CN108153245A - Smooth trajectory forwarding method and system - Google Patents
Smooth trajectory forwarding method and system Download PDFInfo
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- CN108153245A CN108153245A CN201711437252.0A CN201711437252A CN108153245A CN 108153245 A CN108153245 A CN 108153245A CN 201711437252 A CN201711437252 A CN 201711437252A CN 108153245 A CN108153245 A CN 108153245A
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/34—Director, elements to supervisory
- G05B2219/34083—Interpolation general
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Abstract
The present invention provides a kind of smooth trajectory forwarding method and systems, the described method comprises the following steps：Obtain the first transit point on first track and the second transit point on second track；According to first transit point, the second transit point, arrow coefficients to construct switchover condition is cut in introducing；The expression formula for calculating the switching parameter of switching curve according to the switchover condition for cutting arrow coefficient is introduced；Expression formula according to arrow coefficient reference value and the switching parameter is cut is determined with reference to switching curve and its commutated error；According to it is described with reference to switching curve commutated error adjustment described in cut arrow coefficient reference value, until it is described with reference to switching curve commutated error be less than or equal to preset value, using it is corresponding with reference to transfer curve as output switching curve.The present invention swears that coefficients to construct meets the switchover condition of second order geometry continuum, it can be achieved that the second order geometry continuum between any two ends track is transferred by introducing to cut.
Description
Technical field
The present invention relates to digital control system or robot trajectory's interpolation fields, turn more specifically to a kind of smooth trajectory
Connect method and system.
Background technology
In digital control processing or robot trajectory's movement, running orbit (such as cutter path of numerically-controlled machine tool) is not generally by
The full curve of same type is formed, such as straightway, arc section, spline curve section.These general curved sections at connecting points only
There is G0 continuously (i.e. 0 rank geometry continuum).When feed speed is by these connecting points, it will directional velocity is caused to be mutated, so as to
Cause impact, reduce processing quality.
In order to reduce impact, usable centripetal acceleration limits the feed speed at these connecting points.However, to cadion-acceleration
Degree size is limited, therefore the feed speed after limitation is generally very low, so as to which feed speed in process be caused frequently to carry out
Acceleration and deceleration reduce processing efficiency.
For the cutter path of continuous small line segment composition, different types of curve also can be used continuously to be connected these G0
Point is smoothly transferred, and to avoid impact, and significantly promotes the size of transition feed speed.Such as circular arc can be used to difference
The curve of type is smoothly transferred, and can obtain the running orbit of G1 continuous (1 rank geometry continuum) so that feed speed is not
Direction mutation can occur.But circular arc switching can not realize continual curvature, i.e. G2 is continuous (2 rank geometry continuum), therefore acceleration
It will appear mutation, cause soft impulse.
Occur to realize G2 continuously smooth forwarding methods later, such as using B-spline, Bezier spline, PH battens
Curve etc. by setting the control vertex at spline curve first and last end, can realize continual curvature.But although the above method solves
The G2 continuously smooths switching problem of continuous small line segment running orbit, but can not realize that the G2 continuously smooths between arbitrary trajectory are transferred,
As the G2 continuously smooths between straightway and arc section are transferred, the G2 continuously smooths between arc section and arc section are transferred, straight line
The G2 continuously smooths switching between the switching of G2 continuously smooths, arc section and spline curve section between section and spline curve section, sample
G2 continuously smooths switching between curved section and spline curve section etc..
Invention content
The technical problem to be solved in the present invention is, G2 between a variety of tracks can not be realized for above-mentioned smooth forwarding method
The problem of continuously smooth turns provides a kind of smooth trajectory forwarding method and system.
The technical solution that the present invention solves above-mentioned technical problem is to provide a kind of smooth trajectory forwarding method, is used to implement
The smooth switching of adjacent the first track and the second track, and there are one connecting points for first track and the second track tool；Institute
The method of stating includes the following steps：
Obtain the first transit point on first track and the second transit point on second track；
According to first transit point, the second transit point, arrow coefficients to construct switchover condition is cut in introducing；
The expression formula of the switching parameter of switching curve is obtained according to the switchover condition；
Swear that coefficient reference value and the expression formula of the switching parameter are determined with reference to switching curve and its commutated error according to cutting,
The commutated error is the minimum distance with reference to connecting points described in curve distance of transferring；
Arrow coefficient reference value is cut according to the commutated error adjustment with reference to switching curve, until described with reference to switching
The commutated error of curve is less than or equal to preset value, and corresponding reference is transferred curve as output switching curve.
In smooth trajectory forwarding method of the present invention, the switchover condition meets second order geometry continuum, and introduces
Cut arrow coefficient the switchover condition be：
Wherein, C (0) be transfer curve starting point, C ' (0) be transfer the origin of curve single order lead arrow, C " (0) be transfer song
The second order of line starting point leads arrow；C1(u1) for the first transit point in the first track, C1′(u1) it is the first transit point in the first track
Single order lead arrow, C1“(u1) for the second order of the first transit point in the first track lead arrow；C (1) be transfer curve terminal, C ' (1)
Single order for End of Curve of transferring leads the second order that arrow, C " (1) are switching End of Curve and leads arrow；C2(u2) for the in the second track
Two transit points, C2′(u2) for the single order of the second transit point in the second track lead arrow, C2“(u2) it is the second transit point in the second track
Second order lead arrow；C1 and c2 is cuts arrow coefficient.
In smooth trajectory forwarding method of the present invention, the switching parameter includes control vertex, described according to institute
The expression formula that switchover condition determines the switching parameter of switching curve is stated, including：
By 5 BeziersAs the expression formula of switching curve, wherein PiFor Bezier song
The control vertex of line C (u), B5,i(u) it is 5 Bezier basic functions, andWherein symbol
“！" represent that factorial calculates；
The table for the multiple control vertexs for obtaining the switching curve is calculated according to the switchover condition and 5 Beziers
Up to formula.
In smooth trajectory forwarding method of the present invention, the basis cuts arrow coefficient reference value and the switching parameter
Expression formula determine with reference to switching curve and its commutated error and according to it is described with reference to transfer curve commutated error adjust institute
State cut arrow coefficient reference value, until it is described with reference to switching curve commutated error be less than or equal to preset value, by corresponding reference
Curve of transferring is used as output switching curve, including：
(a1) it is corresponding more according to the expression formula acquisition of the reference value and the multiple control vertex of cutting arrow coefficient c1 and c2
It the reference value of a control vertex and is obtained according to the expression formula of the reference value of the multiple control vertex and the switching curve
With reference to switching curve, and the commutated error with reference to switching curve is calculated, then perform (a2)；
(a2) when the commutated error with reference to switching curve is more than the preset value, cut described in adjustment arrow coefficient c1 and
The reference value of c2, and return to step (a1), until the commutated error with reference to switching curve is less than or equal to the preset value
When, the corresponding reference switching curve of the reference value for cutting arrow coefficient c1 and c2 that final adjustment is obtained is as output switching curve.
In smooth trajectory forwarding method of the present invention, the reference for cutting arrow coefficient c1 and c2 in the step (a1)
The initial value of value is c1=c2=0.1；In the step (a2), by the reference value for cutting arrow coefficient c1 and c2 from small to large
Adjustment.
In smooth trajectory forwarding method of the present invention, the first transit point packet obtained on first track
It includes：
Use Numerical Methods Solve equationObtain the first geometric locus ginseng at the first transit point
Number u1, and according to the first geometric locus parameter u1Obtain the first transit point C1(u1), the C1' (u) is the one of the first track
Rank leads arrow, S1For the first preset length, and first length is on first track, and first transit point is to described
The length of connecting points, " | | | | " represent that vector field homoemorphism length calculates；
Second transit point obtained on second track includes：
Use Numerical Methods Solve equationObtain the second geometric locus at the second transit point
Parameter u2, and according to the second geometric locus parameter u2Obtain the first transit point C2(u2), the C2' (u) is the second track
Single order leads arrow, S2For the second preset length, and second length is first transit point to institute on second track
State the length of connecting points.
The present invention also provides a kind of smooth trajectory adapting system, it is used to implement the flat of the first adjacent track and the second track
It trackslips and connects, and there are one connecting points for first track and the second track tool；The adapting system include transit point acquiring unit,
Switchover condition construction unit, switching parameter of curve computing unit, commutated error computing unit and switching curve acquisition unit,
In：
The transit point acquiring unit, for obtaining the first transit point and second track on first track
On the second transit point；
The switchover condition construction unit, for according to first transit point, the second transit point, arrow coefficient structure to be cut in introducing
Make switchover condition；
The switching parameter of curve computing unit, for determining the switching parameter of switching curve according to the switchover condition
Expression formula；
The commutated error computing unit, for being determined according to the expression formula for cutting arrow coefficient reference value and the switching parameter
With reference to switching curve and its commutated error, the commutated error is the most low coverage with reference to connecting points described in curve distance of transferring
From；
The switching curve acquisition unit, for cutting arrow system according to the commutated error adjustment with reference to switching curve
Number reference value, until the commutated error with reference to switching curve is less than or equal to preset value, and will be corresponding bent with reference to switching
Line is as output switching curve.
In smooth trajectory adapting system of the present invention, the switchover condition of the switchover condition construction unit construction is expired
Sufficient second order geometry continuum, and the switchover condition introduced after cutting arrow coefficient is：
Wherein, C (0) be transfer curve starting point, C ' (0) be transfer the origin of curve single order lead arrow, C " (0) be transfer song
The second order of line starting point leads arrow；C1(u1) for the first transit point in the first track, C1′(u1) it is the first transit point in the first track
Single order lead arrow, C1“(u1) for the second order of the first transit point in the first track lead arrow；C (1) be transfer curve terminal, C ' (1)
Single order for End of Curve of transferring leads the second order that arrow, C " (1) are switching End of Curve and leads arrow；C2(u2) for the in the second track
Two transit points, C2′(u2) for the single order of the second transit point in the second track lead arrow, C2“(u2) it is the second transit point in the second track
Second order lead arrow；C1 and c2 is cuts arrow coefficient.
In smooth trajectory adapting system of the present invention, the switching parameter includes control vertex, and the switching is bent
Line parameter calculation unit is by 5 BeziersAs the expression formula of switching curve, wherein PiFor shellfish
The control vertex of Sai Er curve C (u), B5,i(u) it is 5 Bezier basic functions, andWherein
Symbol "！" represent that factorial calculates, and calculated according to the switchover condition and 5 Beziers and obtain the more of the switching curve
The expression formula of a control vertex.
In smooth trajectory adapting system of the present invention, the switching curve acquisition unit unit turns in the reference
The reference value of arrow coefficient is cut when connecing the commutated error of curve more than the preset value described in adjustment, until described with reference to switching curve
Commutated error be less than or equal to the preset value when, using it is described with reference to transfer curve as output switching curve.
The smooth trajectory forwarding method and system of the present invention swears that coefficients to construct meets second order geometry continuum by introducing to cut
Switchover condition, it can be achieved that between any two ends track second order geometry continuum switching, and make switching curve meet switching required precision,
And the computational efficiency of the present invention is high, curve shape adjustment is simple.
Description of the drawings
Fig. 1 is the schematic diagram of smooth trajectory forwarding method embodiment of the present invention；
Fig. 2 is the schematic diagram of the first track to be transferred and the second track；
Fig. 3 is the schematic diagram of switching curve generated by smooth trajectory forwarding method of the present invention；
Fig. 4 be by smooth trajectory forwarding method of the present invention generate switching curve it is adjusted after schematic diagram；
Fig. 5 is the schematic diagram of smooth trajectory adapting system embodiment of the present invention.
Specific embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, it is right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.
As shown in Figure 1, it is the schematic diagram of smooth trajectory forwarding method embodiment of the present invention, which can
The smooth switching of the first adjacent track and the second track is used to implement, and there are one be connected for the first track and the second track tool
Point.It is below object with the first track 21 of two sections of linkings, the second track 22 on X/Y plane shown in Fig. 2, to the method for the present invention
It is described in detail, wherein it is O that above-mentioned first track 21, which can be the center of circle,1=(0,0,0), the circular arc that radius is 10mm；Second rail
Mark 22 can be that the center of circle is O2=(20,0,0), the circular arc that radius is 15mm, the first track 21,22 connecting points of the second track are A=
(6.8750,7.2618,0)。
The smooth trajectory forwarding method of the present invention of the present embodiment includes the following steps：
Step S1：The first transit point is obtained from the first track 21 and from the second track 22 and the second transit point.In reality
In, above-mentioned first track, 21 and second track 22 can also be straightway or spline curve section etc. other than being circular arc.
Above-mentioned first track 21 is represented by C1(u), the second track 22 can be C2(u), wherein parameter u is variable, and is taken
Value is ranging from [0,1].The connecting points A of first track 21 and the second track 22 is both the terminal and the second rail of the first track 21
The starting point of mark 22, i.e. A=C1(1)=C2(0)。
In this step, can be according on the first track, length (the first preset length S of the first transit point to connecting points A1)
To obtain the first transit point.Specifically, the first transit point can be obtained from the first track 21 in the following manner：Use numerical value side
Method solves equationObtain the parameter of curve u at the first transit point1, and according to parameter of curve u1Obtain the
One transit point C1(u1), above-mentioned C1' (u) is that the single order of the first track leads arrow, S1For the first preset length, " | | | | " represent vector
Mould length calculate.
Similarly, can be according on the second track, length (the second preset length S of the second transit point to connecting points A2) obtain
Take the second transit point.Specifically, the second transit point can be obtained from the second track 22 in the following manner：It is asked using numerical method
It solves equationObtain the parameter of curve u at the second transit point2, and obtained according to the parameter of curve
First transit point C2(u2), the C2' (u) is that the single order of the second track leads arrow, S2For the second preset length.
Above-mentioned first preset length S1With the second preset length S2It can be set, such as the first track by distance coefficient of transferring
21 and second the length of track 22 be respectively l1And l2, then the switching distance S on the first track 211For S1=0.5a1l1, the second rail
Switching distance S on mark 222For S2=0.5a2l2, wherein a1 and a2 are switching distance coefficient, and value range is [0,1], separately
The first preset length S also can be directly set outside1With the second preset length S2Value.
Such as two sections of circular arcs shown in Fig. 2, S can be set1=S2=1mm, then corresponding first transit point is C1(u1)
=(6.1157,7.9119,0), the second transit point are C2(u2)=(7.3879,8.1201,0).
Step S2：According to the first transit point and the second transit point, arrow coefficients to construct switchover condition is cut in introducing.
In this step, the first transit point C can be first calculated respectively1(u1) at curve C1(u) single order leads arrow C '1(u1) and two
Rank leads arrow C "1(u1) and the second transit point C2(u) place's curve C2(u) single order leads arrow C '2(u2) and second order lead arrow C "2(u2)。
Such as both ends circular arc shown in Fig. 2, C ' is calculated1(u1)=(7.9119, -6.1157,0), C "1(u1)=(-
6.1157,-7.9119,0)、C′2(u2)=(8.1201,12.6121,0) and C "2(u2)=(12.6121, -8.1201,0).
Then it is C (u) to enable switching curve, and the wherein value range of parameter u is [0,1], to realize second order geometry continuum, is needed
Meet following three conditions
(1) the position condition of continuity, i.e.,：
C (0)=C1(u1), C (1)=C2(u2) (1)
(2) the arrow condition of continuity is cut：
(3) continual curvature condition：
Wherein, C (0) is the starting point of switching curve, and C ' (0) is that the single order of switching origin of curve position leads arrow, C " (0) to turn
The second order for connecing the origin of curve leads arrow；C (1) is the terminal of switching curve, and C ' (1) is that the single order of switching End of Curve leads arrow, C " (1)
Second order for End of Curve of transferring leads arrow.
Then for above three condition, arrow coefficient c is cut in introducing1And c2, and the single order at switching curve first and last end is enabled to lead arrow point
It is not：
C ' (0)=c1C′1(u1), C ' (1)=c2C′2(u2) (4)
Understand that cutting arrow condition of continuity perseverance sets up according to formula (2).And according to formula (3), then to ensure continual curvature condition perseverance into
Vertical, the second order at switching curve first and last end, which leads arrow, to be respectively：
It can must then meet the switching curve head end conditions of second order geometry continuum switchover condition according to formula (1), (4) and (5)
Meet：
Step S3：The expression formula of the switching parameter of switching curve is calculated according to the switchover condition of above-mentioned construction.
In this step, by 5 BeziersAs the expression formula of switching curve, wherein Pi
For the control vertex of Bezier C (u), B5,i(u) it is 5 Bezier basic functions, and
Wherein symbol "！" represent that factorial calculates.Switching parameter at this time includes control vertex, and the expression formula of corresponding switching parameter is
The expression formula of control vertex.Above-mentioned Bezier has Properties of Vertices control as follows：
Then the table for the multiple control vertexs for obtaining switching curve is calculated according to above-mentioned switchover condition and 5 Beziers
Up to formula, i.e., it is according to can must the transfer expression formula of control vertex of curve of formula (6) and formula (7)：
Step S4：Expression formula according to arrow coefficient reference value and parameter of transferring is cut determines to miss with reference to switching curve and its switching
Difference, above-mentioned commutated error are the minimum distance with reference to the curve distance connecting points A that transfers, i.e. commutated error
In the step, corresponded to first according to the expression formula calculating of the reference value and multiple control vertexs of cutting arrow coefficient c1 and c2
Multiple control vertexs reference value and referred to according to the expression formula of the reference values of multiple control vertexs and switching curve
Switching curve, and calculate the minimum distance with reference to switching curve distance connecting points A；The minimum distance obtained is being calculated more than default
During value, the reference value of arrow coefficient c1 and c2 is cut in adjustment, and is calculated again corresponding with reference to the nearest of switching curve distance connecting points A
Distance, so adjustment once or for several times (also can not be adjusted and directly meet minimum distance condition), until above-mentioned minimum distance
During less than or equal to preset value, switching curve will be referred to as switching curve.
Such as it is c1=c2=0.1, and substitute into the control of formula (8) that can first take the initial value of the reference value for cutting arrow coefficient c1 and c2
The reference value that the expression formula on vertex processed obtains multiple control vertexs is：
Above-mentioned control is pinpointed into P0、P1、P2、P3、P4、P5It substitutes into 5 Beziers and can obtain corresponding reference switching
Curve, this is signified with reference to the label 31 in switching curve such as Fig. 3.
This season is C (u with reference to point nearest apart from connecting points A on switching curve C (u)x), then commutated error for ε=| | C
(ux)-A | |, if with reference to point C (u on switching curve C (u)x) at 1 rank lead arrow as C ' (ux), then meet equation<C′(ux),C
(ux)-A>=0, wherein symbol "<>" represent that the scalar product of vector calculates.
In order to calculate ux, using Newton Algorithm Equation f (x)=<C′(ux),C(ux)-A>=0, select unknown quantity ux's
Initial value is calculated asIterative calculating is iterated using following：
Until
U at this timex=uj+1.Wherein ujAnd uj+ 1 be respectively jth and j+1 iteration result, C ' (uj) and C " (uj) it is respectively with reference to switching
Parameter u on curve C (u)jThe single order at place leads resultant second order and leads arrow, and σ is iteration precision.Iterative initial value is hereinEnable iteration precision σ=10-6, C (u are finally calculatedx)=C (0.5385)=(6.8146,
7.7271,0), then commutated error is ε=0.4692mm.
Step S5：Arrow coefficient reference value is cut according to the commutated error adjustment with reference to switching curve, until with reference to curve of transferring
Commutated error be less than or equal to preset value, using it is corresponding with reference to transfer curve as output switching curve.
In step s 4, if the preset value of maximum commutated error is εmaxTurn of=0.3mm, at this time (i.e. c1=c2=0.1)
Connect error ε>εmax, need to adjust and cut arrow coefficient c1=0.2 and c2=0.15, and substitute into the expression of the control vertex of formula (8) again
Formula, the reference value for calculating acquisition control vertex are：
Above-mentioned control is pinpointed into P0、P1、P2、P3、P4、P5It substitutes into 5 Beziers and can obtain corresponding reference switching
Curve, this is signified with reference to the label 41 in switching curve such as Fig. 4, and corresponding commutated error is recalculated as ε according to above method
=0.266mm≤εmax, meet required precision with reference to switching curve at this time, you can above-mentioned reference is transferred into curve as final
Output transfer curve to control device export.Control device can correspond to equipment operation according to output switching curve controlled.
It particularly, need to be since one small to adjusting, and make by apart from connecting points A big when cut arrow coefficient adjustment
Four control vertexs recently (such as the control vertex P in Fig. 31、P2、P3、P4) polygon that forms for convex polygon, avoids
Curve of transferring distorts.
As shown in figure 5, being the schematic diagram of smooth trajectory adapting system embodiment of the present invention, which is used to implement adjacent
First track and the smooth switching of the second track, and there are one connecting points for the first track and the second track tool.The rail of the present embodiment
The smooth adapting system of mark include transit point acquiring unit 51, switchover condition construction unit 52, switching parameter of curve computing unit 53,
Commutated error computing unit 54 and switching curve acquisition unit 55, and above-mentioned transit point acquiring unit 51, switchover condition are built
Unit 52, switching parameter of curve computing unit 53, commutated error computing unit 54 and switching curve acquisition unit 55 can be by depositing
It is stored in memory and can be made of the instruction that processor performs.
Above-mentioned transit point acquiring unit 51 is for the first track C of acquisition1(u) the first transit point C on1(u1) and the second rail
Mark C2(u) the second transit point C on2(u2).It specifically, can be according in the first track C1(u) on, the first transit point C1(u1) extremely hold in the mouth
The length (i.e. the first preset length) of contact A obtains the first transit point and according in the second track C2(u) on, second turn
Contact C2(u2) obtain the second transit point C to the length (i.e. the second preset length) of connecting points A2(u2)。
Switchover condition construction unit 52 for calculate respectively the first transit point single order lead resultant second order lead arrow and second turn
The single order of junction leads resultant second order and leads arrow, and passes through introducing and cut arrow coefficients to construct switchover condition.Specifically, through switchover condition structure
The switchover condition for building the construction of unit 52 meets second order geometry continuum, and the switchover condition introduced after cutting arrow coefficient can be：
Wherein, C (0) is the starting point of switching curve, and C ' (0) is that the single order of switching origin of curve position leads arrow, C " (0) to turn
The second order for connecing the origin of curve leads arrow；C1(u1) for the first transit point in the first track, C1′(u1) it is first turn in the first track
The single order of contact leads arrow, C1“(u1) for the second order of the first transit point in the first track lead arrow；C (1) be transfer curve terminal, C '
(1) be transfer End of Curve single order lead arrow, C " (1) be switching End of Curve second order lead arrow；C2(u2) in the second track
Second transit point, C2′(u2) for the single order of the second transit point in the second track lead arrow, C2“(u2) transfer in the second track second
The second order of point leads arrow；C1 and c2 is cuts arrow coefficient.
Parameter of curve of transferring computing unit 53 is used to obtain the expression formula of the switching parameter of switching curve according to switchover condition.
Specifically, the switching parameter of curve computing unit 53 is by 5 BeziersAs switching curve
Expression formula, wherein PiControl vertex (control vertex as switching parameter at this time, parameter of transferring for Bezier C (u)
Expression formula is the expression formula of control vertex), B5,i(u) it is 5 Bezier basic functions, and
Wherein symbol "！" represent that factorial calculates, and the multiple controls for obtaining switching curve are calculated according to switchover condition and 5 Beziers
The expression formula on vertex processed.
Commutated error computing unit 54 turns for determining to refer to according to the expression formula for cutting arrow coefficient reference value and parameter of transferring
Curve and its commutated error are connect, commutated error is with reference to switching curve distance connecting points (the i.e. rank of the first track and the second track
Contact) minimum distance.Specifically, when switching parameter of curve computing unit 53 is using 5 Beziers as switching curve
During expression formula, the expression formula on the expression formula of parameter of transferring vertex in order to control.
Specifically, which uses the reference value and multiple control vertexs for cutting arrow coefficient c1 and c2
Expression formula obtains corresponding multiple control vertex reference values and according to the reference value of multiple control vertexs and the table of switching curve
It is obtained up to formula with reference to switching curve, and calculates the minimum distance with reference to switching curve distance connecting points.
Switching curve acquisition unit 55 is used to cut arrow coefficient reference value according to the commutated error adjustment with reference to switching curve, directly
The commutated error of reference switching curve cut corresponding to arrow coefficient reference value after to adjustment is less than or equal to the preset value, and
Corresponding reference is transferred into curve as output switching curve.
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art in the technical scope disclosed by the present invention, the change or replacement that can be readily occurred in,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of the claims
Subject to.
Claims (10)
1. a kind of smooth trajectory forwarding method is used to implement the smooth switching of the first adjacent track and the second track, and described
There are one connecting points for first track and the second track tool；It is characterized in that, it the described method comprises the following steps：
Obtain the first transit point on first track and the second transit point on second track；
According to first transit point, the second transit point, arrow coefficients to construct switchover condition is cut in introducing；
The expression formula of the switching parameter of switching curve is determined according to the switchover condition；
Expression formula according to arrow coefficient reference value and the switching parameter is cut is determined with reference to switching curve and its commutated error, described
Commutated error is the minimum distance with reference to connecting points described in curve distance of transferring；
Arrow coefficient reference value is cut according to the commutated error adjustment with reference to switching curve, until described with reference to switching curve
Commutated error be less than or equal to preset value, using it is corresponding with reference to transfer curve as output switching curve.
2. smooth trajectory forwarding method according to claim 1, which is characterized in that the switchover condition meets second order geometry
Continuously, and introduce cut arrow coefficient the switchover condition be：
Wherein, C (0) is the starting point of switching curve, and C ' (0) is that the single order of the switching origin of curve leads arrow, and C " for switching curve rise by (0)
The second order of point leads arrow；C1(u1) for the first transit point in the first track, C1′(u1) it is one of the first transit point in the first track
Rank leads arrow, C1“(u1) for the second order of the first transit point in the first track lead arrow；C (1) is the terminal of switching curve, and C ' (1) is turns
The single order for connecing End of Curve leads arrow, and " (1) is that the second order of switching End of Curve leads arrow to C；C2(u2) for second turn in the second track
Contact, C2′(u2) for the single order of the second transit point in the second track lead arrow, C2“(u2) it is two of the second transit point in the second track
Rank leads arrow；C1 and c2 is cuts arrow coefficient.
3. smooth trajectory forwarding method according to claim 1 or 2, which is characterized in that the switching parameter includes control
Vertex, the expression formula of the switching parameter that switching curve is determined according to the switchover condition, including：
By 5 BeziersAs the expression formula of switching curve, wherein PiFor Bezier C
(u) control vertex, B5, i(u) it is 5 Bezier basic functions, andWherein symbol "！" table
Show that factorial calculates；
The expression for the multiple control vertexs for obtaining the switching curve is calculated according to the switchover condition and 5 Beziers
Formula.
4. smooth trajectory forwarding method according to claim 3, which is characterized in that the basis cut arrow coefficient reference value and
The expression formula of the switching parameter determines with reference to curve of transferring to turn with reference to switching curve and its commutated error and according to described
Connect cut described in error transfer factor arrow coefficient reference value, until it is described with reference to switching curve commutated error be less than or equal to preset value,
Using it is corresponding with reference to transfer curve as output switching curve, including：
(a1) according to the corresponding multiple controls of expression formula acquisition for the reference value and the multiple control vertex for cutting arrow coefficient c1 and c2
It the reference value on vertex processed and is referred to according to the expression formula of the reference value of the multiple control vertex and the switching curve
Switching curve, and calculate the commutated error with reference to switching curve；
(a2) when the commutated error with reference to switching curve is more than the preset value, arrow coefficient c1 and c2 are cut described in adjustment
Reference value, and return to step (a1), will when the commutated error with reference to switching curve is less than or equal to the preset value
What final adjustment obtained cuts the corresponding reference switching curve of reference value of arrow coefficient c1 and c2 as output switching curve.
5. smooth trajectory forwarding method according to claim 4, which is characterized in that cut arrow coefficient in the step (a1)
The initial value of the reference value of c1 and c2 is c1=c2=0.1；In the step (a2), by the ginseng for cutting arrow coefficient c1 and c2
Value is examined to adjust from small to large.
6. smooth trajectory forwarding method according to claim 1, which is characterized in that described to obtain on first track
First transit point includes：
Use Numerical Methods Solve equationObtain the first geometric locus parameter u at the first transit point1,
And according to the first geometric locus parameter u1Obtain the first transit point C1(u1), C1' (u) is that the single order of the first track leads arrow, S1
For the first preset length, and first length is first transit point to the connecting points on first track
Length, " | | | | " represent that vector field homoemorphism length calculates；
Second transit point obtained on second track includes：
Use Numerical Methods Solve equationObtain the second geometric locus parameter at the second transit point
u2, and according to the second geometric locus parameter u2Obtain the first transit point C2(u2), C2' (u) is that the single order of the second track leads arrow,
S2For the second preset length, and second length is first transit point to the connecting points on second track
Length.
7. a kind of smooth trajectory adapting system is used to implement the smooth switching of the first adjacent track and the second track, and described
There are one connecting points for first track and the second track tool；It is characterized in that, the adapting system includes transit point acquiring unit, turns
Narrow bars part construction unit, switching parameter of curve computing unit, commutated error computing unit and switching curve acquisition unit,
In：
The transit point acquiring unit, for obtaining on the first transit point and second track on first track
Second transit point；
The switchover condition construction unit, for according to first transit point, the second transit point, introducing to be cut arrow coefficients to construct and turned
Narrow bars part；
The switching parameter of curve computing unit, for determining the expression of the switching parameter of switching curve according to the switchover condition
Formula；
The commutated error computing unit, for determining to refer to according to the expression formula for cutting arrow coefficient reference value and the switching parameter
Switching curve and its commutated error, the commutated error are the minimum distance with reference to connecting points described in curve distance of transferring；
The switching curve acquisition unit, for cutting arrow coefficient ginseng according to the commutated error adjustment with reference to switching curve
Value is examined, until the commutated error with reference to switching curve is less than or equal to the preset value, and will be corresponding bent with reference to switching
Line is as output switching curve.
8. smooth trajectory adapting system according to claim 6, which is characterized in that the switchover condition construction unit construction
Switchover condition meet second order geometry continuum, and the switchover condition introduced after cutting arrow coefficient is：
Wherein, C (0) is the starting point of switching curve, and C ' (0) is that the single order of the switching origin of curve leads arrow, and C " for switching curve rise by (0)
The second order of point leads arrow；C1(u1) for the first transit point in the first track, C1′(u1) it is one of the first transit point in the first track
Rank leads arrow, C1“(u1) for the second order of the first transit point in the first track lead arrow；C (1) is the terminal of switching curve, and C ' (1) is turns
The single order for connecing End of Curve leads arrow, and " (1) is that the second order of switching End of Curve leads arrow to C；C2(u2) for second turn in the second track
Contact, C2′(u2) for the single order of the second transit point in the second track lead arrow, C2“(u2) it is two of the second transit point in the second track
Rank leads arrow；C1 and c2 is cuts arrow coefficient.
9. smooth trajectory adapting system according to claim 7 or 8, which is characterized in that the switching parameter includes control
Vertex, the switching parameter of curve computing unit is by 5 BeziersTable as switching curve
Up to formula, wherein PiFor the control vertex of Bezier C (u), B5, i(u) it is 5 Bezier basic functions, andWherein symbol "！" represent that factorial calculates, and according to the switchover condition and 5 Bezier
Curve calculates the expression formula for the multiple control vertexs for obtaining the switching curve.
10. smooth trajectory adapting system according to claim 9, which is characterized in that the switching curve acquisition unit exists
The reference value of arrow coefficient is cut when the commutated error with reference to switching curve is more than the preset value described in adjustment, until the ginseng
When examining the commutated error of switching curve less than or equal to the preset value, the reference is transferred into curve as output switching song
Line.
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