Method, device, equipment and storage medium for local fairing transition between tracks
阅读说明：本技术 一种轨迹间的局部光顺过渡方法、装置、设备及存储介质 (Method, device, equipment and storage medium for local fairing transition between tracks ) 是由 贺跃帮 王瑞超 冯均鹏 林铭杰 李兴春 于 2021-08-19 设计创作，主要内容包括：本发明公开了一种轨迹间的局部光顺过渡方法、装置、设备及存储介质,方法包括：取对所有i＝0,1,…N,计算并利用距离公式求出距离p-(1)的距离e(i),若min{e(0),e(1),…e(N)}<ε,则取表示新的可行解；否则取利用求解测试解公式重新得到j＝j+1,若j>cout或者则取作为最终解,否则返回重新执行上述步骤。通过轨迹间的局部光顺过渡方法,可以解决直线与直线,直线与圆弧,圆弧与圆弧之间的光顺过渡问题,且误差可控,能够进一步光顺加工路径,提高了加工效率,进而提升了加工效果。(The invention discloses a method, a device, equipment and a storage medium for local smooth transition between tracks, wherein the method comprises the following steps: get For all i ═ 0,1, … N, calculations And the distance p is calculated by using a distance formula 1 If min { e (0), e (1), … e (N) }<Epsilon, then get Representing a new feasible solution; otherwise get Recovery by solving test solution equations j is j +1, if j>cout or Then get And returning to re-execute the steps as a final solution if not. Through the local fairing transition method between the tracks, the fairing transition problem between a straight line and a straight line, between a straight line and an arc and between an arc and an arc can be solved, the error is controllable, a machining path can be further faired, the machining efficiency is improved, and the machining effect is further improved.)
1. A method for local fairing transitions between traces, the method comprising:
step S1: setting upExpressed in coordinates p0As a starting point, curve f0Three-dimensional coordinates at path length L, while settingIs a curve f0End point of, and total lengthIs composed ofAnd is provided withIs a curve f1By the coordinate p1As a starting point, p2As an end point, the total length isSetting the starting point of the transition curve as curve f0Up and away p1A distance L0Point of (2)End point is curve f1Up and away p1A distance L1Point of (2)Calculating p (u) by using a transition curve formula; wherein p (u) is the three-dimensional coordinate of the transition curve at parameter u;
step S2: setting the given maximum transition length to L2If the transition error is epsilon, the total number of u discrete is N, the number of search times is count, the search precision is delta, and j is 0, then the initial feasible solution L is obtainedfEqual to epsilon, the initial infeasible solution Ln＝L2Test solutions
GetFor all i ═ 0,1, … N, calculationsAnd the distance p is calculated by using a distance formula1If min { e (0), e (1) }<Epsilon, then getRepresenting a new feasible solution; otherwise get
Step S4: recovery by solving test solution equationsj is j +1, if j>cout orThen getOtherwise, the process returns to re-execute the above step S3.
2. The method of claim 1, wherein the transition curve formula is expressed as:
wherein u ∈ (0,1) is a parameter.
3. The method for local smooth transition between tracks according to claim 2, wherein the solving test solution formula is expressed as:
wherein L isfTo be an initial feasible solution, LnIs an initial infeasible solution.
4. The method of claim 3, wherein the distance formula is expressed as:
wherein the content of the first and second substances,for transition curve in parameterThree-dimensional coordinates of (c).
5. A device for localized fairing transitions between traces, comprising:
a first unit for settingExpressed in coordinates p0As a starting point, curve f0Three-dimensional coordinates at path length L, while settingIs a curve f0And a total length ofAnd is provided withIs a curve f1By the coordinate p1As a starting point, p2As an end point, the total length isSetting the starting point of the transition curve as curve f0Up and away p1A distance L0Point of (2)End point is curve f1Up and away p1A distance L1Point of (2)Calculating p (u) by using a transition curve formula; wherein p (u) is the three-dimensional coordinate of the transition curve at parameter u;
a second unit for setting the given maximum transition length to L2If the transition error is epsilon, the total number of u discrete is N, the number of search times is count, the search precision is delta, and j is 0, then the initial feasible solution L is obtainedfEqual to epsilon, the initial infeasible solution Ln＝L2Test solutions
A third unit for takingFor all i ═ 0,1, … N, calculationsAnd the distance p is calculated by using a distance formula1If min { e (0), e (1) }<Epsilon, then getRepresenting a new feasible solution; otherwise get
A fourth unit for retrieving using the solving of the test solution formulaj is j +1, if j>cout orThen getAnd returning to re-execute the third unit as a final solution if not.
6. The apparatus for local fairing transition between tracks of claim 5, wherein said transition curve formula is expressed as:
wherein u ∈ (0,1) is a parameter.
7. The apparatus for local optical smooth transition between tracks according to claim 6, wherein the solving test solution formula is expressed as:
wherein L isfTo be an initial feasible solution, LnIs an initial infeasible solution.
8. The apparatus for local fairing transition between tracks of claim 7, wherein said distance formula is expressed as:
wherein the content of the first and second substances,for transition curve in parameterThree-dimensional coordinates of (c).
9. An apparatus for localized fairing transitions between traces, comprising: at least one processor; at least one memory for storing at least one program; the method of local fairing transitions between trajectories as claimed in any one of claims 1 to 4 when executed by at least one of said processors.
10. A computer-readable storage medium storing computer-executable instructions for performing the method of local fairing transitions between traces of any of claims 1-4.
Technical Field
The present invention relates to the field of automatic control technologies, and in particular, to a method, an apparatus, a device, and a storage medium for local fairing transition between tracks.
Background
At present, the input of the three-axis numerical control system generally adopts straight lines and circular arcs. Because there is a corner between the straight line and the straight line, there is a centripetal force sudden change between the straight line and the circular arc, so if the processing mode of the straight line and the circular arc is directly adopted, the speed or the acceleration is not smooth at the intersection point of the straight line and the straight line, and the processing efficiency and the processing effect are influenced. For this reason, a large number of researchers have discussed the fairing problem between straight lines, such as global fitting fairing methods using a-splines, B-splines, C-splines or NURBS-splines, local transition fairing methods using arcs, parabolas, Hermite curves or bezier curves (B-splines); all the methods can perfectly deal with the problem of smoothness between straight lines and can obtain better processing efficiency and processing effect. However, the above methods can only deal with the problem of smoothness between straight lines, and cannot deal with the problem of transition between straight lines and circular arcs, between fitted curves and straight lines, and between fitted curves, which causes a problem of poor processing effect in some processing applications.
Disclosure of Invention
The present invention is directed to solving at least one of the problems of the prior art.
Therefore, the invention provides a local fairing transition method between tracks, which can further fairing a processing path and improve the processing efficiency.
The invention also provides a device for local fairing transition between tracks by applying the method for local fairing transition between tracks.
The invention also provides a device for local fairing transition between tracks by applying the method for local fairing transition between tracks.
The invention also provides a computer readable storage medium applying the local fairing transition method between the tracks.
A method for local fairing transitions between tracks according to an embodiment of the first aspect of the invention, the method comprising: step S1: setting upExpressed in coordinates p0As a starting point, curve f0Three-dimensional coordinates at path length L, while settingIs a curve f0And a total length ofAnd is provided withIs a curve f1By the coordinate p1As a starting point, p2As an end point, the total length isSetting the starting point of the transition curve as curve f0Up and away p1A distance L0Point of (2)End point is curve f1Up and away p1A distance L1Point of (2)Calculating p (u) by using a transition curve formula; wherein p (u) is the three-dimensional coordinate of the transition curve at parameter u;
step S2: setting the given maximum transition length to L2If the transition error is epsilon, the total number of u discrete is N, the number of search times is count, the search precision is delta, and j is 0, then the initial feasible solution L is obtainedfEqual to epsilon, the initial infeasible solution Ln＝L2Test solutions
Step S3: getFor all i ═ 0,1, … N, calculationsAnd the distance p is calculated by using a distance formula1If min { e (0), e (1), … e (N) }<Epsilon, then getRepresenting a new feasible solution; otherwise get
Step S4: recovery by solving test solution equationsj is j +1, if j>cout orThen getOtherwise, the process returns to re-execute the above step S3.
The method for local smooth transition between the tracks has at least the following beneficial effects: through the local fairing transition method between the tracks, the fairing transition problem between a straight line and a straight line, between a straight line and an arc and between an arc and an arc can be solved, the error is controllable, a machining path can be further faired, the machining efficiency is improved, and the machining effect is further improved.
According to some embodiments of the invention, the transition curve formula may be expressed as:
wherein u ∈ (0,1) is a parameter.
According to some embodiments of the invention, the solving a test solution formula may be expressed as:
wherein L isfTo be an initial feasible solution, LnIs an initial infeasible solution.
According to some embodiments of the invention, the distance formula may be expressed as:
wherein the content of the first and second substances,for transition curve in parameterThree-dimensional coordinates of (c).
The device for local fairing transition between tracks according to the embodiment of the second aspect of the invention comprises:
a first unit for settingExpressed in coordinates p0As a starting point, curve f0At path length LThree-dimensional coordinates of simultaneous devicesIs a curve f0And a total length ofAnd is provided withIs a curve f1By the coordinate p1As a starting point, p2As an end point, the total length isSetting the starting point of the transition curve as curve f0Up and away p1A distance L0Point of (2)End point is curve f1Up and away p1A distance L1Point of (2)Calculating p (u) by using a transition curve formula; wherein p (u) is the three-dimensional coordinate of the transition curve at parameter u;
a second unit for setting the given maximum transition length to L2If the transition error is epsilon, the total number of u discrete is N, the number of search times is count, the search precision is delta, and j is 0, then the initial feasible solution L is obtainedfEqual to epsilon, the initial infeasible solution Ln＝L2Test solutions
A third unit for takingFor all i ═ 0,1, … N, calculationsAnd calculating the distance by using a distance formulap1If min { e (0), e (1), … e (N) }<Epsilon, then getRepresenting a new feasible solution; otherwise get
A fourth unit for retrieving using the solving of the test solution formulaj is j +1, if j>cout orThen getAnd returning to re-execute the third unit as a final solution if not.
According to some embodiments of the invention, the transition curve formula may be expressed as:
wherein u ∈ (0,1) is a parameter.
According to some embodiments of the invention, the solving a test solution formula may be expressed as:
wherein L isfTo be an initial feasible solution, LnIs an initial infeasible solution.
According to some embodiments of the invention, the distance formula may be expressed as:
wherein the content of the first and second substances,for transition curve in parameterThree-dimensional coordinates of (c).
A device for local light-to-transition between tracks according to an embodiment of a third aspect of the invention comprises: at least one processor; at least one memory for storing at least one program; at least one of said programs, when executed by at least one of said processors, implements a method of local fairing transitions between trajectories as described above.
According to a fourth aspect of the present invention, there is provided a computer-readable storage medium storing computer-executable instructions, which when executed by a control processor, implement the local fairing transition method between tracks as described above.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
Drawings
The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a method for local smooth transition between tracks according to an embodiment of the present invention;
FIG. 2 is a cross-plot of curves in a local smooth transition method between tracks provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a local fairing transition device between tracks according to an embodiment of the present invention;
fig. 4 is a schematic diagram of a local fairing transition device between tracks according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
In the description of the present invention, it should be understood that the orientation or positional relationship referred to in the description of the orientation, such as the upper, lower, front, rear, left, right, etc., is based on the orientation or positional relationship shown in the drawings, and is only for convenience of description and simplification of description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, should not be construed as limiting the present invention.
In the description of the present invention, the meaning of a plurality of means is one or more, the meaning of a plurality of means is two or more, and larger, smaller, larger, etc. are understood as excluding the number, and larger, smaller, inner, etc. are understood as including the number. If the first and second are described for the purpose of distinguishing technical features, they are not to be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, unless otherwise explicitly limited, terms such as arrangement, installation, connection and the like should be understood in a broad sense, and those skilled in the art can reasonably determine the specific meanings of the above terms in the present invention in combination with the specific contents of the technical solutions.
Referring to fig. 1 and 2, an embodiment according to the first aspect of the present invention provides a method of local fairing transition between tracks, the method including, but not limited to, step S1, step S2, step S3 and step S4.
Step S1: setting upExpressed in coordinates p0As a starting point, curve f0Three-dimensional coordinates at path length L, while settingIs a curve f0And a total length of Lf0(ii) a And is provided withIs a curve f1By the coordinate p1As a starting point, p2As an end point, the total length isSetting the starting point of the transition curve as curve f0Up and away p1A distance L0Point of (2)End point is curve f1Up and away p1A distance L1Point of (2)Calculating p (u) by using a transition curve formula; wherein p (u) is the three-dimensional coordinate of the transition curve at parameter u;
step S2: setting the given maximum transition length to L2If the transition error is epsilon, the total number of u discrete is N, the number of search times is count, the search precision is delta, and j is 0, then the initial feasible solution L is obtainedfEqual to epsilon, the initial infeasible solution Ln＝L2Test solutions
Step S3: getFor all i ═ 0,1, … N, calculationsAnd the distance p is calculated by using a distance formula1If min { e (0), e (1), … e (N) }<Epsilon, then getRepresenting a new feasible solution; otherwise get
Step S4: recovery by solving test solution equationsj is j +1, if j>cout orThen getOtherwise, the process returns to re-execute the above step S3.
It should be noted that, in the embodiments of the present invention, the problem of fairing transition between a straight line and a straight line, between a straight line and an arc, and between an arc and an arc can be solved by using a local fairing transition method between tracks, and an error is controllable, so that a processing path can be further faired, the processing efficiency is improved, and the processing effect is further improved.
In an embodiment, the transition curve formula according to the embodiment of the present invention can be expressed as:
wherein u ∈ (0,1) is a parameter.
In one embodiment, solving the test solution formula may be expressed as:
wherein L isfTo be an initial feasible solution, LnIs an initial infeasible solution.
In one embodiment, the distance formula may be expressed as:
wherein the content of the first and second substances,for transition curve in parameterThree-dimensional coordinates of (c).
Referring to fig. 3, according to an embodiment of the second aspect of the present invention, there is provided a local fairing transition device 1000 between tracks, including:
a first unit 1100 for settingExpressed in coordinates p0As a starting point, curve f0Three-dimensional coordinates at path length L, while settingIs a curve f0And a total length ofAnd is provided withIs a curve f1By the coordinate p1As a starting point, p2As an end point, the total length isSetting the starting point of the transition curve as curve f0Up and away p1A distance L0Point of (2)End point is curve f1Up and away p1A distance L1Point of (2)Calculating p (u) by using a transition curve formula; wherein p (u) is the three-dimensional extent of the transition curve at parameter uCoordinates;
a second unit 1200 for setting a given maximum transition length L2If the transition error is epsilon, the total number of u discrete is N, the number of search times is count, the search precision is delta, and j is 0, then the initial feasible solution L is obtainedfEqual to epsilon, the initial infeasible solution Ln＝L2Test solutions
A third unit 1300 for fetchingFor all i ═ 0,1, … N, calculationsAnd the distance p is calculated by using a distance formula1If min { e (0), e (1), … e (N) }<Epsilon, then getRepresenting a new feasible solution; otherwise get
A fourth unit 1400 for retrieving using solving the test solution formulaj is j +1, if j>cout orThen getAnd returning to re-execute the third unit as a final solution if not.
In one embodiment, the transition curve formula may be expressed as:
wherein u ∈ (0,1) is a parameter.
In one embodiment, solving the test solution formula may be expressed as:
wherein L isfTo be an initial feasible solution, LnIs an initial infeasible solution.
In one embodiment, the distance formula may be expressed as:
wherein the content of the first and second substances,for transition curve in parameterThree-dimensional coordinates of (c).
It should be noted that, since the apparatus for local fairing transition between tracks in the present embodiment and the method for local fairing transition between tracks in the foregoing embodiment are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the system embodiment, and are not described in detail herein.
Referring to fig. 4, according to an embodiment of the fourth aspect of the present invention, there is provided an apparatus for local fairing transition between tracks, the apparatus comprising: a memory 600, a processor 500, and a computer program stored on the memory 600 and executable on the processor 500.
The processor 500 and the memory 600 may be connected by a bus or other means.
It should be noted that the apparatus for local fairing transition between tracks in the present embodiment and the method for local fairing transition between tracks in the foregoing embodiments belong to the same inventive concept, and therefore, these embodiments have the same implementation principle and technical effect, and are not described in detail herein.
The non-transitory software programs and instructions required to implement the inter-track local fairing transition method of the above-described embodiments are stored in the memory 600 and, when executed by the processor 500, perform the inter-track local fairing transition method of the above-described embodiments, e.g., performing the above-described method steps S1-S4 of fig. 1.
An embodiment according to a fourth aspect of the present invention provides a computer-readable storage medium, which stores computer-executable instructions, and when the computer-executable instructions are executed by a control processor, the method for local smooth transition between tracks in the above-mentioned embodiment is implemented. For example, the above-described method steps S1 to S4 in fig. 1 are performed.
It should be noted that, since the computer-readable storage medium in this embodiment and the method for local fairing transition between tracks in the above-mentioned embodiment are based on the same inventive concept, the corresponding contents in the method embodiment are also applicable to the system embodiment, and are not described in detail herein.
One of ordinary skill in the art will appreciate that all or some of the steps, systems, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components may 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 may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as is well known to those of ordinary skill in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, Digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can accessed by a computer. In addition, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media as known to those skilled in the art.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an illustrative embodiment," "an example," "a specific example," or "some examples" or the like mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.