training before deployment. Dataset construction involves collecting a large number of 3D scanned point clouds of typical spacecraft (such as fairings, wing leading edges, and reentry capsules). These points are manually labeled by process experts, assigning each data point a corresponding ground truth class label (e.g., class 0 for smooth aerodynamic surfaces, class 1 for high-curvature transition regions, and class 2 for occlusion and narrow-slit interference regions). The pre-trained loss function uses the cross-entropy loss function to measure the difference between the probability distribution characteristics predicted by the graph convolutional neural network and the ground truth class labels. The calculation formula is as follows:

[0126] ;

[0127] in, Represents the cross-entropy loss function. This is an index for the topological region of the spraying application. This represents the total number of topological regions to be coated. The first in the dataset used for pre-training One-hot encoding of the true class label for each data point is used as an indicator variable. for The probability distribution characteristics predicted by the corresponding graph convolutional neural network. This represents the total number of data points in the dataset used for pre-training; This is a logarithmic calculation.

[0128] During pre-training, the Adam optimization algorithm is used to optimize the learnable parameter weight matrix. An iterative update based on gradient descent is performed (with an initial learning rate of 0.001). After sufficient training and convergence, the GCN model can accurately and adaptively segment the large-scale complex curved surface point cloud of the spacecraft into multiple independent spraying topology regions based on the input local geometric features and graph topology relationships. This provides accurate region boundaries and geometric prior data for subsequent adaptive parameter optimization of sag penalty and trajectory isometric mapping.

[0129] S5. Calculate the cumulative coating thickness of each data point within the spraying topology region, and then construct the sagging deformation penalty factor by combining the global gravity direction vector. Construct a joint optimization objective function for the spray gun moving speed and spraying overlap distance in each spraying topology region.

[0130] As a preferred embodiment of step S5, the specific process includes:

[0131] S51. Set the theoretical spraying trajectory axis and establish the single-pass spatial deposition rate function. .

[0132] In practical engineering, the single-pass spray pattern is not a uniform, ideal rectangle, but rather exhibits a continuous distribution with a thicker center and thinner edges. This embodiment uses a Gaussian spatial distribution model to characterize the spray gun deposition rate under static conditions, and calculates the dynamic deposition amount of the spraying robot's spray gun as follows:

[0133] ;

[0134] in, This represents the data points in the sprayed topology region. Indicates the overlap distance of the coating; The first part of the spray gun of the painting robot Dynamic deposition amount along the spray trajectory axis of the theoretical spraying method; This indicates the maximum deposition amount at the center axis of the spray gun on the painting robot. This represents an exponential function with the natural constant e as its base. The effective radius parameter, which characterizes the spray width, was obtained through prior offline spraying process experiments. For data points To the The vertical Euclidean distance of the theoretical spray trajectory axis (this distance is affected by the spray overlap distance) (control) Represents the cosine function; This indicates the axis of the spray jet (referring to the direction of paint spraying in three-dimensional space) and the data points. The angle between the local tangent plane and the normal.

[0135] The spray trajectory axis is the geometric center line of the spray gun center sweeping along the curved surface during the spraying operation. In the current stage of joint optimization of process parameters, the actual continuous spray trajectory has not yet been generated. The theoretical spray trajectory axis can be obtained through the following algorithm: using the outer contour geometric boundary of the current spray topology region as the offset starting line, the current spray overlap distance... As the equidistant offset step size, an offset operation is performed on the curved surface towards the interior of the current spraying topology region, with an offset distance of [value missing]. The spatially equidistant contour lines formed at that time are the first... The theoretical spraying trajectory axis.

[0136] Dynamic sedimentation The design takes into account the spatial distance between the spray gun and the workpiece, the spray angle, and the Gaussian spatial distribution characteristics of the spray pattern.

[0137] S52. Considering that the large-size curved surface spraying of spacecraft needs to be completed through multiple overlapping trajectories, in the process of multi-channel dynamic continuous spraying, assuming that the spraying robot's spray gun moves at a constant speed along the trajectory, the data points within the spraying topology area are... Cumulative coating thickness This represents the sum of the dynamic deposition amounts from each pass. It is based on the dynamic deposition amount from the spray gun of the spraying robot. Calculate the cumulative coating thickness at each data point within the spraying topology region. as follows:

[0138] ;

[0139] in, This indicates the speed at which the spray gun of the painting robot moves; This represents the total number of theoretical spraying trajectory axes within the current spraying topology region.

[0140] S53. Spacecraft coatings typically exhibit high viscosity. Under gravitational fields, coatings with large curvatures or steep angles are prone to "sagging" defects, where they tangentially slide and accumulate. Based on the simplified Navier-Stokes equations of fluid mechanics under the thin-film fluid approximation, the tangential shear stress is proportional to the cube of the liquid film thickness and is driven by the tangential component of gravity on curved surfaces.

[0141] A sagging deformation penalty factor is constructed based on the unit normal vector of data points and the cumulative coating thickness, combined with the global gravity direction vector. :

[0142] ;

[0143] in, The comprehensive physical property constants that characterize the fluid properties of the coating (related to coating density, dynamic viscosity and gravitational acceleration, and can be obtained through prior process rheological experiments); For data points The unit normal vector; Represents the global gravity direction vector (usually set to...). ); Indicates the calculation of the modulus; It strictly represents the sine value of the inclination angle of the surface at that point relative to the direction of gravity, reflecting the real tangential driving force that causes the sag (i.e. the driving force of gravity along the tangential direction of the surface).

[0144] sag deformation penalty factor The physical meaning is clear: the greater the thickness and the greater the tangential gravity component, the greater the risk of sagging.

[0145] S54. Taking into account both the process compliance of coating thickness and the suppression of sagging defects, in each spraying topology area ( (This represents the index of the spray topology region) to construct information about the spray gun movement speed. Spraying overlap distance The joint optimization objective function is defined as follows:

[0146] ;

[0147] in, Indicates the first The joint optimization objective function for each sprayed topology region; The target process thickness for the coating; and These represent the thickness error terms. With the risk of slippage Weighting coefficients; Indicates the first One sprayed topological area; Indicates the first A spraying topology area Inner spraying topology area Do double integral, Indicates the first A spraying topology area Inner spraying topology area Do The double integral.

[0148] S6. Under the constraints of process safety conditions, the joint optimization objective function is solved to obtain the optimal spray gun moving speed and the optimal spray overlap distance for each spraying topology region.

[0149] As a preferred embodiment of step S6, the specific process includes:

[0150] S61. Since the input three-dimensional measurement data is a discrete point cloud, the joint optimization objective function is transformed into a weighted summation approximation of discrete data points within the spraying topology region, mathematically represented as follows:

[0151] ;

[0152] in, Representing data points The corresponding local infinitesimal approximation area.

[0153] S62. Further define process safety constraints.

[0154] Upper and lower limits are set for the spray gun movement speed and spray overlap distance (determined by the physical limits of the spraying actuator). The process safety constraints are defined as follows:

[0155] ;

[0156] ;

[0157] in, , These represent the upper and lower limits of the spray gun's movement speed, respectively; , These represent the upper and lower limits of the spray overlap distance, respectively.

[0158] S63. Under the constraints of process safety conditions, the Sequential Quadratic Programming (SQP) algorithm is used to iteratively minimize the joint optimization objective function after it is transformed into a weighted sum approximation, and the optimal spray gun moving speed for each spraying topology region is output. Optimal spray overlap distance .

[0159] During algorithm execution, based on the analytical gradient of the objective function and the approximation information of the Hessian matrix, the original nonlinear optimization problem is approximated as a quadratic programming subproblem in each iteration step. Finally, the optimal spray gun movement speed corresponding to each spraying topology region that satisfies the KKT (Karush-Kuhn-Tucker) optimality condition is output. Optimal spray overlap distance .

[0160] S7. Reconstruct each spraying topology region into a continuous three-dimensional curved manifold mesh and construct a global geodesic distance scalar field. Then, combine the optimal spraying overlap distance to construct discrete isosurfaces in each spraying topology region, generate smooth spraying curves for each theoretical spraying trajectory axis, and construct the local spraying trajectory for each spraying topology region.

[0161] As a preferred embodiment of step S7, the specific process includes:

[0162] S71, For any sprayed topology area The geometric boundary point set of its outer contour is extracted using the Alpha-Shape edge contour detection algorithm or the Principal Component Analysis (PCA) boundary detection method. .

[0163] S72. Since the original three-dimensional measurement point cloud is essentially a discrete, disordered set of coordinates, lacking the continuous topological connectivity required for solving partial differential equations, this invention first reconstructs the spraying topological region through restricted Delaunay triangulation. That is, using the set of geometric boundary points of the outer contour as the constraint boundary, the spraying topological region is divided by Delaunay triangulation. The discrete data points are connected to give them topological edge connectivity, thereby reconstructing them into a continuous three-dimensional curved surface mesh with local connectivity.

[0164] S73, in the sprayed topology area A continuous geodesic distance scalar field is established on the corresponding continuous three-dimensional curved manifold mesh. Set of geometric boundary points of the outer contour The geodesic distance scalar field of the points in the field is initialized to 0.

[0165] Specifically, the set of geometric boundary points of the outer contour As a scalar field of geodesic distance The initial zero level set for the sprayed topological region arbitrary boundary data points The initial geodesic distance boundary conditions are as follows: .

[0166] S74. Using the outer contour geometric boundary point set as the wavefront evolution reference, the Fast Marching Method (FMM) is used in each continuous three-dimensional manifold grid to solve for the minimum value of all data points in the current spraying topology region reaching the outer contour geometric boundary point set along the surface of the continuous three-dimensional manifold grid, thereby constructing a global geodesic distance scalar field containing all data points in the current spraying topology region.

[0167] Specifically, the geodesic equation (i.e., the Eikonal equation) satisfying the equidistant evolution constraint is first solved in a continuous three-dimensional curved manifold mesh. The equidistant evolution constraint means that the propagation velocity of the wavefront extending inward along the local normal on the manifold surface is kept constant at a unit rate, thus ensuring that the obtained distance strictly corresponds to the shortest physical connection on the surface. This equation geometrically constrains the geodesic distance scalar field. The intrinsic gradient magnitude on the manifold surface is always 1, meaning the wavefront expands inward on the surface at a unit velocity for any data point. Its spatial partial differential equation is expressed as: ,in Indicates the calculation of the modulus. The intrinsic surface gradient operator represents the tangent space of a continuous three-dimensional surface.

[0168] In practice, a minimum heap data structure is maintained, and the nodes of the continuous three-dimensional curved manifold mesh are divided into three states: "Accepted", "Trial", and "Far". The algorithm always pops the node with the smallest current geodesic distance from the trial point set and adds it to the Accepted state, and updates the geodesic distance of its adjacent unknown nodes using the upwind difference scheme.

[0169] The spraying topology region is obtained through mesh iterative solution using the FMM algorithm. All data points Reaching the geometric boundary along the surface The minimum geodesic distance is obtained, thus constructing a globally complete global geodesic distance scalar field. .

[0170] S75. Based on the optimal spraying overlap distance and the global geodesic distance scalar field, discrete isosurfaces are extracted from the current spraying topology region, mathematically represented as follows:

[0171] ;

[0172] in, This represents the index of the theoretical spray trajectory axis within the current spray topology region; Indicates the first position within the current spraying topology region. The equidistant mapping trajectory curves of the spraying trajectory axis in the theory of topology divide the current spraying topology region into discrete isosurfaces; Indicates the current (i.e., the first) (Number) data points in the sprayed topology area; Represents information about data points The global geodesic distance scalar field; This indicates the optimal spray overlap distance.

[0173] This step is completed entirely within the intrinsic space of the curved surface, completely eliminating the defects in trajectory spacing contraction or distortion caused by the external plane slicing method in the aerodynamic transition zone with high curvature.

[0174] S76. To avoid sudden changes in joint acceleration and body vibration during discrete point interpolation of the painting robot, the following measures are adopted: The subuniform rational B-spline curves are used to perform spatial smoothing fitting on the equidistant mapped trajectory curves of each theoretical spray trajectory axis within the spray topology region, generating all smooth spray curves within the spray topology region.

[0175] More specifically, step S76 includes the following process:

[0176] S761. Constructing parameterized curve equations for non-uniform rational B-spline curves in three-dimensional space:

[0177] ;

[0178] in, Indicates the first The parameterized curves of non-uniform rational B-splines (NURBS) obtained by fitting the isometric mapped trajectory curves; Denotes the normalized independent continuous parameter used to describe the parameterized curve of a non-uniform rational B-spline, with a value range of 1. ; Indicates the control point index. This represents the total number of control points required for a smooth spatial fitting of the current equidistant mapped trajectory curve. Indicates the first A control point, wherein the control point is a spatial vertex used to control the spatial geometry of a non-uniform rational B-spline parameterized curve. For the first Weighting factors corresponding to each control point; For the first control points Subuniform rational B-spline basis functions.

[0179] To ensure the smooth motion of the end effector of the painting robot, this embodiment sets the polynomial order. (i.e., a cubic NURBS curve), thereby ensuring that the generated trajectory has [certain characteristics] in three-dimensional space. Continuity (curvature continuity).

[0180] S762. Based on the cumulative chord length parameterization method for each data point on the discrete equidistant mapped trajectory curve, a non-decreasing real number sequence is constructed as the node vector. Combination number All B-spline basis function values ​​were derived and calculated, including the initial zero-order basis function. Defined as:

[0181] ;

[0182] Higher-order basis functions The recursive calculation formula is:

[0183] ;

[0184] in, Represents the node vector The first in A fixed set of discrete node values ​​is used to define the local support interval of the basis function; the node vector... The total number of nodes in the system is .

[0185] S763. To prevent anomalies caused by denominators being zero in the recursive calculation of higher-order basis functions, boundary protection constraints are set: when When a fractional rational B-spline basis function with a denominator of 0 occurs during the solution process, the corresponding fractional term is defined as 0 as a whole.

[0186] S764. Construct a system of linear equations relating the data points, the basis function matrix, and the control points: ;in Let be the coordinate matrix composed of known data points on the equidistant mapped trajectory curve. This is the rational basis function matrix constructed by normalizing the basis functions. The matrix to be determined is constructed from the control points; the control points are solved by inversely calculating the matrix using the least squares method. and their corresponding weighting factors This allows for the construction of a smooth spraying curve within the spraying topology region.

[0187] S77. Connect the smoothed spraying curves of each theoretical spraying trajectory axis in a single spraying topology area end to end according to the index order of the number of theoretical spraying trajectory axes (i.e., connect them in a "bow" shape) to form a local spraying trajectory.

[0188] S8. Perform global path planning on the spraying topology region to obtain the globally optimal region traversal sequence, thereby obtaining the global spraying trajectory and the expected pose matrix of the spraying robot's spray gun at each trajectory point.

[0189] As a preferred embodiment of step S8, the specific process includes:

[0190] S81. In order to minimize the spatial idle transition time of the spray gun in the non-spraying state, the start and end points of the local spraying trajectory of each spraying topology region are regarded as traversal nodes. The traditional path planning method that only uses spatial distance or tangent as weight is abandoned. The innovative method uses the surface normal continuity (i.e., the cosine value of the angle between the unit normal vectors) and the spatial Euclidean distance at the boundary of each region (the start and end points of the local spraying trajectory of each spraying topology region) as edge weights. The heuristic ant colony algorithm is used to solve the globally optimal region traversal sequence (i.e., the Traveling Salesman Problem (TSP) model).

[0191] Specifically, the present invention defines nodes. To the node The transfer cost weight is not only proportional to the Euclidean distance between the two points, but also to the node With nodes Unit normal vector , The included angle cosine value Related ( (Angle) The larger the value, the higher the penalty cost, thus forcing the algorithm to prioritize transitions to regions with gentle changes in normal direction, greatly reducing the risk of sudden attitude changes during cross-regional movements.

[0192] S82. After determining the globally optimal region traversal sequence, link the local spraying trajectories of each spraying topology region end to end to obtain the global spraying trajectory.

[0193] S83. Calculate the unit normal vector for each trajectory point in the global spraying trajectory, and then calculate the desired pose matrix of the spray gun. This ensures that the axis of the spray jet remains collinear with the normal vector of the trajectory point at all times. The final output includes the spatial position and the desired pose matrix of the spray gun. Optimal spray gun movement speed The global continuous spraying trajectory instruction set completes the offline planning process of the spraying trajectory, and then directly drives the spraying robot to perform high-precision spraying operations, thus completing the entire trajectory planning and control process.

[0194] In summary, the topology-aware spraying trajectory planning method proposed in this invention for large-size, multi-curvature spacecraft spraying achieves high-precision trajectory collaborative planning that overcomes spatial projection distortion and coating sag defects under large-size, complex curved surfaces of spacecraft by employing high-dimensional topological feature perception via graph convolutional neural networks, parameter adaptive optimization by fusing a sag physical model, geodesic distortion-free mapping based on manifold equations, and global smooth stitching based on surface normal continuity.

[0195] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0196] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0197] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft, characterized in that, include: The original three-dimensional point cloud data of the spacecraft surface is acquired, and the original three-dimensional point cloud data is preprocessed and spatially calibrated to obtain the spacecraft surface point cloud data in the base coordinate system of the spraying robot. Calculate the unit normal vector, maximum principal curvature, and minimum principal curvature of each data point in the point cloud data of the spacecraft surface, and then obtain the surface shape index of each data point; An undirected topological graph is constructed using all data points in the spacecraft surface point cloud data as vertices. The high-dimensional fused feature vectors of each vertex are constructed by combining the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature and surface shape index of each data point. The undirected topological graph and the high-dimensional fused feature vectors of each vertex are fed into a pre-trained graph convolutional neural network to segment the point cloud data on the spacecraft surface into several sprayed topological regions. The cumulative coating thickness at each data point within the spraying topology region is calculated. Then, a sagging deformation penalty factor is constructed by combining the global gravity direction vector. A joint optimization objective function is then built for each spraying topology region, considering the spray gun movement speed and the spray overlap distance. This includes: Define the theoretical spraying trajectory axis and calculate the dynamic deposition amount of the spraying robot's spray gun: ； in, This represents the data points in the sprayed topology region. Indicates the overlap distance of the coating; The first part of the spray gun of the painting robot Dynamic deposition amount along the spray trajectory axis of the theoretical spraying method; This indicates the maximum deposition amount at the center axis of the spray gun on the painting robot. This represents an exponential function with the natural constant e as its base. The effective radius parameter characterizing the spray width; For data points To the The vertical Euclidean distance of the spraying trajectory axis in the theoretical spraying method; Represents the cosine function; Indicates the axis of the spray jet and the data points The angle between the unit normal vectors at that location; Calculating the cumulative coating thickness at each data point within the spraying topology region based on the dynamic deposition amount of the spraying robot's spray gun. : ； in, This indicates the speed at which the spray gun of the painting robot moves; This represents the total number of theoretical spraying trajectory axes within the current spraying topology region; A sagging deformation penalty factor is constructed based on the unit normal vector of data points and the cumulative coating thickness, combined with the global gravity direction vector. : ； in, The comprehensive physical property constants that characterize the fluid properties of the coating; For data points The unit normal vector; This represents the global gravity direction vector; Indicates the calculation of the modulus; Construct information about the spray gun movement speed in each spraying topology region. Spraying overlap distance The joint optimization objective function is defined as follows: ； in, Indicates the first The joint optimization objective function for each sprayed topology region; The target process thickness for the coating; and These represent the thickness error terms. With the risk of slippage Weighting coefficients; Indicates the first One sprayed topological area; Indicates the first A spraying topology area Inner spraying topology area Do double integral, Indicates the first A spraying topology area Inner spraying topology area Do The double integral; Under the constraints of process safety conditions, the joint optimization objective function is solved to obtain the optimal spray gun moving speed and the optimal spray overlap distance for each spraying topology region. Each spraying topology region is reconstructed into a continuous three-dimensional curved manifold mesh and a global geodesic distance scalar field is constructed. Then, combined with the optimal spraying overlap distance, discrete isosurfaces are constructed in each spraying topology region to generate smooth spraying curves for each theoretical spraying trajectory axis and construct the local spraying trajectory for each spraying topology region. Global path planning is performed on the topological region of the spraying to obtain the globally optimal region traversal sequence, thereby obtaining the global spraying trajectory and the expected pose matrix of the spraying robot's spray gun at each trajectory point.

2. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 1, characterized in that: The process of acquiring the original three-dimensional point cloud data of the spacecraft surface, preprocessing and spatially calibrating the original three-dimensional point cloud data to obtain the spacecraft surface point cloud data in the base coordinate system of the painting robot includes: Drive the three-dimensional measurement equipment to perform a global scan of the spacecraft surface and obtain raw three-dimensional point cloud data; Voxel grid filtering is used to uniformly downsample the original 3D point cloud data to reduce data redundancy, and a statistical outlier removal algorithm is combined to remove noise points, thus obtaining preprocessed 3D point cloud data. Solve for the rigid body transformation matrix between the coordinate system of the 3D measuring equipment and the base coordinate system of the spraying robot, and map the preprocessed 3D point cloud data to the base coordinate system of the spraying robot to obtain the point cloud data of the spacecraft surface.

3. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 1, characterized in that: The calculation of the unit normal vector, maximum principal curvature, and minimum principal curvature of each data point in the spacecraft surface point cloud data, thereby obtaining the surface shape index of each data point, includes: The K-nearest neighbor algorithm is used to obtain the local spatial neighborhood point set of each data point in the point cloud data of the spacecraft surface; Principal component analysis is performed on the local spatial neighborhood point set of each data point to obtain the unit normal vector of each data point and construct the local tangent plane of each data point. The least squares method is used to fit the quadratic microsurface in the local tangent plane of each data point to construct the local curvature tensor of each data point. Solve for the eigenvalues ​​and eigenvectors of the local curvature tensor, and analytically obtain the maximum and minimum principal curvatures of each data point; The mathematical representation of the surface shape index for each data point in the spacecraft surface point cloud data is as follows: ； in, This indicates the first point cloud data on the spacecraft surface. The surface shape index for each data point; Pi; It is the arctangent function; , These represent the points in the spacecraft surface point cloud data, respectively. The maximum and minimum principal curvatures of the data points satisfy the constraints. ; To prevent positive integers with a denominator of 0 from taking values ​​in the range of... .

4. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 1, characterized in that: The construction of an undirected topological graph using all data points in the spacecraft surface point cloud data as vertices includes: generating an undirected edge if the Euclidean distance between two data points is less than a preset threshold, thus forming the edge set of the undirected topological graph; The process of constructing a high-dimensional fusion feature vector for each vertex by combining the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature, and surface shape index of each data point includes: concatenating and splicing the position coordinate vector, unit normal vector, maximum principal curvature, minimum principal curvature, and surface shape index of the data point to obtain the high-dimensional fusion feature vector of the vertex corresponding to the data point.

5. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 1, characterized in that: The process involves feeding the undirected topological graph and the high-dimensional fused feature vectors of each vertex into a pre-trained graph convolutional neural network to segment the spacecraft surface point cloud data into several sprayed topological regions, including: By transposing and stacking the high-dimensional fused feature vectors of all vertices, we obtain the fused feature matrix. ; The graph convolutional neural network includes an input layer, several graph convolutional hidden layers, and an output layer. The graph convolutional hidden layer uses the following normalized approximation formula based on spectral graph theory to propagate the high-dimensional fused feature vectors of each vertex: ； in, The graph convolutional neural network represents the first... The input node feature matrix of the graph convolutional hidden layer, the initial graph convolutional hidden layer Set as ; The graph convolutional neural network represents the first... The output node feature matrix of the nth graph convolutional hidden layer, i.e., the nth... The input node feature matrix of the graph convolutional hidden layer; The self-loop adjacency matrix is ​​defined as follows: , The standard adjacency matrix of an undirected topological graph. It is the identity matrix; Let denote the self-circularity matrix, which is a diagonal matrix whose diagonal elements are scalars. The sum of the elements in the corresponding row; The graph convolutional neural network represents the first... The learnable parameter weight matrix of each graph convolutional hidden layer; Represents a nonlinear activation function; The output layer outputs the probability distribution characteristics of the sprayed topology region to which each vertex belongs, that is, the probability distribution characteristics of the sprayed topology region to which each data point belongs, thereby dividing the spacecraft surface point cloud data into several sprayed topology regions.

6. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 1, characterized in that: Under the constraints of process safety conditions, the joint optimization objective function is solved to obtain the optimal spray gun moving speed and optimal spray overlap distance for each spraying topology region, including: The joint optimization objective function is transformed into a weighted summation approximation of discrete data points within the spraying topology region, mathematically represented as follows: ； in, Representing data points The corresponding local infinitesimal approximation area; Upper and lower limits are set for the spray gun movement speed and spray overlap distance. The process safety constraints are defined as follows: ； ； in, , These represent the upper and lower limits of the spray gun's movement speed, respectively; , These represent the upper and lower limits of the coating overlap distance, respectively. Under the constraints of process safety conditions, a sequential quadratic programming algorithm is used to minimize the joint optimization objective function after iterative solution by weighted summation approximation, and the optimal spray gun moving speed and optimal spray overlap distance of each spraying topology region are output.

7. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 1, characterized in that: The process involves reconstructing each spraying topology region into a continuous three-dimensional curved manifold mesh and constructing a global geodesic distance scalar field. Then, by combining the optimal spraying overlap distance, discrete isosurfaces are constructed within each spraying topology region to generate smooth spraying curves for each theoretical spraying trajectory axis, thus constructing the local spraying trajectory for each spraying topology region. This includes: A point cloud edge feature detection algorithm is used to extract the set of geometric boundary points of the outer contour of each sprayed topological region; Using the set of geometric boundary points of the outer contour as the constraint boundary, the discrete data points in each spraying topological region are connected by Delaunay triangulation to make them have topological edge connectivity, thereby reconstructing a continuous three-dimensional curved surface manifold mesh. A continuous geodesic distance scalar field is established on the continuous three-dimensional curved manifold mesh corresponding to each spraying topology region, and the geodesic distance scalar field of the points in the outer contour geometric boundary point set is initialized to 0; Using the outer contour geometric boundary point set as the wavefront evolution reference, the fast travel method is used in each continuous three-dimensional manifold grid to solve the minimum value of all data points in the current spraying topology region reaching the outer contour geometric boundary point set along the surface of the continuous three-dimensional manifold grid, thereby constructing a global geodesic distance scalar field containing all data points in the current spraying topology region. Based on the optimal spray overlap distance and the global geodesic distance scalar field, discrete isosurfaces are extracted from the current spray topology region, mathematically represented as follows: ； in, This represents the index of the theoretical spray trajectory axis within the current spray topology region; Indicates the first position within the current spraying topology region. The equidistant mapping trajectory curves of the spraying trajectory axis in the theory of topology divide the current spraying topology region into discrete isosurfaces; Indicates the first Data points in each sprayed topology region; Represents information about data points The global geodesic distance scalar field; Indicates the optimal spray overlap distance; use The subuniform rational B-spline curves are used to perform spatial smoothing fitting on the equidistant mapped trajectory curves of each theoretical spray trajectory axis within the spray topology region, thereby generating all smooth spray curves within the spray topology region. The smooth spraying curves corresponding to the theoretical spraying trajectory axes within a single spraying topology area are connected end to end in the order of the number of theoretical spraying trajectory axes to form a local spraying trajectory.

8. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 7, characterized in that: The use The sub-uniform rational B-spline curves are used to perform spatial smoothing fitting on the equidistant mapped trajectory curves of each theoretical spray trajectory axis within the spraying topology region, generating all smooth spray curves within that spraying topology region, including: Constructing parameterized curve equations for non-uniform rational B-splines in three-dimensional space: ； in, Indicates the first The non-uniform rational B-spline parameterized curve obtained by fitting the isochronous mapped trajectory curve; Denotes the normalized independent continuous parameter used to describe the parameterized curve of a non-uniform rational B-spline. ; indicates the control point index. This represents the total number of control points required for a smooth spatial fitting of the current equidistant mapped trajectory curve. Indicates the first A control point, wherein the control point is a spatial vertex used to control the spatial geometry of a non-uniform rational B-spline parameterized curve. For the first Weighting factors corresponding to each control point; For the first control points Subuniform rational B-spline basis functions; Based on the cumulative chord length parameterization method for each data point on the discrete isometric mapping trajectory curve, a non-decreasing sequence of real numbers is constructed as the node vector. Combination number The values ​​of all B-spline basis functions were derived and calculated, including the initial zero-order basis function. Defined as: ； Higher-order basis functions The recursive calculation formula is: ； in, Represents the node vector The first in A fixed set of discrete node values ​​is used to define the local support interval of the basis function; Set boundary protection constraints: when When a denominator of a subuniform rational B-spline basis function is zero during the solution process, the corresponding fractional term is defined as zero as a whole. Construct a system of linear equations relating the data points, the basis function matrix, and the control points: ;in Let be the coordinate matrix composed of known data points on the equidistant mapped trajectory curve. This is the rational basis function matrix constructed by normalizing the basis functions. The matrix to be found is constructed from the control points; the control points are solved by inverse calculation using the least squares method. and their corresponding weighting factors This allows for the construction of a smooth spraying curve within the spraying topology region.

9. The topology-aware spraying trajectory planning method for spraying large-size, multi-curvature spacecraft according to claim 7, characterized in that: The process of performing global path planning on the spraying topology region to obtain the globally optimal region traversal sequence, thereby obtaining the global spraying trajectory, and the expected pose matrix of the spraying robot's spray gun at each trajectory point, includes: The starting and ending points of the local spraying trajectories of each spraying topology region are regarded as traversal nodes. A traveling salesman problem model is constructed. The cosine of the angle between the unit normal vectors at the starting and ending points of the local spraying trajectories of each spraying topology region and the spatial Euclidean distance are used as edge weights. The heuristic ant colony algorithm is used to solve the globally optimal region traversal sequence. The global spraying trajectory is obtained by linking the local spraying trajectories of each spraying topology region based on the globally optimal region traversal sequence. Calculate the unit normal vector for each trajectory point in the global spraying trajectory, and then calculate the expected pose matrix of the spray gun to ensure that the axis of the spray jet is always collinear with the normal vector of the trajectory point.

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