Robot path planning method for mixed-flow water turbine runner blade defect inspection

Abstract

The invention provides a robot path planning method for mixed-flow water turbine runner blade defect inspection. The robot path planning method comprises the following steps that S1, feasibility analysis of robot defect inspection is conducted on a blade, and an effective detection area is determined; s2, extracting a three-dimensional mesh model of the blade surface from the effective detection area, and establishing bidirectional mapping between a three-dimensional space and a two-dimensional UV parameter space by projecting the three-dimensional mesh model to the two-dimensional UV parameter space; s3, generating a boundary offset path of the two-dimensional UV parameter space and a robot arch scanning path; and S4, based on the bidirectional mapping, processing the boundary offset path and the arch scanning path of the robot, and generating a path back projection and three-dimensional detection track. Through accurate curved surface parameterization, an efficient path generation algorithm and an accurate three-dimensional mapping strategy, the method aims at improving the detection efficiency and quality of the runner blade of the mixed-flow water turbine, and technical guarantee is provided for safe and stable operation of a hydropower station.

Description

Technical Field

[0001] The invention relates to the technical field of automatic detection of hydropower equipment, and in particular to a robot path planning method for defect inspection of a Francis turbine runner blade. Background Art

[0002] As the core component of hydropower equipment, the performance of the turbine directly affects the power generation efficiency and the stability of power station operation. During long-term operation, the runner blades may be damaged by factors such as water flow impact and foreign object impact. If not discovered and handled in time, the power generation efficiency will be reduced and even safety accidents will be caused. It is said that traditional manual inspection methods have problems such as low efficiency, inconsistent accuracy, incomplete coverage, and face safety risks. In order to improve detection efficiency and accuracy while reducing personnel risks, the introduction of automated robot systems for regular inspection of runner blades has become a new trend.

[0003] However, the Francis turbine runner blades have a complex three-dimensional curved surface structure, which poses a huge challenge to the robot's path planning. The existing path planning methods have the following main problems: insufficient surface modeling accuracy, making it difficult to accurately represent the complex blade structure; full coverage is difficult, making it difficult to balance the comprehensiveness and efficiency of detection; poor local feature adaptability, making it difficult to dynamically adjust the path according to the local geometric features of the blade surface; and high computational complexity, making it difficult to achieve rapid planning. Summary of the invention

[0004] The present invention aims to provide a robot path planning method for defect inspection of Francis turbine runner blades to solve the above-mentioned problems.

[0005] The present invention provides a robot path planning method for defect inspection of Francis turbine runner blades, comprising the following steps:

[0006] S1. Feasibility analysis of robot defect inspection on blades and determination of effective inspection area;

[0007] S2, extracting a three-dimensional mesh model of the blade surface from the effective detection area, and establishing a bidirectional mapping between the three-dimensional space and the two-dimensional UV parameter space by projecting the three-dimensional mesh model into the two-dimensional UV parameter space;

[0008] S3, generating a boundary offset path and a robot bow scanning path in a two-dimensional UV parameter space;

[0009] S4. Based on the bidirectional mapping, the boundary offset path and the robot bow scanning path are processed to generate a path back projection and a three-dimensional detection trajectory.

[0010] In some embodiments, step S1 includes the following sub-steps:

[0011] S11. Conduct feasibility analysis based on the geometric characteristics and curvature distribution of turbine runner blades and the motion characteristics and magnetic attraction capability of wheeled crawling robots.

[0012] S12. Determine the effective detection area of ​​the robot on the blade surface by calculating the crawlability index of each point on the surface of the turbine runner blade.

[0013] In some embodiments, step S2 includes the following sub-steps:

[0014] S21, extracting a three-dimensional mesh model of the blade surface from the effective detection area, projecting the three-dimensional mesh model into a two-dimensional UV parameter space, calculating the corresponding coordinates of each vertex in the three-dimensional mesh model in the two-dimensional UV parameter space, and establishing a hash table from vertex index to UV coordinates;

[0015] S22. Based on the hash table, construct a forward mapping between the three-dimensional space and the two-dimensional UV parameter space;

[0016] S23. Based on the reverse query of the hash table, a reverse mapping between the two-dimensional UV parameter space and the three-dimensional space is constructed.

[0017] In some embodiments, step S22 specifically includes:

[0018] Use the space partitioning structure to quickly locate the triangular surface element where the given 3D point is located, and calculate the centroid coordinates of the given 3D point in the triangular surface element;

[0019] Based on the hash table, obtaining vertex coordinates of a UV triangle corresponding to the barycentric coordinates of the given three-dimensional point in the triangle face;

[0020] Based on the vertex coordinates of the corresponding UV triangle, accurate UV coordinates are obtained by performing linear interpolation in the two-dimensional UV parameter space using the same center of gravity coordinates as those in the three-dimensional space, thereby achieving accurate conversion of points from the three-dimensional space to the two-dimensional UV parameter space.

[0021] In some embodiments, step S23 specifically includes:

[0022] Use the point positioning algorithm in the two-dimensional UV parameter space to quickly find the UV triangle containing the given UV coordinates. This UV triangle directly corresponds to the projection of the three-dimensional mesh model in the two-dimensional UV parameter space. Calculate the centroid coordinates of the given UV coordinates in the UV triangle.

[0023] Perform a reverse query based on the hash table to obtain vertex coordinates of a triangular face element in a three-dimensional space corresponding to the barycentric coordinates of the given UV coordinate in the UV triangle;

[0024] Based on the vertex coordinates of the triangular face elements in the corresponding three-dimensional space, accurate three-dimensional Cartesian coordinates are obtained by performing linear interpolation in the three-dimensional space using the same centroid coordinates as the two-dimensional UV parameter space, thereby achieving accurate conversion of points from the two-dimensional UV parameter space to the three-dimensional space.

[0025] In some embodiments, step S3 includes the following sub-steps:

[0026] S31, in the two-dimensional UV parameter space, using a boundary detection algorithm to extract a boundary contour point set of the three-dimensional mesh model projected in the two-dimensional UV parameter space;

[0027] S32, performing smoothing and internal bias operation on the extracted boundary contour to generate a boundary bias path with no self-intersection and high smoothness;

[0028] S33. In the internal area defined by the boundary offset path, based on the motion characteristics of the wheeled crawling robot and the coverage of the detection sensor, calculate and optimize the robot's bow scanning path.

[0029] In some embodiments, in step S31, the boundary detection algorithm includes:

[0030] Construct the spatial partition structure of the point cloud;

[0031] Calculate the angle distribution in the local neighborhood of each point in the spatial partition structure;

[0032] Based on the angle distribution, by setting the angle threshold and the minimum number of neighbors, it is determined whether a point is a boundary point. The initially determined boundary points are optimized through multiple iterations to finally obtain an accurate boundary contour point set.

[0033] In some embodiments, step S32 specifically includes:

[0034] Perform nearest neighbor sorting on the boundary contour point set to ensure the continuity of the point sequence;

[0035] The sorted boundary contour point set is smoothed using B-spline curve fitting technology;

[0036] The normal vector of each point on the smooth curve is calculated, and an internal bias operation is performed along the normal direction. During the biasing process, the result is further smoothed by detecting and processing self-intersections, and finally a self-intersection-free and highly smooth boundary bias path is generated.

[0037] In some embodiments, step S33 specifically includes:

[0038] The principal directions of the two-dimensional boundary offset path curves are calculated by principal component analysis;

[0039] generating a series of cutting lines perpendicular to the main direction and equally spaced;

[0040] Calculating the intersection points of the cutting line and the two-dimensional boundary offset path curve, and alternately generating arcuate paths according to the parity of the intersection point pairs; in the process of path generation, fully considering the minimum turning radius of the robot and the effective coverage width of the detection sensor, adjusting the spacing between adjacent paths and the curvature of the arcuate;

[0041] A path smoothing algorithm is applied to optimize the generated arcuate path, eliminating sharp turns and ensuring the continuity and smoothness of the path.

[0042] In some embodiments, step S4 includes the following sub-steps:

[0043] S41, optimizing and sampling the boundary offset path and the robot arc scanning path planned in the two-dimensional UV parameter space, and projecting the sampling points back to the three-dimensional space by using the bidirectional mapping to obtain discrete points in the three-dimensional space;

[0044] S42, generating a smooth and continuous three-dimensional detection trajectory for the sampling points projected back into the three-dimensional space through an interpolation algorithm and a curve fitting technique.

[0045] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0046] 1. The present invention realizes high-precision conversion of complex three-dimensional blade surface to two-dimensional UV parameter space through precise surface parameterization and bidirectional mapping technology, ensuring that path planning can accurately reflect the actual geometric characteristics of the blade.

[0047] 2. The arc scanning path generation algorithm proposed in the present invention can efficiently generate a comprehensive detection path in the two-dimensional UV parameter space, taking into account the robot's motion characteristics, and improving the efficiency and accuracy of defect detection.

[0048] 3. The present invention utilizes precise bidirectional mapping relationships to accurately convert the two-dimensional planning path into a three-dimensional detection trajectory. Combined with the optimization algorithm, the generated trajectory not only conforms to the blade surface shape, but also meets the robot movement requirements, thereby improving the reliability of automated detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The present invention is a flowchart of a robot path planning method for inspecting defects of a Francis turbine runner blade in an embodiment of the present invention.

[0050] Figure 2 Graph showing the curvature distribution of the runner blades in an embodiment of the present invention.

[0051] Figure 3 This is a rendering of the effective detection area of ​​the blade in an embodiment of the present invention.

[0052] Figure 4 This is a projection effect diagram of a three-dimensional mesh model in a two-dimensional UV parameter space in an embodiment of the present invention.

[0053] Figure 5 This is a diagram showing the accuracy verification result of the forward direction mapping in an embodiment of the present invention.

[0054] Figure 6 This is a diagram showing the effect of boundary extraction in a two-dimensional UV parameter space in an embodiment of the present invention.

[0055] Figure 7 4 is a diagram showing the effect of a boundary bias path in a two-dimensional UV parameter space in an embodiment of the present invention.

[0056] Figure 8 This is a diagram showing the effect of the arcuate scanning path in an embodiment of the present invention.

[0057] Fig. 9 This is a rendering of the detection path of a crawling robot for a mixed flow runner blade in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0059] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] Example

[0061] like Figure 1 As shown, this embodiment proposes a robot path planning method for defect inspection of Francis turbine runner blades, comprising the following steps:

[0062] S1. Feasibility analysis of robot defect inspection on blades and determination of effective inspection area.

[0063] In some embodiments, step S1 includes the following sub-steps:

[0064] S11. Based on the geometric characteristics and curvature distribution of the turbine runner blades, combined with the motion characteristics and magnetic attraction ability of the wheeled crawling robot, a feasibility analysis is performed; for example: first, the main curvature and Gaussian curvature distribution of the blade surface are calculated, such as the main curvature and Gaussian curvature distribution of the Francis turbine runner blade surface of a hydropower station. Figure 2 As shown. Then, based on the structural parameters of the robot, the robot kinematic model is established. For example, the structural parameters of the wheeled crawling robot include wheelbase, wheel diameter, and body size. Finally, the feasibility analysis is carried out by combining the main curvature and Gaussian curvature distribution of the blade surface with the robot kinematic model. For example, the local curvature radius and the inclination angle with the horizontal plane at each position of the blade surface are calculated, and the maximum adsorption force under different local curvature radii and inclination angles is calculated by combining the robot's magnetic suction device.

[0065] S12, by calculating the crawlability index of each point on the surface of the turbine runner blade, including the local curvature radius and the inclination angle, etc., determine the effective detection area of ​​the robot on the blade surface, such as Figure 3 shown.

[0066] S2. Extract the three-dimensional mesh model of the blade surface from the effective detection area, and establish a bidirectional mapping between the three-dimensional space and the two-dimensional UV parameter space by projecting the three-dimensional mesh model into the two-dimensional UV parameter space.

[0067] In some embodiments, step S2 includes the following sub-steps:

[0068] S21, extracting the three-dimensional mesh model of the blade surface from the effective detection area, and projecting the three-dimensional mesh model into the two-dimensional UV parameter space, such as Figure 4 As shown, the corresponding coordinates of each vertex in the three-dimensional mesh model in the two-dimensional UV parameter space are calculated, and a hash table of vertex index to UV coordinates is established. In this embodiment, an algorithm such as Least Square Conformal Mapping (LSCM) is used to implement step S21.

[0069] S22. Based on the hash table, construct a forward mapping between the three-dimensional space (three-dimensional Cartesian coordinate system) and the two-dimensional UV parameter space:

[0070] Use the space partitioning structure (such as kd tree) to quickly locate the triangle surface element where the given 3D point is located, and calculate the centroid coordinates of the given 3D point in the triangle surface element;

[0071] Based on the hash table, obtaining vertex coordinates of a UV triangle corresponding to the barycentric coordinates of the given three-dimensional point in the triangle face;

[0072] Based on the vertex coordinates of the corresponding UV triangle, accurate UV coordinates are obtained by performing linear interpolation in the two-dimensional UV parameter space using the same center of gravity coordinates as those in the three-dimensional space, thereby achieving accurate conversion of points from the three-dimensional space to the two-dimensional UV parameter space.

[0073] S23, based on the reverse query of the hash table, construct a reverse mapping between the two-dimensional UV parameter space and the three-dimensional space (three-dimensional Cartesian coordinate system):

[0074] Use the point positioning algorithm in the two-dimensional UV parameter space to quickly find the UV triangle containing the given UV coordinates. This UV triangle directly corresponds to the projection of the three-dimensional mesh model in the two-dimensional UV parameter space. Calculate the centroid coordinates of the given UV coordinates in the UV triangle.

[0075] Perform a reverse query based on the hash table to obtain vertex coordinates of a triangular face element in a three-dimensional space corresponding to the barycentric coordinates of the given UV coordinate in the UV triangle;

[0076] Based on the vertex coordinates of the triangular face elements in the corresponding three-dimensional space, accurate three-dimensional Cartesian coordinates are obtained by performing linear interpolation in the three-dimensional space using the same centroid coordinates as the two-dimensional UV parameter space, thereby achieving accurate conversion of points from the two-dimensional UV parameter space to the three-dimensional space.

[0077] To evaluate the accuracy of the established bidirectional mapping relationship, 5 test points (non-vertices) are randomly selected on the blade surface and their original 3D coordinates are recorded. First, these points are converted to the 2D UV parameter space using the forward mapping in step S21, and then the UV coordinates are remapped back to the 3D space using the reverse mapping in step S22. By comparing the original 3D coordinates with the remapped coordinates, the Euclidean distance between them is calculated as the mapping error. The results are shown in Figure 2. Figure 5 shown.

[0078] S3, generating a boundary offset path in a two-dimensional UV parameter space and a robot bow scanning path.

[0079] In some embodiments, step S3 includes the following sub-steps:

[0080] S31, in the two-dimensional UV parameter space, using the boundary detection algorithm to extract the boundary contour point set of the three-dimensional mesh model projected in the two-dimensional UV parameter space, such as Figure 6 As shown. The boundary detection algorithm is:

[0081] Construct a spatial partitioning structure of the point cloud (such as a kd tree);

[0082] Calculate the angle distribution in the local neighborhood of each point in the spatial partition structure;

[0083] Based on the angle distribution, by setting the angle threshold and the minimum number of neighbors, it is determined whether a point is a boundary point. The initially determined boundary points are optimized through multiple iterations to finally obtain an accurate boundary contour point set.

[0084] S32, performing smoothing and internal biasing operations on the extracted boundary contour to generate a boundary biasing path with no self-intersection and high smoothness, such as Figure 7 The details are as follows:

[0085] Perform nearest neighbor sorting on the boundary contour point set to ensure the continuity of the point sequence;

[0086] The sorted boundary contour point set is smoothed using B-spline curve fitting technology;

[0087] The normal vector of each point on the smooth curve is calculated, and an internal bias operation is performed along the normal direction. During the biasing process, the result is further smoothed by detecting and processing self-intersections, and finally a self-intersection-free and highly smooth boundary bias path is generated.

[0088] S33, in the internal area defined by the boundary offset path, based on the motion characteristics of the wheeled crawling robot and the coverage of the detection sensor, calculate and optimize the robot's bow scanning path, such as Figure 8 The details are as follows:

[0089] The principal direction of the two-dimensional boundary offset path curve is calculated by principal component analysis (PCA);

[0090] generating a series of cutting lines perpendicular to the main direction and equally spaced;

[0091] Calculating the intersection points of the cutting line and the two-dimensional boundary offset path curve, and alternately generating arcuate paths according to the parity of the intersection point pairs; in the process of path generation, fully considering the minimum turning radius of the robot and the effective coverage width of the detection sensor, adjusting the spacing between adjacent paths and the curvature of the arcuate;

[0092] A path smoothing algorithm is applied to optimize the generated arcuate path, eliminating sharp turns and ensuring the continuity and smoothness of the path.

[0093] S4, based on the bidirectional mapping, the boundary offset path and the robot arc scanning path are processed to generate a path back projection and a three-dimensional detection trajectory, such as Fig. 9 shown.

[0094] In some embodiments, step S4 includes the following sub-steps:

[0095] S41, optimizing and sampling the boundary offset path and the robot arc scanning path planned in the two-dimensional UV parameter space, and using the bidirectional mapping, projecting the sampling points back to the three-dimensional space to obtain discrete points in the three-dimensional space. The details are as follows:

[0096] The boundary offset path and the robot bow scanning path in the two-dimensional UV parameter space are uniformly sampled to ensure that the sampling points can fully represent the geometric characteristics of the curve;

[0097] By using the reverse mapping established in step S23, each sampling point is accurately projected from the two-dimensional UV parameter space back to the three-dimensional space to obtain a discrete point in the three-dimensional space.

[0098] S42, generating a smooth and continuous three-dimensional detection trajectory for the sampling points projected back into the three-dimensional space through an interpolation algorithm and a curve fitting technique.

[0099] In this embodiment, a cubic spline interpolation algorithm is used to process discrete points in three-dimensional space: first, these discrete points in three-dimensional space are used as control points to construct a parameterized cubic spline curve; then, the shape of the curve is optimized by adjusting the tension and deviation parameters of the spline curve to ensure the smoothness and continuity of the path, thereby generating a three-dimensional detection trajectory suitable for the motion characteristics of a wheeled crawling robot.

[0100] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A robot path planning method for defect inspection of Francis turbine runner blades, characterized in that: The steps include: S1. Feasibility analysis of robot defect inspection on blades and determination of effective inspection area; S2, extracting a three-dimensional mesh model of the blade surface from the effective detection area, and establishing a bidirectional mapping between the three-dimensional space and the two-dimensional UV parameter space by projecting the three-dimensional mesh model into the two-dimensional UV parameter space; S3, generating a boundary offset path and a robot bow scanning path in a two-dimensional UV parameter space; S4. Based on the bidirectional mapping, the boundary offset path and the robot bow scanning path are processed to generate a path back projection and a three-dimensional detection trajectory.

2. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 1, characterized in that: Step S1 includes the following sub-steps: S11. Conduct feasibility analysis based on the geometric characteristics and curvature distribution of turbine runner blades and the motion characteristics and magnetic attraction capability of wheeled crawling robots. S12. Determine the effective detection area of ​​the robot on the blade surface by calculating the crawlability index of each point on the surface of the turbine runner blade.

3. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 1, characterized in that: Step S2 includes the following sub-steps: S21, extracting a three-dimensional mesh model of the blade surface from the effective detection area, projecting the three-dimensional mesh model into a two-dimensional UV parameter space, calculating the corresponding coordinates of each vertex in the three-dimensional mesh model in the two-dimensional UV parameter space, and establishing a hash table of vertex indexes to UV coordinates; S22, constructing a forward mapping between the three-dimensional space and the two-dimensional UV parameter space based on the hash table; S23. Based on the reverse query of the hash table, a reverse mapping between the two-dimensional UV parameter space and the three-dimensional space is constructed.

4. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 3, characterized in that: Step S22 specifically includes: Use the space partitioning structure to quickly locate the triangular surface element where the given 3D point is located, and calculate the centroid coordinates of the given 3D point in the triangular surface element; Based on the hash table, obtaining vertex coordinates of a UV triangle corresponding to the centroid coordinates of the given three-dimensional point in the triangle face; Based on the vertex coordinates of the corresponding UV triangle, accurate UV coordinates are obtained by performing linear interpolation in the two-dimensional UV parameter space using the same center of gravity coordinates as those in the three-dimensional space, thereby achieving accurate conversion of points from the three-dimensional space to the two-dimensional UV parameter space.

5. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 3, characterized in that: Step S23 specifically includes: Use the point positioning algorithm in the two-dimensional UV parameter space to quickly find the UV triangle containing the given UV coordinates. This UV triangle directly corresponds to the projection of the three-dimensional mesh model in the two-dimensional UV parameter space. Calculate the centroid coordinates of the given UV coordinates in the UV triangle. Perform a reverse query based on the hash table to obtain vertex coordinates of a triangular face element in a three-dimensional space corresponding to the barycentric coordinates of the given UV coordinate in the UV triangle; Based on the vertex coordinates of the triangular face elements in the corresponding three-dimensional space, accurate three-dimensional Cartesian coordinates are obtained by performing linear interpolation in the three-dimensional space using the same centroid coordinates as the two-dimensional UV parameter space, thereby achieving accurate conversion of points from the two-dimensional UV parameter space to the three-dimensional space.

6. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 1, characterized in that: Step S3 includes the following sub-steps: S31, in the two-dimensional UV parameter space, using a boundary detection algorithm to extract a boundary contour point set of the three-dimensional mesh model projected in the two-dimensional UV parameter space; S32, performing smoothing and internal bias operation on the extracted boundary contour to generate a boundary bias path with no self-intersection and high smoothness; S33. In the internal area defined by the boundary offset path, based on the motion characteristics of the wheeled crawling robot and the coverage of the detection sensor, calculate and optimize the robot's bow scanning path.

7. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 6, characterized in that: In step S31, the boundary detection algorithm includes: Construct the spatial partition structure of the point cloud; Calculate the angle distribution in the local neighborhood of each point in the spatial partition structure; Based on the angle distribution, by setting the angle threshold and the minimum number of neighbors, it is determined whether a point is a boundary point. The initially determined boundary points are optimized through multiple iterations to finally obtain an accurate boundary contour point set.

8. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 6, characterized in that: Step S32 specifically includes: Perform nearest neighbor sorting on the boundary contour point set to ensure the continuity of the point sequence; The sorted boundary contour point set is smoothed using B-spline curve fitting technology; The normal vector of each point on the smooth curve is calculated, and an internal bias operation is performed along the normal direction. During the biasing process, the result is further smoothed by detecting and processing self-intersections, and finally a self-intersection-free and highly smooth boundary bias path is generated.

9. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 6, characterized in that: Step S33 specifically includes: The principal directions of the two-dimensional boundary offset path curves are calculated by principal component analysis; generating a series of cutting lines perpendicular to the main direction and equally spaced; Calculating the intersection points of the cutting line and the two-dimensional boundary offset path curve, and alternately generating arcuate paths according to the parity of the intersection point pairs; in the process of path generation, fully considering the minimum turning radius of the robot and the effective coverage width of the detection sensor, adjusting the spacing between adjacent paths and the curvature of the arcuate; A path smoothing algorithm is applied to optimize the generated arcuate path, eliminating sharp turns and ensuring the continuity and smoothness of the path.

10. The robot path planning method for defect inspection of Francis turbine runner blades according to claim 1, characterized in that: Step S4 includes the following sub-steps: S41, optimizing and sampling the boundary offset path and the robot arc scanning path planned in the two-dimensional UV parameter space, and projecting the sampling points back to the three-dimensional space by using the bidirectional mapping to obtain discrete points in the three-dimensional space; S42, generating a smooth and continuous three-dimensional detection trajectory for the sampling points projected back into the three-dimensional space through an interpolation algorithm and a curve fitting technique.

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