CN109164759A - Curve interpolating method, equipment and computer readable storage medium - Google Patents
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Abstract
本发明提供了一种曲线插补方法、设备及计算机可读存储介质，所述曲线插补方法，包括：根据待处理轨迹曲线上的起点、终点以及位于所述起点和终点之间的N‑1个取样点创建引导数组，所述引导数组中的N+1个值分别对应所述起点至起点、起点至各个取样点、起点至终点的弧长，其中N为整数；对所述待处理轨迹曲线进行速度规划，获得所述待处理轨迹曲线上各点的弧长关于时间t的弧长时间函数；依次根据所述引导数组、弧长时间函数、前一插补周期的插补参数及对应的弧长，计算后一插补周期的插补参数。本发明可以对任意参数化曲线以弧长进行插补，使进给速度规划路径距离与实际插补路径距离一致，在实际应用中可使各轴运动更加平稳精确。
The present invention provides a curve interpolation method, a device and a computer-readable storage medium. The curve interpolation method includes: according to the starting point, the ending point on the to-be-processed trajectory curve, and the N-point between the starting point and the ending point. 1 sampling point to create a guide array, and N+1 values in the guide array correspond to the arc length from the starting point to the starting point, the starting point to each sampling point, and the starting point to the end point, where N is an integer; Carry out speed planning on the trajectory curve, and obtain the arc length function of the arc length of each point on the trajectory curve to be processed with respect to time t; Corresponding arc length, calculate the interpolation parameters of the next interpolation cycle. The invention can interpolate any parameterized curve with arc length, so that the distance of the planned path of the feed speed is consistent with the distance of the actual interpolation path, and the movement of each axis can be more stable and accurate in practical application.
Description
Technical field
The present invention relates to automation fields, can more specifically to a kind of curve interpolating method, equipment and computer
Read storage medium.
Background technique
Parametric curve interpolation technique is used by more and more commercial digital control systems or robot control system, these
Even if system does not provide the personal code work of parametric curve interpolation directly, also rail can be carried out using parametric curve in internal system
Mark is smooth, therefore is directed to the Interpolation Process of parametric curve.
Precision is followed in order to improve the track of system, speed is carried out using the preceding plus-minus short-cut counting method generally before locus interpolation
Planning obtains rate curve, then obtains the interpolation distance in a cycle in each interpolation cycle and carries out locus interpolation.At present
Existing general parameter curve interpolating method includes Taylor expansion, feedback interpolation and polynomial fitting method.Taylor expansion
Method calculates new interpolation parameters by building feed speed, parameter of curve and the relationship of time, wherein applying at most is one
Rank and the second Taylor series method；Feedback interpolation ensures the distance between adjacent interpolated point and planning distance one by iterative calculation
It causes；Polynomial fitting method realizes height by pre-generating a large amount of piecewise polynomial functions between parameter of curve and interpolation distance
Accuracy computation.
At present in parametric curve interpolation, the accuracy of interpolating method, i.e. phase are usually judged using velocity perturbation as standard
Deviation between the distance between neighbor interpolation point and planning distance accounts for the percentage of planning distance.Therefore above-mentioned interpolating method all with
This standard carries out interpolation algorithm design, makes every effort to minimum velocity perturbation.
However, using the arc length of geometric locus as path distance when due to carrying out feed speed planning, and with low velocity
Fluctuation is that the existing interpolating method of target is actually to carry out interpolation with chord length, this results in feed speed planning distance and reality
(arc length distance is greater than chord length distance) inconsistent between distance, hangover can be caused existing to ensure that current path interpolation finishes
As velocity jump can be caused if directly carrying out next section of locus interpolation if ignoring the deviation.
Summary of the invention
The technical problem to be solved in the present invention is that cannot be considered in terms of hangover and speed for above-mentioned parameter curve interpolating scheme
The problem of degree mutation, provide a kind of curve interpolating method, equipment and computer readable storage medium.
The technical solution that the present invention solves above-mentioned technical problem is to provide a kind of curve interpolating method, comprising:
According to starting point, terminal and the N-1 sampling between the beginning and end on geometric locus to be processed
Point creation guidance array, the N+1 value guided in array respectively correspond the starting point and take to starting point, the starting point to each
The arc length of sampling point, the starting point to the end, wherein N is integer；
Speed planning is carried out to the geometric locus to be processed, the arc length for obtaining each point on the geometric locus to be processed is closed
In the arc length function of time of time t；
Successively according to the guidance array, the arc length function of time, the interpolation parameters of previous interpolation cycle and corresponding
Arc length calculates the interpolation parameters of latter interpolation cycle.
In curve interpolating method of the present invention, in the geometric locus to be processed, the starting point, N-1 sampling
The parameter of geometric locus to be processed corresponding to point and terminal constitutes arithmetic progression.
In curve interpolating method of the present invention, it is described according to the guidance array, it is the arc length function of time, preceding
The interpolation parameters of one interpolation cycle and corresponding arc length, the interpolation parameters for calculating latter interpolation cycle include:
(a) according to the interpolation parameters of previous interpolation cycle, corresponding first arc length of previous interpolation cycle, latter interpolation cycle
Value in corresponding second arc length and the guidance array, obtains interpolation a reference value and arc length increment；
(b) the interpolation parameters discreet value of latter interpolation cycle is calculated according to the interpolation a reference value, and is calculated described wait locate
Manage the absolute value of the interpolation a reference value on geometric locus to the arc length between the interpolation parameters discreet value of latter interpolation cycle；
(c) according in the interpolation parameters discreet value of the latter interpolation cycle and the geometric locus to be processed
Interpolation a reference value to the arc length between the interpolation parameters discreet value of latter interpolation cycle constructs multinomial；
(d) interpolation parameters in latter period are determined according to the arc length increment and the multinomial.
In curve interpolating method of the present invention, corresponding first arc length of the previous interpolation cycle is inserted according to previous
It mends corresponding time in period and the arc length function of time is calculated and obtained, corresponding second arc length of the latter interpolation cycle is according to latter
Interpolation cycle corresponding time and the arc length function of time, which calculate, to be obtained；
The guidance array includes multiple numerical intervals, and each numerical intervals are made of two adjacent values, described
In step (a): described if the value of first arc length and the second arc length is located in the same numerical intervals of the guidance array
Interpolation a reference value is the interpolation parameters of the previous interpolation cycle, and the arc length increment is the difference of the second arc length and the first arc length；
Otherwise, the interpolation a reference value is the parameter of value L [m] corresponding geometric locus to be processed, and the arc length increment is described second
The difference of arc length and value L [m], wherein described value L [m] is the starting point of the numerical intervals of the guidance array where the second arc length, and 0≤
m≤N。
In curve interpolating method of the present invention, the step (b) includes:
(b1) 1 to the k rank for calculating the geometric locus to be processed at interpolation a reference value leads arrow, and the k is whole greater than zero
Number；
(b2) the interpolation parameters discreet value of latter interpolation cycle is calculated using k rank Taylor expansion；
(b3) it calculates 1 to k rank of the geometric locus to be processed at discreet value and leads arrow, and institute is calculated using numerical integration method
It is absolute to the arc length between the interpolation parameters discreet value of latter interpolation cycle to state interpolation a reference value on geometric locus to be processed
Value.
In curve interpolating method of the present invention, in the step (b2):
When the k is 1, the interpolation parameters discreet value u of the latter interpolation cyclepIt is obtained by the calculating of following calculating formula
:" | | | | " indicate the long calculating of vector field homoemorphism, ubFor interpolation a reference value, △ sbFor arc length increasing
Amount, C ' (ub) it is that single order of the geometric locus to be processed at interpolation a reference value leads arrow；
When the k is 2, the interpolation parameters discreet value u of the latter interpolation cyclepIt is obtained by the calculating of following calculating formula
:"<>" indicates that the scalar product of vector calculates, C " (ub) be to
It handles second order of the geometric locus at interpolation a reference value and leads arrow；
When the k is 3, the interpolation parameters discreet value u of the latter interpolation cyclepIt is obtained by the calculating of following calculating formula
:
C″′(ub) it is that three ranks of the geometric locus to be processed at interpolation a reference value lead arrow.
Multinomial in curve interpolating method of the present invention, in the step (c) are as follows:
And the multinomial meets:
WhereinJth order derivative of the parameter u about arc length parameters s for indicating geometric locus C (u) to be processed, works as j=
It is calculated when 1,2,3 are as follows:
C ' (u) is that single order of the geometric locus C (u) to be processed at parameter u leads arrow, C, and " (u) is geometric locus C to be processed
(u) second order at parameter u leads arrow and C " ' (u) is that three ranks of the geometric locus C (u) to be processed at parameter u lead arrow；
aiFor multinomial coefficient, and in k=1:
In k=2:
In k=3:
In curve interpolating method of the present invention, numerical integration is respectively adopted in N+1 value in the guidance array
Algorithm, which calculates, to be obtained.
The present invention also provides a kind of curve interpolating equipment, including memory and processor, being stored in the memory can
The computer program run on the processor, which is characterized in that the processor is realized when executing the computer program
The step of method as described above.
The present invention also provides a kind of computer readable storage medium, computer program, institute are stored on the storage medium
When stating computer program and being executed by processor, the step of realizing method as described above.
Curve interpolating method, equipment and computer readable storage medium of the invention can be with by carrying out interpolation with arc length
Interpolation is carried out with arc length to arbitrary parameter curve, keeps feed speed planning path distance consistent with practical interpolation path distance,
So as to avoid existing using low velocity fluctuation as hangover or velocity jump problem existing for the interpolating method of target, in practical application
In keep the movement of each axis more steady accurate.
The present invention also has many advantages, such as that space efficiency is high, computational accuracy is high, computational efficiency is high.
Detailed description of the invention
Fig. 1 is the flow diagram of curve interpolating method embodiment of the present invention；
Fig. 2 is the flow diagram that the interpolation parameters of latter interpolation cycle are obtained in curve interpolating method of the present invention；
Fig. 3 is the schematic diagram of 5 bezier curves to be processed；
Fig. 4 is showing corresponding to the arc length function of time of the geometric locus to be processed of Fig. 3 in curve interpolating method of the present invention
It is intended to；
Fig. 5 is to rule when using curve interpolating method of the present invention to geometric locus interpolation to be processed shown in Fig. 3 shown in Fig. 3
Deviation schematic diagram between long and interpolation arc length of making an arc；
Fig. 6 is the schematic diagram of curve interpolating apparatus embodiments of the present invention.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, with reference to the accompanying drawings and embodiments, 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, being the schematic diagram of curve interpolating method embodiment of the present invention, this method can be to arbitrary parameter curve
Interpolation is carried out, and eliminates the deviation between feed speed planning path distance and Actual path distance.Method in the present embodiment
It specifically includes:
S1: according to geometric locus C (u) to be processed (u ∈ [us,ue]) on starting point, terminal and be located at beginning and end it
Between the creation of N-1 sample point include N+1 value guidance array L, in above-mentioned guidance array L, the 1st value L [1] is wait locate
The starting point of geometric locus C (u) is managed to the arc length (i.e. 0) of starting point, a value L [i+1] of i+1 (i=1,2 ..., N-1) is to be processed
For the starting point of geometric locus C (u) to the arc length of i-th of sample point, the last one value L [N+1] is geometric locus C (u) to be processed
The arc length of starting point to the end, wherein N is integer.Above-mentioned N can be arranged according to arc length, control accuracy requirement of C (u) etc..
In above-mentioned geometric locus C (u) to be processed, u is parameter, i.e. independent variable, usFor the corresponding parameter of starting point, ueFor terminal
Corresponding parameter.To reduce computation complexity, track to be processed corresponding to above-mentioned starting point, N-1 sample point and terminal is bent
The parameter of line C (u) constitutes arithmetic progression.
Specifically, N+1 arc length in above-mentioned guidance array is respectively adopted numerical integration algorithm and calculates acquisition.Certainly, on
Stating arc length can also be used other modes calculating acquisition.
Such as when geometric locus to be processed is that 5 bezier curve C (u) shown in Fig. 3 (u ∈ [0,1]) (Betsy that is bent
The control vertex sequence of line are as follows: (6.1731656763491,0,0), and (10,0,0), (10,0,0), (10,
1.54287027426666,0),(10.6001836626339,2.6712514744994,0),(11.4644660940673,
3.53553390593274,0)), can use N=4, and create guidance array L=0,2.9426958,4.2247336,
5.63402696 7.1577073 }.
Step S2: carrying out speed planning to geometric locus C (u) to be processed, obtains each on the geometric locus C (u) to be processed
Arc length function of time s (t) (t > 0) of the arc length of point about time t.
In this step, trapezoidal or S type or other rate curve planing methods specifically can be used to geometric locus C to be processed
(u) speed planning is carried out.For 5 bezier curve C (u) shown in Fig. 3 (u ∈ [0,1]), arc length function of time s (t) is such as
Shown in Fig. 4.
Step S3: successively according to guidance array L, arc length function of time s (t), the interpolation parameters of previous interpolation cycle and right
The arc length answered calculates the interpolation parameters of latter interpolation cycle.In this step, the starting point of geometric locus C (u) to be processed can be made
For first interpolated point, and subsequent interpolated point is successively obtained, until the interpolated point of acquisition reaches geometric locus C (u) to be processed
Terminal or terminal outside.
As shown in Fig. 2, being the process signal for obtaining the interpolation parameters of latter interpolation cycle in curve interpolating method of the present invention
Figure, this method specifically includes the following steps:
Step S31: according to the interpolation parameters of previous interpolation cycle, corresponding first arc length of previous interpolation cycle, it is latter insert
The value (arc length) in period corresponding second arc length and guidance array is mended, interpolation a reference value u is obtainedbWith arc length increment Delta sb。
Specifically, above-mentioned first arc length specifically can (time can be according to interpolation according to the previous interpolation cycle corresponding time
Period calculates) and step S2 in the arc length function of time s (t) that obtains calculate and obtain, the second arc length then can be according to latter interpolation week
Phase corresponding time and arc length function of time s (t), which are calculated, to be obtained.
Guiding array includes multiple numerical intervals, and each numerical intervals are made of two adjacent values, in this step,
If the value of the first arc length and the second arc length is located in the same numerical intervals of guidance array, interpolation a reference value is previous interpolation week
The interpolation parameters of phase, arc length increment Delta sbFor the difference of the second arc length and the first arc length；Otherwise, interpolation a reference value ubIt is right for value L [m]
The parameter for the geometric locus to be processed answered, arc length increment Delta sbFor the second arc length and value L [m] difference (value of the second arc length between
It guides between the value L [m] and value L [m+1] in array).Above-mentioned value L [m] is m-th of the value guided in array, and L [m+1] is to draw
The m+1 value in derivative group, and 0≤m≤N.
Specifically, it is assumed that the corresponding first arc length s of previous cycle (i-th of interpolation cycle)i=s (iTs) (wherein TsIt is slotting
Mend the period) it is located between n-th of value of guidance array L and (n+1)th value (0≤n≤N), i.e. L [n]≤si<L[n+1]；It is latter
Period (i+1 interpolation cycle) corresponding second arc length si+1=s ((i+1) Ts) it is located at m-th of the value and m of guidance array L
Between+1 value (0≤m≤N), i.e. L [m]≤si+1<L[m+1].If n=m, the first arc length siWith the second arc length si+1Positioned at drawing
The same section of derivative group L enables interpolation a reference value ub=ui(wherein uiFor the interpolation parameters of previous interpolation cycle), the latter period
Arc length increment between the corresponding interpolation a reference value of interpolation parameters is then Δ sb=si+1-si；Otherwise ub=us+m(ue-us)/N, then
Δsb=si+1- L [m], i.e. interpolation a reference value ubValue be the second arc length si+1The starting point L of the numerical intervals of the guidance array at place
[m], arc length increment are the second arc length si+1And the difference of above-mentioned starting point L [m].
Step S32: the interpolation parameters discreet value u of latter interpolation cycle is calculated according to interpolation a reference valuep, and calculate to be processed
Interpolation a reference value on geometric locus to the arc length between the interpolation parameters discreet value of latter interpolation cycle absolute value | Δ sp|,
Wherein arc length Δ spWith arc length increment Delta sbJack per line (i.e. with just or with negative).
In this step, 1 to the k rank that need to first calculate geometric locus to be processed at interpolation a reference value leads arrow, above-mentioned k be greater than
Zero integer；Then the interpolation parameters discreet value of latter interpolation cycle is calculated using k rank Taylor expansion；Using numerical integration side
Method calculates the interpolation a reference value on geometric locus to be processed to the arc length between the interpolation parameters discreet value of latter interpolation cycle
Absolute value | Δ sp|。
The value of above-mentioned k can be set as needed, and k value is bigger, and the precision for generally approaching arc length is higher, but calculation amount is bigger,
Usually when the curvature of curve C (u) to be processed is smaller, k can use smaller value, and when the curvature of curve C (u) to be processed is larger, k is desirable
The larger value.
K generally takes 1,2 or 3, when k is 1, the interpolation parameters discreet value u of latter interpolation cyclepPass through following calculating formula meter
It calculates and obtains:
" | | | | " indicate the long calculating of vector field homoemorphism, ubFor interpolation a reference value, △ sbFor arc length increment, C ' (ub) it is to be processed
Geometric locus C (u) is in interpolation a reference value ubThe single order at place leads arrow；
When k is 2, the interpolation parameters discreet value u of latter interpolation cyclepIt is calculated and is obtained by following calculating formula:
"<>" indicates that the scalar product of vector calculates, C " (ub) it is geometric locus C (u) to be processed in interpolation a reference value ubPlace
Second order leads arrow；
When k is 3, the interpolation parameters discreet value u of latter interpolation cyclepIt is calculated and is obtained by following calculating formula:
C″′(ub) it is geometric locus C (u) to be processed in interpolation a reference value ubThree ranks at place lead arrow.
Interpolation a reference value u on geometric locus C (u) to be processedbTo the interpolation parameters discreet value u of latter interpolation cyclepArc length
Absolute value | Δ sp| numerical integration method can be used and calculate acquisition.
Step S33: geometric locus C (u) to be processed is calculated in discreet value up1 to the k rank at place leads arrow, and according to latter interpolation
The interpolation parameters discreet value u in periodpAnd arc length Δ spConstruct multinomial
And above-mentioned multinomial (4) meets:
WhereinJth order derivative of the parameter u about arc length parameters s for indicating geometric locus C (u) to be processed, works as j=
It is calculated when 1,2,3 are as follows:
C ' (u) is that single order of the geometric locus C (u) to be processed at parameter u leads arrow, C, and " (u) is geometric locus C to be processed
(u) second order at parameter u leads arrow and C " ' (u) is that three ranks of the geometric locus C (u) to be processed at parameter u lead arrow；
In multinomial (4), aiFor multinomial coefficient, and in k=1:
In k=2:
In k=3:
Step S34: the arc length increment Delta s that will be obtained in step S3bSubstituting into multinomial (4) can be obtained inserting for latter period
Mend parameter ui+1=f (Δ sb)。
As shown in figure 5, being the method for the present invention arc length that theory is planned in Interpolation Process (i.e. according to arc length function of time s
(t) arc length calculated) and practical interpolation arc length between aberration curve.From the figure, it can be seen that deviation maximum value is -2nm
Left and right, it is very small, it is basic in practical applications to can consider that theoretical planning arc length is equal with practical interpolation arc length, therefore the present invention
Can carry out interpolation when method interpolation 5 bezier curves shown in Fig. 3 with arc length, eliminate feed speed planning path distance with
Deviation between Actual path distance, ensure that the steady and accurate of motion process.
It will appreciated by the skilled person that whole or certain steps in above-mentioned the present embodiment disclosed method,
It may be implemented as software, firmware, hardware and its combination appropriate.
As shown in fig. 6, the present invention also provides a kind of curve interpolating equipment, which can be applied to numerically-controlled machine tool or machine
People, and the equipment includes memory 61 and processor 62, and the meter that can be run on the processor 62 is stored in memory 61
The step of calculation machine program, processor 62 realizes method as described above when executing computer program.Parameter interpolation in the present embodiment
Curve interpolating method in equipment and above-mentioned Fig. 2,3 corresponding embodiments belongs to same design, and specific implementation process is shown in pair in detail
The embodiment of the method answered, and the technical characteristic in embodiment of the method is corresponding applicable in this apparatus embodiments, it is no longer superfluous here
It states.
The present invention also provides a kind of computer readable storage medium, computer program, the meter are stored on storage medium
When calculation machine program is executed by processor, the step of realizing method as described above.In above-mentioned storage medium and Fig. 2,3 corresponding embodiments
Curve interpolating method belong to same design, specific implementation process is shown in corresponding embodiment of the method, and embodiment of the method in detail
In technical characteristic it is corresponding in the present embodiment be applicable in, which is not described herein again.
The foregoing is only a preferred embodiment of the present invention, but scope of protection of the present invention is not limited thereto,
In the technical scope disclosed by the present invention, any changes or substitutions that can be easily thought of by anyone skilled in the art,
It should be covered by the protection scope of the present invention.Therefore, protection scope of the present invention should be with scope of protection of the claims
Subject to.
Claims (10)
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| CN116787448A (en) * | 2023-08-14 | 2023-09-22 | 遨博(北京)智能科技股份有限公司 | A trajectory interpolation method, device, computer equipment and storage medium |
| CN116880341A (en) * | 2023-09-07 | 2023-10-13 | 上海泛腾电子科技有限公司 | High-precision motion control system based on industrial Ethernet bus |
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