CN109799785A - A kind of spline curve localization method and storage medium - Google Patents
A kind of spline curve localization method and storage medium Download PDFInfo
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Abstract
Embodiment of the invention discloses a kind of spline curve localization methods, belong to planning algorithm technical field.A kind of spline curve localization method, comprising: obtain data point array S [j].Knot vector array u [m] is obtained according to the data point array S [j].Control point array P [n] is obtained according to the data point array S [j] and the knot vector array u [m].The knot vector array u [m] and the control point array P [n] obtain spline curve C [u].Fitting multi-section-line L [n] is obtained according to the spline curve C [u].Speed planning is carried out according to the fitting multi-section-line L [n].The positioning planning of spline curve positioning dispensing is rapidly completed in spline curve localization method described in the embodiment of the present invention, realizes the described point process of smooth curve, improves the working efficiency of equipment.
Description
Technical field
The embodiment of the present invention is related to planning algorithm technical field more particularly to a kind of spline curve localization method.
Background technique
In industrial processes, the work for needing that multiple workpiece are carried out with viscose glue reinforcing can be encountered often, wherein how
Carrying out viscose glue to the gap of spline curve irregular between workpiece is the problem faced in production.
Inventor has found during studying the application, and in dispensing technology field, existing glue dispensing machine can not lead to
It crosses effective spline curve positioning to complete to draw the pattern of spline curve, causes to need to carry out during workpiece dispensing artificial
Dispensing is assisted, more manpower and material resources is consumed, can not accomplish the spline curve of mass work purpose for dispensing glue.Therefore, how
The positioning planning of spline curve positioning dispensing is rapidly completed, becomes urgent problem to be solved.
Summary of the invention
How the embodiment of the present invention is the technical problem to be solved is that, to be rapidly completed the positioning of spline curve positioning dispensing
Planning.
In order to solve the above-mentioned technical problem, a kind of spline curve localization method described in the embodiment of the present invention use with
Under technical solution.
A kind of spline curve localization method, comprising:
It obtains data point array S [j].
Knot vector array u [m] is obtained according to the data point array S [j].
Control point array P [n] is obtained according to the data point array S [j] and the knot vector array u [m].
The knot vector array u [m] and the control point array P [n] obtain spline curve C [u].
Fitting multi-section-line L [n] is obtained according to the spline curve C [u].
Speed planning is carried out according to the fitting multi-section-line L [n].
In an embodiment of the present invention, >=3 element j in the data point array S [j].
In an embodiment of the present invention, knot vector array u [m] is obtained according to the data point array S [j], specifically included:
Total chord length of spline curve after each element is linked in sequence in A1, the calculating data point array S [j]；
The relationship of element j in element m and the data point array S [j] in A2, the knot vector array u [m] are as follows: m
=j+8；
A3, it is overlapped to make finally to fit the curve starting point for the spline curve come with first knot vector, it need to be by u
U [0] in [m] to U [j] setting value be 0.The calculate node vector value since U [j+1] a node, one by one by iterative algorithm
Calculate all knot vector value array u [m].The iterative algorithm refers to: present node vector value=upper node arrow
Magnitude+when leading portion chord length/total chord length；
A4, it is overlapped to make finally to fit the end point for the spline curve come with the last one knot vector, setting institute
The value for stating the U [m-j] to u [m] in knot vector value array u [m] is 1, and so far knot vector calculating finishes.
In an embodiment of the present invention, it is controlled according to the data point array S [j] and the knot vector array u [m]
Point array P [n], specifically includes:
B1, according to knot vector value u [m], calculate α, β and g in the corresponding triple diagonal matrix of each node；
B2, the multiplicity according to knot vector, accordingly modify corresponding triple diagonal matrix；
B3, P vector, q vector sum Z vector in control point are calculated according to triple diagonal matrix parameter alpha, β and g；
B4, the control point P [n] that spline curve is calculated according to P vector, q vector sum Z vector, detailed process is as follows:
B41, the value for determining the last one control point are as follows: P [m] .x=ZX [m]；P [m] .y=ZY [m]；
B42, control point P [m] is brought to following algorithm: P [i] .x=(ZX [i]-Q [i] * P [i+1] .x) into；P [i] .y=
(ZY [i]-Q [i] * P [i+1] .y), obtains P [m-1], and then recursion obtains control point array P [m].
In an embodiment of the present invention, P vector, q vector sum Z vector respectively refer to X, Y and Z in respective nodes vector space coordinate
All directions vector component；Z vector is divided into ZX and/or ZY.
In an embodiment of the present invention, the knot vector array u [m] and the control point array P [n] obtain spline curve
C [u], specific algorithm are as follows:
Wherein, PiFor preset control point；For the basic function of spline curve.
In an embodiment of the present invention, fitting multi-section-line L [n] is obtained according to the spline curve C [u], specifically convert mode
Include:
The fitting multi-section-line L [n] is to be replaced in the case where determining fitting precision using the straight-line segment of limited item number
Spline curve C [u] drawing image；
Guaranteeing to draft currently by preset two vectors point in the coordinate of X-axis and Y-axis in the case where default precision
The straight-line segment L of two o'clock.
In an embodiment of the present invention, it includes: more to the fitting for carrying out speed planning according to the fitting multi-section-line L [n]
Section line L [n] carries out accelerating sections, the planning of constant-speed section and braking section.
In an embodiment of the present invention, accelerating sections, the planning of constant-speed section and braking section are carried out to the fitting multi-section-line L [n]
Include:
C1, be fitted multi-section-line L [n], preset speed V and preset acceleration A be input projecting parameter；
C2, the total length AL for calculating fitting multi-section-line L [n] and acceleration are away from SL；
C3, the distance for calculating the default line segment that fitting multi-section-line L [n] is arrived are TL, >=0 n.
In an embodiment of the present invention, accelerating sections, the planning of constant-speed section and braking section are carried out to the fitting multi-section-line L [n]
Further include: when TL < SL is then accelerating sections, calculating speed TL/AL*V；
As TL > SL and compare TL > (AL-SL), be then braking section, calculating speed is (AL-TL)/SL*V；
When TL > SL is constant-speed section, calculating speed V.
In an embodiment of the present invention, a kind of storage medium, which is characterized in that instruction is stored in the storage medium, this refers to
Order executes the processor according to claim 1 to use described in any one of 9 claims
In spline curve localization method；The storage medium is used to obtain knot vector array u according to the data point array S [j]
[m], and then obtain control point array P [n]；Spline curve C [u] is obtained by the control point array P [n] again.According to described
Spline curve C [u] obtains fitting multi-section-line L [n], while carrying out speed planning to the fitting multi-section-line L [n].
Compared with prior art, the embodiment of the present invention mainly have it is following the utility model has the advantages that
Spline curve localization method described in the embodiment of the present invention, comprising: obtain data point array S [j], according to described
Data point array S [j] obtains knot vector array u [m].According to the data point array S [j] and the knot vector array u
[m] obtains control point array P [n].The knot vector array u [m] and the control point array P [n] obtain spline curve C
[u].Vector array u [m] is obtained by trigonometric function, control point array P [n] is being obtained by vector array u [m], and then obtain
To spline curve C [u], the reliability converted before data point to spline curve is enhanced.Further according to the spline curve C [u]
Fitting multi-section-line L [n] is obtained, speed planning is carried out according to the fitting multi-section-line L [n].Curve is replaced by the straight line of multistage
It realizes and speed planning is carried out to the straight line of particular end, strengthen equipment to workpiece flexibility for dispensing glue and stationarity.To sum up institute
It states, the positioning planning of spline curve positioning dispensing is rapidly completed in spline curve localization method described in the embodiment of the present invention, real
The described point process for having showed smooth curve, improves the working efficiency of equipment.
Detailed description of the invention
It, below will be to required use in each embodiment in order to illustrate more clearly of the technical solution of the embodiment of the present invention
Attached drawing be briefly described, it should be apparent that, drawings in the following description are only some embodiments of the invention, for this
For the those of ordinary skill of field, under the premise of not making the creative labor power, it can also be obtained according to these attached drawings other
Attached drawing.
Fig. 1 is the schematic diagram of spline curve localization method described in the embodiment of the present invention；
Fig. 2 is the instance graph of spline curve described in the embodiment of the present invention；
Fig. 3 is the exemplary diagram of spline curve speed planning described in the embodiment of the present invention.
Specific embodiment
Below in conjunction with the attached drawing in various embodiments of the present invention, the technical solution in various embodiments of the present invention is carried out
Understand and completely describes.Described embodiment is a part of preferred embodiment of the present invention, rather than all feasible realities
Apply example.Based on each embodiment in the specific embodiment of the invention, any person skilled in the art is not making creation
Property labour under the premise of other embodiments obtained, all should belong to the scope of protection of the invention.
Unless otherwise defined, all technical and scientific terms used herein and person skilled in the art of the present invention
Normally understood meaning is identical.Any term used herein is intended merely to description specific embodiment, it is not intended that limit
Protection scope of the present invention processed.
It is the schematic diagram of spline curve localization method described in the embodiment of the present invention with reference to Fig. 1.Implementation of the invention
Spline curve localization method described in example, is related to the dispensing process of multiple product, advises for the gap to product
Curve dispensing then, and carry out the optimization of dispensing speed.
Spline curve localization method includes the following contents described in the embodiment of the present invention:
Step 101: obtaining data point array S [j].
Step 102: knot vector array u [m] is obtained according to the data point array S [j].
Step 103: control point array P is obtained according to the data point array S [j] and the knot vector array u [m]
[n]。
Step 104: the knot vector array u [m] and the control point array P [n] obtain spline curve C [u].
Step 105: fitting multi-section-line L [n] is obtained according to the spline curve C [u].
Step 106: speed planning is carried out according to the fitting multi-section-line L [n].
Wherein, the data point array S [j] of acquisition is to pass through reading by being drafted according to the design requirement of product
Corresponding data point array S [j] is taken to carry out drafting spline curve.Since the positioning of spline curve has certain radian, because
3 scheduled numerical value need be at least written when designing spline curve and moving towards in this, that is, refer to: first in the data point array S [j]
Plain >=3 j.
In step 102 of the embodiment of the present invention, what is be previously mentioned obtains knot vector array u according to the data point array S [j]
[m], specifically includes:
Total chord length of spline curve after each element is linked in sequence in A1, the calculating data point array S [j].
Processing curve corresponding with process is formed by connecting the data point array S [j], obtains total chord length of spline curve.
In the process, the processing curve is the curve that one end only has single wave crest, when identifying the curve is dual waves curve,
It can take and dual waves are divided into the acquisition that single ridge curves carry out the total chord length of single ridge curves, subsequent processing section similarly uses
The curved section at the unicast peak of the segmentation is planned and is handled.
The relationship of element j in element m and the data point array S [j] in A2, the knot vector array u [m] are as follows: m
=j+8.
A3, it is overlapped to make finally to fit the curve starting point for the spline curve come with first knot vector, it need to be by u
U [0] in [m] to U [j] setting value be 0.The calculate node vector value since U [j+1] a node, one by one by iterative algorithm
Calculate all knot vector value array u [m].The iterative algorithm refers to: present node vector value=upper node arrow
Magnitude+when leading portion chord length/total chord length；
A4, it is overlapped to make finally to fit the end point for the spline curve come with the last one knot vector, setting institute
The value for stating the U [m-j] to u [m] in knot vector value array u [m] is 1, and so far knot vector calculating finishes.
In step 103 of the embodiment of the present invention, obtained according to the data point array S [j] and the knot vector array u [m]
To control point array P [n], specifically include:
B1, according to knot vector value u [m], knot vector value u [m] is passed to triple diagonal matrix formula as input parameter
In, α, β and g in the corresponding triple diagonal matrix of each node are calculated by triple diagonal matrix formula.
B2, the multiplicity according to knot vector, accordingly modify corresponding triple diagonal matrix.According to the opposite of adjacent data point
The modification of position progress α, β and g corresponding points.
B3, P vector, q vector sum Z vector in control point are calculated according to triple diagonal matrix parameter alpha, β and g.According to section
Angle parameter α, β and g of point vector calculate the vector component of all directions of X, Y and Z in respective nodes vector space coordinate
P, Q and Z.Wherein, P vector, q vector sum Z vector respectively refer to all directions of X, Y and Z in respective nodes vector space coordinate
Vector component, Z vector are divided into ZX and/or ZY.
B4, the control point P [n] that spline curve is calculated according to P vector, q vector sum Z vector, detailed process is as follows:
B41, the value for determining the last one control point are as follows: P [m] .x=ZX [m]；P [m] .y=ZY [m]；
B42, control point P [m] is brought to following algorithm: P [i] .x=(ZX [i]-Q [i] * P [i+1] .x) into；P [i] .y=
(ZY [i]-Q [i] * P [i+1] .y), obtains P [m-1], and then recursion obtains control point array P [m].
In step 104 of the embodiment of the present invention, the knot vector array u [m] and the control point array P [n] obtain sample
Curve C [u], specific algorithm are as follows:
Wherein, PiFor preset control point, it includes i be count tag.For the base letter of spline curve
Number, it includes p be PiIn one value.In the conversion process of spline curve C [u], N thereinI, p(u) it refers to: working as P
Value be 0 when, Pi, according to the judgement N for judging algorithmI, 0(u) value.Judge that algorithm is as follows:
When the value of P is other numerical value other than 0, N is obtained according to algorithmI, p(u):
In step 105 of the embodiment of the present invention, fitting multi-section-line L [n], the fitting are obtained according to the spline curve C [u]
Multi-section-line L [n], which refers to, retouches side using a plurality of straight-line segment progress spline curve C [u], the case where determining fitting precision
Under, the image of the spline curve C [u] is overlapped using a plurality of straight-line segment.Guaranteeing to lead in the case where default precision
Cross the straight-line segment L that preset two vectors point drafts current two o'clock in the coordinate of X-axis and Y-axis.
It is the instance graph of spline curve described in the embodiment of the present invention with reference to Fig. 2.It is explained using instance graph described quasi-
Close multi-section-line L [n] is how to convert to obtain from the spline curve C [u].Assuming that curve is the spline curve C [u] in figure
Realistic model, wherein point t0 and point t2 are control point, the intermediate point of chord length after point t12 connects for point t0 with point t2, t12's
Coordinate is X and Y-axis (t0+t2)/2 obtains.Point t1 is the coordinate value of the intermediate point of t0 and t2 curve overall length, and L is point t1 and point
The distance of t12.By preset fitting precision e, the relationship of L and e are judged.As L >=e, then by the coordinate value assignment of point t1
Give point t2, t2=t1.Until stopping is calculated in the fitting multi-section-line L [n] when judging the relationship of L and e for L < e
It challengees straight line L by oneself, the value of each element in fitting multi-section-line L [n] is obtained by the circulation of finite number of time.
It is the exemplary diagram of spline curve speed planning described in the embodiment of the present invention with reference to Fig. 3.According to the fitting
It includes: to carry out accelerating sections, the rule of constant-speed section and braking section to the fitting multi-section-line L [n] that multi-section-line L [n], which carries out speed planning,
It draws.Accelerating sections is carried out to the fitting multi-section-line L [n], the planning of constant-speed section and braking section includes:
C1, be fitted multi-section-line L [n], preset speed V and preset acceleration A be input projecting parameter.It is preset
The value of speed V and acceleration A is user's input parameter value.
C2, the total length AL for calculating fitting multi-section-line L [n] and acceleration are away from SL.Pass through calculation formulaIt obtains
Acceleration distance and deceleration distance.
C3, the distance for calculating the default line segment that fitting multi-section-line L [n] is arrived are TL, >=0 n.
Accelerating sections is being carried out to the fitting multi-section-line L [n], when the planning of constant-speed section and braking section, when TL < SL is then
Accelerating sections, calculating speed TL/AL*V.As TL > SL and compare TL > (AL-SL), be then braking section, calculating speed is (AL-
TL)/SL*V.When TL > SL is constant-speed section, calculating speed V.To the fitting multi-section-line L [n] carry out accelerating sections, constant-speed section and
The planning of braking section is in order to keep starting and stopping for motor during dispensing more gentle, as shown in the figure.
In addition, a kind of storage medium of non-transient computer is also disclosed in the embodiment of the present invention, the storage medium is used for
It is stored with the executable instruction of computer, the executable instruction of the computer is any in above method embodiment for executing
A kind of algorithm.
The storage medium is used to obtain knot vector array u [m] according to the data point array S [j], and then is controlled
System point array P [n]；Spline curve C [u] is obtained by the control point array P [n] again.It is obtained according to the spline curve C [u]
Speed planning is carried out to fitting multi-section-line L [n], while to the fitting multi-section-line L [n], realizes and spline curve is rapidly completed
The positioning planning of positioning dispensing, reaches the described point process of smooth curve, and then improves mechanical production efficiency.
Spline curve localization method described in the embodiment of the present invention, mainly there is following technical effect:
Spline curve localization method described in the embodiment of the present invention, comprising: obtain data point array S [j], according to described
Data point array S [j] obtains knot vector array u [m].According to the data point array S [j] and the knot vector array u
[m] obtains control point array P [n].The knot vector array u [m] and the control point array P [n] obtain spline curve C
[u].Vector array u [m] is obtained by trigonometric function, control point array P [n] is being obtained by vector array u [m], and then obtain
To spline curve C [u], the reliability converted before data point to spline curve is enhanced.Further according to the spline curve C [u]
Fitting multi-section-line L [n] is obtained, speed planning is carried out according to the fitting multi-section-line L [n].Curve is replaced by the straight line of multistage
It realizes and speed planning is carried out to the straight line of particular end, strengthen equipment to workpiece flexibility for dispensing glue and stationarity.To sum up institute
It states, the positioning planning of spline curve positioning dispensing is rapidly completed in spline curve localization method described in the embodiment of the present invention, realizes
The described point process of smooth curve, improves the working efficiency of equipment.
Those of ordinary skill in the art are it is to be understood that one of the various embodiments described above spline curve localization method may be used also
To realize by other means.
Finally, it should be noted that the above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are simultaneously
Be not restricted to the described embodiments, it is other it is any without departing from the spirit and principles of the present invention made by change, modification,
Substitution, simplifies combination, should be equivalent substitute mode, is included within the scope of the present invention.
Claims (10)
1. a kind of spline curve localization method characterized by comprising
It obtains data point array S [j]；
Knot vector array u [m] is obtained according to the data point array S [j]；
Control point array P [n] is obtained according to the data point array S [j] and the knot vector array u [m]；
The knot vector array u [m] and the control point array P [n] obtain spline curve C [u]；
Fitting multi-section-line L [n] is obtained according to the spline curve C [u]；
Speed planning is carried out according to the fitting multi-section-line L [n].
2. spline curve localization method according to claim 1, which is characterized in that element in the data point array S [j]
>=3 j.
3. spline curve localization method according to claim 2, which is characterized in that obtained according to the data point array S [j]
To knot vector array u [m], specifically include:
Calculate total chord length of the spline curve after each element is linked in sequence in the data point array S [j]；
The relationship of element j in element m and the data point array S [j] in the knot vector array u [m] are as follows: m=j+8；
It is overlapped to make finally to fit the curve starting point for the spline curve come with first knot vector, it need to will be in u [m]
U [0] to U [j] setting value be 0；The calculate node vector value since U [j+1] a node, institute is calculated by iterative algorithm one by one
Some knot vector value array u [m]；The iterative algorithm refers to: a present node vector value=upper knot vector value+current
Section chord length/total chord length；
In order to be overlapped the end point for finally fitting the spline curve come with the last one knot vector, the node arrow is set
The value of U [m-j] to u [m] in magnitude array u [m] is 1, and so far knot vector calculating finishes.
4. spline curve localization method according to claim 3, which is characterized in that according to the data point array S [j] and
The knot vector array u [m] obtains control point array P [n], specifically includes:
According to knot vector value u [m], α, β and g in the corresponding triple diagonal matrix of each node are calculated；
According to the multiplicity of knot vector, corresponding triple diagonal matrix is accordingly modified；
According to triple diagonal matrix parameter alpha, β and g；Calculate P vector, the q vector sum Z vector in control point；
The control point P [n] of spline curve is calculated according to P vector, q vector sum Z vector, detailed process is as follows: determining last
The value at a control point are as follows: P [m] .x=ZX [m]；P [m] .y=ZY [m]；
Bring control point P [m] into following algorithm: P [i] .x=(ZX [i]-Q [i] * P [i+1] .x)；P [i] .y=(ZY [i]-Q
[i] * P [i+1] .y), it obtains P [m-1], and then recursion obtains control point array P [m].
5. spline curve localization method according to claim 4, which is characterized in that P vector, q vector sum Z vector respectively refer to
The vector component of all directions of X, Y and Z in respective nodes vector space coordinate；Z vector is divided into ZX and/or ZY.
6. spline curve localization method according to claim 4 or 5, which is characterized in that the knot vector array u [m]
Spline curve C [u], specific algorithm are obtained with the control point array P [n] are as follows:
Wherein, PiFor preset control point；
For the basic function of spline curve.
7. spline curve localization method according to claim 6, which is characterized in that obtained according to the spline curve C [u]
It is fitted multi-section-line L [n], specific conversion mode includes:
The fitting multi-section-line L [n] is to be overlapped the batten using a plurality of straight-line segment in the case where determining fitting precision
The image of curve C [u]；
Guaranteeing to draft current two o'clock in the coordinate of X-axis and Y-axis by preset two vectors point in the case where default precision
Straight-line segment L.
8. spline curve localization method according to claim 1, which is characterized in that according to the fitting multi-section-line L [n] into
Row speed planning includes: to carry out accelerating sections, the planning of constant-speed section and braking section to the fitting multi-section-line L [n]；
Accelerating sections is carried out to the fitting multi-section-line L [n], the planning of constant-speed section and braking section includes:
To be fitted the projecting parameter that multi-section-line L [n], preset speed V and preset acceleration A are input；
It calculates the total length AL of fitting multi-section-line L [n] and accelerates away from SL；
The distance for calculating the default line segment that fitting multi-section-line L [n] is arrived is TL, >=0 n.
9. spline curve localization method according to claim 8, which is characterized in that carried out to the fitting multi-section-line L [n]
The planning of accelerating sections, constant-speed section and braking section further include: when TL < SL is then accelerating sections, calculating speed TL/AL*V；
As TL > SL and compare TL > (AL-SL), be then braking section, calculating speed is (AL-TL)/SL*V；
When TL > SL is constant-speed section, calculating speed V.
10. a kind of storage medium, which is characterized in that be stored with instruction in the storage medium, which makes when being executed by processor
The processor executes according to claim 1 to being used for spline curve localization method described in any one of 9 claims；
The storage medium is used to obtain knot vector array u [m] according to the data point array S [j], and then obtains control point
Array P [n]；Spline curve C [u] is obtained by the control point array P [n] again；Intended according to the spline curve C [u]
It closes multi-section-line L [n], while speed planning is carried out to the fitting multi-section-line L [n].
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| WO2021248797A1 (en) * | 2020-06-08 | 2021-12-16 | 苏州艾吉威机器人有限公司 | B-spline curve-based path planning method and system, and motion control method and system |
| CN116551457A (en) * | 2023-07-11 | 2023-08-08 | 济南邦德激光股份有限公司 | Method and equipment for connecting and processing straight line segment and circular arc segment through spline curve |
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