Free-form surface polishing path planning method and device, storage medium and equipment

Abstract

The application discloses a free curved surface polishing path planning method and device, a storage medium and equipment. The method comprises the following steps: acquiring a polishing tool radius and a three-dimensional point cloud of a workpiece to be polished, extracting a normal vector and a second type of basic form coefficient of each point, and constructing an enhanced point cloud; generating an initial polishing path and establishing a Frenet frame; calculating a normal curvature along a subnormal vector direction, deducing a maximum allowable path distance arc length of each point based on the spatial geometric relationship between the normal curvature radius and the polishing tool radius, taking the minimum value as a bias path distance arc length, and generating a next polishing path; iterating the above process until a plurality of ordered polishing sub-paths are obtained by covering a preset polishing area; calculating a tangential normal curvature for each sub-path, deducing an adaptive step length, and resampling to generate a fully covered polishing path. The application does not require a complete workpiece curved surface model, effectively improves polishing processing efficiency, and can simultaneously guarantee the polishing coverage integrity of adjacent paths and path tool position points.

Description

Technical Field

[0001] This invention relates to the field of polishing path planning technology, and more specifically to a method, apparatus, storage medium, and device for polishing path planning of free-form surfaces. Background Technology

[0002] In aerospace, automotive manufacturing, rail transportation, and mold manufacturing, many key components have complex free-form surface structures, such as turbine blades, automotive body panel molds, and high-speed rail car shells. The grinding quality of these components directly affects their aerodynamic performance, appearance quality, and service life. Robotic automated grinding technology is an important means of grinding these components. The goal of grinding path planning is to generate an ordered set of paths on the surface of the workpiece to be ground, enabling the grinding tool to completely cover the area to be processed, while avoiding missed areas or excessive overlap.

[0003] Existing grinding path planning methods mainly fall into the following categories: First, methods based on surface parametric models, using parametric representations such as NURBS to generate isoparametric paths. These methods offer high path quality but rely on CAD models and cannot be directly used when only 3D scanned point cloud data of the workpiece is available. Second, methods using equal cross-section methods or isoparametric lines to generate grinding paths with fixed row spacing. These methods are simple to implement, but the fixed row spacing cannot adapt to local curvature variations. In areas with high curvature, excessive spacing between adjacent paths can lead to missed grinding, while in flat areas with low curvature, insufficient spacing can cause path overlap and reduced grinding efficiency. Third, methods based on point cloud grid division or edge tracking rely on manual experience to set the row spacing, lacking a quantitative correlation with surface geometric features. Finally, methods using data-driven approaches such as reinforcement learning have limited generalization and lack interpretability.

[0004] Existing methods only focus on path planning in the row spacing direction, ignoring the problem of missed wear caused by curvature changes in the tangential direction of the path. This results in coverage gaps that may still exist within the same path, making it impossible to guarantee full coverage.

[0005] Therefore, how to effectively refine path planning methods to address the deficiencies and shortcomings of existing technologies has become an important issue that researchers in this field urgently need to solve. Summary of the Invention

[0006] The purpose of this invention is to address the above-mentioned problems by providing a method, apparatus, storage medium, and device for planning grinding paths on free-form surfaces.

[0007] The technical solution of this invention is: a grinding path planning method for free-form surfaces, comprising the following steps:

[0008] S1: Obtain the radius of the grinding tool and the three-dimensional point cloud of the workpiece to be ground, extract the normal vector and the coefficients of the second type of basic form of each point in the three-dimensional point cloud, and construct an enhanced point cloud; S2: Generate an initial polishing path based on the enhanced point cloud, and establish a Frenet frame for each point on the initial polishing path. The Frenet frame includes the normal vector, the tangent vector of the initial polishing path, and the binormal vector obtained by the cross product of the normal vector and the tangent vector. S3: Calculate the normal curvature along the direction of the subnormal vector based on the Frenet frame, deduce the maximum allowable row spacing arc length at each point on the initial grinding path based on the spatial geometric relationship between the normal curvature radius corresponding to the normal curvature and the radius of the grinding tool, and take the minimum value among the maximum row spacing arc lengths as the offset row spacing arc length, and generate the next grinding path based on the Frenet frame and the offset row spacing arc length; S4: Take the next polishing path as the current polishing path, and repeatedly execute the operation of establishing a Frenet frame for each point on the current polishing path and generating the next polishing path until the generated polishing sub-paths cover the preset polishing area of ​​the 3D point cloud, and obtain several ordered polishing sub-paths. S5: Calculate the normal curvature along the tangent vector direction of each grinding sub-path, derive the maximum allowable step arc length for each point on the same path in combination with the radius of the grinding tool, take the minimum value among the maximum step arc lengths as the processing step length, and resample the grinding sub-path based on the processing step length to generate a fully covered grinding path.

[0009] As an improvement to this embodiment of the invention, in step S1, the method for constructing the enhanced point cloud is as follows: performing neighborhood retrieval on each point in the three-dimensional point cloud to obtain the corresponding neighborhood point set, constructing the covariance matrix of the neighborhood point set and extracting the normal vector by eigenvalue decomposition of the covariance matrix, obtaining the second type of basic form coefficients by fitting a local quadratic surface, and associating the normal vector, the second type of basic form coefficients, and the coordinates of the three-dimensional point cloud to obtain the enhanced point cloud.

[0010] As an improvement to an embodiment of the present invention, step S2 specifically includes: obtaining the initial cutting plane equation, solving for the intersection points of the initial cutting plane and the hidden surface corresponding to the enhanced point cloud and sorting them to obtain the initial polishing path; calculating the tangent vector of each point on the initial polishing path using the central difference method, and determining the binormal vector by the cross product of the tangent vector and the normal vector to obtain the Frenet frame of each point.

[0011] As an improvement to this embodiment of the invention, in step S3, the derivation process of the maximum row spacing arc length is as follows: calculate the normal curvature radius of the binormal vector direction according to Euler's formula; based on the geometric constraint relationship between the normal curvature radius and the radius of the grinding tool, establish row spacing calculation models for convex surfaces, concave surfaces and planes respectively; and obtain the maximum allowed row spacing arc length for each point on the initial grinding path according to the row spacing calculation model.

[0012] As an improvement to this embodiment of the invention, the line spacing calculation model is specifically as follows: For a convex surface, the maximum allowable line spacing is calculated based on the critical intersection condition that the center distance formed by the centers of two adjacent grinding tools on the trajectory offset outward along the surface normal vector is equal to the diameter of the grinding tool; for a concave surface, the maximum allowable line spacing is calculated based on the critical intersection condition that the center distance formed by the centers of two adjacent grinding tools on the trajectory offset inward along the surface normal vector is equal to the diameter of the grinding tool, and it is determined whether the radius of the grinding tool is greater than the radius of the local trajectory of the concave surface; if so, the corresponding point is marked as an unreachable point; and the diameter of the grinding tool is determined as the maximum allowable line spacing.

[0013] As an improvement to this embodiment of the invention, in step S3, the method for generating the next polishing path is as follows: the offset line spacing arc length is divided into small step lengths, a temporary intermediate point is obtained by moving along the subnormal direction in the local tangent plane, several nearest neighbor points of the temporary intermediate point are searched in the three-dimensional point cloud, the local surface is fitted using the nearest neighbor points, and the temporary intermediate point is projected onto the local surface along the normal direction of the local surface to obtain a new path point, the normal vector and Frenet frame are updated until each point of the initial polishing path is updated, and the updated points are deduplicated and sorted to obtain the next polishing path.

[0014] As an improvement of this embodiment of the invention, the method for calculating the maximum step arc length in step S5 is as follows: calculate the normal radius of curvature of the tangent vector direction of the path, and establish arc length step length calculation models for convex surfaces, concave surfaces and planes respectively; obtain the maximum allowable arc length step length of adjacent tool positions on the same path according to the arc length step length calculation model.

[0015] To achieve one of the above-mentioned objectives, one embodiment of the present invention provides a grinding path planning device for free-form surfaces, comprising the following modules: The point cloud enhancement module is used to obtain the radius of the grinding tool and the three-dimensional point cloud of the workpiece to be ground, extract the normal vector and the coefficient of the second type of basic form of each point in the three-dimensional point cloud, and construct the enhanced point cloud. The path initialization module is used to generate an initial polishing path based on the enhanced point cloud, and to establish a Frenet frame for each point on the initial polishing path. The Frenet frame includes the normal vector, the tangent vector of the initial polishing path, and the binormal vector obtained by the cross product of the normal vector and the tangent vector. The sub-path generation module is used to calculate the normal curvature along the direction of the sub-normal vector based on the Frenet frame, deduce the maximum allowable row spacing arc length for each point on the initial grinding path based on the spatial geometric relationship between the normal curvature radius corresponding to the normal curvature and the radius of the grinding tool, take the minimum value among the maximum row spacing arc lengths as the offset row spacing arc length, and generate the next grinding path based on the Frenet frame and the offset row spacing arc length. The sub-path iteration module is used to take the next polishing path as the current polishing path, repeatedly execute the operation of establishing a Frenet frame for each point on the current polishing path, and generating the next polishing path, until the generated polishing sub-paths cover the preset polishing area of ​​the 3D point cloud, and obtain several ordered polishing sub-paths. The grinding path generation module is used to calculate the normal curvature along the tangent vector direction of each grinding sub-path, derive the maximum allowable step arc length for each point on the same path in combination with the radius of the grinding tool, take the minimum value among the maximum step arc lengths as the processing step length, and resample the grinding sub-paths based on the processing step length to generate a full-coverage grinding path.

[0016] To achieve one of the above-mentioned objectives, one embodiment of the present invention provides a computer-readable storage medium storing program instructions, which, when executed, implement the grinding path planning method for freeform surfaces as described in any of the preceding claims.

[0017] To achieve one of the above-mentioned objectives, one embodiment of the present invention provides an electronic device, including a processor and a memory, wherein the memory stores program instructions, and the processor executes the program instructions to implement the grinding path planning method for freeform surfaces as described in any of the preceding claims.

[0018] The grinding path planning method, apparatus, storage medium, and device for free-form surfaces provided in this invention have the following advantages: This invention performs path planning based on extracting local differential geometric parameters of the surface from a 3D point cloud, eliminating the need for a complete workpiece surface model. It adaptively solves for row spacing and step size based on the geometric constraints of curvature in different regions of the surface and the radius of the grinding tool, effectively improving grinding efficiency. Furthermore, by calculating and adaptively constraining the normal curvature along the sub-normal and path tangential directions, it simultaneously ensures the grinding coverage integrity of adjacent paths and tool positions along the same path, reducing dependence on fixed empirical row spacing and fixed sampling step size, and enabling full-coverage grinding of free-form surfaces. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the grinding path planning method for free-form surfaces described in this invention. Figure 2 This is a schematic diagram of the structure of the grinding path planning device for free-form surfaces described in this invention; Figure 3 This is a schematic diagram of the structure of the electronic device described in this invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Embodiment 1 of the present invention provides a method for planning the grinding path of a free-form surface, such as... Figure 1 As shown, it includes the following steps: Step S1: Obtain the radius of the grinding tool and the three-dimensional point cloud of the workpiece to be ground, extract the normal vector and the coefficients of the second type of basic form of each point in the three-dimensional point cloud, and construct an enhanced point cloud; In practice, the grinding tool can be a disc-type grinding wheel, including industrial grinding consumables such as sanding discs, flap wheels, and belt wheels. The radius of the grinding tool is determined based on the specifications of the consumables used with the equipment; if different specifications of grinding consumables are used, the corresponding radius is updated accordingly. The workpieces to be ground are all smooth, continuous, second-order differentiable free-form surfaces, such as turbine blades in the aerospace industry, mold covers in the automotive industry, and high-speed rail shells in the rail transit industry. The surface of the workpiece to be ground does not have a uniform curvature value; local areas can be convex, concave, or planar. The three-dimensional point cloud of the workpiece to be ground can be obtained using a structured light 3D camera or a laser line scan sensor as a visual acquisition device, with the workpiece positioned and clamped using an industrial fixture. The visual acquisition device completely scans the preset grinding area of ​​the workpiece from multiple spatial angles, generating the three-dimensional point cloud. ,in, The unit of measurement for each point in the three-dimensional point cloud is uniformly set in millimeters, and it is used to completely represent the curved surface shape of the workpiece to be polished.

[0022] In practice, the normal vector can be implemented using methods based on local Voronoi diagrams, analytical differentiation based on moving least squares surface fitting, deep learning point cloud normal vector prediction networks, or eigenvalue decomposition of the covariance matrix. The coefficients of the second type of fundamental form can be obtained through local cubic surface fitting, implicit surface differentiation of radial basis functions, quadratic surface fitting, or directly taking the covariant derivative of the normal vector field.

[0023] In this embodiment, the method for constructing the enhanced point cloud is as follows: for each point in the three-dimensional point cloud, a neighborhood search is performed to obtain the corresponding neighborhood point set; the covariance matrix of the neighborhood point set is constructed and the normal vector is extracted by eigenvalue decomposition of the covariance matrix; the second type of basic form coefficients are obtained by fitting a local quadratic surface; and the normal vector, the second type of basic form coefficients, and the coordinates of the three-dimensional point cloud are associated to obtain the enhanced point cloud.

[0024] Here, for the points in the three-dimensional point cloud A point can be searched using a KD-tree. The coordinates are the origin and the radius. The set of all neighborhood points inside the sphere ,in, The neighboring points in the three-dimensional point cloud The global index in the range, where k is the number of points contained in the neighborhood. Radius The average sampling interval of the 3D point cloud Times, preferably, the radius To ensure the numerical stability of the quadratic surface fitting, if It can increase the radius Search again. Then, calculate the mean of the neighborhood points. , ,in, It is a local index within the neighborhood point set. Point The neighborhood point set of the first The three-dimensional coordinates of each point.

[0025] Construct the covariance matrix of the neighborhood point set based on the mean of the neighborhood point set and the neighborhood points. , ,in, This represents the transpose of a vector or matrix. For the covariance matrix... Perform eigenvalue decomposition to extract normal vectors. Specifically, let the three eigenvalues ​​be... ,and The corresponding unit eigenvectors are respectively The smallest eigenvalue corresponding feature vector As a point The initial normal vector is adjusted globally to ensure it uniformly points to the outside of the surface. Specifically, if... Then In the opposite direction, among which, As a reference direction, the reference direction can be determined by the center of the 3D point cloud bounding box pointing outwards, ultimately yielding the point... normal vector , ,in, Let be the set of all normal vectors, used to represent a unit sphere in three-dimensional space.

[0026] Then, the coefficients of the second type of fundamental form are obtained through local quadratic surface fitting; specifically, using points... Origin and normal vector Let w be the axis, and arbitrarily choose two mutually orthogonal unit vectors within the tangent plane. As shaft and Establish a local orthogonal coordinate system (axis) ),in, , neighboring points Transform to the local orthogonal coordinate system: ,in, Neighboring points The coordinate components in the local coordinate system, with units of . For the transformed points Fitting a quadratic surface using the least squares method: ,in, These are coefficients of the second type of basic form, all in units of... Fitting requires... To minimize the sum of squared errors, the coefficients of the first kind of fundamental form of the local orthogonal coordinate system are: The enhanced point cloud is obtained by associating the normal vector, the coefficients of the second type of basic form, and the coordinates of the 3D point cloud. Understandably, this allows for the acquisition of local differential geometric information of a surface using only 3D point clouds, without relying on a complete parametric CAD surface model.

[0027] Step S2: Generate an initial polishing path based on the enhanced point cloud, and establish a Frenet frame for each point on the initial polishing path. The Frenet frame includes the normal vector, the tangent vector of the initial polishing path, and the binormal vector obtained by the cross product of the normal vector and the tangent vector. In practice, the initial polishing path can be obtained by projecting a user-specified boundary curve onto a 3D point cloud, walking along the geodesic of the 3D point cloud from one end to the other, intersecting the plane with the point cloud, or directly selecting a point sequence of the 3D point cloud boundary as the initial polishing path.

[0028] In this embodiment, the initial polishing path is generated by finding the intersection of a plane and a point cloud. Specifically, the equation of the initial cutting plane is obtained, the intersection points of the initial cutting plane and the hidden surface corresponding to the enhanced point cloud are solved and sorted to obtain the initial polishing path; the tangent vector of each point on the initial polishing path is calculated using the central difference method, and the binormal vector is determined by the cross product of the tangent vector and the normal vector to obtain the Frenet frame of each point.

[0029] Here, the initial cutting plane can be specified by the user or automatically selected based on the minimum principal direction of the 3D point cloud, and the equation of the initial cutting plane... : , ,in, Let be the planar parameters, and let the initial cutting plane satisfy . The point, among which, The planar distance threshold can be the radius. of By multiplying the values ​​by a factor of two, the exact intersection point can be obtained by interpolating along the plane normal to the corresponding local quadratic surface: The initial polishing path is obtained by sorting all intersection points according to their spatial location. ,in, The total number of points contained in the initial path, indicated by the superscript. Indicates the path number, each intersection point Inherit normal vector from the nearest point cloud point and curvature coefficient , , Then, the tangent vector at each point on the initial grinding path is calculated using the central difference method. ,in, Describes the Euclidean norm of a vector. , Each is the current point Along the path, the beginning and end points are analyzed using one-sided differences. To ensure the tangent vector lies within the tangent plane of the surface, projection and normalization are performed: , ,in, Represents the vector dot product. For point The tangent vector at the given point. The binormal vector is determined by the cross product of the tangent vector and the normal vector. ,in, Represents the cross product of vectors. Located in the tangent plane and with the tangent vector Vertically, pointing in the direction of advancement for the next path, and obtaining the Frenet frame for each point in the initial polishing path: It is understandable that generating the initial grinding path based on the intersection of the cutting planes does not require manual hand-drawing of curves or pre-setting of complex boundary contours. It is suitable for various irregular free-form workpieces and provides a unified and standardized geometric calculation benchmark for the generation of the next grinding path.

[0030] Step S3: Calculate the normal curvature along the direction of the binormal vector based on the Frenet frame. Based on the spatial geometric relationship between the normal curvature radius corresponding to the normal curvature and the radius of the grinding tool, derive the maximum allowable row spacing arc length at each point on the initial grinding path. Take the minimum value among the maximum row spacing arc lengths as the offset row spacing arc length. Generate the next grinding path based on the Frenet frame and the offset row spacing arc length. Specifically, the derivation process of the maximum row spacing arc length is as follows: calculate the normal curvature radius along the direction of the binormal vector according to Euler's formula; based on the geometric constraint relationship between the normal curvature radius and the radius of the grinding tool, establish row spacing calculation models for convex surfaces, concave surfaces, and planes respectively; obtain the maximum allowable row spacing arc length at each point on the initial grinding path according to the row spacing calculation model.

[0031] Here, in the local orthogonal coordinate system, the binormal vector The coordinates are represented as ,Right now , , Normal curvature in this direction , normal radius of curvature ,in, The unit is ,like The composition rate is considered to be zero. For the curvature threshold, preferably, Radius of normal curvature This indicates that the surface in this direction is locally approximated as a plane. Based on the row spacing calculation model, the maximum allowable row spacing arc length for each point on the initial grinding path is obtained, and the maximum row spacing arc length for valid points on the initial grinding path, excluding unreachable points, is calculated. Take the minimum value as the offset line spacing arc length , where superscript Indicates from the first path to the first The +1 line spacing of the path can be understood as using the minimum value to ensure that all points on the path are fully covered, resulting in no missed grinding along the entire path. In practice, in addition to taking the minimum value, the determination of the offset line spacing arc length can also adopt a segmented line spacing strategy. Specifically, the initial grinding path is divided into segments according to curvature clustering, and the minimum value is taken independently for each segment; a continuously varying line spacing function is used to directly calculate the local offset line spacing arc length of each point as a function of curvature, and then the next path is obtained by integration along the binormal direction.

[0032] In this embodiment, the row spacing calculation model is as follows: For convex surfaces, the maximum allowable row spacing is calculated based on the critical intersection condition that the center distance between the centers of two adjacent grinding tools on the trajectory offset outward along the surface normal vector is equal to the diameter of the grinding tool; for concave surfaces, the maximum allowable row spacing is calculated based on the critical intersection condition that the center distance between the centers of two adjacent grinding tools on the trajectory offset inward along the surface normal vector is equal to the diameter of the grinding tool, and it is determined whether the radius of the grinding tool is greater than the radius of the local trajectory of the concave surface; if so, the corresponding point is marked as an unreachable point; and the diameter of the grinding tool is determined as the maximum allowable row spacing.

[0033] Here, in the line spacing calculation model, if the normal curvature The surface is a convex surface, and the center trajectory of the grinding tool is an arc. The arc is concentric with the surface, and its radius is the radius R of the grinding tool and the normal radius of curvature. The sum of the centers of two adjacent grinding tools and the distance between their centers. , ,in, This represents the maximum row spacing arc length along the direction of the secondary normal vector between the centers of two adjacent grinding tools. For common curved surfaces... Using a small angle approximation )get If the curvature Then the surface is a concave surface, when At that time, the radius of the center trajectory of the grinding tool is the radius R of the grinding tool and the normal radius of curvature. The difference is the distance between the centers of two adjacent grinding tools. .when When the curvature is constant, mark it as an unreachable point; if the normal curvature is constant... Then the curved surface is a plane. .

[0034] In practice, the generation method of the next grinding path can be adopted by directly advancing based on the geodesic distance field of point cloud, advancing along the grid edge after point cloud meshing, solving the geodesic equation after implicit reconstruction of curved surface, and offset method of tangent plane stepping plus projection, etc.

[0035] In this embodiment, the method for generating the next polishing path is as follows: the offset line spacing arc length is divided into small step lengths, and a temporary intermediate point is obtained by moving along the subnormal direction in the local tangent plane. Several nearest neighbor points of the temporary intermediate point are searched in the three-dimensional point cloud. The local surface is fitted using the nearest neighbor points, and the temporary intermediate point is projected onto the local surface along the normal direction of the local surface to obtain a new path point. The normal vector and Frenet frame are updated until each point of the initial polishing path is updated. The updated points are deduplicated and sorted to obtain the next polishing path.

[0036] In practice, the offset line spacing arc length is divided into M microsteps, with each microstep being... , ,in, It is a positive integer; a temporary intermediate point is obtained by moving along the secondary normal direction within the local tangent plane. , , , , Search for temporary intermediate points of Find the nearest neighbor points, fit the local plane using the normal vectors and positions of the nearest neighbors, and then use the temporary intermediate points. Move along the local average normal until the projection point is obtained by landing on the local surface. ,in, The number of projection reference points, preferably, From enhanced point clouds Query distance from projection point The normal vector of the nearest point is used as To preserve the invariance of the tangent vector's direction on the surface, we approximate it as... Then project it onto the new tangent plane and normalize it: Update the secondary normal vector Obtain new path points The updated points are deduplicated and sorted to obtain the next polishing path. .

[0037] Step S4: Take the next polishing path as the current polishing path, and repeatedly perform the operation of establishing a Frenet frame for each point on the current polishing path and generating the next polishing path until the generated polishing sub-paths cover the preset polishing area of ​​the 3D point cloud, and obtain several ordered polishing sub-paths. In practice, the criteria for determining whether the preset grinding area is completely covered are divided into two categories, and the iterative calculation can be terminated if either category is met. The first criterion is that all points on the newly generated grinding path fall outside the effective boundary of the 3D point cloud, and there is a significant spatial gap between all coordinate points on the path and the main area of ​​the point cloud, meaning there are no surface areas available for further grinding. The second criterion is that when most points on the newly generated path are projected onto a surface, no corresponding effective neighboring points can be found within the 3D point cloud, and the local quadratic surface fitting lacks sufficient neighborhood points for support, indicating that the path has exceeded the boundary range of the preset grinding area surface of the workpiece to be ground. When either of the above conditions is met, it means that all current grinding sub-paths can completely cover the preset grinding area corresponding to the 3D point cloud. The generated grinding sub-paths are then aggregated to form an ordered complete grinding sub-path set, and the Frenet frame set of the grinding sub-paths is obtained. .

[0038] Step S5: Calculate the normal curvature along the tangent vector direction of each grinding sub-path, derive the maximum allowable step arc length at each point on the same path in combination with the radius of the grinding tool, take the minimum value among the maximum step arc lengths as the processing step length, and resample the grinding sub-path based on the processing step length to generate a full-coverage grinding path.

[0039] Here, the normal curvature of the polishing path along the direction of the path tangent vector is... , , ,in, The tangent vector, The components in the local orthogonal coordinate system are The method for calculating the maximum step size arc length is as follows: calculate the normal radius of curvature in the tangent vector direction of the path, and establish arc length step size calculation models for convex surfaces, concave surfaces, and planes respectively; based on the arc length step size calculation model, obtain the maximum allowable arc length step size for adjacent tool positions on the same path. Specifically, the arc length step size calculation model... , ,in, The normal radius of curvature is the direction of the tangent vector of the path. The minimum value among the maximum step size arc lengths is taken as the processing step size, and equidistant resampling is performed along the path arc length using this processing step size. If co-generated... There are 1 processing point, and the position of each processing point is output. and normal vector Combined with the tangent vector The full-coverage polishing path is obtained. The fully covered grinding path can be converted into the end-effector pose of a six-axis robot. ,in, It is a three-dimensional rotation group. It is understood that this invention can simultaneously constrain the processing coverage of the tangential direction of the path, thereby avoiding localized missed grinding defects within the same grinding trajectory, achieving complete bidirectional coverage of the curved surface in both the horizontal and vertical directions. The entire process relies on geometric analytical formulas to solve the step size, without depending on manually setting fixed sampling intervals, thus balancing the integrity of the grinding process with overall processing efficiency.

[0040] Embodiment 2 of the present invention provides a grinding path planning device for free-form surfaces, such as... Figure 2 As shown, it includes the following modules: The point cloud enhancement module 201 is used to obtain the radius of the grinding tool and the three-dimensional point cloud of the workpiece to be ground, extract the normal vector and the coefficient of the second type of basic form of each point in the three-dimensional point cloud and construct the enhanced point cloud. The path initialization module 202 is used to generate an initial polishing path based on the enhanced point cloud, and to establish a Frenet frame containing the normal vector, tangent vector and binormal vector for each point on the initial polishing path; The sub-path generation module 203 is used to calculate the normal curvature along the direction of the subnormal vector based on the Frenet frame, deduce the maximum allowable row spacing arc length for each point on the initial grinding path based on the spatial geometric relationship between the normal curvature radius corresponding to the normal curvature and the radius of the grinding tool, take the minimum value among the maximum row spacing arc lengths as the offset row spacing arc length, and generate the next grinding path based on the Frenet frame and the offset row spacing arc length. The sub-path iteration module 204 is used to take the next polishing path as the current polishing path, repeatedly execute the operation of establishing a Frenet frame for each point on the current polishing path, and generating the next polishing path, until the generated polishing sub-paths cover the preset polishing area of ​​the 3D point cloud, and obtain several ordered polishing sub-paths. The grinding path generation module 205 is used to calculate the normal curvature along the tangent vector direction of each grinding sub-path, derive the maximum allowable step arc length at each point on the same path in combination with the radius of the grinding tool, take the minimum value among the maximum step arc lengths as the processing step length, and resample the grinding sub-path based on the processing step length to generate a full-coverage grinding path.

[0041] Embodiment 3 of the present invention provides a computer-readable storage medium storing program instructions, which, when executed, implement the grinding path planning method for free-form surfaces as described in any of the preceding embodiments.

[0042] Embodiment 4 of the present invention provides an electronic device, such as... Figure 3 As shown, it includes a processor and a memory, the memory storing program instructions, and the processor executing the program instructions to implement the grinding path planning method for freeform surfaces as described in any of the preceding claims.

[0043] This invention can be an apparatus, method, and / or computer program product. A computer program product may include a readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of the invention.

[0044] Storage media can be tangible devices that hold and store instructions for use by instruction execution devices. Storage media can include, but are not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof.

[0045] It should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This way of describing the specification is only for clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0046] The detailed descriptions listed above are merely specific descriptions of feasible embodiments of the present invention, and are not intended to limit the scope of protection of the present invention. All equivalent embodiments or modifications made without departing from the spirit of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for planning grinding paths on freeform surfaces, characterized in that, Includes the following steps: S1: Obtain the radius of the grinding tool and the three-dimensional point cloud of the workpiece to be ground, extract the normal vector and the coefficients of the second type of basic form of each point in the three-dimensional point cloud, and construct an enhanced point cloud; S2: Generate an initial polishing path based on the enhanced point cloud, and establish a Frenet frame for each point on the initial polishing path. The Frenet frame includes the normal vector, the tangent vector of the initial polishing path, and the binormal vector obtained by the cross product of the normal vector and the tangent vector. S3: Calculate the normal curvature along the direction of the subnormal vector based on the Frenet frame, deduce the maximum allowable row spacing arc length at each point on the initial grinding path based on the spatial geometric relationship between the normal curvature radius corresponding to the normal curvature and the radius of the grinding tool, and take the minimum value among the maximum row spacing arc lengths as the offset row spacing arc length, and generate the next grinding path based on the Frenet frame and the offset row spacing arc length; S4: Take the next polishing path as the current polishing path, and repeatedly execute the operation of establishing a Frenet frame for each point on the current polishing path and generating the next polishing path until the generated polishing sub-paths cover the preset polishing area of ​​the 3D point cloud, and obtain several ordered polishing sub-paths. S5: Calculate the normal curvature along the tangent vector direction of each grinding sub-path, derive the maximum allowable step arc length for each point on the same path in combination with the radius of the grinding tool, take the minimum value among the maximum step arc lengths as the processing step length, and resample the grinding sub-path based on the processing step length to generate a fully covered grinding path.

2. The grinding path planning method for freeform surfaces according to claim 1, characterized in that, In step S1, the method for constructing the enhanced point cloud is as follows: for each point in the three-dimensional point cloud, a neighborhood search is performed to obtain the corresponding neighborhood point set; the covariance matrix of the neighborhood point set is constructed and the normal vector is extracted by eigenvalue decomposition of the covariance matrix; the second type of basic form coefficients are obtained by fitting a local quadratic surface; and the normal vector, the second type of basic form coefficients, and the coordinates of the three-dimensional point cloud are associated to obtain the enhanced point cloud.

3. The grinding path planning method for freeform surfaces according to claim 1, characterized in that, Step S2 specifically includes: obtaining the initial cutting plane equation, solving for the intersection points of the initial cutting plane and the hidden surface corresponding to the enhanced point cloud and sorting them to obtain the initial polishing path; calculating the tangent vector of each point on the initial polishing path using the central difference method, and determining the binormal vector by the cross product of the tangent vector and the normal vector to obtain the Frenet frame of each point.

4. The grinding path planning method for freeform surfaces according to claim 1, characterized in that, In step S3, the derivation process of the maximum row spacing arc length is as follows: calculate the normal curvature radius of the binormal vector direction according to Euler's formula; based on the geometric constraint relationship between the normal curvature radius and the radius of the grinding tool, establish row spacing calculation models for convex surfaces, concave surfaces and planes respectively; and obtain the maximum allowed row spacing arc length for each point on the initial grinding path according to the row spacing calculation model.

5. The grinding path planning method for freeform surfaces according to claim 4, characterized in that, The line spacing calculation model is as follows: For convex surfaces, the maximum allowable line spacing is calculated based on the critical intersection condition that the center distance between the centers of two adjacent grinding tools on the trajectory offset outward along the surface normal vector is equal to the diameter of the grinding tool; for concave surfaces, the maximum allowable line spacing is calculated based on the critical intersection condition that the center distance between the centers of two adjacent grinding tools on the trajectory offset inward along the surface normal vector is equal to the diameter of the grinding tool, and it is determined whether the radius of the grinding tool is greater than the radius of the local trajectory of the concave surface; if so, the corresponding point is marked as an unreachable point; and the diameter of the grinding tool is determined as the maximum allowable line spacing.

6. The grinding path planning method for freeform surfaces according to claim 1, characterized in that, In step S3, the method for generating the next polishing path is as follows: the offset line spacing arc length is divided into small step lengths, and a temporary intermediate point is obtained by moving along the binormal direction in the local tangent plane. Several nearest neighbor points of the temporary intermediate point are searched in the three-dimensional point cloud. The local surface is fitted using the nearest neighbor points, and the temporary intermediate point is projected onto the local surface along the normal direction of the local surface to obtain a new path point. The normal vector and Frenet frame are updated until each point of the initial polishing path is updated. The updated points are deduplicated and sorted to obtain the next polishing path.

7. The grinding path planning method for freeform surfaces according to claim 1, characterized in that, The method for calculating the maximum step arc length in step S5 is as follows: calculate the normal radius of curvature in the tangent vector direction of the path, and establish arc length step length calculation models for convex surfaces, concave surfaces, and planes respectively; obtain the maximum allowable arc length step length of adjacent tool positions on the same path according to the arc length step length calculation model.

8. A grinding path planning device for free-form surfaces, characterized in that, Includes the following modules: The point cloud enhancement module is used to obtain the radius of the grinding tool and the three-dimensional point cloud of the workpiece to be ground, extract the normal vector and the coefficient of the second type of basic form of each point in the three-dimensional point cloud, and construct the enhanced point cloud. The path initialization module is used to generate an initial polishing path based on the enhanced point cloud, and to establish a Frenet frame for each point on the initial polishing path. The Frenet frame includes the normal vector, the tangent vector of the initial polishing path, and the binormal vector obtained by the cross product of the normal vector and the tangent vector. The sub-path generation module is used to calculate the normal curvature along the direction of the sub-normal vector based on the Frenet frame, deduce the maximum allowable row spacing arc length for each point on the initial grinding path based on the spatial geometric relationship between the normal curvature radius corresponding to the normal curvature and the radius of the grinding tool, take the minimum value among the maximum row spacing arc lengths as the offset row spacing arc length, and generate the next grinding path based on the Frenet frame and the offset row spacing arc length. The sub-path iteration module is used to take the next polishing path as the current polishing path, repeatedly execute the operation of establishing a Frenet frame for each point on the current polishing path, and generating the next polishing path, until the generated polishing sub-paths cover the preset polishing area of ​​the 3D point cloud, and obtain several ordered polishing sub-paths. The grinding path generation module is used to calculate the normal curvature along the tangent vector direction of each grinding sub-path, derive the maximum allowable step arc length for each point on the same path in combination with the radius of the grinding tool, take the minimum value among the maximum step arc lengths as the processing step length, and resample the grinding sub-paths based on the processing step length to generate a full-coverage grinding path.

9. A computer-readable storage medium storing program instructions, characterized in that, When the program instructions are executed, they implement the grinding path planning method for freeform surfaces as described in any one of claims 1 to 7.

10. An electronic device, characterized in that, It includes a processor and a memory, the memory storing program instructions, and the processor executing the program instructions to implement the grinding path planning method for free-form surfaces as described in any one of claims 1 to 7.

Images