A point cloud registration method, a gradual forming mirror surface compensation method and system

Abstract

The application provides a point cloud registration method, a gradual forming mirror surface compensation method and system, acquires two point cloud data to be registered; after extracting edge points of the point cloud by using a PCA method, edge planes of reference point cloud and registered point cloud are fitted by using the edge points; a rotation matrix between normal vectors of the two edge planes is calculated, so that the normal vector of the edge plane of the registered point cloud is aligned to the normal vector of the edge plane of the reference point cloud; the convex hull directions of the reference point cloud and the registered point cloud are aligned; fine alignment is performed, so that the Euclidean distance between the edge points of the two point clouds is minimized. Based on the mirror principle, robot machining error compensation is carried out, the point cloud of the actual machining surface is measured by using a scanner, the target surface is regarded as a mirror surface, and the actual machining surface is mirrored to the other side through the target surface, so that the compensation surface is obtained, and the geometric precision of the formed part is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of three-dimensional curved surface forming, and particularly relates to a point cloud registration method, a progressive forming mirror surface compensation method and system. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute the prior art.

[0003] Robot progressive forming of sheet metal is a flexible processing method for three-dimensional curved surface forming of sheet metal, and uses an industrial robot to drive a hemispherical tool head to process point by point and layer by layer. Progressive forming directly manufactures a sample part using a three-dimensional digital model of a target component, greatly reduces the cycle from design to production, and has many advantages in manufacturing sheet metal parts.

[0004] However, this method also has some disadvantages:

[0005] (1) The rigidity of the robot body is insufficient, and the robot end will produce a certain disturbance error when subjected to external force.

[0006] (2) The sheet metal itself will produce a certain springback after processing, resulting in a certain springback error.

[0007] (3) When the point cloud of the formed part and the standard point cloud are analyzed for error, manual registration is required, which has a certain registration error. SUMMARY

[0008] To solve the above problems, the present application provides a point cloud registration method, a progressive forming mirror surface compensation method and system, which improves the geometric accuracy of the formed part and also improves the registration accuracy of the progressive forming part scanning point cloud.

[0009] According to some embodiments, the present application adopts the following technical scheme:

[0010] A point cloud registration method comprises the following steps:

[0011] Obtain two point cloud data to be registered;

[0012] After extracting the edge points of the point cloud using the PCA method, the edge planes of the reference point cloud and the registered point cloud are fitted using the edge points;

[0013] Calculate the rotation matrix between the normal vectors of the two edge planes, so that the normal vector of the edge plane of the registered point cloud is aligned to the normal vector of the edge plane of the reference point cloud;

[0014] Align the convex hull directions of the reference point cloud and the registered point cloud;

[0015] Fine alignment is performed to minimize the Euclidean distance between the edge points of the two point clouds.

[0016] As an alternative embodiment, the process of aligning the convex hull directions of the reference point cloud and the point cloud to be registered comprises: for the edge planes A and B in the two point clouds, let their fitting plane equations be ax+by+cz+d=0;

[0017] For each point in each point cloud, calculate its distance to the corresponding plane. For a point P(x, y, z) and a plane ax+by+cz+d=0, the signed distance D of the point to the plane can be expressed as:

[0018] The signed distance represents the position of the point relative to the plane: if D>0, the point is on one side of the plane; if D<0, the point is on the other side of the plane; if D=0, the point is on the plane;

[0019] For each point cloud, according to the calculated signed distance, count the number of points on both sides of the plane, and calculate the number of points with D>0 and D<0;

[0020] Compare the number of points on both sides of each point cloud to determine which side of which plane has more points, and then the side of the plane is the convex hull direction of the point cloud;

[0021] If the convex hull directions of the two point clouds are opposite, rotate the point cloud to be registered by 180 degrees, otherwise, do not calculate.

[0022] As an alternative embodiment, fine alignment is performed using the ICP algorithm to minimize the Euclidean distance between the edge points.

[0023] A progressive forming mirror surface compensation method, comprising the following steps:

[0024] Based on the above point cloud registration method, the point cloud of the actual machined surface and the point cloud of the target surface are registered, and the point cloud of the actual machined surface is taken as the reference point cloud and the point cloud of the target surface is taken as the point cloud to be registered.

[0025] For each point in the point cloud to be registered, find the nearest neighbor point in the reference point cloud;

[0026] For each set of nearest neighbor points, fit a plane to determine the parameters of the plane equation;

[0027] For each point in the point cloud to be registered, based on the parameters, calculate its mirror point on the fitted plane;

[0028] Generate a mirror compensation surface point cloud according to all the mirror points.

[0029] The generated mirror compensation surface point cloud is reversely generated into a three-dimensional geometric model, and a machining path is determined according to the three-dimensional geometric model.

[0030] As an alternative embodiment, the k-nearest neighbor algorithm is used to find the nearest neighbor point in the reference point cloud for each point in the registered point cloud.

[0031] As an alternative embodiment, the least square method is used to calculate the parameters of the plane equation.

[0032] As an alternative embodiment, based on the parameters, the process of calculating the mirror point of each point p i in the registered point cloud on the fitting plane includes: i calculating the mirror point p

[0033] p i ′=p i -2(n·p i +d)n

[0034] wherein n is the normal vector of the plane, determined by the parameters, n·p i +d represents the directed distance of p i to the plane.

[0035] A point cloud registration system comprises:

[0036] A data acquisition module configured to acquire two point cloud data to be registered;

[0037] A fitting module configured to extract edge points of the point clouds by using the PCA method, and then fit edge planes of the reference point cloud and the registered point cloud using the edge points;

[0038] A coarse alignment module configured to calculate a rotation matrix between normal vectors of the two edge planes, so that the normal vector of the edge plane of the registered point cloud is aligned to the normal vector of the edge plane of the reference point cloud, and the convex hull directions of the reference point cloud and the registered point cloud are aligned;

[0039] A fine alignment module configured to perform fine alignment to minimize the Euclidean distance between the edge points of the two point clouds.

[0040] A progressive forming mirror surface compensation system comprises:

[0041] A point cloud registration system configured to register point clouds of an actual machining surface and a target surface, with the point cloud of the actual machining surface as a reference point cloud and the point cloud of the target surface as a registered point cloud;

[0042] A neighbor point determination module configured to find the nearest neighbor point in the reference point cloud for each point in the registered point cloud;

[0043] a fitting module configured to fit, for each set of nearest neighbor points, into a plane, and determine parameters of a plane equation;

[0044] a mirror point calculation module configured to calculate, for each point in the registered point cloud, a mirror point thereof on the fitted plane based on the parameters;

[0045] a third point cloud generation module configured to generate a mirror compensation surface point cloud according to all the mirror points;

[0046] a compensation module configured to generate a three-dimensional geometric model from the generated mirror compensation surface point cloud, and determine a machining path according to the three-dimensional geometric model.

[0047] A computer readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps in the above method.

[0048] An electronic device comprising a memory and a processor, and computer instructions stored on the memory and running on the processor, which, when executed by the processor, complete the steps in the above method.

[0049] Compared with the prior art, the present application has the following beneficial effects:

[0050] The point cloud registration algorithm based on PCA-icp improves the registration accuracy of the scanned point cloud of the incremental forming part, and the incremental forming mirror surface compensation algorithm based on the point cloud registration algorithm compensates the machining error of the robot based on the mirror principle, measures the point cloud of the actual machining surface through the scanner, regards the target surface as a mirror surface, mirrors the actual machining surface to the other side through the target surface, and thus obtains the compensation surface, thereby improving the geometric accuracy of the formed part.

[0051] In order to make the above objectives, characteristics and advantages of the present application more apparent and easy to understand, a preferred embodiment is described below in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0052] The drawings constituting a part of the specification of the present application are used to provide a further understanding of the present application, and the schematic embodiments of the present application and the description thereof are used to explain the present application, and do not constitute an improper limitation on the present application.

[0053] Figure 1 It is a mirror surface compensation algorithm principle diagram of an embodiment;

[0054] Figure 2 It is a point cloud registration algorithm effect diagram of an embodiment;

[0055] Figure 3 It is a part cross-sectional schematic diagram of an embodiment;

[0056] Figure 4 is a schematic diagram of a progressive forming workpiece modeling according to an embodiment;

[0057] Figure 5 is a schematic diagram of a conical part according to an embodiment;

[0058] Figure 6 is a schematic diagram of a two point cloud alignment process according to an embodiment;

[0059] Figure 7 is a schematic diagram of a two point cloud alignment result according to an embodiment;

[0060] Figure 8 is a schematic diagram of mirror point determination according to an embodiment;

[0061] Figure 9 is a schematic diagram of a generated compensated point cloud according to an embodiment. DETAILED DESCRIPTION

[0062] The application will be further described below in conjunction with the accompanying drawings and embodiments.

[0063] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0064] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0065] The embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0066] Embodiment One

[0067] A point cloud registration method, as shown in Figure 2 includes the following steps:

[0068] Obtain two point cloud data to be registered;

[0069] After extracting the edge points of the point cloud using the PCA method, the edge planes of the reference point cloud and the registered point cloud are fitted using the edge points;

[0070] Calculate the rotation matrix between the normal vectors of the two edge planes, so that the normal vector of the edge plane of the registered point cloud is aligned to the normal vector of the edge plane of the reference point cloud;

[0071] Convex hull direction of the aligned base point cloud and the registered point cloud;

[0072] Fine alignment is performed to minimize the Euclidean distance between the edge points of the two point clouds.

[0073] First, a brief introduction is given.

[0074] As shown in Figure 3 , the forming force of incremental forming gradually increases with the machining depth, and the springback phenomenon in sheet metal machining mainly occurs in the area with large machining depth under the action of the simple support die.

[0075] In addition, the geometric shape of the incremental forming workpiece is mostly "open" shape, and all are machined from the z=0 plane, that is, the cross-sectional area of the z=0 plane is the largest, and the cross-sectional area of the upper or lower layer is gradually reduced. Therefore, this paper uses the edge points of the initial machining plane as the reference for point cloud registration, which is more in line with the compensation requirements of the incremental forming process.

[0076] For incremental forming parts, it is a sheet metal machining process that forms a surface layer by layer from a flat sheet. Therefore, when analyzing the part forming geometric accuracy, only the forming surface needs to be analyzed, and the initial machining surface of the part is always flat, and the cross-sectional area gradually decreases during layer-by-layer processing. Therefore, projecting the overall geometric shape onto the initial machining plane can retain as much information as possible.

[0077] PCA analysis is a powerful dimensionality reduction algorithm that cleverly combines projection variance using the square of the 2-norm to reduce three-dimensional data to two-dimensional data. The purpose of using principal component analysis is to reduce the dimensionality of the data while retaining as much information as possible.

[0078] For a single-layer surface point cloud M containing n points, the coordinates of each point m i = [x i , y i , z i ], the data matrix is represented as:

[0079]

[0080] Calculate the mean vector of each column:

[0081]

[0082] Center the data:

[0083]

[0084] The centered data matrix is:

[0085]

[0086] The covariance matrix C is:

[0087]

[0088] The unfolded covariance matrix is:

[0089]

[0090] where, The other elements in the matrix are the same.

[0091] Eigenvalue decomposition is performed on the covariance matrix C.

[0092] CV = VD

[0093] where V is the eigenvector matrix and D is the eigenvalue matrix.

[0094]

[0095] V = [v1 v2 v3]

[0096] Definition of eigenvalue decomposition:

[0097] Cv i = λ i v i

[0098] where the eigenvalue λ i represents the variance of the data in the direction of the eigenvector v i .

[0099] Arrange the eigenvalues in descending order:

[0100] λ1≥λ2≥λ3

[0101] The eigenvector direction corresponding to the maximum eigenvalue is the principal component direction, i.e. the projection direction of the point cloud.

[0102] In addition, assuming that the point cloud is uniformly distributed in space, the variance is positively correlated with the projection area. The projection area refers to the convex hull area of the projection points when the point cloud is projected onto a certain plane. For a uniformly distributed three-dimensional point cloud, projecting the point cloud onto different planes, the size of the projection area is related to the expansion degree of the points on the plane.

[0103] For a uniformly distributed point cloud, the expansion degree of the projection points determines the projection area. The expansion degree of the projection points is determined by the variance in the projection direction. The larger the eigenvalue, the greater the expansion degree in that direction, and the larger the corresponding projection area.

[0104] To demonstrate the universality of principal component analysis (PCA) in incremental forming parts, a conical part with a wall angle of α is taken as an example. Figure 5 As shown.

[0105] Compare the base area S with the projected area W of the front view:

[0106] S=πr 2

[0107]

[0108] That is, tanα < π. Solving for α, we get α = 72°. Furthermore, the depth can reach 3r. This is sufficient for most incrementally formed shapes.

[0109] This embodiment uses typical parts for verification and the results are satisfactory.

[0110] The specific process includes:

[0111] like Figure 6 As shown, after extracting the edge points of the point cloud using PCA, the edge planes of point clouds A and B are fitted using these edge points. The rotation matrix between the normal vectors of the two planes is calculated so that the normal vector of plane B is aligned with the normal vector of plane A.

[0112] The normal vectors are then aligned with the convex hull directions of the two point clouds by further rotation matrix calculation.

[0113] The process of aligning the convex hull directions of the reference point cloud and the point cloud to be registered includes: for edge plane A and edge plane B in the two point clouds, let their fitting plane equation be: ax + by + cz + d = 0;

[0114] For each point in the point cloud, calculate its distance to the corresponding plane. For point P(x,y,z) and plane ax+by+cz+d=0, the signed distance D from the point to the plane can be expressed as:

[0115] Signed distance represents the position of a point relative to a plane: if D > 0, the point is on one side of the plane; if D < 0, the point is on the other side of the plane; if D = 0, the point is on the plane.

[0116] For each point cloud, based on the calculated signed distance, count the number of points located on both sides of the plane, and calculate the number of points where D>0 and D<0;

[0117] Compare the number of points on both sides of each point cloud to determine which side of which plane has more points. Then, that side of the plane is the convex hull direction of the point cloud.

[0118] If the convex hulls of the two point clouds are in opposite directions, the registered point cloud will be rotated 180 degrees; otherwise, it will not be calculated.

[0119] Fine alignment is performed using the ICP (Iterative Closest Point) algorithm to minimize the Euclidean distance between the edge points, as shown in Figure 7 .

[0120] Embodiment Two

[0121] A mirror surface compensation method, based on the method provided in Embodiment One, first performs registration of the two point clouds.

[0122] As shown in Figure 1 , this method is based on the mirror principle to compensate for robot machining errors. The point cloud of the actual machined surface is measured by a scanner, the target surface is regarded as a mirror surface, and the actual machined surface is mirrored to the other side through the target surface, and the compensation surface is obtained.

[0123] Specifically includes:

[0124] Given two point clouds ptCloudA and ptCloudB, create a new point cloud ptCloudC, where each point is the mirror transformed point of the point in ptCloudB through the nearest neighbor point fitting plane in ptCloudA.

[0125] First, find the nearest neighbor point in ptCloudA for each point in ptCloudB. Use the k-nearest neighbor algorithm. For a point in ptCloudB, find its nearest neighbor point in ptCloudA.

[0126] For each set of nearest neighbor points, fit a plane. Let the equation of the fitted plane be:

[0127] ax+by+cz+d=0

[0128] Using the least squares method, we can get the parameters n = [a, b, c] and d of the plane equation.

[0129] For each point p i in ptCloudB, calculate its mirror point p i ' on the fitted plane, as shown in Figure 8 , calculated by the following formula:

[0130] p i ′=p i -2(n·p i +d)n

[0131] Where n is the normal vector of the plane, and n·p i +d represents the directed distance from p i to the plane.

[0132] AsFigure 9 The generated point cloud is reversely generated into a three-dimensional geometric model, and a tool path is generated for machining.

[0133] The point cloud is repaired and reversely modeled into a three-dimensional model in stp format using the designX software. Then, the machining tool path is generated using UG, and the next step of trajectory planning is performed.

[0134] Those skilled in the art will appreciate that embodiments of the application can be provided as methods, systems, or computer program products. Accordingly, the application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the application can be embodied in the form of a computer program product on one or more computer readable storage media (including, but not limited to, disk memory, CD-ROMs, optical storage media, etc.) having computer usable program code embodied therein.

[0135] The present application is described in reference to the flowchart and / or block diagrams of the method, apparatus (system), and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as a combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce an apparatus that implements the functions specified in the flowchart and / or block diagram. Figure 1 one or more flows and / or blocks Figure 1 means for performing the function specified by the flow or flows and / or block or blocks.

[0136] These computer program instructions can also be stored in a computer readable storage medium that can direct the computer or other programmable data processing apparatus to work in a specific manner, so that the instructions stored in the computer readable storage medium produce a product including an instruction apparatus that implements the functions specified in the flowchart and / or block diagram. Figure 1 one or more flows and / or blocks Figure 1 means for performing the function specified by the flow or flows and / or block or blocks.

[0137] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable data processing apparatus to produce a computer implemented process, so that the instructions executed on the computer or other programmable data processing apparatus provide a process for implementing the functions specified in the flowchart and / or block diagram. Figure 1 one or more flows and / or blocks Figure 1 means for performing the function specified by the flow or flows and / or block or blocks.

[0138] The above merely describes the preferred embodiments of the present application and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made by those skilled in the art without departing from the spirit and principle of the present application shall fall within the protection scope of the present application.

Claims

1. A method of point cloud registration, characterized in that, The method comprises the following steps: Obtaining two point cloud data to be registered; Using PCA method to extract edge points of the point cloud, and fitting edge planes of the reference point cloud and the registered point cloud using the edge points; Calculating a rotation matrix between normal vectors of the two edge planes, so that the normal vector of the edge plane of the registered point cloud is aligned to the normal vector of the edge plane of the reference point cloud; Aligning the convex hull directions of the reference point cloud and the registered point cloud; Performing fine alignment to minimize the Euclidean distance between edge points of the two point clouds; The process of aligning the base point cloud and the convex hull direction of the registered point cloud specifically comprises: for the edge planes A and B in the two point clouds, let their fitting plane equations be: ; For each point in each point cloud, the distance of it to the corresponding plane is calculated, for a point P(x, y, z) and a plane The signed distance D of a point to a plane is expressed as: ; The signed distance represents the position of a point relative to a plane: if D > 0, the point is on one side of the plane; if D < 0, the point is on the other side of the plane; if D = 0, the point is on the plane; For each point cloud, according to the calculated signed distance, the number of points on both sides of the plane is counted, and the number of points with D > 0 and D < 0 is calculated; Comparing the number of points on both sides of each point cloud to determine which side of which plane has more points, and the side of the plane is the convex hull direction of the point cloud; If the convex hull directions of the two point clouds are opposite, the registered point cloud is rotated by 180 degrees, otherwise, no rotation is performed; The process of performing fine alignment to minimize the Euclidean distance between edge points of the two point clouds specifically comprises: performing fine alignment using an ICP algorithm to minimize the Euclidean distance between edge points.

2. A method of mirror surface compensation by incremental forming, characterized in that The method comprises the following steps: Based on the point cloud registration method of claim 1, the point cloud of the actual machining surface and the point cloud of the target surface are registered, and the point cloud of the actual machining surface is taken as the reference point cloud, and the point cloud of the target surface is taken as the registered point cloud; Finding the nearest neighbor point in the reference point cloud for each point in the registered point cloud; For each set of nearest neighbor points, fitting into a plane to determine the parameters of the plane equation; For each point in the registered point cloud, based on the parameters, calculating its mirror point on the fitted plane; Generating a mirror compensation surface point cloud according to all the mirror points; Generating a three-dimensional geometric model in reverse from the generated mirror compensation surface point cloud, and determining a machining path according to the three-dimensional geometric model.

3. A method of mirror surface compensation by incremental forming according to claim 2, characterized in that The k-nearest neighbor algorithm is used to find the nearest neighbor point in the reference point cloud for each point in the registered point cloud.

4. A method of mirror surface compensation by incremental forming according to claim 2, characterized in that, The least squares method is used to calculate the parameters of the plane equation.

5. A method of mirror surface compensation by incremental forming according to claim 2, characterized in that, Based on the parameters, the process of computing the mirror point of each point in the registered point cloud on the fitting plane comprises computing the mirror point of each point in the registered point cloud on the fitting plane : wherein is a normal vector to the plane, determined by the parameters denotes the directed distance to the plane.

6. A point cloud registration system, characterized in that, It comprises: A data acquisition module configured to obtain two point cloud data to be registered; A fitting module configured to use PCA method to extract edge points of the point cloud, and fit edge planes of the reference point cloud and the registered point cloud using the edge points; A coarse alignment module configured to calculate a rotation matrix between normal vectors of the two edge planes, so that the normal vector of the edge plane of the registered point cloud is aligned to the normal vector of the edge plane of the reference point cloud, and align the convex hull directions of the reference point cloud and the registered point cloud; A fine alignment module configured to perform fine alignment to minimize the Euclidean distance between edge points of the two point clouds; The process of aligning the base point cloud and the convex hull direction of the registered point cloud specifically includes: for the edge planes A and B in the two point clouds, let their fitting plane equations be: ; For each point in each point cloud, the distance of it to the corresponding plane is calculated, for a point P(x, y, z) and a plane , the signed distance D of the point to the plane is expressed as: ; The signed distance represents the position of a point relative to a plane: if D > 0, the point is on one side of the plane; if D < 0, the point is on the other side of the plane; if D = 0, the point is on the plane; For each point cloud, according to the calculated signed distance, the number of points located on both sides of the plane is counted, and the number of points of D > 0 and D < 0 is calculated; Compare the number of points on both sides of each point cloud to determine which side of which plane has more points, and then the side of the plane is the convex hull direction of the point cloud; If the convex hull directions of the two point clouds are opposite, the registered point cloud is rotated by 180 degrees, otherwise, it is not rotated; The process of fine alignment to minimize the Euclidean distance between the edge points of the two point clouds specifically includes: fine alignment using the ICP algorithm to minimize the Euclidean distance between the edge points.

7. A system for mirror surface compensation by incremental forming, characterized by Comprise: A point cloud registration system configured to register the point cloud of the actual machining surface and the point cloud of the target surface based on the point cloud registration method of claim 1, taking the point cloud of the actual machining surface as the reference point cloud and the point cloud of the target surface as the registered point cloud; A neighbor point determination module configured to find the nearest neighbor point in the reference point cloud for each point in the registered point cloud; A fitting module configured to fit each set of nearest neighbor points into a plane to determine the parameters of the plane equation; A mirror point calculation module configured to calculate the mirror point of each point in the registered point cloud on the fitted plane based on the parameters; A third point cloud generation module configured to generate a mirror compensation surface point cloud according to all mirror points; A compensation module configured to generate a three-dimensional geometric model from the generated mirror compensation surface point cloud, and determine a machining path according to the three-dimensional geometric model.

8. An electronic device, characterized by comprising: A computer program product comprising a memory and a processor and computer instructions stored on the memory and running on the processor, when the computer instructions are run by the processor, the steps in the method of claim 1 or any one of claims 2-5 are completed.

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