Topology preserving type curved surface trajectory planning algorithm based on surface curvature induction and multi-domain coupling optimization

Abstract

The invention belongs to the technical field of intelligent manufacturing, relates to the directions of numerical control machining, industrial robot trajectory control, complex curved surface path planning and the like, and provides a topology maintenance type curved surface trajectory optimization algorithm fusing surface curvature induction and multi-domain coupling optimization. The method comprises the steps of curved surface preprocessing, initial path construction, multi-domain coupling optimization, topology maintenance, trajectory output and the like. The method comprises the following steps: extracting local curvature characteristics of a free-form surface, adaptively arranging path points, constructing a multi-target optimization model containing indexes such as path uniformity, normal consistency and track fairness, and ensuring that the path direction is consistent with the normal height of the surface through an optimization process. The algorithm adopts an evolutionary optimization strategy to globally adjust the path, and introduces a topology maintenance mechanism to ensure that the original curved surface structure is not damaged in the optimization process. The method is suitable for CNC machining, industrial robot trajectory control and three-dimensional modeling, and has the advantages of being reasonable in path distribution, high in geometric consistency, stable in optimization effect and the like.

Description

Technical Field

[0001] This invention relates to the technical fields of intelligent manufacturing, CNC machining, industrial robot trajectory control, neural network geometric feature extraction and complex surface path planning. Specifically, it is an intelligent trajectory optimization method that integrates surface geometric feature sensing and multi-domain coupling optimization. It is applicable to high-precision machining path generation, robot trajectory control and trajectory planning and optimization tasks in the process of geometric modeling of free-form surfaces or irregular three-dimensional surfaces. Background Technology

[0002] With the development of intelligent manufacturing technology, complex freeform surfaces are increasingly being used in aerospace, medical devices, mold manufacturing, and robotics. To achieve high-precision, high-efficiency machining, measurement, or trajectory control on these surfaces, path planning algorithms, as one of the core supporting technologies, are particularly crucial.

[0003] Existing freeform surface path planning methods typically rely on regular mesh generation, fixed-direction scanning, or path generation based on empirical rules. These methods often suffer from the following problems when dealing with highly non-uniform and complex surfaces: 1. Uneven distribution of path points: Insufficient consideration of surface geometric changes leads to excessively dense paths in high curvature areas and excessively sparse paths in low curvature areas, affecting processing efficiency and quality; 2. Path direction deviates from surface normal: Failure to dynamically adjust the relationship between the path tangent and the surface normal may result in improper tool contact angle, trajectory distortion, and reduced machining consistency; 3. Lack of multi-objective collaborative optimization mechanism: Existing algorithms mostly focus on a single optimization index and cannot effectively coordinate multiple objectives such as path smoothness, processing efficiency, and error control; 4. Missing or distorted surface topology: Some path planning algorithms neglect to preserve the original surface topology or shape during path unfolding, leading to geometric deviations.

[0004] In addition, although some studies have used techniques such as multi-axis linkage, scanning path planning, and grinding trajectory control to process complex surfaces, most of them focus on specific applications (such as laser repair and blade processing), and have insufficient dynamic perception of free-form surface geometric features, making it difficult to adapt to the path adaptive optimization requirements under irregular structures.

[0005] Therefore, there is an urgent need for an intelligent trajectory planning method that can integrate surface geometric feature sensing with multi-objective coupling optimization mechanism. This method can not only improve the rationality of path point distribution and direction, but also achieve a global improvement in trajectory quality while ensuring surface topological consistency, thereby meeting the application needs of freeform surfaces in high-end manufacturing. Summary of the Invention

[0006] The purpose of this invention is to overcome the problems of uneven path development, orientation mismatch, topology distortion, and difficulty in coordinating multiple objectives in existing complex surface path planning methods. It provides a topology-preserving intelligent surface trajectory optimization algorithm that integrates surface curvature sensing and multi-domain coupling optimization to achieve high-quality path generation and trajectory planning on free-form surfaces. To achieve the above objective, this invention proposes the following technical solutions.

[0007] like Figure 1 As shown, the method of the present invention includes the following steps: surface input and discretization, geometric feature extraction, direction field generation, initial path layout, multi-domain coupling optimization, topology preservation adjustment, and trajectory output. 1. Surface curvature feature sensing module: Discretizes the input freeform surface model and calculates principal curvature, average curvature or higher-order differential features to achieve fine perception of the geometric changes of the target surface, which serves as the constraint basis for subsequent path planning; 2. Initial path construction mechanism: An initial path network is generated based on the curvature gradient field and normal distribution to ensure that the path direction is as consistent as possible with the surface normal and to avoid path distortion or overlap; 3. Multi-domain coupled optimization model: Construct a multi-objective coupled optimization framework, comprehensively consider multiple optimization indicators such as path uniformity, normal consistency, processing efficiency, and trajectory smoothness, and perform global path scheduling through weight adjustment; 4. Topology-preserving path adjustment strategy: In the post-processing stage of the path, operations such as surface boundary constraints, path continuity analysis, and topology mapping preservation mechanisms are used to ensure that the trajectory distribution does not destroy the original surface structure features; 5. Intelligent trajectory output module: Combines geometric optimization results to output data formats for CNC machining, robot path control, or 3D modeling.

[0008] Through the above technical solution, the present invention has the following beneficial effects: • It can accurately perceive the geometric features of complex freeform surfaces and adaptively adjust the path. • The generated paths exhibit greater consistency in terms of point distribution and direction matching; • Supports multi-objective collaborative optimization, enabling balanced control across different application objectives; • Maintain the original surface topology and avoid geometric distortion caused by path errors; • It can be widely used in high-precision manufacturing and automation scenarios such as 3D surface modeling, complex workpiece processing, and robot trajectory control. Attached Figure Description

[0009] Figure 1 This is a schematic diagram of the overall process of a topology-preserving surface trajectory optimization method according to the present invention.

[0010] Figure 2 This is a schematic diagram of curvature feature extraction and GNN estimation according to the present invention.

[0011] Figure 3 This is a block diagram of the multi-objective coupling optimization process of the present invention. Detailed Implementation

[0012] To more clearly illustrate the technical solution of this invention, the following detailed description is provided in conjunction with a typical application scenario. The method is applicable to path planning tasks on complex three-dimensional freeform surfaces and can be applied to intelligent manufacturing systems such as CNC machining, robot control, and 3D modeling. The trajectory optimization method of this invention includes the following steps.

[0013] Step 1. Surface input and preprocessing.

[0014] like Figure 2 As shown, this invention discretizes the input freeform surface and performs curvature estimation through a grid neighborhood feature input graph neural network (GNN). The results are then fused with those from the traditional fitting method to obtain stable curvature features.

[0015] Step 1.1: Model import and discretization.

[0016] Import the freeform surface model to be processed as a triangular mesh (such as STL format), a parametric model (such as NURBS surface), etc. If it is a parametric model, perform meshing to facilitate subsequent curvature estimation.

[0017] Step 1.2: Geometric feature extraction.

[0018] The local curvature features of a discrete mesh are calculated, including principal curvature, mean curvature, and curvature gradient. A method based on mesh neighborhood fitting and second-order difference is used to estimate curvature, and a graph neural network (GNN) is introduced for deep learning of the mesh structure to improve the accuracy of curvature perception and the robustness of geometric feature extraction. The input to the GNN is the geometric neighborhood features of each mesh point (such as normal, side length, angle, etc.), and the output is the local curvature estimation result. The network structure is constructed using a graph convolution mechanism and can be trained based on existing publicly available graph neural network models.

[0019] Step 2. Initial path construction.

[0020] Step 2.1: Generating the orientation field.

[0021] Based on the curvature gradient field and surface normal information, a direction field for guiding path construction is generated. The path direction is preferentially set to be perpendicular to the principal curvature direction to improve machining stability.

[0022] Step 2.2: Initial trajectory layout.

[0023] Based on the orientation field, the starting points of the path are arranged, and an adaptive point placement strategy is adopted: dense points are placed in high curvature areas and sparse points are placed in low curvature areas to form an initial trajectory network.

[0024] Step 3. Multi-objective coupling optimization.

[0025] like Figure 3 As shown, the multi-objective optimization process includes steps such as path encoding, objective function evaluation, non-dominated sorting and selection, crossover and mutation, and constraint repair, until the Pareto front solution set is obtained.

[0026] Step 3.1: Construction of multi-objective function.

[0027] Construct a path optimization model that includes the following sub-objectives: • Uniformity of path point spacing; • The angle between the path direction and the normal is minimal; • Minimize path duplication rate; • Minimize the total path length; • Trajectory smoothness (curvature continuity); • Maximize processing efficiency; • Maximize area coverage.

[0028] The weights of each optimization objective are dynamically adjusted based on the actual application scenario (such as fine machining, rough machining, and 3D scanning) to form an adaptive weight allocation mechanism.

[0029] Step 3.2: Optimize algorithm execution.

[0030] A multi-objective optimization algorithm is employed to globally optimize the position and orientation of path points. The algorithm can be one of the mainstream multi-objective optimization algorithms currently available, such as NSGA-II, MOEA / D, or alternatively, particle swarm optimization, multi-objective differential evolution, etc. The appropriate algorithm for practical deployment depends on the path size and required optimization accuracy.

[0031] Step 4. Topology preservation and path correction.

[0032] Step 4.1: Boundary detection and topology consistency adjustment.

[0033] Boundary constraint checks are performed on the optimized path to ensure it does not go out of bounds or break. Curvature-preserving interpolation and path continuity repair are used to maintain the geometric and topological consistency of the original surface. Furthermore, for surface regions with mesh noise or boundary sharp angles, constraint-preserving path stretching algorithms or neighborhood normal correction strategies are introduced to enhance trajectory stability.

[0034] Step 5. Trajectory output and application integration.

[0035] Step 5.1: Trajectory output format conversion.

[0036] Transform the final path into a data format supported by the application system, including but not limited to: • G-code (applicable to CNC machining); • A sequence of trajectory points containing attitude information (suitable for multi-degree-of-freedom robots); • Curve control points or path fitting functions (used for modeling and simulation systems).

[0037] When handling multi-axis linkage robot control tasks, the attitude angle optimization algorithm is combined to jointly schedule and optimize the attitude of trajectory points, thereby improving the consistency of trajectory control and the accuracy of equipment execution.

[0038] Step 5.2: Trajectory simulation and visualization.

[0039] Before the trajectory is output, an integrated visualization simulation module is used to preview and verify the path, and output auxiliary information such as path density map, orientation field map, and processing simulation map, so that users can interactively adjust and verify the rationality of the trajectory.

[0040] Through the above steps, the present invention can achieve accurate perception and adaptive path optimization of the geometric features of freeform surfaces, generate trajectory paths with high directional consistency, topology preservation and multi-objective balance, significantly improve processing quality and control efficiency, and is applicable to various complex surface automated processing scenarios.

Claims

1. A topology-preserving intelligent surface trajectory optimization algorithm that integrates surface curvature sensing and multi-domain coupling optimization, comprising the following steps: (1) Obtain the target freeform surface model, discretize the model, and extract the curvature-related geometric features of each discrete unit; (2) Based on the geometric features, a path is generated to construct a direction field, and an initial path is generated adaptively according to the direction field. The density of path points is related to the curvature change. (3) Construct a multi-objective optimization model that includes indicators such as path distribution uniformity, path direction and normal consistency, trajectory smoothness, and processing efficiency, and perform global optimization on the initial path based on a multi-domain coupled optimization algorithm; (4) Perform topology preservation adjustments based on the optimization results, including boundary constraint detection, path continuity repair, and surface structure consistency preservation; (5) Convert the optimized trajectory into a data format usable by the target system for processing or trajectory control.

2. The method according to claim 1, wherein, The geometric features include one or more of principal curvature, mean curvature, and curvature gradient.

3. The method according to claim 1, wherein, The curvature information is obtained using curvature estimation methods based on local grid neighborhood fitting, second-order difference, and graph neural networks.

4. The method according to claim 1, wherein, The path construction direction field is generated based on the curvature gradient field and the surface normal. The path direction is preferably perpendicular to the principal curvature direction, and the path point density is higher in the high curvature region than in the low curvature region.

5. The method according to claim 1, wherein, The optimization algorithm for the multi-objective optimization model is selected from the non-dominated sorting genetic algorithm (NSGA-II), the decomposition-type multi-objective optimization algorithm (MOEA / D), the multi-objective particle swarm optimization algorithm, or the multi-objective differential evolution algorithm.

6. The method according to claim 1, wherein, The weights of each indicator in the multi-objective optimization are adaptively adjusted according to the processing type, accuracy requirements, or surface characteristics.

7. The method according to claim 1, wherein, Topology preservation adjustments include interpolation compensation based on curvature features, path stretching, or normal correction to improve trajectory continuity and stability.

8. The method according to claim 1, wherein, The trajectory output format includes G-code, a sequence of trajectory points containing attitude information, or a set of curve control points.

9. A surface trajectory optimization apparatus for implementing the method of claim 1, characterized in that, include: (1) Geometric feature sensing unit: used to discretize the input freeform surface and extract geometric features such as curvature; (2) Initial path generation unit: used to generate a direction field based on geometric features and adaptively lay out the initial path; (3) Multi-domain coupled optimization unit: used to construct and execute a multi-objective optimization model containing multiple optimization indices to perform global optimization of the path; (4) Topology Preservation Adjustment Unit: Used to correct boundary constraints, path continuity and topology consistency of the optimized path; (5) Trajectory output unit: used to convert the optimized trajectory into a data format usable by the target system.

10. The apparatus according to claim 9, wherein, The geometric feature sensing unit includes a curvature estimation algorithm module based on grid neighborhood fitting, second-order difference, or graph neural network.

11. The apparatus according to claim 9, wherein, The multi-domain coupled optimization unit supports the switching and combination of various evolutionary optimization algorithms.

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