A Trajectory Generation Method for Multi-Region Fusion

Abstract

A trajectory generation method for multi-region fusion. For the target surface of the trajectory to be generated that has been divided into several regions, calculate the distance from a given reference benchmark in each region to each point in that region. For the common boundary between two adjacent regions, respectively extract the distance values from the common boundary to the two reference benchmarks and establish a linear mapping relationship of the distance values to achieve distance registration, and use this linear relationship to update the distance values of each point in the region. Then, perform Laplace fusion on the distance values in the neighborhood of the common boundary to achieve smooth transition. For all other adjacent regions, also use the above method for fusion in turn. Finally, extract the isometric lines to obtain a fusion trajectory that meets the requirements. The present invention is simple and effective, has universality, and can be used in many fields such as the partitioned manufacturing of complex surface parts, the additive manufacturing of 3D printed parts, and the manufacturing process of automatic fiber placement of composite materials.

Description

Technical Field

[0001] The present invention relates to the technical field of computer-aided (CAX), and particularly relates to a trajectory generation method for multi-region fusion. Background Art

[0002] When it is difficult to balance all requirements to obtain a global optimal solution, divide and conquer is a common problem-solving idea. Whether it is the zoning plan of a city, the design and arrangement of the tool path movement trajectory on a complex surface, the path planning of 3D printing, or the path design of automatic composite material placement, according to different conditional requirements, using the zoning method is a common idea, and it can often provide a solution for finding a better solution.

[0003] However, there is an inevitable problem in planning the trajectory by the zoning method, that is, the trajectory transition problem between different regions. At present, some studies do not consider the transition connection after zoning, which will inevitably have certain defects. If no post-processing is performed, the trajectories of each region are independent, the trajectories between different regions are discontinuous, and the trajectory directions at the boundaries are inconsistent. Then this trajectory will cause the tool to lift, the wire breakage in 3D printing, or the wire breakage in composite material placement, which will inevitably have a certain negative impact on the performance of the workpiece.

[0004] Some studies have proposed some methods for zoning trajectory transition on the basis of completing the zoning trajectory planning, which can be roughly divided into two categories:

[0005] The first type of method is to first obtain the tool paths of each region, and then consider the transition connection between each region. This is the most common type of transition connection method. Some scholars have proposed to use Nurbs curves or cubic B-spline curves to fit local transition curves at the region boundaries to complete the smooth transition connection between regions. This method can usually meet the G1 continuity of the local transition region, and the trajectory is also relatively smooth. However, if the direction difference of the trajectories between two regions at the boundary is too large and the number of trajectories is inconsistent, this method cannot well complete the transition of the trajectories between regions, and there is still a phenomenon similar to the tool mark. In addition, for complex surfaces with high precision requirements, the fitting of local transition curves cannot achieve good results.

[0006] The second type of method is zoning trajectory optimization, which optimizes each region separately from an overall perspective to make the trajectories between regions tend to be smooth. This method seemingly connects each region together, but in fact, it does not really achieve the trajectory transition connection, and the adjustment of the trajectories within each region is relatively large, making it difficult to meet the original requirements of each region for the trajectory. In short, there is a trade-off between the optimization of the trajectories within the region and the smoothness of the boundary transition, and it is difficult to balance both the whole and the local.

[0007] The present invention proposes a trajectory generation method for multi-region fusion, aiming to consider both the requirements for the trajectory within each region and the transitional connection between regions. This method provides a more efficient, robust, and unified operation, offering a new idea for generating a multi-region fusion trajectory with continuous and smooth transitions. Summary of the Invention

[0008] The object of the present invention is to invent a trajectory generation method for multi-region fusion to solve the problem that there is no fusion transition between regions after trajectory planning by region division.

[0009] The technical solution of the present invention is as follows:

[0010] A trajectory generation method for multi-region fusion, characterized in that: for the target surface of the trajectory to be generated that has been divided into several regions, calculate the distance from a given reference benchmark within each region to each point in the region. For the common boundary between two adjacent regions, respectively extract the distance values from the common boundary to the two reference benchmarks and establish a linear mapping relationship of the distance values to achieve distance registration, and use this linear relationship to update the distance values of each point within the region; then perform Laplacian fusion on the distance values in the neighborhood of the common boundary to achieve smooth transition. For all other adjacent regions, also use the above method for fusion in turn, and finally extract the isometric lines to obtain the fusion trajectory that meets the requirements. To facilitate the calculation and processing of this discrete variable of the distance value, the image rasterization method can be used to realize the discretization of the distance value, so as to facilitate a series of operations such as subsequent mapping transformation and interpolation filling.

[0011] The beneficial effects of the present invention are as follows:

[0012] The present invention provides a trajectory generation method for multi-region fusion, which considers both the requirements for the trajectory within each region and the transitional connection between regions. First, the trajectory boundary is smooth, and there is no place where the curvature changes suddenly greatly in the connection of the transition region. Second, it is unified and efficient. Compared with the method of local transition curve fitting used in previous methods, the algorithm similar to image processing provides a more efficient, robust, and unified operation to handle geometric problems. Finally, the overall trajectory is optimized, and the trajectory fusion optimization of all regions can be realized to meet the requirements of the coincidence degree with the given vector field direction and the equal step distance constraint.

[0013] The present invention is simple and effective, has universality, and can be used in many fields such as the divided manufacturing of complex surface parts, the additive manufacturing of 3D printed parts, and the manufacturing process of automatic fiber placement of composite materials. Brief Description of the Drawings

[0014] Figure 1 It is the overall flowchart of the present invention.

[0015] Figure 2Is the target surface of the trajectory to be generated that has been divided into several regions.

[0016] Figure 3 Is the given reference vector field.

[0017] Figure 4 Is the reference benchmark calculated for each partition.

[0018] Figures 5(a) and 5(b) are grayscale images generated by each sub-region according to the Euclidean distance of the reference points.

[0019] Figure 6 Are the grayscale images and their boundaries of two adjacent regions.

[0020] Figure 7 Is the linear mapping relationship of the least squares fitting of the boundary value.

[0021] Figure 8 Is the grayscale image updated by the linear mapping.

[0022] Figure 9 Is the grayscale image after interpolation filling in the narrowband transition region.

[0023] Figure 10 Is the laying trajectory generated before fusion.

[0024] Figure 11 、 Figure 12 Is the finally generated laying trajectory.

[0025] Figure 13 、 Figure 14 Is the comparison result of Example 2. Specific implementation method

[0026] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0027] Such as Figures 1-14 shown.

[0028] A trajectory generation method for multi-region fusion, the specific steps are as follows:

[0029] First, for the target surface of the trajectory to be generated that has been divided into several regions, calculate the reference standard corresponding to each partition according to the trajectory generation requirements. Here, the reference benchmark is given in the form of reference points.

[0030] Second, calculate the distance value of each point in the corresponding region according to the reference benchmark, that is, the distance value to the reference point. For the convenience of discrete representation, the region is rasterized here to form the form of a grayscale image, and the grayscale value of the image is the above distance value.

[0031] Third, for the two grayscale images I1 and I2 of the adjacent regions, their adjacent boundary pixel points {pb} The gray values on I1 and I2 are p b1 and p b2 , respectively. The coefficients A and b of the linear mapping are obtained by least squares calculation, such that ‖A·p b2 +b - p b1 ‖ is minimized, and the gray value of I2 is adjusted and updated to obtain I2 = A·I2 + b.

[0032] Fourth, simultaneously, taking {p b} as the benchmark, image dilation is performed to obtain the common boundary neighborhood M. The pixel gray values within the common boundary neighborhood M are obtained through image Laplacian fusion, and then the gray value correction of I1 and I2 is completed.

[0033] Finally, by analogy, the distance values of all adjacent regions are corrected according to the above steps, and finally the isometric line is extracted to obtain the fusion trajectory that meets the requirements. The overall process is as Figure 1 shown.

[0034] Where:

[0035] 1. For the to-be-generated trajectory described above, it is required that the trajectory direction at each point coincides with the reference direction to a certain extent, that is, the included angle between the tangent direction of each point on the trajectory and the reference direction at that point is less than a given value, and the adjacent trajectory spacing is equal everywhere, that is, the trajectory can be regarded as an isometric line formed by equidistant offset from a reference benchmark outward. The reference direction refers to a vector field of a given area to be planned for the trajectory, which is used as the basis for the theoretical trajectory trend. It is hoped that the to-be-generated trajectory approaches it, and it is usually obtained through finite element simulation calculation.

[0036] 2. The reference benchmark described above is composed of points and line elements on the target surface. Each region corresponds to a reference benchmark, and the corresponding trajectory is obtained by offsetting the reference benchmark outward at different distances. The reference benchmark of this patent adopts the form of a reference point. The specific method is as follows: A series of key points corresponding to straight lines in each region are subjected to dual transformation to obtain the point set coordinates. The key region is mapped to the dual space, and a curve is fitted using weighted linear least squares method, and then mapped back to the plane rectangular coordinate system through inverse duality to obtain the reference point. For each region, there is one and only one reference point.

[0037] 3. The Laplacian fusion of the common boundary neighborhood described above refers to re-filling the values within a given transition region. The common boundary neighborhood means that the shortest distance from any point in this neighborhood to the common boundary is less than a given value. The specific method is as follows: Values are inserted inward from the values on the outer boundary of this region, a discrete Laplacian equation on the region is established, and it is solved based on the Dirichlet boundary value condition, which can ensure that on the basis of not changing the gradient change trend, an interpolation of this transition region is generated to achieve a smooth transition of the distance value with the external region.

[0038] IV. The isometric lines are extracted to obtain a fusion trajectory that meets the requirements, which is characterized in that: the shortest distance value from any point on the target surface to the reference can be calculated. After the above fusion operation, the points with equal distance values are extracted to form a line, which is the isometric line. According to the trajectory generation requirements, appropriate distance values are selected to generate a series of isometric lines to obtain the final trajectory. The final trajectory meets the requirements of the coincidence degree with the given vector field direction, and also meets the trajectory equidistant step constraint. The trajectory in the boundary transition region is smooth and continuous, and its curvature has no obvious mutation.

[0039] Example 1:

[0040] S1: The target surface of the trajectory to be generated that has been divided into several regions is as Figure 2 shown. The given reference vector field is as shown in Figure 3. The magnitude and direction of the vector are consistent with the size and direction of the arrow. According to the trajectory generation requirements, the reference standards corresponding to each partition are calculated. Here, the reference benchmark is given in the form of a reference point, as Figure 4 shown. The circles in the figure are the calculated reference points.

[0041] S2: According to this reference benchmark, the distance values of each point in the corresponding region are calculated, that is, the distance values to the reference point. For the convenience of discrete representation, the region is rasterized here to form the form of a grayscale image. The grayscale value of the image is the above-mentioned distance value, as shown in Figures 5(a) and 5(b).

[0042] S3: For two grayscale images I1 and I2 of adjacent regions, as Figure 6 shown, the gray values of their adjacent boundary pixel points {p b} on I1 and I2 are p b1 and p b2 . As Figure 7 shown, the coefficients A and b of the linear mapping are obtained through least-squares calculation. The abscissa is I2, and the ordinate is I1. The slope of this fitting line is A, and the intercept is b. Make ‖A·p b2 + b - p b1 ‖ minimized, and the gray value of I2 is adjusted and updated to get I2 = A·I2 + b, as Figure 8 shown.

[0043] S4: At the same time, taking {p b} as the benchmark, using the image dilation algorithm in morphology, with a 15*15 square unit structure as the kernel, the {p b} is dilated outward by 10 pixel points to obtain the common boundary neighborhood M, as Figure 9 shown.

[0044] S5: Perform Laplacian fusion on the common boundary neighborhood: Discard the original pixel values in the common boundary neighborhood M, regard the pixels around M as Dirichlet boundary conditions, solve the Laplace equation, perform interpolation calculation of the pixel values within M, refill the pixel values of this narrow-band transition region, obtain a grayscale image M' with smooth gradient changes, and then complete the grayscale value correction of I1 and I2. The result is as Figure 10 shown.

[0045] S6: By analogy, correct the distance values of all adjacent regions according to the above steps, and finally extract the isometric lines to obtain a fusion trajectory that meets the requirements, as Figure 12 shown, and compared with the trajectory generated by the grayscale image before fusion as shown in Figure 11 , it can prove the effectiveness of this fusion method.

[0046] Example 2:

[0047] This example aims at the target surfaces of multiple regions. The specific steps are the same as those in Example 1. The finally generated trajectory is as Figure 14 shown, and compared with the trajectory generated by the grayscale image before fusion as shown in Figure 13 , it can prove the generality of this fusion method.

[0048] The present invention provides a method for generating a trajectory for multi-region fusion, which not only considers the requirements for the trajectory within each region, but also takes into account the transitional connection between regions. It innovatively adopts an algorithm similar to image processing to solve this problem, providing more efficient, robust and unified operations. The method is simple, effective and general.

[0049] The parts not involved in the present invention are the same as or can be implemented by the prior art.

Claims

1. A trajectory generation method for multi-region fusion, characterized in that: For the target surface whose trajectory is to be generated and which has been divided into several regions, calculate the distances from a given reference benchmark in each region to each point in the region. For the common boundary between two adjacent regions, respectively extract the distance values from the common boundary to the two reference benchmarks and establish a linear mapping relationship of the distance values to achieve distance registration, and use this linear relationship to update the distance values of each point in the region; then perform Laplacian fusion on the distance values in the neighborhood of the common boundary to achieve smooth transition; for all other adjacent regions, also use the above method for fusion in turn. Finally, extract the isometric lines to obtain a fused trajectory that meets the requirements; the reference benchmark is in the form of a benchmark point. The specific approach is as follows: Take a series of key-point corresponding lines in each region and perform a dual transformation to obtain the point-set coordinates, map the key region to the dual space, use the weighted linear least squares method to fit the curve, and then map back to the plane rectangular coordinate system through the inverse dual mapping to obtain the benchmark point; there is one and only one benchmark point for each region; calculate the distance values of each point in the corresponding region according to this reference benchmark, that is, the distance values to the benchmark point. For the convenience of discrete representation, here it is rasterized into the form of a grayscale image, and the grayscale value of the image is the above-mentioned distance value; for two grayscale images I1 and I2 of adjacent regions, the grayscale values of their adjacent boundary pixel points {p b} on I1 and I2 are p b1 and p b2 respectively. Calculate the coefficients A and b of the linear mapping through the least squares method to minimize ‖A·p b2 + b - p b1 ‖, and adjust and update the grayscale value of I2 to obtain I2 = A·I2 + b; at the same time, perform image dilation with {p b} as the benchmark to obtain the neighborhood M of the common boundary, and obtain the pixel grayscale values in the neighborhood M of the common boundary through image Laplacian fusion, thereby completing the grayscale value correction of I1 and I2; the Laplacian fusion of the neighborhood of the common boundary refers to re-filling the values in the given transition region; the neighborhood of the common boundary means that the shortest distance from any point in this neighborhood to the common boundary is less than a given value. The specific approach is as follows: Insert from the values on the outer boundary of the region, establish a discrete Laplacian equation on the region, and solve it based on the Dirichlet boundary value condition, which can ensure that on the basis of not changing the gradient change trend, generate the interpolation of this transition region and achieve smooth transition with the distance values of the external region.

2. The method according to claim 1, characterized in that: The reference benchmark is composed of points and line elements on the target surface, and each divided area corresponds to a reference benchmark.

3. The method according to claim 1, characterized in that: The linear mapping mentioned above means minimizing the two-norm of the distance values on the common boundary between two adjacent regions by least squares, that is, finding A and b such that ‖A·p b2 +b - p b1 ‖ is minimized, where p b2 and p b1 are respectively the distance value samples from the boundary to the two regions, and A and b are the coefficients calculated by least squares.

4. The method according to claim 1, characterized in that: The shortest distance from any point on the common boundary neighborhood to the common boundary is less than a given value.

5. The method according to claim 1, characterized in that: The Laplace fusion mentioned above refers to refilling the values within a given transition region; inserting values from the outer boundary of the region inward, establishing a discrete Laplace equation on the region, and solving it based on the Dirichlet boundary value condition, which can ensure generating the interpolation of the transition region without changing the gradient change trend and achieving a smooth transition of the distance values with the external region.

6. The method according to claim 1, characterized in that: The extraction of the isometric line to obtain a fusion trajectory that meets the requirements means that the shortest distance value from any point on the target surface to the benchmark can be calculated. After the fusion operation, the points with equal distance values are extracted to form a line, which is the isometric line. According to the trajectory generation requirements, a series of isometric lines can be generated by selecting the set distance values to obtain the final trajectory.

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