Grinding track full-coverage planning method, system and equipment and storage medium

By generating and discretizing the initial trajectory line on the complex curved surface, calculating the effective grinding width, selecting the offset direction for offsetting, and iteratively adjusting the trajectory point position, the problem of under-grinding of the grinding trajectory with curvature changes is solved, and the grinding coverage and quality are improved.

CN121596829APending Publication Date: 2026-03-03AVIC BEIJING AERONAUTICAL MFG TECH RES INST
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Patent Information

Application Number
CN202511651412.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-11-12
Publication Date
2026-03-03

AI Technical Summary

Technical Problem

Existing grinding trajectory planning methods are difficult to adapt to curvature changes on complex surfaces, resulting in under-grinding and reduced grinding quality.

Method used

By generating an initial trajectory line and discretizing it, calculating the effective grinding width, selecting an offset direction for offsetting, and iteratively adjusting the trajectory points so that the distance between adjacent points is covered by the effective grinding width, a new trajectory that adapts to changes in surface curvature is generated.

Benefits of technology

It effectively avoids under-sanding, increases sanding coverage, and improves the sanding quality of complex curved surfaces.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention relates to a polishing track full-coverage planning method, system and device and a storage medium. The polishing track full coverage planning method comprises the steps that an initial track line is generated on an input curved surface and discretized to obtain a track point column, and the effective polishing width of each track point position is calculated; selecting an offset direction to offset discrete points on the initial track line to obtain an initial point position of a next polishing track, and calculating an effective polishing width at each initial point position; and the initial point position is adjusted so that the distance between the adjacent point positions on the two tracks can be covered by the effective polishing width of the two points, loop iteration is conducted till no under-polishing area exists between the two tracks, and a new track line is obtained. Based on the relation between the effective polishing width and the curvature of the polishing point position, the track capable of adapting to the curvature change of the curved surface is generated by iteratively adjusting the polishing track point position, the situation of insufficient polishing is avoided, and the overall coverage rate is increased.
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Description

Technical Field

[0001] This application relates to the field of complex surface grinding trajectory planning technology, and in particular to a grinding trajectory full-coverage planning method, system, device and storage medium. Background Technology

[0002] The grinding path refers to the relative motion trajectory of the machining tool on the surface being machined, affecting the efficiency of the machining process, the surface roughness of the machined surface, and the shape accuracy. Current methods for generating grinding paths mainly include the parametric line method, the parallel section method, and the equidistant offset method.

[0003] The parametric line method uses equally spaced parametric lines in the parameter space as grinding trajectory lines, which is simple and efficient in calculation. However, the trajectory spacing in the parameter space will significantly increase or decrease with the curvature changes of complex surfaces in 3D space. Therefore, when planning trajectories on complex surfaces, there is a problem of uneven grinding paths, which can easily lead to under-grinding. The parallel section method divides the processing surface into a set of equally spaced parallel planes and uses the intersection line as the grinding path. This method is highly efficient, but it cannot adapt well to changes in surface curvature. For complex surfaces, it is prone to under-grinding and over-grinding. The equidistant offset method uses a series of geodesic equidistant curves as grinding trajectories, which can adapt well to changes in surface curvature. However, it ignores the change in effective grinding width with the curvature at each point on the trajectory. Under-grinding may occur if the offset distance is too large relative to the effective grinding width, reducing the grinding coverage.

[0004] The trajectories generated by the parametric line method and the parallel section method are difficult to adapt to changes in surface curvature, resulting in insufficient trajectory density in areas with large curvature. Although the equidistant offset method can adapt to changes in curvature, there may still be problems with excessive offset distances, exceeding the actual effective grinding width of the trajectory. These problems can easily lead to under-grinding of the surface and reduce grinding quality. Summary of the Invention

[0005] This application provides a method, system, device, and storage medium for full coverage planning of grinding tracks to solve the problems in the background art.

[0006] Firstly, this application provides a method for planning full coverage of polished trajectories, including: An initial trajectory line is generated on the input surface and discretized to obtain a series of trajectory points. The effective grinding width at each trajectory point is then calculated. The discrete points on the initial trajectory are offset by a selected offset direction to obtain the initial position of the next grinding trajectory, and the effective grinding width at each initial position is calculated. The initial points are adjusted so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and the process is repeated until there are no under-grinding areas between the two trajectories, thus obtaining a new trajectory line.

[0007] Further, the step of generating an initial trajectory line on the input surface and discretizing it to obtain a sequence of trajectory points includes: Generate the minimum bounding box of the input surface, select a suitable mid-face of the minimum bounding box as the tangent plane, and calculate the intersection line of the tangent plane and the input surface as the initial trajectory line; The initial trajectory line is discretized using an adaptive discretization method based on surface curvature to obtain a sequence of trajectory points.

[0008] Further, the selection of the bias direction to bias discrete points on the initial trajectory line includes: For each discrete point on the initial trajectory, a geodesic offset is applied in a direction perpendicular to the feed direction and consistent with the overall direction.

[0009] Further, after adjusting the initial points so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and performing iterative iterations until there are no under-grinding areas between the two trajectories to obtain a new trajectory line, the process further includes: Repeat the steps of discretizing and biasing the new trajectory line to generate a new trajectory line until the generated new trajectory line exceeds the surface range; Return to the initial trajectory line and select the opposite direction to perform the steps of discretization and bias generation of a new trajectory line until no new trajectory can be generated.

[0010] Furthermore, the effective grinding width is the maximum width of the contact area between the grinding tool and the curved surface in the direction perpendicular to the feed when the grinding tool is at that position.

[0011] Secondly, this application provides a system for planning full coverage of polished trajectories, including: The trajectory discretization module is used to generate an initial trajectory line on the input surface and discretize it to obtain a sequence of trajectory points, and calculate the effective grinding width at each trajectory point. The point offset module is used to select the offset direction to offset discrete points on the initial trajectory line to obtain the initial point of the next grinding trajectory, and to calculate the effective grinding width at each initial point. The trajectory adjustment module is used to adjust the initial point so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and to perform cyclic iteration until there is no under-grinding area between the two trajectories, thus obtaining a new trajectory line.

[0012] Thirdly, this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the full coverage planning method for the polishing trajectory as described above.

[0013] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the full-coverage planning method for grinding trajectories as described above.

[0014] The above-mentioned technical solution of this application has the following advantages: The grinding trajectory full-coverage planning method provided in the first aspect of this application generates an initial trajectory line on the input surface and discretizes it to obtain a sequence of trajectory points, and calculates the effective grinding width at each trajectory point; it selects an offset direction to offset the discrete points on the initial trajectory line to obtain the initial point of the next grinding trajectory, and calculates the effective grinding width at each initial point; it adjusts the initial point so that the distance between adjacent points on two trajectories can be covered by the effective grinding width of the two points, and performs iterative iteration until there is no under-grinding area between the two trajectories, obtaining a new trajectory line. By iteratively adjusting the grinding trajectory points, a trajectory that can adapt to changes in surface curvature is generated, effectively avoiding under-grinding and improving coverage.

[0015] It is understood that the beneficial effects of the second, third and fourth aspects mentioned above can be found in the relevant descriptions in the first aspect above, and will not be repeated here. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0017] Figure 1 A flowchart of the grinding trajectory full coverage planning method provided in the embodiments of this application; Figure 2 A schematic diagram of the intersection line between the curved surface and the surface in the minimum bounding box provided in the embodiments of this application; Figure 3 This is a schematic diagram showing the initial trajectory and effective grinding width at discrete points provided in the embodiments of this application; Figure 4 The bias direction provided for the embodiments of this application Select a diagram; Figure 5 The bias direction provided for the embodiments of this application Select a diagram; Figure 6 This is a schematic diagram of trajectory point offset provided in an embodiment of this application; Figure 7 This is a schematic diagram of the reverse movement points provided in the embodiments of this application; Figure 8 This is a schematic diagram of surface trajectory point processing provided in an embodiment of this application. Detailed Implementation

[0018] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0019] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0020] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0021] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized. "A plurality" means "two or more."

[0022] The specific embodiments of this application will be described in further detail below with reference to the accompanying drawings and examples. The following examples are used to illustrate this application, but are not intended to limit the scope of this application.

[0023] This application provides a method for full coverage planning of grinding trajectories, specifically including the following steps: generating an initial trajectory line on the input surface and discretizing it to obtain a sequence of trajectory points, and calculating the effective grinding width at each trajectory point; selecting an offset direction to offset the discrete points on the initial trajectory line to obtain the initial point of the next grinding trajectory, and calculating the effective grinding width at each initial point; adjusting the initial point so that the distance between adjacent points on two trajectories can be covered by the effective grinding width of the two points, and performing iterative iterations until there is no under-grinding area between the two trajectories, thus obtaining a new trajectory line.

[0024] The purpose of this application is to address the problem of insufficient trajectory density in high-curvature areas, leading to under-grinding, in the process of planning grinding trajectories for complex curved surfaces. This is due to the failure to consider the impact of surface curvature variations on the grinding width. Simultaneously, it addresses the under-grinding issue caused by excessively large spacing in the equidistant offset algorithm. Therefore, a full-coverage grinding trajectory planning method based on the effective grinding width is proposed. During trajectory planning, based on the relationship between the grinding width, tool feed direction, and tool posture, the grinding trajectory points are iteratively adjusted to generate a trajectory that adapts to changes in surface curvature, effectively avoiding under-grinding and improving coverage.

[0025] In some embodiments, generating an initial trajectory line on the input surface and discretizing it to obtain a sequence of trajectory points includes: generating a minimum bounding box of the input surface; selecting a suitable mid-plane of the minimum bounding box as a tangent plane; calculating the intersection of the tangent plane and the input surface as the initial trajectory line; and discretizing the initial trajectory line using an adaptive discretization method based on surface curvature to obtain a sequence of trajectory points.

[0026] In some embodiments, the selection of the offset direction to offset discrete points on the initial trajectory line includes: for each discrete point on the initial trajectory line, performing a geodesic offset in a direction perpendicular to the feed direction and consistent with the overall direction.

[0027] In some embodiments, after adjusting the initial point position so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and performing iterative iterations until there is no under-grinding area between the two trajectories to obtain a new trajectory line, the method further includes: repeating the steps of discretizing and biasing to generate a new trajectory line on the new trajectory line until the generated new trajectory exceeds the surface range; returning to the initial trajectory line and selecting the opposite direction to perform the steps of discretizing and biasing to generate a new trajectory line until no new trajectory can be generated.

[0028] In some embodiments, the effective grinding width is the maximum width of the contact area between the grinding tool and the curved surface in the direction perpendicular to the feed direction when the grinding tool is at that point.

[0029] The technical solution of this application is as follows: First, an initial trajectory line is generated on the input surface. This trajectory is discretized to obtain the contact points between the tool and the workpiece. An offset direction is selected, and the discrete points on the initial trajectory are offset to obtain the initial points of the next grinding trajectory. Based on the relationship between the grinding width and the curvature of the surface, the initial points are adjusted one by one so that the geodesic distance between adjacent points on two trajectories can be covered by the effective grinding width of the two points. This process is iterated until there is no under-grinding area between the two trajectories. New trajectory points are generated iteratively according to the above steps until no new trajectory points can be generated. Then, the initial trajectory is returned, and the opposite offset direction is selected, repeating the above steps. The specific steps are as follows: 1) Initial trajectory generation and discretization Generate the minimum bounding box of the input surface, select a suitable mid-face of the bounding box as the tangent plane, and calculate the intersection of the tangent plane and the surface as the initial trajectory. Define the effective grinding width at each trajectory point as the maximum width of the contact area between the grinding tool and the surface in the direction perpendicular to the feed when the grinding tool is at that point. Discretize the initial trajectory using an adaptive discretization method based on surface curvature to obtain the trajectory point sequence, and calculate the effective grinding width at each trajectory point.

[0030] 2) Offset initial trajectory point For each point on the initial trajectory, a geodesic offset is applied in a direction perpendicular to the feed direction and consistent with the overall direction, and the effective grinding width at each trajectory point is calculated.

[0031] 3) Iteratively adjust the position of each point on the bias trajectory Based on the polishing width at each trajectory point, adjust the position of each trajectory point one by one so that the distance between adjacent points can be covered by the effective polishing width at the two points, thus obtaining a new sequence of trajectory points. Iterate this step until there are no under-polished areas between the new trajectory and the initial trajectory.

[0032] 4) Generate new trajectory points based on the points of the initial trajectory. Use the trajectory generated in step 3) as the trajectory, and repeat steps 2) and 3) until the trajectory generated in step 3) exceeds the surface range.

[0033] 5) Return to the initial trajectory and select the opposite offset direction to generate a new trajectory. Use the trajectory generated in step 1) as the initial trajectory, change to another direction, and repeat steps 2) to 4) until no new trajectory can be generated, at which point the planning ends.

[0034] The following is a description through specific embodiments.

[0035] Example In this embodiment, given the known relationship between the normal curvature at each point on the surface and the effective grinding width at the grinding point as a function of curvature, a grinding trajectory is planned to adapt to changes in curvature and avoid under-grinding. For example... Figure 1 As shown, the process includes the following main steps: initial trajectory generation and discretization, offsetting points on the trajectory, iteratively adjusting points on the trajectory, repeating offsetting and iterative generation of new trajectories until the trajectory grinding range and the surface have no intersection, and changing the translation direction from the initial trajectory to generate a new trajectory.

[0036] Step 1: Generate the minimum bounding box of the surface, take a suitable mid-face of the bounding box as the tangent plane, and calculate the intersection line between the tangent plane and the surface, such as... Figure 2 As shown, the initial trajectory is discretized using an adaptive discretization method based on surface curvature to obtain the trajectory point sequence. The intersection of the tangent plane and the surface is taken as the initial trajectory and denoted as... , The discrete points above are denoted as , Calculate the different effective grinding widths at each trajectory point and record them as follows: ,like Figure 3 As shown. Select The left or right side perpendicular to the feed direction is used as the reference offset direction. Each discrete point is denoted as . All are offset along the reference direction. Taking the right side of the feed direction as the reference direction as an example, such as... Figure 4 As shown.

[0037] Step 2: If the initial trajectory If the trajectory is not generated in step one, then determine it based on the trajectory offset direction in step one. Upper point Bias direction , and On the same side of the feed direction, such as Figure 5 As shown. For the point location. Along the bias direction Offset distance The offset point is recorded as All locations The trajectory formed is denoted as .

[0038] Step 3: For Points on The effective grinding width at each point is calculated based on the curvature. , and The geodetic distance between them is If all All meet If so, proceed to step four; otherwise, if... Figure 7 As shown, points that do not meet the above conditions are respectively offset along the bias direction in step two. Reverse movement distance Repeat step three until all points no longer change. and The polishing condition between them is as follows Figure 7 If the adjustment is completed, all points will be... There are points that extend beyond the surface. ,and .Pick and The intersection of the line connecting the two surfaces with the boundary of the surface is used as... ,like Figure 8 As shown. After completing the above operations, all points will be... Record as trajectory ,like All points on the surface are located on the surface boundary; proceed to step five. Step 4: Track As the initial trajectory ,right Repeat steps two and three; Step 5: Return to the trajectory generated in Step 1, with the offset direction. Reverse the direction and implement step two until step five is implemented again to end the trajectory planning.

[0039] The full-coverage grinding trajectory planning method provided in this application effectively avoids under-grinding and improves grinding coverage by iteratively moving the trajectory point positions and dynamically adjusting the grinding trajectory spacing. It requires fewer input parameters and can automatically generate full-coverage grinding trajectories, improving the algorithm's adaptability and grinding trajectory planning efficiency. This method is suitable for complex surfaces with significant curvature variations, addressing the problem of existing methods struggling to adapt to curvature changes. By adjusting the trajectory spacing according to curvature changes, this method avoids under-grinding during planning and improves the grinding quality of complex surfaces.

[0040] Corresponding to the full coverage planning method for grinding trajectories described in the above embodiments, this application also provides a full coverage planning system for grinding trajectories, which includes: The trajectory discretization module is used to generate an initial trajectory line on the input surface and discretize it to obtain a sequence of trajectory points, and calculate the effective grinding width at each trajectory point. The point offset module is used to select the offset direction to offset discrete points on the initial trajectory line to obtain the initial point of the next grinding trajectory, and to calculate the effective grinding width at each initial point. The trajectory adjustment module is used to adjust the initial point so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and to perform cyclic iteration until there is no under-grinding area between the two trajectories, thus obtaining a new trajectory line.

[0041] It should be noted that the information interaction and execution process between the above modules / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0042] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the system can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0043] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the grinding trajectory full coverage planning method provided in the first aspect.

[0044] In applications, electronic devices may include, but are not limited to, processors and memory. These are merely examples of electronic devices and do not constitute a limitation on the electronic device. They may include more or fewer components, combinations of certain components, or different components, such as input / output devices, network access devices, etc. Input / output devices may include cameras, audio capture / playback devices, displays, etc. Network access devices may include network modules for wireless network communication with external devices.

[0045] In applications, the processor can be a Central Processing Unit (CPU), but it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0046] In applications, memory can be an internal storage unit of an electronic device in some embodiments, such as a hard drive or RAM. In other embodiments, memory can be an external storage device of the electronic device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card. Memory can also include both internal and external storage units of the electronic device. Memory is used to store operating systems, applications, bootloaders, data, and other programs, such as program code for computer programs. Memory can also be used to temporarily store data that has been output or will be output.

[0047] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, can implement the steps in the above-described method embodiments.

[0048] This application implements all or part of the processes in the methods of the above embodiments, which can be accomplished by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium can at least include: any entity or device capable of carrying the computer program code to an electronic device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, such as a USB flash drive, a portable hard drive, a magnetic disk, or an optical disk.

[0049] Those skilled in the art will recognize that the device and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0050] In the embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interface, or the device may be indirectly coupled or communicated, and may be electrical, mechanical, or other forms.

[0051] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for planning a full-coverage grinding trajectory, characterized in that, include: An initial trajectory line is generated on the input surface and discretized to obtain a series of trajectory points. The effective grinding width at each trajectory point is then calculated. The discrete points on the initial trajectory are offset by a selected offset direction to obtain the initial position of the next grinding trajectory, and the effective grinding width at each initial position is calculated. The initial points are adjusted so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and the process is repeated until there are no under-grinding areas between the two trajectories, thus obtaining a new trajectory line.

2. The grinding trajectory full-coverage planning method as described in claim 1, characterized in that, The step of generating an initial trajectory line on the input surface and discretizing it to obtain a sequence of trajectory points includes: Generate the minimum bounding box of the input surface, select a suitable mid-face of the minimum bounding box as the tangent plane, and calculate the intersection line of the tangent plane and the input surface as the initial trajectory line; The initial trajectory line is discretized using an adaptive discretization method based on surface curvature to obtain a sequence of trajectory points.

3. The grinding trajectory full-coverage planning method as described in claim 1, characterized in that, The selected bias direction biases discrete points on the initial trajectory line, including: For each discrete point on the initial trajectory, a geodesic offset is applied in a direction perpendicular to the feed direction and consistent with the overall direction.

4. The grinding trajectory full-coverage planning method as described in claim 1, characterized in that, After adjusting the initial points so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and performing iterative iterations until there are no under-grinded areas between the two trajectories to obtain a new trajectory line, the process further includes: Repeat the steps of discretizing and biasing the new trajectory line to generate a new trajectory line until the generated new trajectory line exceeds the surface range; Return to the initial trajectory line and select the opposite direction to perform the steps of discretization and bias generation of a new trajectory line until no new trajectory can be generated.

5. The grinding trajectory full-coverage planning method as described in claim 1, characterized in that, The effective grinding width is the maximum width of the area in contact with the curved surface when the grinding tool is at that point, perpendicular to the feed direction.

6. A grinding trajectory full-coverage planning system, characterized in that, include: The trajectory discretization module is used to generate an initial trajectory line on the input surface and discretize it to obtain a sequence of trajectory points, and calculate the effective grinding width at each trajectory point. The point offset module is used to select the offset direction to offset discrete points on the initial trajectory line to obtain the initial point of the next grinding trajectory, and to calculate the effective grinding width at each initial point. The trajectory adjustment module is used to adjust the initial point so that the distance between adjacent points on the two trajectories can be covered by the effective grinding width of the two points, and to perform cyclic iteration until there is no under-grinding area between the two trajectories, thus obtaining a new trajectory line.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the full coverage planning method for grinding trajectory as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the full coverage planning method for grinding trajectory as described in any one of claims 1 to 5.