CN113171913B - Spraying path generation method based on three-dimensional point cloud of seat furniture - Google Patents

Abstract

A spraying path generation method based on three-dimensional point cloud of seating furniture relates to a furniture spraying method. Importing a three-dimensional point cloud model of a seat workpiece; clustering and dividing the to-be-sprayed area according to the sparsity of the point cloud characteristic distribution; for the topology of the characteristic dense area obtained by segmentation as a full filling entity, generating a spraying path by using a point cloud slicing algorithm, clustering the characteristic sparse area into a single narrow beam unit, and generating the spraying path by using a midline extraction algorithm; planning paths and combining, and simulating the coating thickness; and generating a total spraying path of the surface of the seat workpiece, and guiding the path into a spraying robot controller. Aiming at the requirement of the flexibility degree of a spraying system, the spraying path generation method based on the three-dimensional point cloud of the seat furniture is provided, the generated spraying path can ensure the uniformity of the thickness of the coating, and simultaneously can ensure higher spraying efficiency and save the coating.

Description

Spraying path generation method based on three-dimensional point cloud of seat furniture

Technical Field

The invention relates to a furniture spraying method, in particular to a spraying path generation method based on three-dimensional point cloud of furniture such as chairs, and belongs to the technical field of intelligent spraying processing.

Background

Painting robots have been used in many production scenarios because they can separate workers from the painting environment and work continuously and stably. In the spraying process, a spray gun of the spraying robot moves along the surface of a workpiece according to a set path by using set spraying parameters, so the reasonability of the design of the spraying path directly influences the spraying uniformity, the spraying efficiency and the utilization rate of the coating. At present, the spraying path generation method mainly comprises two methods of manual teaching and off-line programming. The manual teaching has low working efficiency and the spraying quality depends on the experience of a teaching person. Therefore, in recent years, off-line programming based on three-dimensional models has become a research hotspot for the requirements of flexible spraying systems of robots.

Many previous spray path algorithm studies were based on CAD models of the workpieces, which required that accurate three-dimensional models of the workpieces had to be obtained in advance, which is very disadvantageous for increasing the flexibility of the spray system. In some occasions, the CAD model of the workpiece to be sprayed is not easy to obtain, and the traditional path planning algorithm is limited. In recent years, high-precision vision sensors are rapidly developed, and generation of a high-quality spraying path based on object three-dimensional point cloud becomes a new research direction.

In recent years, some methods for generating a workpiece point cloud spraying path based on point cloud have appeared, but most of the methods do not consider workpiece features, and plan the whole workpiece as a fully-filled topological entity on the basis of the workpiece features.

Disclosure of Invention

Aiming at the requirement of the flexibility degree of a spraying system, the invention provides a spraying path generation method based on three-dimensional point cloud of chair furniture, and the generated spraying path can ensure the uniformity of the thickness of a coating, can ensure higher spraying efficiency and saves the coating.

In order to achieve the purpose, the invention adopts the following technical scheme: a spraying path generation method based on three-dimensional point cloud of seating furniture comprises the following steps:

the method comprises the following steps: importing a three-dimensional point cloud model of the seat workpiece: importing the pcd-formatted file of the seat workpiece into a PCL (personal computer) library-based point cloud reading program, calculating a main characteristic vector of the point cloud by adopting a main component analysis algorithm, and finishing characteristic direction identification and posture transformation according to the rotation of the characteristic vector of the point cloud and the translation of the centroid position of the point cloud;

step two: clustering and segmenting the to-be-sprayed area according to the sparsity of point cloud characteristic distribution:

201. establishing a minimum point cloud bounding box lambda { [ x ] with each side parallel to the corresponding characteristic direction and capable of containing all point clouds_min,x_max]×[y_min,y_max]×[z_min,z_max]}；

202. Establishing a plurality of equally spaced slice planes in a main characteristic direction z axis, wherein the space between the slice planes is the moving space w of a spray gun, and cutting a point cloud bounding box of a seat workpiece into a cube Y_i：

Wherein i represents the number of the slice surface;

203. a cube Y_iN in_iPoints are taken as a sample point set and are recorded as omega_i＝{P_i(x_i,y_i,z_i),i＝1,2,,···,n_i}, calculate Ω_iAll points inside and omega_iCenter of mass P_ciDistance between, is recorded as

Calculating the void fraction within each block

204. The void ratio of each block is obtained, and the average value is used as the threshold rho of the void ratio_aveIf Ω is_iCalculated void fraction in excess of rho_aveJudging the region as a feature dense region, and recording the combined point set as omega t, otherwise, judging the region as a feature sparse region, and recording the combined point set as omega s;

205. and carrying out quadratic segmentation on omega s Euclidean clustering of the characteristic sparse region, finishing the Euclidean clustering segmentation when the original point set becomes an empty set, and recording the kth new segmentation point cloud subset as omega c_k；

Step three: for the topology of the characteristic dense area obtained by segmentation as a full filling entity, generating a spraying path by using a point cloud slicing algorithm, clustering the characteristic sparse area into a single narrow beam unit, and generating the spraying path by using a midline extraction algorithm:

301. generating a plurality of equally spaced slice planes in a main characteristic direction z axis, wherein the thickness between the adjacent slice planes is the moving distance w of a spray gun;

302. calculating the contour of the point cloud on the plane by intersection method, deducing the position of the point on the slice by using the point near the slice, representing the point cloud distribution near the slice by using the data on the slice, finding the nearest matching point pairs at both sides of the slice, and calculating the intersection point of the space straight line formed by connecting the point pairs and the slice plane to obtain the contour point, the straight line

And section E_jPoint of intersection P_si(x_si,y_si,z_si) Calculating formula:

wherein j is the serial number of the slice, δ is the thickness between adjacent slices, and t is the coefficient of the spatial straight line;

303. performing cubic spline interpolation on the solved contour path;

304. the characteristic sparse area is clustered into a single narrow beam unit, and the implementation method for generating the spraying path by the midline extraction algorithm comprises the following steps: to point cloud set omega c_kExtracting edges to obtain edge outer contours;

305. the extracted edges are sorted in a clockwise mode because the edge point set is unordered, and then the product of the unit vector of the maximum characteristic direction and the gradient vector of the adjacent edge points after sorting is calculated

Deleting the points with the product smaller than the set threshold from the point set, namely eliminating the points on the short edge;

306. performing Euclidean clustering on the residual point sets, dividing the residual point sets into contour two-side edge line point sets in the maximum characteristic direction, and storing the contour two-side edge line point sets in a set Ed_1kAnd Ed_k2In, to the set Ed_k1And Ed_k2Scattered point cubic spline interpolation, Ed in (E)_k1Interpolated point set Ed_k1'＝{P_{Edk1_i}(x_{Edk1_i},y_{Edk1_i},z_{Edk1_i}),Edk1_i＝1,2,,···,n_Edk1}，Ed_k2Point set Ed of interpolated element reverse order_k2'＝{P_{Edk2_i}(x_{Edk2_i},y_{Edk2_i},z_{Edk2_i}),Edk2_i＝1,2,,···,n_Edk2To Ed_k1' and Ed_k2' the corresponding element coordinate in (1) takes the midpoint P_{Emk_i}：

The obtained path points are spraying path points in a characteristic sparse area;

step four: merging planned paths, and simulating the coating thickness:

401. calculating the attitude direction of the spray gun, namely the normal direction of the surface of the seat workpiece, wherein the calculation method is the principal component analysis method, and the ambiguity of the normal can be removed by orienting all normal directions to the viewpoint uniformly;

402. for the contour path of the surface of the seat workpiece obtained by the two methods, the height of the spray gun is deviated along the attitude direction of the spray gun, namely the normal direction of the surface of the seat workpiece, through path point interpolation, and then the actual running path of the spraying robot can be obtained;

403. calculating the paint thickness deposition model on the free-form surface by using a infinitesimal method, and deducing the accumulated thickness th of the coating at one point on the free-form surface according to the projection similar geometric relationship_w'：

Wherein h represents the vertical height from the spray gun to the spraying experiment plane, h' represents the vertical height from the spray gun to the free-form surface, gamma represents the vertical angle between a point on the free-form surface and the center connecting line of the spray gun, psi represents the normal angle between a point on the free-form surface and the center connecting line of the spray gun, and th_wThe cumulative thickness of the coating at the point on the spray test plane is shown;

404. substituting the spraying model and the spraying parameters to verify the spraying uniformity and the spraying efficiency caused by the spraying path;

step five: and generating a total spraying path of the surface of the seat workpiece, and guiding the path into a spraying robot controller.

Compared with the prior art, the invention has the beneficial effects that: the spraying path generated based on the three-dimensional point cloud generating robot has the advantages that the spraying path is directly generated by combining with external measuring equipment to directly operate on the point cloud, the flexibility degree of a spraying system is improved, automation in the spraying process is realized, the actual spraying operation time can be reduced under the condition that the spraying uniformity is not reduced, the production efficiency can be greatly improved in actual production, the paint waste is reduced, and the application prospect is wide.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a schematic diagram illustrating determination of a cut area void fraction of a bounding box of a seat back of a seat workpiece according to an exemplary embodiment;

FIG. 3 is a schematic diagram illustrating a segmentation result of a spray area of a chair back of a chair workpiece according to sparsity in an embodiment;

FIG. 4 is a schematic diagram of cross-sectional contour points determined by point cloud slice intersection in accordance with an embodiment;

FIG. 5 is a schematic diagram of cross-sectional path points generated by a chair back point cloud slicing algorithm for a chair workpiece in accordance with an exemplary embodiment;

FIG. 6 is a schematic illustration of a leg centerline extraction for a seat workpiece in an exemplary embodiment;

FIG. 7 is a schematic view of a surface spray path planned by the method of the present invention;

FIG. 8 is a schematic view of a coating deposition model on a free-form surface according to an embodiment;

FIG. 9 is a schematic diagram illustrating the thickness distribution of the coating on the surface of the workpiece as a result of the planned spray path of the method of the present invention;

FIG. 10 is a schematic illustration of the surface spray paths generated on the four surfaces of a seat workpiece using the method of the present invention.

Detailed Description

The technical solutions in the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.

As shown in fig. 1, a spraying path generation method based on a three-dimensional point cloud of seating furniture includes the following steps:

the method comprises the following steps: leading in a three-dimensional point cloud model of a seat workpiece, specifically: importing the pcd-formatted file of the seat workpiece into a PCL (personal computer) library-based point cloud reading program, calculating a main characteristic vector of the point cloud by adopting a Principal Component Analysis (PCA) algorithm, and finishing characteristic direction identification and posture transformation according to the rotation of the characteristic vector of the point cloud and the translation of the centroid position of the point cloud;

the embodiment adopts a three-dimensional point cloud model, the data format is a pcd format, the three-dimensional point cloud model is obtained by scanning and measuring the surface of a seat workpiece through a visual sensor, the application occasion is wide, the three-dimensional point cloud model is easy to obtain, the detailed description is carried out on the chair back of the seat workpiece, and the point cloud data is expressed as follows: m ═ P_i(x_i,y_i,z_i) I ═ 1,2,, n }, where P is_iThe ith point constituting the surface of the seat workpiece is indicated, and n represents the total number of points.

101. The process of calculating the principal eigenvector of the point cloud by using a Principal Component Analysis (PCA) algorithm comprises the following steps: calculating a semi-positive definite covariance matrix after point cloud decentralization:

wherein, (x, y, z) is the coordinate of the three-dimensional point cloud model under the pcd format, and the eigenvalue matrix U of 3 multiplied by 1 can be obtained by half and positive definite covariance matrix decomposition_aAnd a 3 × 3 eigenvector matrix U_c；

102. The coordinate transformation matrix for realizing the alignment of the characteristic directions is as follows:

wherein, U_c ^TIs the transpose of the eigenvector matrix, P is the centroid coordinate column vector (x)_c,y_c,z_c)^TThe result of the feature direction conversion is shown by the coordinate axis of fig. 2;

step two: clustering and partitioning the to-be-sprayed area according to the sparsity of point cloud characteristic distribution, specifically:

201. referring to FIG. 2, a minimum point cloud bounding box λ { [ x ] is established, each side of which is parallel to the corresponding feature direction and can contain all the point clouds_min,x_max]×[y_min,y_max]×[z_min,z_max]}；

202. Referring to fig. 2, a plurality of equally spaced slicing planes are established on the z-axis in the main characteristic direction, the spacing between the slicing planes is equal to the moving distance w of the spray gun, and the point cloud bounding box of the seat workpiece is cut into a cube Y_i：

Wherein i represents the number of slice planes;

203. a cube Y_iN in_iPoints are taken as a sample point set and are recorded as omega_i＝{P_i(x_i,y_i,z_i),i＝1,2,,···,n_i}, calculate Ω_iAll points inside and omega_iCenter of mass P_ciDistance between, is recorded as

Calculating the void fraction within each block

204. The void ratio of each block is obtained, and the average value is used as the threshold rho of the void ratio_aveIf Ω is_iCalculated void fraction in excess of rho_aveJudging the region as a characteristic dense region, otherwise, judging the region as a characteristic sparse region, merging point sets judged as the chair back characteristic dense region, marking the merged point set as omega t, merging point sets judged as the chair leg characteristic sparse region, and marking the merged point set as omega s;

205. performing Euclidean clustering quadratic segmentation on the chair leg characteristic sparse area, randomly selecting one point in a point set omega s combined with the characteristic sparse area, searching r neighborhood of sampling points smaller than a set distance threshold value by using Kdtree, taking all neighborhood points as sampling points, searching r neighborhood of the sampling points until r neighborhood points meeting the requirement cannot be found in the origin set, and separating to finish a clustering point cloud set omega s₁Deleting the clustered points from the originAnd when the original point set becomes an empty set, the Euclidean clustering segmentation of all the points is completed, and the kth new segmentation point cloud subset is marked as omega c_kThe segmentation result is shown in fig. 3;

step three: for the topology of the chair back feature dense area obtained by segmentation as a full filling entity, a point cloud slicing algorithm is used for generating a spraying path, the feature sparse area is clustered into a single narrow beam unit, and a midline extraction algorithm is used for generating the spraying path, wherein the method specifically comprises the following steps:

301. for the topology of the chair back feature dense area obtained by segmentation as a full-filling entity, referring to fig. 4, the realization method for generating the spraying path by the point cloud slicing algorithm comprises the steps of generating a plurality of equally spaced slicing planes in the main feature direction z-axis, wherein the thickness between the adjacent slicing planes is the moving distance w of a spray gun;

302. referring to fig. 4, calculating the contour of the point cloud on the plane by intersection method, using the points near the slice to deduce the position of the points on the slice, using the data on the slice to represent the point cloud distribution near the slice, finding the nearest matching point pairs at both sides of the slice, calculating the intersection point of the space straight line formed by connecting the point pairs and the slice plane to obtain the contour point, the straight line

And section E_jPoint of intersection P_si(x_si,y_si,z_si) Calculating formula:

wherein j is the serial number of the slice, δ is the thickness between adjacent slices, t is the coefficient of the spatial straight line, and the result of the contour calculation is shown in fig. 5;

303. performing cubic spline interpolation on the solved contour path;

304. the characteristic sparse area is clustered into a single chair leg narrow beam unit, and the implementation method for generating the spraying path by the midline extraction algorithm comprises the following steps: to point cloud set omega c_kEdge extraction to obtainAn edge profile;

305. the edge point sets of the chair legs are disordered, the extracted edges are sorted in a clockwise mode, and then the product of the unit vector of the maximum characteristic direction and the gradient vector of the adjacent edge points after sorting is calculated

Deleting the points with the product smaller than the set threshold from the point set, namely eliminating the points on the short edge;

306. carrying out Euclidean clustering on the remaining chair leg point sets, dividing the remaining chair leg point sets into contour two side line point sets in the maximum characteristic direction, and storing the contour two side line point sets in a set Ed_1kAnd Ed_k2In, to the set Ed_k1And Ed_k2Scattered point cubic spline interpolation, Ed in (E)_k1Interpolated point set Ed_k1'＝{P_{Edk1_i}(x_{Edk1_i},y_{Edk1_i},z_{Edk1_i}),Edk1_i＝1,2,,···,n_Edk1}，Ed_k2Point set of interpolated elements in reverse order

Ed_k2'＝{P_{Edk2_i}(x_{Edk2_i},y_{Edk2_i},z_{Edk2_i}),Edk2_i＝1,2,,···,n_Edk2To Ed_k1' and Ed_k2' the corresponding element coordinate in (1) takes the midpoint P_{Emk_i}：

The obtained path points are spraying path points in a characteristic sparse area, and are shown in fig. 6;

step four: combining planned paths, and simulating the coating thickness, specifically comprising the following steps:

401. calculating the attitude direction of the spray gun, namely the normal direction of the surface of the seat workpiece, wherein the calculation method is the principal component analysis method, and the ambiguity of the normal can be removed by orienting all normal directions to the viewpoint uniformly;

402. referring to fig. 7, for the contour path of the surface of the seat workpiece obtained by the two methods, the height of the spray gun is shifted along the attitude direction of the spray gun, i.e. the normal direction of the surface of the seat workpiece, through path point interpolation, so that the actual running path of the spraying robot can be obtained;

403. referring to FIG. 8, a paint thickness deposition model on a free-form surface is calculated by using a infinitesimal method, and the cumulative thickness th of a coating layer at one point on the free-form surface can be derived from a projection similarity geometric relationship_w：

Wherein h represents the vertical height from the spray gun to the spraying experiment plane, h' represents the vertical height from the spray gun to the free-form surface, gamma represents the vertical angle between a point on the free-form surface and the center connecting line of the spray gun, psi represents the normal angle between a point on the free-form surface and the center connecting line of the spray gun, and th_wThe cumulative thickness of the coating at the point on the spray test plane is shown;

404. referring to fig. 9, substituting the spraying model and the spraying parameters to verify the spraying uniformity and the spraying efficiency caused by the spraying path;

step five: the generation of the total spraying path of the surface of the seat workpiece is conducted into a spraying robot controller, the method provided by the invention is applied to the spraying path planning of the seat workpieces on four sides, the obtained planning result is shown in figure 10, and the actual requirements of engineering can be met.

Aiming at the requirement of a flexible spraying system, the invention provides a spraying path generation method aiming at low paint waste of a seat workpiece with complex geometric characteristics under the condition that a three-dimensional model is unknown. The innovation of the invention is to provide an automatic segmentation method for point cloud of a spraying area, which specifically comprises the steps of 201-306, adopting different path planning strategies according to the feature density degree, specifically the step of 301-306, and establishing a coating thickness model to perform quantitative simulation verification on the provided path planning effect, specifically the step of 401-404. The method can reduce the actual spraying operation time under the condition of ensuring that the spraying uniformity is not reduced, can greatly improve the production efficiency in the actual production and reduce the paint waste.

In addition, the method can be expanded to automatic path planning of other spraying scenes such as wood, masonry, steel and the like.

It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.

Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (1)

1. A spraying path generation method based on three-dimensional point cloud of seat furniture is characterized by comprising the following steps: the method comprises the following steps:

the method comprises the following steps: importing a three-dimensional point cloud model of the seat workpiece: importing the pcd-formatted file of the seat workpiece into a PCL (personal computer) library-based point cloud reading program, calculating a main characteristic vector of the point cloud by adopting a main component analysis algorithm, and finishing characteristic direction identification and posture transformation according to the rotation of the characteristic vector of the point cloud and the translation of the centroid position of the point cloud;

step two: clustering and segmenting the to-be-sprayed area according to the sparsity of point cloud characteristic distribution:

201. establishing a minimum point cloud bounding box lambda { [ x ] with each side parallel to the corresponding characteristic direction and capable of containing all point clouds_min,x_max]×[y_min,y_max]×[z_min,z_max]}；

202. Establishing a plurality of equally spaced slice planes in a main characteristic direction z axis, wherein the space between the slice planes is the moving space w of a spray gun, and cutting a point cloud bounding box of a seat workpiece into a cube Y_i：

Wherein i represents the number of the slice surface;

203. a cube Y_iN in_iPoints are taken as a sample point set and are recorded as omega_i＝{P_i(x_i,y_i,z_i),i＝1,2,,…,n_i}, calculate Ω_iAll points inside and omega_iCenter of mass P_ciDistance between, is recorded as

Calculating the void fraction within each block

204. The void ratio of each block is obtained, and the average value is used as the threshold rho of the void ratio_aveIf Ω is_iCalculated void fraction in excess of rho_aveJudging the region as a feature dense region, and recording the combined point set as omega t, otherwise, judging the region as a feature sparse region, and recording the combined point set as omega s;

205. and carrying out quadratic segmentation on omega s Euclidean clustering of the characteristic sparse region, finishing the Euclidean clustering segmentation when the original point set becomes an empty set, and recording the kth new segmentation point cloud subset as omega c_k；

Step three: for the topology of the characteristic dense area obtained by segmentation as a full filling entity, generating a spraying path by using a point cloud slicing algorithm, clustering the characteristic sparse area into a single narrow beam unit, and generating the spraying path by using a midline extraction algorithm:

301. generating a plurality of equally spaced slice planes in a main characteristic direction z axis, wherein the thickness between the adjacent slice planes is the moving distance w of a spray gun;

302. calculating the contour of the point cloud on the plane by intersection method, deducing the position of the point on the slice by using the point near the slice, representing the point cloud distribution near the slice by using the data on the slice, finding the nearest matching point pairs at both sides of the slice, and calculating the intersection point of the space straight line formed by connecting the point pairs and the slice plane to obtain the contour point, the straight line

And section E_jPoint of intersection P_si(x_si,y_si,z_si) Calculating formula:

wherein j is the serial number of the slice, δ is the thickness between adjacent slices, and t is the coefficient of the spatial straight line;

303. performing cubic spline interpolation on the solved contour path;

304. the characteristic sparse area is clustered into a single narrow beam unit, and the implementation method for generating the spraying path by the midline extraction algorithm comprises the following steps: to point cloud set omega c_kExtracting edges to obtain edge outer contours;

305. the extracted edges are sorted in a clockwise mode because the edge point set is unordered, and then the product of the unit vector of the maximum characteristic direction and the gradient vector of the adjacent edge points after sorting is calculated

Deleting the points with the product smaller than the set threshold from the point set, namely eliminating the points on the short edge;

306. performing Euclidean clustering on the residual point sets, dividing the residual point sets into contour two-side edge line point sets in the maximum characteristic direction, and storing the contour two-side edge line point sets in a set Ed_1kAnd Ed_k2In, to the set Ed_k1And Ed_k2Scattered point cubic spline interpolation inValue, Ed_k1Interpolated point set Ed_k1'＝{P_{Edk1_i}(x_{Edk1_i},y_{Edk1_i},z_{Edk1_i}),Edk1_i＝1,2,,…,n_Edk1}，Ed_k2Point set Ed of interpolated element reverse order_k2'＝{P_{Edk2_i}(x_{Edk2_i},y_{Edk2_i},z_{Edk2_i}),Edk2_i＝1,2,,…,n_Edk2To Ed_k1' and Ed_k2' the corresponding element coordinate in (1) takes the midpoint P_{Emk_i}：

The obtained path points are spraying path points in a characteristic sparse area;

step four: merging planned paths, and simulating the coating thickness:

401. calculating the attitude direction of the spray gun, namely the normal direction of the surface of the seat workpiece, wherein the calculation method is the principal component analysis method, and the ambiguity of the normal can be removed by orienting all normal directions to the viewpoint uniformly;

402. for the contour path of the surface of the seat workpiece obtained by the two methods, the height of the spray gun is deviated along the attitude direction of the spray gun, namely the normal direction of the surface of the seat workpiece, through path point interpolation, and then the actual running path of the spraying robot can be obtained;

403. calculating the paint thickness deposition model on the free-form surface by using a infinitesimal method, and deducing the accumulated thickness th of the coating at one point on the free-form surface according to the projection similar geometric relationship_w'：

Wherein h represents the vertical height from the spray gun to the spraying experiment plane, h' represents the vertical height from the spray gun to the free-form surface, gamma represents the vertical angle between a point on the free-form surface and the center connecting line of the spray gun, psi represents the normal angle between a point on the free-form surface and the center connecting line of the spray gun, and th_wThe cumulative thickness of the coating at the point on the spray test plane is shown;

404. substituting the spraying model and the spraying parameters to verify the spraying uniformity and the spraying efficiency caused by the spraying path;

step five: and generating a total spraying path of the surface of the seat workpiece, and guiding the path into a spraying robot controller.

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