Archimedean spiral-based interpolation method and related devices

Abstract

The application discloses an interpolation method based on an Archimedes spiral and a related device, and the method comprises the following steps: acquiring setting parameters of a curve to be processed, the setting parameters comprising a starting radius, a pitch coefficient and an angle parameter; determining a calculated arc length of the curve to be processed according to the starting radius, the pitch coefficient and the angle parameter; acquiring a current arc length of an interpolation device, and iteratively optimizing the calculated arc length according to the current arc length and the calculated arc length until the difference between the current arc length and the calculated arc length meets an iteration end condition; determining the angle parameter of the current arc length at the iteration end as a target polar angle; and outputting an interpolation result according to the starting radius, the pitch coefficient and the target polar angle. By establishing an accurate relationship between the arc length and the polar angle, combining speed planning to realize an even and efficient interpolation algorithm, and using the Newton iteration method to quickly solve the interpolation point coordinates, the real-time requirement is met while the trajectory accuracy is ensured, and high-precision and high-efficiency trajectory control is realized.

Description

Technical Field

[0001] This application relates to the field of motion control technology, and in particular to an interpolation method and related apparatus based on the Archimedes spiral. Background Technology

[0002] The Archimedean spiral is a common planar curve whose polar diameter is determined by the polar angle, initial radius, and pitch coefficient. It is widely used in dispensing, 3D printing, and CNC machining. Existing Archimedean spiral interpolation schemes partially employ the equal-angle incremental method, which involves velocity planning based on the polar angle and calculating the corresponding interpolation point coordinates according to the polar coordinate equation. While this method is computationally simple, it ignores the linear velocity fluctuations caused by changes in the polar diameter. This results in faster speeds at larger radii and slower speeds at smaller radii, leading to uneven adhesive application in dispensing and inconsistent surface quality in CNC machining. In other scenarios, the Archimedean spiral is calculated using an approximate arc length method, achieving equal-step interpolation through geometric approximations (such as using chord length instead of arc length). This low-order approximation replaces precise calculations, resulting in minor computational simplification, but leads to significant error accumulation under high-precision requirements, hindering high-speed, high-precision machining. Summary of the Invention

[0003] This application provides an interpolation method and related apparatus based on the Archimedes spiral, which can ensure trajectory accuracy while meeting real-time requirements, and achieve high-precision and high-efficiency trajectory control.

[0004] In a first aspect, embodiments of this application provide an interpolation method based on an Archimedean spiral, the method comprising the following steps: Obtain the setting parameters of the curve to be processed, including the starting radius, pitch coefficient, and angle parameters; The calculated arc length of the curve to be processed is determined based on the starting radius, the pitch coefficient, and the angle parameter. Obtain the current arc length of the interpolation device, iteratively optimize the calculated arc length based on the current arc length and the calculated arc length until the difference between the current arc length and the calculated arc length satisfies the iteration termination condition, and determine the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle; The interpolation result is output based on the starting radius, the pitch coefficient, and the target polar angle; Based on the interpolation result, the interpolation device is controlled to perform the interpolation operation.

[0005] In some embodiments, determining the calculated arc length of the curve to be processed based on the starting radius, the pitch coefficient, and the angle parameter includes: Based on the polar coordinate equation of the curve to be processed, determine the integral formula for the arc length of the curve to be processed; The initial radius, the pitch coefficient, and the angle parameter are substituted into the arc length integral formula to determine the calculated arc length.

[0006] In some embodiments, determining the integral formula of the curve to be processed based on its polar coordinate equation includes: Differentiate the polar coordinate equation of the curve to be processed and substitute it into the arc length formula of the curve to be processed to obtain the first transformation formula; Extracting like terms from the first conversion formula yields the second conversion formula; The second conversion formula is subjected to coefficient conversion processing to establish a unique correspondence between the calculated arc length and polar angle of the curve to be processed, thereby obtaining the integral formula of the curve to be processed.

[0007] In some embodiments, the setting parameters further include feed rate and interpolation cycle; The step of iteratively optimizing the calculated arc length based on the current arc length and the calculated arc length includes: The current arc length is determined based on the feed rate and the interpolation cycle; Based on the integral formula of the curve to be processed, the calculated arc length, and the current arc length, the objective function is determined; The iteration termination condition is determined based on the objective function, the calculated arc length, and the preset threshold.

[0008] In some embodiments, determining the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle includes: The derivative of the objective function is obtained by taking the derivative of the objective function. The angle parameter is calculated iteratively based on the objective function and the derivative function; When the angle parameter satisfies the iteration termination condition, the current angle parameter is determined to be the target polar angle.

[0009] In some embodiments, after iteratively calculating the angle parameters based on the objective function and the derivative function, the interpolation method further includes: When the angle parameter does not meet the iteration termination condition, the current angle parameter is substituted into the arc length integral formula to obtain the updated arc length. Substitute the current angle parameter and the updated arc length into the objective function, and iteratively optimize the calculated arc length until the angle parameter satisfies the iteration termination condition.

[0010] In some embodiments, outputting the interpolation result based on the starting radius, the pitch coefficient, and the target polar angle includes: Substituting the initial radius, the pitch coefficient, and the target polar angle into the rectangular coordinate formula, we obtain the coordinate information; Based on the coordinate information, the interpolation result for the current period is obtained.

[0011] Secondly, embodiments of this application provide an interpolation device based on an Archimedean spiral, which is used to implement the interpolation method based on an Archimedean spiral of the first aspect, including: The acquisition module is used to acquire the setting parameters of the curve to be processed, including the starting radius, pitch coefficient and angle parameters; The determination module is used to determine the calculated arc length of the curve to be processed based on the starting radius, the pitch coefficient, and the angle parameter; An iterative module is used to obtain the current arc length of the interpolation device, iteratively optimize the calculated arc length based on the current arc length and the calculated arc length, until the difference between the current arc length and the calculated arc length satisfies the iteration termination condition, and determine the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle; The output module is used to output the interpolation result based on the starting radius, the pitch coefficient, and the target polar angle; The interpolation module is used to control the interpolation device to perform interpolation operations based on the interpolation results.

[0012] Thirdly, embodiments of this application provide an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the interpolation method based on the Archimedean spiral of the first aspect.

[0013] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the Archimedean spiral-based interpolation method of the first aspect.

[0014] The interpolation method, apparatus, and storage medium based on the Archimedean spiral of this application have at least the following beneficial effects: By acquiring the set parameters of the curve to be processed, including the initial radius, pitch coefficient, and angle parameters; determining the arc length of the curve to be processed based on the initial radius, pitch coefficient, and angle parameters; determining the objective function of the angle parameters based on the arc length; iteratively calculating the angle parameters based on the objective function to obtain the target polar angle; and outputting the interpolation result based on the initial radius, pitch coefficient, and target polar angle. By establishing a precise relationship between the arc length and the polar angle, and combining it with velocity planning to achieve a uniform and efficient interpolation algorithm, and using Newton's iteration method to quickly solve for the coordinates of the interpolation points, the real-time requirements are met while ensuring trajectory accuracy, thus achieving high-precision and high-efficiency trajectory control.

[0015] Other features and advantages of this application will be set forth in the following description and will be apparent in part from the description or may be learned by practicing the application. The objectives and other advantages of this application may be realized and obtained by means of the structures particularly pointed out in the description and the accompanying drawings. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating an interpolation method based on the Archimedean spiral according to an embodiment of the present invention; Figure 2 for Figure 1 Flowchart of step S2000; Figure 3 for Figure 2 Flowchart of step S2100; Figure 4 for Figure 1 Flowchart of step S3000; Figure 5 for Figure 1 The flowchart of step S3000 when the angle parameter satisfies the iteration termination condition; Figure 6 for Figure 1 The flowchart for step S3000 when the angle parameter does not meet the iteration termination condition; Figure 7 for Figure 1 Flowchart of step S4000; Figure 8 This is a structural diagram of an interpolation device based on an Archimedean spiral according to an embodiment of the present invention; Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. Furthermore, the features, operations, or characteristics described in the specification can be combined in any suitable manner to form various implementations. Simultaneously, the steps or actions described in the method description can be rearranged or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0018] In the description of this application, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0019] The serial numbers assigned to components in this document, such as "first" and "second," are used only to distinguish the described objects and have no sequential or technical meaning. The terms "connection" and "linkage" used in this application, unless otherwise specified, include both direct and indirect connections (linkages).

[0020] This invention relates to an interpolation method and related apparatus based on the Archimedean spiral. The Archimedean spiral is a common planar curve, also known as a constant-velocity spiral. A ray rotates uniformly around a pole, while a moving point moves uniformly outward along the ray; the trajectory of the moving point is the Archimedean spiral, and its polar coordinate equation is... ,in Polar radius, Polar angle; The initial radius; The pitch coefficient is used to control the density of the helix. Archimedes' spirals are widely used in fluid transport and hydraulic engineering, mechanical transmission and machine tool processing, specifically in areas such as dispensing, 3D printing, and CNC machining.

[0021] In practical applications, Archimedean spiral interpolation schemes employ the constant-angle increment method and the approximate arc-length method. The constant-angle increment method plans the velocity based on the polar angle and calculates the corresponding interpolation point coordinates according to the polar coordinate equation. While this method is computationally simple, it ignores the linear velocity fluctuations caused by changes in the polar radius, resulting in higher speeds at larger radii and lower speeds at smaller radii. This can lead to uneven adhesive application in dispensing scenarios and inconsistent surface quality in CNC machining. Furthermore, the approximate arc-length method achieves constant-step interpolation through geometric approximations (such as using chord length instead of arc length), replacing precise calculations with lower-order approximations for minor computational simplification. However, under high-precision requirements, significant error accumulation hinders high-speed, high-precision machining. Therefore, there is an urgent need for an Archimedean spiral interpolation method that can accurately plan the velocity based on the arc length, ensuring uniform linear velocity during machining.

[0022] Based on the above, this invention provides an interpolation method and related apparatus based on an Archimedean spiral. The method involves acquiring set parameters of the curve to be processed, including the initial radius, pitch coefficient, and angle parameters; determining the arc length of the curve based on these parameters; determining the objective function for the angle parameters based on the arc length; iteratively calculating the angle parameters based on the objective function to obtain the target polar angle; and outputting the interpolation result based on the initial radius, pitch coefficient, and target polar angle. By establishing a precise relationship between the arc length and polar angle through integration, and combining this with velocity planning to achieve a uniform and efficient interpolation algorithm, the method utilizes Newton's iteration method to quickly solve for the interpolation point coordinates. This ensures both trajectory accuracy and real-time performance, achieving high-precision and high-efficiency trajectory control.

[0023] Please see Figure 1 , Figure 1 The flowchart illustrates an interpolation method based on the Archimedean spiral provided by an embodiment of the present invention. For example... Figure 1 As shown, the interpolation method based on the Archimedean spiral in this embodiment of the invention includes the following steps: Step S1000: Obtain the setting parameters of the curve to be processed. The setting parameters include the starting radius, pitch coefficient and angle parameters.

[0024] It is understandable that, as shown in the polar coordinate equation of the Archimedean spiral, determining the position and characteristics of the curve to be processed requires obtaining the set parameters of the curve. Specifically, the set parameters include the initial radius, pitch coefficient, and angle parameters. Among these, the initial polar radius... Polar angle The distance from the starting point to the center of the spiral. This indicates that the spiral originates from the origin. This represents the initial segment of the inner circle of the helix. Pitch coefficient. Used to control the density of the spiral. The larger the spiral, the looser it is. Angular parameters include the initial angle. and termination angle The unit is rad, total number of revolutions Total number of laps This makes the input of setting parameters more intuitive and is often used for CNC macro program variables.

[0025] In some embodiments, the setting parameters also include feed rate. and interpolation period Feed rate Interpolation cycle is the rate at which the workpiece moves relative to the machining component in the feed direction during machining, directly determining machining efficiency and surface quality. It is the time interval at which the CNC system performs a curve interpolation calculation and outputs position commands for each axis at fixed intervals.

[0026] It should be noted that the setting parameters of the curve to be processed can be obtained through manual input, system default generation, or reading from the database, which are existing technologies and will not be elaborated here.

[0027] Step S2000: Determine the calculated arc length of the curve to be processed based on the starting radius, pitch coefficient, and angle parameters.

[0028] Understandably, to ensure the accuracy of the machining curve trajectory while meeting real-time requirements, it is necessary to calculate the arc length of the curve to be machined based on the starting radius, pitch coefficient, and angle parameters. In this embodiment, the above-mentioned polar coordinate equation is used... The angle is calculated from the initial angle. to the termination angle The arc length.

[0029] Please see Figure 2 , Figure 2 A schematic diagram illustrating the specific implementation process of step S2000 above is shown. For example... Figure 2 As shown, step S2000 includes at least the following steps: Step S2100: Determine the arc length integral formula of the curve to be processed based on the polar coordinate equation of the curve to be processed.

[0030] Understandably, based on the polar coordinate equation of the curve to be processed, the arc length integral is obtained as follows:

[0031] Please see Figure 3 , Figure 3 A schematic diagram illustrating the specific implementation process of step S2100 above is shown. For example... Figure 3 As shown, step S2100 further includes at least the following steps: Step S2110: Differentiate the polar coordinate equation of the curve to be processed and substitute it into the arc length formula of the curve to be processed to obtain the first transformation formula.

[0032] Understandably, differentiating the polar coordinate equation of the curve to be processed yields the following formula:

[0033] Substituting the values ​​into the arc length formula of the curve to be processed, we obtain the first conversion formula as shown below:

[0034] Step S2120: Extract like terms from the first conversion formula to obtain the second conversion formula.

[0035] Understandably, the first transformation formula, after extracting like terms, yields the second transformation formula as shown below:

[0036] Step S2130: Perform coefficient conversion processing on the second conversion formula to establish a unique correspondence between the calculated arc length and polar angle of the curve to be processed, and obtain the integral formula of the curve to be processed.

[0037] It is understandable that the coefficient conversion process for the second conversion formula is performed in this embodiment by setting parameters. As shown below:

[0038] Substituting into the indefinite integral formula:

[0039] The integral formula for obtaining the curve to be processed is shown below:

[0040] in, .

[0041] It should be noted that the integral formula for the curve to be processed establishes the arc length. With polar angle The unique correspondence enables precise calculation of the arc length of the Archimedes spiral, providing accurate arc length data support for subsequent velocity planning.

[0042] Step S2200: Substitute the initial radius, pitch coefficient, and angle parameters into the arc length integral formula to determine the calculated arc length.

[0043] It is understandable that after determining the integral formula for the curve to be processed, the calculated arc length of the curve can be determined by substituting the starting radius, pitch coefficient, and angle parameters. Compared with the approximate calculation method, the integral calculation method of this application significantly improves the accuracy of arc length calculation and ensures the accuracy of the interpolation trajectory.

[0044] Step S3000: Obtain the current arc length of the interpolation device, and iteratively optimize the calculated arc length based on the current arc length and the calculated arc length until the difference between the current arc length and the calculated arc length meets the iteration termination condition. Then, determine the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle.

[0045] Understandably, after obtaining the calculated arc length of the curve to be processed, the feed rate is then considered. and interpolation period This yields the expected arc length increment for each cycle. .

[0046] Please see Figure 4 , Figure 4 A schematic diagram illustrating the specific implementation process of step S3000 above is shown. For example... Figure 4 As shown, step S3000 further includes at least the following steps: Step S3100: Determine the current arc length based on the feed rate and interpolation cycle.

[0047] As can be understood from the above steps, setting parameters also includes feed rate. and interpolation period Therefore, the expected arc length increment for each cycle is obtained. The calculation process is as follows:

[0048] Meanwhile, the current arc length is known. The corresponding polar angle needs to be solved. , making Specifically, within the first interpolation cycle, the current arc length equals the expected arc length increment, i.e. .

[0049] Step S3200: Based on the integral formula of the curve to be processed, calculate the arc length and the current arc length, and determine the objective function.

[0050] It is understandable that the arc length obtained from the above steps... With polar angle The relationship is a nonlinear equation that cannot be solved directly. In this embodiment, Newton's iteration method is used to solve the problem. This is achieved by constructing the objective function. As shown in the following formula:

[0051] Step S3300: Determine the iteration termination condition of the objective function based on the objective function, the calculated arc length, and the preset threshold.

[0052] Understandably, after determining the objective function, to ensure the accuracy of the interpolation trajectory, the size of the objective function needs to be controlled within a certain precision range. That is, the smaller the absolute value of the objective function, the smaller the difference between the arc length obtained in the above steps and the current arc length position. The iteration termination condition for the objective function is shown in the following formula:

[0053] in, The polar angle corresponding to the current cycle. This is the preset threshold.

[0054] Please see Figure 5 , Figure 5 The diagram illustrates the specific implementation process of step S3000 above when the angle parameter satisfies the iteration termination condition. For example... Figure 5 As shown, step S3000 further includes at least the following steps: Step S3400: Perform a derivative operation on the objective function to obtain the derivative of the objective function.

[0055] It is understandable that by taking the derivative of the objective function, we obtain its derivative, as shown in the following formula:

[0056] Step S3500: Iteratively calculate the angle parameters based on the objective function and the derivative function.

[0057] It is understandable that, based on the objective function and derivative function obtained from the above steps, and according to Newton's iteration formula, the following formula is obtained:

[0058] in, This represents the polar angle corresponding to the next cycle. The angle parameter is iteratively calculated using the above formula until the iteration termination condition of the objective function determined in the previous steps is met.

[0059] Step S3600: When the angle parameter meets the iteration termination condition, determine the current angle parameter as the target polar angle.

[0060] Understandably, after the above iterative steps are completed, when the angle parameter meets the iteration termination condition, the current angle parameter is determined to be the target polar angle. .

[0061] Please see Figure 6 , Figure 6 The diagram illustrates the specific implementation process of step S3000 above when the angle parameter does not meet the iteration termination condition. For example... Figure 6 As shown, step S3000 further includes at least the following steps: Step S3700: When the angle parameter does not meet the iteration termination condition, substitute the current angle parameter into the arc length integral formula to obtain the updated arc length.

[0062] It is understandable that when the angle parameter does not meet the iteration termination condition, i.e. To further reduce the number of iterations, the interpolation method in this embodiment uses the current angle parameter as the angle parameter for the next cycle to obtain a more accurate updated arc length.

[0063] Step S3800: Substitute the current angle parameter and the updated arc length into the objective function, and iteratively optimize the calculation of the arc length until the angle parameter meets the iteration termination condition.

[0064] Understandably, by substituting the current angle parameter and the updated arc length into the objective function, and repeating steps S3100 to S3500, the angle parameter satisfies the iteration termination condition, thus obtaining a more accurate target polar angle. .

[0065] Step S4000: Output the interpolation result based on the starting radius, pitch coefficient, and target polar angle.

[0066] It is understandable that the target polar angle is obtained through the above steps. Then, by combining the starting radius and pitch coefficient, the interpolation coordinate information for this cycle can be accurately obtained, thereby ensuring the accuracy of the interpolation trajectory.

[0067] Please see Figure 7 , Figure 7 A schematic diagram illustrating the specific implementation process of step S4000 above is shown. For example... Figure 7 As shown, step S4000 includes at least the following steps: Step S4100: Substitute the starting radius, pitch coefficient, and target polar angle into the rectangular coordinate formula to obtain the coordinate information.

[0068] It is understandable that the target polar angle is obtained through the above steps. Then, substitute the values ​​into the rectangular coordinate formula to obtain the coordinate information. The specific process is shown in the following formula:

[0069] Step S4200: Obtain the interpolation result for the current period based on the coordinate information.

[0070] Understandably, after obtaining the coordinate information through the above steps, the interpolation device can output accurate interpolation results for the current period. This allows for precise control of the interpolation device to execute interpolation commands.

[0071] Step S5000: Based on the interpolation results, control the interpolation device to perform the interpolation operation.

[0072] It is understood that the interpolation method based on the Archimedean spiral in this application uses arc length as the interpolation parameter to ensure that the displacement (linear velocity) is consistent in each interpolation cycle, avoiding the uneven density problem caused by constant angle interpolation. Simultaneously, the interpolation method in this application uses an integral method to accurately calculate the arc length of the Archimedean spiral, avoiding arc length errors caused by approximate formulas, providing accurate data support for velocity planning and coordinate solving, and significantly improving the accuracy of the interpolation trajectory. Since the Newton iteration method has second-order convergence characteristics under this mathematical model, it typically only requires 1-3 iterations to achieve the machine accuracy requirements, utilizing the polar angle of the previous cycle. As an initial value, the number of iterations is further reduced, improving the real-time performance of the interpolation method based on the Archimedean spiral. The interpolation method of this application embodiment can also be extended to arc-length parameterized interpolation of other parametric curves (such as logarithmic spirals, involutes, etc.), improving applicability and compatibility.

[0073] In practical applications, it is necessary to machine a section of Archimedean spiral, with the parameters set as follows: , Starting angle Termination angle feed rate interpolation period Substituting the above parameters into the arc length formula above, the total arc length is calculated as follows: Assuming the velocity curve is a uniform velocity curve, the expected arc length increment for each cycle is: .

[0074] The polar angle and coordinates are solved iteratively using the above steps, with a preset accuracy threshold. The initial value for the first interpolation cycle is... Target arc length position ,but , Substituting into Newton's iterative formula, we get... Substitute into the arc length formula to calculate Because the objective function Therefore, a second iteration is required. The result from the previous calculation... Substituting the initial value into Newton's iterative formula, we get Substitute into the arc length formula to calculate Because the objective function If the iteration termination condition is met, the iteration stops, and the polar angle of the first interpolation cycle is... Substituting into the rectangular coordinate formula, we can obtain , The coordinates are output to the interpolation device, completing the first interpolation cycle.

[0075] Next, the initial value of the second interpolation cycle is the polar angle of the first interpolation cycle. Target arc length position Following the steps outlined above, the polar angle is solved using Newton's iterative method. and , Coordinates. The initial value for the third interpolation cycle is the polar angle of the second interpolation cycle. This process continues until the entire Archimedes spiral interpolation is completed.

[0076] The specific calculation process yielded the interpolation results for the first 20 interpolation cycles, as shown in the table below for the number of iterations and error values: Table 1: Number of iterations and error values

[0077] As shown in Table 1, the error value of each interpolation cycle is very small, and the accuracy requirement can be achieved in just two iterations. This indicates that the interpolation method based on the Archimedes spiral in this application has a fast convergence speed, high calculation accuracy, and uniform interpolation length, which verifies the feasibility and superiority of the interpolation method proposed in this application.

[0078] like Figure 8 As shown, Figure 8 This is a schematic diagram of the structure of the interpolation device 600 based on the Archimedean spiral provided in the embodiments of this application. The entire process of the interpolation method based on the Archimedean spiral provided in the embodiments of this application involves the following modules in the interpolation device 600 based on the Archimedean spiral: acquisition module 610, determination module 620, iteration module 630, output module 640 and interpolation module 650.

[0079] The acquisition module 610 is used to acquire the setting parameters of the curve to be processed, including the starting radius, pitch coefficient and angle parameters. The determination module 620 is used to determine the calculated arc length of the curve to be processed based on the starting radius, pitch coefficient, and angle parameters. The iteration module 630 is used to obtain the current arc length of the interpolation device, and iteratively optimize the calculated arc length based on the current arc length and the calculated arc length until the difference between the current arc length and the calculated arc length meets the iteration termination condition. The angle parameter of the current arc length corresponding to the end of the iteration is determined as the target polar angle. Output module 640 is used to output interpolation results based on the starting radius, pitch coefficient and target polar angle; The interpolation module 650 is used to control the interpolation device to perform interpolation operations based on the interpolation results.

[0080] like Figure 9 As shown, Figure 9 This is a schematic diagram of a controller 700 provided in one embodiment of this application.

[0081] The controller 700 in this embodiment includes one or more processors 710 and a memory 720. Figure 9 The example uses a processor 710 and a memory 720.

[0082] The processor 710 and memory 720 can be connected via a bus or other means. Figure 9 Taking the example of a connection between China and Israel via a bus.

[0083] Memory 720, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory 720 may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory 720 may optionally include memory 720 remotely located relative to processor 710, and these remote memories can be connected to controller 700 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0084] Those skilled in the art will understand that Figure 9 The device structure shown does not constitute a limitation on the controller 700 and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0085] This application embodiment also provides a storage medium storing computer-executable instructions for executing the above-described interpolation method based on the Archimedean spiral.

[0086] In one embodiment, the storage medium stores computer-executable instructions that are executed by one or more processors 710, such as one of the processors 710 in the controller 700, to enable the one or more processors 710 to perform the Archimedes spiral-based interpolation method provided in any embodiment of this application.

[0087] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network nodes. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0088] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0089] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0090] In the several embodiments provided in this application, it should be understood that the disclosed systems, instruments, and methods can be implemented in other ways. For example, the instrument embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the shown or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between instruments or units may be electrical, mechanical, or other forms. Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, i.e., they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0091] It should also be understood that the various implementation methods provided in this application can be combined arbitrarily to achieve different technical effects.

[0092] The above is a detailed description of the preferred embodiments of this application. However, this application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. An interpolation method based on the Archimedean spiral, characterized in that, The method includes the following steps: Obtain the setting parameters of the curve to be processed, including the starting radius, pitch coefficient, and angle parameters; The calculated arc length of the curve to be processed is determined based on the starting radius, the pitch coefficient, and the angle parameter. Obtain the current arc length of the interpolation device, iteratively optimize the calculated arc length based on the current arc length and the calculated arc length until the difference between the current arc length and the calculated arc length satisfies the iteration termination condition, and determine the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle; The interpolation result is output based on the starting radius, the pitch coefficient, and the target polar angle; Based on the interpolation result, the interpolation device is controlled to perform the interpolation operation.

2. The interpolation method based on the Archimedean spiral according to claim 1, characterized in that, The step of determining the calculated arc length of the curve to be processed based on the initial radius, the pitch coefficient, and the angle parameter includes: Based on the polar coordinate equation of the curve to be processed, determine the integral formula for the arc length of the curve to be processed; The initial radius, the pitch coefficient, and the angle parameter are substituted into the arc length integral formula to determine the calculated arc length.

3. The interpolation method based on the Archimedean spiral according to claim 2, characterized in that, The step of determining the integral formula of the curve to be processed based on its polar coordinate equation includes: Differentiate the polar coordinate equation of the curve to be processed and substitute it into the arc length formula of the curve to be processed to obtain the first transformation formula; Extracting like terms from the first conversion formula yields the second conversion formula; The second conversion formula is subjected to coefficient conversion processing to establish a unique correspondence between the calculated arc length and polar angle of the curve to be processed, thereby obtaining the integral formula of the curve to be processed.

4. The interpolation method based on the Archimedean spiral according to claim 2, characterized in that, The setting parameters also include feed rate and interpolation cycle; The step of iteratively optimizing the calculated arc length based on the current arc length and the calculated arc length includes: The current arc length is determined based on the feed rate and the interpolation cycle; Based on the integral formula of the curve to be processed, the calculated arc length, and the current arc length, the objective function is determined; The iteration termination condition is determined based on the objective function, the calculated arc length, and the preset threshold.

5. The interpolation method based on the Archimedean spiral according to claim 4, characterized in that, The step of determining the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle includes: The derivative of the objective function is obtained by taking the derivative of the objective function. The angle parameter is calculated iteratively based on the objective function and the derivative function; When the angle parameter satisfies the iteration termination condition, the current angle parameter is determined to be the target polar angle.

6. The interpolation method based on the Archimedean spiral according to claim 5, characterized in that, After iteratively calculating the angle parameters based on the objective function and the derivative function, the interpolation method further includes: When the angle parameter does not meet the iteration termination condition, the current angle parameter is substituted into the arc length integral formula to obtain the updated arc length. Substitute the current angle parameter and the updated arc length into the objective function, and iteratively optimize the calculated arc length until the angle parameter satisfies the iteration termination condition.

7. The interpolation method based on the Archimedean spiral according to claim 1, characterized in that, The step of outputting the interpolation result based on the initial radius, the pitch coefficient, and the target polar angle includes: Substituting the initial radius, the pitch coefficient, and the target polar angle into the rectangular coordinate formula, we obtain the coordinate information; Based on the coordinate information, the interpolation result for the current period is obtained.

8. An interpolation device based on an Archimedean spiral, used to implement the interpolation method based on an Archimedean spiral as described in any one of claims 1 to 7, characterized in that, include: The acquisition module is used to acquire the setting parameters of the curve to be processed, including the starting radius, pitch coefficient and angle parameters; The determination module is used to determine the calculated arc length of the curve to be processed based on the starting radius, the pitch coefficient, and the angle parameter; An iterative module is used to obtain the current arc length of the interpolation device, iteratively optimize the calculated arc length based on the current arc length and the calculated arc length, until the difference between the current arc length and the calculated arc length satisfies the iteration termination condition, and determine the angle parameter of the current arc length corresponding to the end of the iteration as the target polar angle; The output module is used to output the interpolation result based on the starting radius, the pitch coefficient, and the target polar angle; The interpolation module is used to control the interpolation device to perform interpolation operations based on the interpolation results.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the interpolation method based on the Archimedean spiral as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The system contains a computer program that, when executed by a processor, implements the interpolation method based on the Archimedean spiral as described in any one of claims 1 to 7.

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