A method for generating robot operation trajectory based on NURBS fitting of complex mesh surfaces

Abstract

The present invention discloses a method for generating robot operation trajectories based on NURBS fitting of complex mesh surfaces. The method is mainly used in the simulation environment of offline programming software. After determining the mesh surface to be processed, the mesh parameters obtained by the least squares conformal mapping mesh parameterization and the parameter adjustment of the minimum bounding box criterion are first used as the pre-input of the NURBS fitting parameterization, and then the least squares NURBS fitting method is used to construct the NURBS surface of the irregular complex mesh surface through the step of normal compensation of the parameter missing area, and finally, an equidistant trajectory is generated in a two-dimensional parameter domain along a straight line or in a manner that fits the curve boundary through the NURBS surface to obtain an equidistant trajectory in three-dimensional space. The present invention obtains a fitting NURBS surface of a complex mesh surface through the proposed NURBS fitting method, and can generate an operation trajectory with a better equidistant effect or a boundary fit.

Description

Technical Field

[0001] The invention belongs to the field of robot trajectory planning and computer-aided manufacturing, and in particular relates to a robot operation trajectory generation method based on complex mesh surface NURBS fitting. Background Art

[0002] With the improvement of robot intelligence, the progress of industrial control systems and the reduction of CAD costs for graphic programming, offline programming technology has flourished and has become the development trend of industrial robot programming in the future. At the same time, since industrial robot automated processing is the key to improving the economic benefits of the manufacturing industry, industrial robot simulation and planning based on offline programming has also become a research hotspot for scholars. Therefore, this paper will study the key technologies in industrial robot simulation and planning based on offline programming, which has positive and important significance for meeting the needs of modern industrial production.

[0003] From the current research status of robot operation trajectory generation for complex surfaces, it can be seen that the current trajectory generation methods for CAD mesh models are mostly for planes, and some are for analyzed quadratic regular surfaces. This patent takes the robot operation trajectory generation in the automobile spraying scene as an example. For example, the surface of the car body has holes, irregular boundaries and many locations with sudden changes in curvature. The smooth implementation of traditional methods depends on appropriate surface segmentation strategies. Currently, most spray surface segmentation mainly relies on manual segmentation, and traditional trajectory generation methods are difficult to generate equidistant trajectories or trajectories that fit the boundary lines when dealing with complex surfaces. Therefore, how to conveniently generate the robot's operation trajectory for complex mesh surfaces is a major difficulty in the current robot operation trajectory generation based on offline programming. Summary of the invention

[0004] The present invention aims to provide a method for generating robot operation trajectories based on NURBS fitting of complex mesh surfaces, so as to solve the technical problem that it is difficult to generate equidistant operation trajectories for complex surfaces in existing off-line programming software.

[0005] In order to solve the above technical problems, the specific technical solution of a robot operation trajectory generation method based on complex mesh surface NURBS fitting of the present invention is as follows:

[0006] A method for generating robot operation trajectory based on NURBS fitting of complex mesh surface includes the following steps:

[0007] Step 1: Parameterize the mesh based on the least squares conformal mapping;

[0008] Step 2: Re-adjust the grid parameters based on the minimum bounding box criterion;

[0009] Step 3: Perform normal interpolation on the vertex missing area of ​​the two-dimensional parameter domain after mesh parameterization;

[0010] Step 4: Use the least squares method to fit the NURBS mesh surface;

[0011] Step 5: Generate an equidistant trajectory in the two-dimensional parameter domain and restore it to a three-dimensional trajectory through the NURBS surface;

[0012] Step 6: Generate the biased robot operation trajectory by normal averaging.

[0013] Furthermore, the step 1 uses least squares conformal mapping to parameterize the mesh as a mesh parameterization method for NURBS surface fitting, mapping the three-dimensional mesh vertices to a two-dimensional parameter domain, where the horizontal axis is called the u direction and the vertical axis is called the v direction. During the mapping process, the deformation of the mesh after parameterization is suppressed by minimizing the violation of the Riemann condition, so that the equidistant trajectories generated in the two-dimensional parameter domain will still be approximately equidistant when corresponding to the three-dimensional space.

[0014] Furthermore, step 2 obtains the minimum bounding box of the vertex set in the parameter domain through the convex hull solution algorithm of the plane point set and the rotating caliper algorithm, and converts the vertex parameters into a coordinate system formed by two vertical edges of the minimum bounding box. When the operation trajectory is subsequently generated, one operation trajectory is generated one by one in the two-dimensional parameter domain along the fixed u or v direction, that is, the direction of the two edges of the rectangle.

[0015] Furthermore, step 3 divides the two-dimensional parameter domain into N×N sub-regions with a fixed step size. If there are vertices in the sub-region, the average normal vector of all vertices in the sub-region is calculated as the value of the corresponding position matrix. If there are no vertices in the sub-region, the row and column of the sub-region are found in the matrix and the average normal interpolation is performed as the average normal of the region.

[0016] Furthermore, the specific steps of step 3 are as follows:

[0017] The two-dimensional space Θ after model parameterization is divided into C regions by cross-section and longitudinal section. u ×C v sub-regions, traverse these sub-regions, if the sub-region Θ i,j (i∈[1,C u ],j∈[0,C v ]) If there is a sampling point of the model, then the average normal vector of the area is recorded as If there is no sampling point in the region, find the two sub-regions θ closest to the sub-region in the horizontal and vertical directions. i,near_c With Θ i,near_r , then Θ i,j The average normal vector of the region is:

[0018]

[0019] Furthermore, step 4 generates node vectors of the NURBS surface in the u direction and the v direction in a uniform manner, and uses the least squares method to fit the NURBS surface with the goal of minimizing the sum of square errors between the NURBS surface and the three-dimensional mesh vertices and the normal error of each sub-region.

[0020] Furthermore, the step 4 includes the following specific steps:

[0021] The NURBS surface expression is:

[0022]

[0023] in are called the control points of the surface. is the weight of each control point. When the order m and n of the NURBS surface in the u and v directions are determined, the control point matrix P, the weight matrix w and the node vector S in the u and v directions are u , S v Together they determine the shape of the surface, collectively referred to as NURBS shape parameters;

[0024] Given a triangle mesh, the vertex set consisting of all vertices is Ω, where each point Ω i , i∈[1,N] has the position of the point Ω pi The normal vector Ω of the point ni Now we need to fit the NURBS surface to the point set, that is, to find a set of NURBS shape parameters so that the sum of the distances from each point in the point cloud to the NURBS surface is minimized, and the normal vector deviation is minimized:

[0025]

[0026] After the previous interpolation step, for those (u, v) parameter points P that do not exist I The position of the point is assigned the normal vector method to the Θ of the subregion to which it belongs. i,j The average normal vector Add the interpolation point P to the least squares fitting objective function I The normal vector deviation of , then the normal deviation penalty term of the parameter void defect can be written as:

[0027]

[0028] After introducing the penalty term of normal interpolation, the objective function can be obtained as shown in the following formula:

[0029]

[0030] Furthermore, the step 5 includes the following specific steps:

[0031] Generate equidistant straight line clusters along the u direction or v direction in the two-dimensional parameter domain, and then transform these equidistant straight line clusters into trajectories on the mesh surface in three-dimensional space through the expression of NURBS surface;

[0032] When there are two curve boundaries that are nearly parallel, you can also specify four vertices of the mesh surface in the two-dimensional parameter domain, then divide the two parallel edges into equal parts, connect all the equally divided points, and then divide the lines connecting the equally divided points into equal parts to obtain the internal points. Finally, connect the points horizontally to obtain the trajectory in the two-dimensional parameter domain, and finally generate the corresponding operation trajectory in the three-dimensional space through the NURBS surface.

[0033] Furthermore, step 6 includes the following specific steps:

[0034] The neighborhood average normal vector of all points on the three-dimensional surface trajectory is solved to replace the original normal vector of the trajectory point. The trajectory is offset by the average normal vector to generate the motion trajectory of the robot end. The expression of the average normal vector is:

[0035]

[0036] The robot operation trajectory generation method based on complex mesh surface NURBS fitting of the present invention has the following advantages:

[0037] 1. Use least squares conformal mapping to map the surface mesh vertices to the two-dimensional parameter domain with minimum mesh deformation to generate two-dimensional isometric trajectories. The isometric trajectories generated in the two-dimensional parameter domain are still close to isometric when corresponding to the three-dimensional space, reducing the dimension of the problem solution.

[0038] 2. A NURBS fitting method for irregular mesh surfaces based on missing area normal compensation is proposed to deal with the problem of NURBS fitting surface distortion caused by vacancies in the parameter domain after mesh parameterization using least squares conformal mapping, and obtain a suitable fitting surface.

[0039] 3. After fitting the NURBS surface, the NURBS surface is used to convert the operating trajectory generated in the two-dimensional parameter domain that is equidistant or fits the surface boundary into an equidistant full-coverage operating trajectory of a complex surface in three-dimensional space. Compared with the traditional trajectory generation method based on plane projection, the method of the present invention generates an operating trajectory with better equidistant effect or fits the boundary. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A flow chart of a method for generating a robot operation trajectory according to the present invention;

[0041] Figure 2 This is the effect diagram of the grid parameter domain after least squares conformal mapping;

[0042] Figure 3 Determine the best trajectory sweep direction map for the minimum bounding box;

[0043] Figure 4 This is the NURBS surface fitting effect diagram of the car's front bumper and fender;

[0044] Figure 5 To convert the linear equidistant trajectory of the parameter domain into a three-dimensional trajectory diagram;

[0045] Figure 6 A schematic diagram of the trajectory for generating a fitted curve boundary in a two-dimensional parameter domain;

[0046] Figure 7 To generate a three-dimensional trajectory map of the car hood fitting curve boundary;

[0047] Figure 8 This is the effect diagram of the spray trajectory offset of the car's front bumper. DETAILED DESCRIPTION

[0048] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a robot operation trajectory generation method based on complex mesh surface NURBS fitting of the present invention in conjunction with the accompanying drawings.

[0049] The method proposed in the present invention can be used to generate robot operation trajectories for complex triangular mesh surfaces, especially for the generation of operation trajectories in spraying scenes. The mesh surfaces used for simulation testing in the present invention are mainly the front bumper and fender of the car. Figure 1 As shown, the specific implementation steps of the present invention are as follows:

[0050] Step 1: Parameterize the mesh based on the least squares conformal mapping.

[0051] The least squares conformal mapping was originally used for texture mapping of general mesh model vertices. Its biggest advantage is that it minimizes the violation of the Riemann condition during the vertex parameter mapping process to suppress the deformation of the mesh parameterized. Here, we introduce the mesh parameterization method as a NURBS surface fitting. The main function of this method is to map the three-dimensional mesh vertices to the two-dimensional parameter domain. The horizontal axis is called the u direction and the vertical axis is called the v direction. In the mapping process, it minimizes the violation of the Riemann condition to suppress the deformation of the mesh parameterized. Figure 2 As shown, the cylindrical patch and the car fender patch are mapped to the two-dimensional parameter domain after vertex parameterization based on least squares conformal mapping. Then, the isometric trajectory generated in the two-dimensional parameter domain will still be approximately isometric when corresponding to the three-dimensional space.

[0052] Step 2: Re-adjust the grid parameters based on the minimum bounding box criterion.

[0053] like Figure 3 As shown, the minimum bounding box of the vertex set in the parameter domain is obtained by the convex hull solution algorithm of the plane point set and the rotating caliper algorithm, and the vertex parameters are converted into the coordinate system formed by the two vertical sides of the minimum bounding box. The purpose of this step is to determine the best sweeping direction for generating the trajectory. When the operation trajectory is generated later, one operation trajectory is generated one by one in the two-dimensional parameter domain along the fixed u or v direction (the direction of the two sides of the rectangle);

[0054] Step 3: Perform normal interpolation on the vertex missing areas of the two-dimensional parameter domain after mesh parameterization. The two-dimensional parameter domain is divided into N×N sub-regions (N×N matrix) with a fixed step size. If there are vertices in the sub-region, the average normal vector of all vertices in the sub-region is calculated as the value of the corresponding position matrix. If there are no vertices in the sub-region, the average normal interpolation is performed on the row and column of the sub-region in the matrix as the average normal of the region.

[0055] like Figure 2 After parameterization, there are a lot of areas without vertices, which will cause the subsequent NURBS surface after fitting to be distorted. Therefore, normal interpolation compensation is performed on the sub-areas with missing vertices in the two-dimensional parameter domain. The two-dimensional space Θ after model parameterization is divided into C regions by cross-section and longitudinal section. u ×C v sub-regions, traverse these sub-regions, if the sub-region Θ i,j (i∈[1,C u ],j∈[0,C v ]) If there is a sampling point of the model, then the average normal vector of the area is recorded as If there is no sampling point in the region, find the two sub-regions θ closest to the sub-region in the horizontal and vertical directions. i,near_c With Θ i,near_r , then Θ i,j The average normal vector of the region is:

[0056]

[0057] Step 4: Use the least squares method to mesh the surface for NURBS fitting.

[0058] The node vectors of the NURBS surface in the u and v directions are generated in a uniform manner. The least squares method is used to fit the NURBS surface with the goal of minimizing the sum of square errors between the NURBS surface and the 3D mesh vertices and the normal error of each sub-region.

[0059] The NURBS surface expression is:

[0060]

[0061] in are called the control points of the surface. is the weight of each control point. When the order m and n of the NURBS surface in the u and v directions are determined, the control point matrix P, the weight matrix w and the node vector S in the u and v directions are u , S v Together they determine the shape of the surface and are collectively referred to as NURBS shape parameters.

[0062] Given a triangle mesh, the vertex set consisting of all vertices is Ω, where each point Ω i , i∈[1,N] has the position of the point Ω pi The normal vector Ω of the point ni Now we need to fit the NURBS surface to the point set, that is, to find a set of NURBS shape parameters so that the sum of the distances from each point in the point cloud to the NURBS surface is minimized, and the normal vector deviation is minimized:

[0063]

[0064] After the previous interpolation step, for those (u, v) parameter points P that do not exist I The position of the point is assigned the normal vector method to the Θ of the subregion to which it belongs. i,j The average normal vector Add the interpolation point P to the least squares fitting objective function I The normal vector deviation of , then the normal deviation penalty term of the parameter void defect can be written as:

[0065]

[0066] After introducing the penalty term of normal interpolation, the objective function can be obtained as shown in the following formula. This objective function can help obtain a suitable fitting surface after the optimization target is executed, and can be solved by the quasi-Newton method, such as Figure 4 The figure shows the result of mesh surface fitting of the car's front bumper and fender.

[0067]

[0068] Step 5: Generate an equidistant trajectory in the two-dimensional parameter domain and restore it to a three-dimensional trajectory through the NURBS surface.

[0069] like Figure 5As shown in Figure 1, equidistant straight line clusters are generated in the two-dimensional parameter domain along the u direction or v direction, and then these equidistant straight line clusters are transformed into the trajectory of the mesh surface in three-dimensional space through the expression of the NURBS surface. Figure 6 As shown, in addition, when there are two curve boundaries that are close to parallel, you can also specify four vertices of the mesh surface, in the two-dimensional parameter domain, and then divide the two parallel edges into equal parts, connect all the equal-division points, and then connect the equal-division points ( Figure 6 The dashed line) is also divided equally, and we get Figure 6 Finally, the points are connected horizontally to obtain the trajectory in the two-dimensional parameter domain ( Figure 6 Finally, the corresponding operation trajectory is generated in three-dimensional space through the NURBS surface, such as Figure 7 The figure shows the spraying operation track on the surface of the car front cover.

[0070] Step 6: Generate the biased robot end motion trajectory by normal averaging.

[0071] Solve the neighborhood average normal vector of all points on the three-dimensional surface trajectory to replace the original normal vector of the trajectory point. The expression of the average normal vector is:

[0072]

[0073] By offsetting the trajectory with the average normal vector to generate the motion trajectory of the robot end, the curvature mutation can be reduced. For the spraying scene, it can ensure that the trajectory point of the spray gun can face most of the area being sprayed, such as Figure 8 shown.

[0074] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A robot operation trajectory generation method based on complex mesh surface NURBS fitting, characterized in that: The steps include: Step 1: Parameterize the mesh based on the least squares conformal mapping; Step 2: Re-adjust the grid parameters based on the minimum bounding box criterion; Step 3: Perform normal interpolation on the vertex missing area of the two-dimensional parameter domain after mesh parameterization; Step 4: Use the least squares method to fit the NURBS mesh surface; The NURBS surface expression is: in are called the control points of the surface. is the weight of each control point. When the order m and n of the NURBS surface in the u and v directions are determined, the control point matrix P, the weight matrix w and the node vector S in the u and v directions are u , S v Together they determine the shape of the surface, P, w, S u , S v Collectively referred to as the shape parameters of NURBS; given a vertex set consisting of all vertices in a triangular mesh is Ω, where each point There are some locations Normal vector to the point Now we need to fit the NURBS surface to the point set, that is, to find a set of NURBS shape parameters so that the sum of the distances from each point in the point cloud to the NURBS surface is minimized, and the normal vector deviation is minimized: After the previous interpolation step, for those (u, v) parameter points P that do not exist I The position of the point is assigned to the sub-region to which it belongs. The average normal vector Add the interpolation point P to the least squares fitting objective function I The normal vector deviation of the parameter is PF, then the normal deviation penalty term PF of the parameter void defect inorm writing: After introducing the penalty term of normal interpolation, the objective function E2 is obtained as shown in the following formula: Step 5: Generate an equidistant trajectory in the two-dimensional parameter domain and restore it to a three-dimensional trajectory through the NURBS surface; Step 6: Generate the biased robot operation trajectory by normal averaging.

2. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 1, characterized in that: The step 1 uses least squares conformal mapping to parameterize the mesh as a mesh parameterization method for NURBS surface fitting, and maps the three-dimensional mesh vertices to a two-dimensional parameter domain, where the horizontal axis is called the u direction and the vertical axis is called the v direction. During the mapping process, the deformation of the mesh after parameterization is suppressed by minimizing the violation of the Riemann condition, so that the equidistant trajectories generated in the two-dimensional parameter domain will still be approximately equidistant when corresponding to the three-dimensional space.

3. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 2, characterized in that: The step 2 obtains the minimum bounding box of the vertex set in the parameter domain through the convex hull solution algorithm of the plane point set and the rotating caliper algorithm, and converts the vertex parameters into the coordinate system formed by the two vertical sides of the minimum bounding box. When the operation trajectory is subsequently generated, the operation trajectories are generated one by one in the two-dimensional parameter domain along the fixed u or v direction, that is, the direction of the two sides of the rectangle.

4. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 1, characterized in that: The step 3 divides the two-dimensional parameter domain into N×N sub-regions with a fixed step size. If there are vertices in the sub-region, the average normal vector of all vertices in the sub-region is calculated as the value of the corresponding position matrix. If there are no vertices in the sub-region, the row and column of the sub-region are found in the matrix and the average normal interpolation is performed as the average normal of the region.

5. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 4, characterized in that: The specific steps of step 3 are as follows: The two-dimensional space Θ after model parameterization is divided into C regions by cross-section and longitudinal section. u ×C v sub-regions, traverse these sub-regions, if the sub-region If there is a sampling point of the model, the average normal vector of the area is recorded as If there is no sampling point in the area, find the two sub-areas closest to the sub-area in the horizontal and vertical directions. and but The average normal vector of the region for:

6. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 1, characterized in that: The step 4 generates node vectors of the NURBS surface in the u direction and the v direction in a uniform manner, and uses the least squares method to fit the NURBS surface with the goal of minimizing the sum of square errors between the NURBS surface and the three-dimensional mesh vertices and the normal error of each sub-region.

7. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 1, characterized in that: The step 5 comprises the following specific steps: Generate equidistant straight line clusters along the u direction or v direction in the two-dimensional parameter domain, and then transform these equidistant straight line clusters into trajectories on the mesh surface in three-dimensional space through the expression of NURBS surface; When there are two curve boundaries that are nearly parallel, specify the four vertices of the mesh surface in the two-dimensional parameter domain, then divide the two parallel edges into equal parts, connect all the equally divided points, and then divide the lines connecting the equally divided points into equal parts to obtain the internal points. Finally, connect the points horizontally to obtain the trajectory in the two-dimensional parameter domain, and finally generate the corresponding operation trajectory in the three-dimensional space through the NURBS surface.

8. The method for generating robot operation trajectory based on complex mesh surface NURBS fitting according to claim 6, characterized in that: The step 6 comprises the following specific steps: Solve the neighborhood average normal vector of all points on the three-dimensional surface trajectory to replace the original normal vector of the trajectory point, and offset the trajectory through the average normal vector to generate the motion trajectory of the robot end. The expression is:

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