CN103048954A - Segmented interpolation method of NURBS (Non-Uniform Rational B-Spline) curve based on ARM9 (Advanced RISC Machines) embedded system and FPGA (Field Programmable Gate Array) - Google Patents

Abstract

The invention discloses a segmented interpolation method of a NURBS (Non-Uniform Rational B-Spline) curve based on an ARM9 (Advanced RISC Machines) embedded system and an FPGA (Field Programmable Gate Array). Rough interpolation is carried out on the NURBS curve by adopting the ARM9 embedded system, so that segmented pre-processing of the NURBS curve is completed; fine interpolation is carried out on the segmented curve by adopting the FPGA; and finally, component motion of each feed shaft is output to a signal control port of a motor in the form of a pulse signal by an external circuit, so that a servo control of the motor is realized. According to the segmented interpolation method disclosed by the invention, a direct processing technology for a complex-surface component which is described by the NURBS curve is realized, so that the processing efficiency is improved when the processing precision is ensured.

Description

A kind of nurbs curve subsection interpolation method based on ARM9 embedded system and FPGA

Technical field

The present invention relates to fields of numeric control technique, relate in particular to a kind of based on ARM9 embedded system and FPGA(field programmable gate array) NURBS (Non-Uniform Rational B-Splines, non-uniform rational B-spline) curve segmentation interpolating method.

Background technology

The NURBS technology has obtained more successful application in the CAD/CAM field.In CAD/CAM software, non-uniform rational B-spline (NURBS) expression is often adopted in the design of part free form surface, and relatively lags behind in the application in CNC field.Traditional CNC system only provides straight line and circular interpolation function, can not directly process the free curve curved surface.Thereby the processing of Complex Surface Part (such as mould, aerospace vehicle model, car model etc.) must be by means of CAD/CAM system, part curve, curved surface profile is separated into a large amount of little section straight lines or circular arc is processed.There is many-sided limitation in this job operation: at first, in order to obtain than high manufacturing accuracy, the CAM system need to generate the less straight line of crypto set and the segment of curve of circular fitting, just need to describe with more NC code, and along with the raising of requirement on machining accuracy, the NC size of code can become how much multiples to increase, such processing mode has not only increased the weight of the transmission burden of CAD/CAM system and CNC system, also taken simultaneously too much CNC storage space, therefore, consider that process time and processing expend, conventional interpolation mode efficient is low and uneconomical; Secondly, because curve is to be formed by little line segment and circular fitting, can cause discontinuous at the speed of Nodes and acceleration of curve, can cause like this feed rate fluctuation in the process excessive, reduce machining precision and surface quality; In addition, also can exist frequently acceleration and deceleration processing, Two Interpolate precision the problem such as to lose, limit the further raising of numerical control (NC) Machining Accuracy and efficient.

Summary of the invention

The invention provides a kind of nurbs curve subsection interpolation method based on ARM9 embedded system and FPGA, solve traditional C NC system and when the processed complex part, need be separated into a large amount of little section straight lines or circular arc, cause the problems such as the poor efficient of machining precision is low, realize the direct process technology of complex part of being described by nurbs curve.

A kind of nurbs curve subsection interpolation method based on ARM9 embedded system and FPGA of the present invention comprises 2 steps:

1) rough interpolation

From the NC code file, extract the workpiece information that nurbs curve is described, controlled some set { P _i, weight factor set { w _iAnd instruction speed F;

Adopt the second Taylor series method of approximation that nurbs curve is carried out pre-interpolation, obtain pre-interpolation point set and close { (u _i, v _i, ρ _i), system identifies curve small curvature radius district automatically according to bow high level error situation of change, and dynamically adjusts pre-interpolated point speed of feed, the interpolated point sets of speeds after being adjusted:

V ^m(u _i)={v|v(u _i)<F}

System extracts small curvature radius district velocity characteristic point: C according to small curvature radius district interpolated point sets of speeds and curvature situation of change ^m(u _i)={ u _i| min (V ^m(u _i))

With adjacent velocity characteristic point nurbs curve is carried out segmentation, obtains sectional curve:

L _m={(C ^m(u _i),C ^m+1(u _i+1))}

Adopt self-adaptation Simpson method to calculate sectional curve length, obtain four-tuple { u _s, u _e, v _i, S _iThe segment of curve data of expression, these data comprise the information of segment of curve head and the tail endpoint parameter, speed of feed, segment of curve length; The segment of curve data are written in the fifo queue of FPGA by the ARM9 embedded system by bus;

2) smart interpolation

FPGA reads segment of curve data in the fifo queue, adopts S type acceleration and deceleration method to carry out acceleration and deceleration and processes, and generates in real time the interpolated point coordinate according to the nurbs curve definition;

Peripheral circuit with the signal controlling port of pulsed quantity formal output to motor, is realized motor servo control with each feed shaft component motion.

Described system extracts small curvature radius district velocity characteristic point according to small curvature radius district interpolated point sets of speeds and curvature situation of change, and concrete steps are:

The pre-interpolation spot speed set in described small curvature radius district is:

V ^m(u _i)={v|v(u _i)<F}

Wherein:

Be m small curve radius district initial parameters;

Adopt greedy algorithm that the small curvature radius district is scanned, extract the minimum speed interpolated point in small curvature radius district, be specially:

Step1 velocity characteristic point initialization: make unique point speed of feed V _f=F, parameter U _f=1;

Step2 interpolated point calculation of parameter: by parameters u _i, speed of feed V (u _i) according to the second Taylor series formula calculating parameter u _I+1

The Step3 sensitive spot is judged: calculate string C (u according to the approximate error of interpolation model of circular arc _i) C (u _i+ 1) bow high level error ER _iIf, ER _iGreater than longbow high level error restriction δ _Max, then dynamically adjust speed of feed V (u _i), this moment C (u _i) be sensitive spot, carry out Step4; If ER _iLess than or equal to longbow high level error restriction δ _Max, when curved scanning finishes, carry out Step5; Otherwise, carry out Step2;

Step4 velocity characteristic point detects: if V _fU _f, then current sensitive spot is new velocity characteristic point, makes V _f=V (u _i), U _f=u _i, carry out Step2; If V _f≤ U _f, pre-interpolated point C (u _i) be small curvature radius district velocity characteristic point, when curved scanning finishes, carry out Step5; Otherwise, continue to detect next small curvature radius district velocity characteristic point, carry out Step1;

The Step5 algorithm finishes: obtain the set of nurbs curve velocity characteristic point

C ^m(u _i)={u _i|min(V ^m(u _i))}

The present invention has following advantage:

(1) adopt high ARM9 embedded system and the FPGA(field programmable gate array of real-time) control technology, the interpolation of nurbs curve is divided into rough interpolation and two stages of smart interpolation, the rough interpolation function of ARM9 Implementation of Embedded System nurbs curve, FPGA realizes the smart interpolation function of NURBS sectional curve, solved traditional C NC need be separated into a large amount of little section straight lines or circular arc at processing parts curve, curved surface profile problem, realized the direct process technology of complex curved surface parts that nurbs curve is described, when guaranteeing machining precision, improved working (machining) efficiency.

When (2) traditional nurbs curve acceleration and deceleration are processed, only carrying out acceleration and deceleration for the small curvature radius district processes, easy formation speed wedge angle, produce sudden change of acceleration, and the present invention has carried out staging treating on the basis that takes into full account the nurbs curve geometric properties, acceleration and deceleration processing to sectional curve when smart interpolation can not form the speed wedge angle, so that the speed transition is more level and smooth.

Description of drawings

Fig. 1 is system framework figure of the present invention;

Fig. 2 is the process flow diagram that segmentation pre-service of the present invention realizes rough interpolation;

Fig. 3 is segment of curve type synoptic diagram among the present invention;

Each stage acceleration of Fig. 4 S type of the present invention curve acceleration and deceleration, speed, acceleration and displacement concern chart.

Below in conjunction with the drawings and specific embodiments the present invention is further described.

Embodiment

As shown in Figure 1, the FPGA(field programmable gate array that the present invention includes the ARM9 embedded system and be attached thereto through bus), this ARM9 embedded system is carried out the segmentation pre-service in off-line phase to nurbs curve, finish the rough interpolation function, and the sectional curve data are written in the fifo queue of FPGA, FPGA is according to interpolation cycle, definition according to nurbs curve calculates each feed shaft component motion, finish smart interpolation function, and the pulse interpolation value outputed to the signal controlling port of motor, realize in real time, accurately motor servo control.

A kind of nurbs curve subsection interpolation method based on ARM9 embedded system and FPGA of the present invention specifically comprises the steps:

Step 1, as shown in Figure 2, by the ARM9 embedded system in off-line phase according to the nurbs curve geometrical property, nurbs curve is carried out the segmentation pre-service, realize the rough interpolation function, then the ARM9 embedded system is written to the sectional curve data in the fifo queue of FPGA by bus:

(1) user selection NC code file reads out the NC machining code, and this NC machining code comprises reference mark set { P _i, weight factor set { w _i, the nurbs curve characteristic information of knot vector and instruction speed F;

(2) adopt the second Taylor series method of approximation that nurbs curve is carried out pre-interpolation, the nurbs curve parameters u is carried out the second Taylor series to time t, by current interpolated point parameters u _iAnd speed of feed v(u _i) obtain the pre-interpolated point parameters u of next interpolated point _I+1:

$u_{i+1}=u_i+\frac{\mathrm{du}}{\mathrm{dt}}{|}_{t=t_i}{T}_s+\frac{1}{2}\frac{d^{2}u}{d{t}^2}{|}_{t=t_i}{T}_s^2+H.O.T$

Wherein: $\frac{\mathrm{du}}{\mathrm{dt}}{|}_{t=t_i}=\frac{V\left(u_i\right)}{\left|\right|\frac{\mathrm{dC}\left(u\right)}{\mathrm{du}}|{|}_{u=u_i}}$

$\frac{d^{2}u}{d{t}^2}{|}_{t=t_i}=-\frac{V^2\left(u_i\right)T_s^2(\frac{\mathrm{dC}\left(u\right)}{\mathrm{du}}\&CenterDot;\frac{d{C}^2\left(u\right)}{d{u}^2}){|}_{u=u_i}}{\left|\right|\frac{\mathrm{dC}\left(u\right)}{\mathrm{du}}|{|}_{u=u_i}^4}$

Above-mentioned H.O.T is that high-order is infinitely small, can ignore;

(3) calculate interpolated point bow high level error, system identifies curve small curvature radius district automatically according to bow high level error situation of change, and dynamically adjusts pre-interpolated point speed of feed, the interpolated point sets of speeds V after being adjusted ^m(u _i)={ v|v (u _i)＜F}

The error of interpolation model is:

$E{R}_i={\mathrm{\&rho;}}_i-\sqrt{{\mathrm{\&rho;}}_i^2-{\left(\frac{V\left(u_i\right)\&CenterDot;T}{2}\right)}^2},{\mathrm{\&rho;}}_i=1/k_i$

k _iFor curve in parameters u _iThe curvature at place has:

$k_i=\frac{\frac{d{C}_x\left(u\right)}{\mathrm{du}}\&CenterDot;\frac{d^2{C}_y\left(u\right)}{d{u}^2}-\frac{d{C}_y\left(u\right)}{\mathrm{du}}\&CenterDot;\frac{d^2{C}_x\left(u\right)}{d{u}^2}}{{\left|\right|\frac{\mathrm{dC}\left(u\right)}{\mathrm{du}}\left|\right|}_{u=u_i}^3}$

According to interpolation bow high level error and longbow high level error restriction relation, dynamically adjust interpolation speed of feed equation and be:

$V\left(u_i\right)=\left\{\begin{array}{cc}F& E{R}_i\&le;{\mathrm{\&delta;}}_{\max }\\ \frac{2}{T}\sqrt{{\mathrm{\&rho;}}_i^2-{({\mathrm{\&rho;}}_i-{\mathrm{\&delta;}}_{\max })}^2}& \mathrm{otherwise}\end{array}\right.$

(4) system identifies the small curvature radius district on the curve automatically according to the nurbs curve curvature variation, finishes the extraction of small curvature radius district velocity characteristic point:

The pre-interpolation spot speed set in described small curvature radius district is:

V ^m(u _i)={v|v(u _i)<F}

Wherein:

Be m small curve radius district initial parameters;

Adopt greedy algorithm that the small curvature radius district is scanned, extract the minimum speed interpolated point in small curvature radius district, concrete steps are:

Step1 velocity characteristic point initialization: make unique point speed of feed V _f=F, parameter U _f=1;

Step2 interpolated point calculation of parameter: by parameters u _i, speed of feed V (u _i) according to the second Taylor series formula calculating parameter u _I+1

The Step3 sensitive spot is judged: calculate string C (u according to the approximate error of interpolation model of circular arc _i) C (u _I+1) bow high level error ER _iIf, ER _iGreater than longbow high level error restriction δ _Max, then dynamically adjust speed of feed V (u _i), this moment C (u _i) be sensitive spot, carry out Step4; If ER _iLess than or equal to longbow high level error restriction δ _Max, when curved scanning finishes, carry out Step5; Otherwise, carry out Step2;

Step4 velocity characteristic point detects: if V _fU _f, then current sensitive spot is new velocity characteristic point, makes V _f=V (u _i), U _f=u _i, carry out Step2; If V _f≤ U _f, pre-interpolated point C (u _i) be small curvature radius district velocity characteristic point, when curved scanning finishes, carry out Step5; Otherwise, continue to detect next small curvature radius district velocity characteristic point, carry out Step1;

The Step5 algorithm finishes: obtain the set of nurbs curve velocity characteristic point:

C ^m(u _i)={u _i|min(V ^m(u _i))}

(5) with small curvature radius district velocity characteristic point nurbs curve is carried out segmentation:

For n velocity characteristic point, curve is divided into the n+1 section, the sectional curve set is:

L _m={(C ^m(u _i),C ^m+1(u _i+1))}；

(6) adopt self-adaptation Simpson method calculated curve segment length, from a C (u ₁) to a C (u ₂) length of curve S be expressed as:

$S={\&Integral;}_{u_1}^{u_2}\left|\right|\frac{\mathrm{dC}}{\mathrm{du}}\left|\right|\mathrm{du}$

Wherein $\left|\right|\frac{\mathrm{dC}}{\mathrm{du}}\left|\right|=\sqrt{{\left(\frac{\mathrm{dx}\left(u\right)}{\mathrm{du}}\right)}^2+{\left(\frac{\mathrm{dy}\left(u\right)}{\mathrm{du}}\right)}^2+{\left(\frac{\mathrm{dz}\left(u\right)}{\mathrm{du}}\right)}^2};$

(7) NURBS sectional curve data rough interpolation is finished, and obtains four-tuple { u _s, u _e, v _i, S _iThe segment of curve data of expression, these segment of curve data comprise the information of segment of curve head and the tail endpoint parameter, speed of feed, segment of curve length, the ARM9 embedded system is written to these segment of curve data in the fifo queue of FPGA by bus;

Step 2, FPGA read segment of curve data in the fifo queue, adopting S type acceleration and deceleration method to carry out acceleration and deceleration processes, generate in real time the interpolated point coordinate according to the nurbs curve definition, in each interpolation cycle, calculate in real time the feeding component of each axle, realize smart interpolation function, peripheral circuit calculates institute's pulsed quantity formal output that is able to each feed shaft component motion to the signal controlling port of motor, and the realization motor servo is controlled:

(1) the NURBS fine interpolator reads the sectional curve data of FIFO storage;

(2) carry out acceleration and deceleration control according to segment of curve length:

Fig. 4 has disclosed the relation of each stage acceleration of S type curve acceleration and deceleration, speed, acceleration and displacement, wherein J _mBe maximum acceleration, A _mBe peak acceleration, T1, T2 ... T7 is each duration in stage, as shown in Figure 4

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="T"\; filenames="HDA00002728178300022.png"\; state="\{\{state\}\}">T</figure-callout>}}_1=T_2=T_5=T_7=\frac{J_m}{A_m}\\ T_2=\frac{f_2-f_1}{A_m}\\ T_6=\frac{f_6-f_5}{A_m}\end{array}\right.$

Make S _AccBe boost phase displacement, S _EvenBe phase displacement at the uniform velocity, S _DecBe the decelerating phase displacement, can be got by Fig. 4:

$\left\{\begin{array}{c}{S}_{\mathrm{acc}}={\mathrm{<figure-callout\; id="1"\; label="S"\; filenames="HDA00002728178300022.png"\; state="\{\{state\}\}">S</figure-callout>}}_1+S_2+S_3\\ S_{\mathrm{even}}=S_4\\ S_{\mathrm{dec}}=S_5+S_6+S_7\end{array}\right.$

Then minimum acceleration and deceleration distance is:

S _min=s _acc+s _dec=s ₁+s ₂+s ₃+s ₅+s ₆+s ₇

When the sectional curve acceleration and deceleration were processed, segment of curve head and the tail end points was the acceleration and deceleration starting point, according to the segment of curve arc length S _iWith minimum acceleration and deceleration apart from S _MinRelation, segment of curve can be divided into four kinds of situations, as shown in Figure 3:

A is I type segment of curve: work as S _iS _Min, comprise acceleration, at the uniform velocity, the segment of curve of moderating process

B is II type segment of curve: work as S _Acc≤ S _i＜S _Min, comprise the segment of curve of acceleration, moderating process

C is III type segment of curve: work as S _i＜S _AccAnd V _s≤ V _e, only comprise the segment of curve of accelerator

D is IV type segment of curve: work as S _i＜S _AccAnd V _sV _e, only comprise the segment of curve of moderating process

Wherein: S _AccBe boost phase displacement, V _sBe the first node speed of feed of sectional curve, V _eBe sectional curve tail node speed of feed.

(3) calculate in real time next interpolated point C (u according to the nurbs curve definition _I+1):

Article one, p nurbs curve definition is:

$C\left(u\right)=\frac{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{N}_{i,p}\left(u\right)w_i{P}_i}{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{N}_{i,p}\left(u\right)w_i},a\&le;u\&le;b$

Here { P _iThe reference mark set, { w _iThe weight factor set, { N _{I, p}(u) } be p the B spline base function that is defined on non-periodic and the non-uniform knot vector U, wherein:

$N_{i,p}\left(u\right)=\frac{(u-u_i)N_{i,p-1}\left(u\right)}{u_{i+p}-u_i}+\frac{(u_{i+p+1}-u)N_{i+1,p-1}\left(u\right)}{u_{i+p+1}-u_{p+1}}$

By reference mark { P _iAnd corresponding weight factor { w _i, can make up one group of weighting reference mark

Can in four-dimentional space, ask for nurbs curve according to the definition of nurbs curve with this group reference mark:

$C^w\left(u\right)=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{N}_{i,p}\left(u\right)P_i^w$

There is a mapping H, with the C on the four-dimentional space ^w(u) be mapped to three dimensions C (u), H satisfies equation: $C\left(u\right)=H\left\{C^w\left(u\right)\right\}=H\left\{\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{N}_{i,p}\left(u\right)P_i^w\right\}=\underset{i=0}{\overset{n}{\mathrm{\&Sigma;}}}{R}_{i,p}\left(u\right)P_i$

Wherein C (u) is C ^w(u) projection on the w=1 lineoid.

According to the nurbs curve definition, by parameters u _I+1Can get the four-dimentional space point:

C ^w(u _i+1)

Again with C ^w(u _I+1) the four-dimentional space point carries out projection, obtains three-dimensional data points C (u _I+1), that is:

C(u _i+1)={x(u _i+1),y(u _i+1),z(u _i+1)}

(4) peripheral circuit calculates institute's pulsed quantity formal output that is able to each feed shaft component motion to the signal controlling port of motor, and the realization motor servo is controlled.

The above, it only is preferred embodiment of the present invention, be not that technical scope of the present invention is imposed any restrictions, so every foundation technical spirit of the present invention all still belongs in the scope of technical solution of the present invention any trickle modification, equivalent variations and modification that above embodiment does.

Claims (2)

1. nurbs curve subsection interpolation method based on ARM9 embedded system and FPGA is characterized in that comprising 2 steps:

1) rough interpolation

From the NC code file, extract the workpiece information that nurbs curve is described, controlled some set { P _i, weight factor set { w _iAnd instruction speed F;

Adopt the second Taylor series method of approximation that nurbs curve is carried out pre-interpolation, obtain pre-interpolation point set and close { (u _i, v _i, ρ _i), system identifies curve small curvature radius district automatically according to bow high level error situation of change, and dynamically adjusts pre-interpolated point speed of feed, the interpolated point sets of speeds after being adjusted:

V ^m(u _i)={v|v(u _i)<F}

System extracts small curvature radius district velocity characteristic point: C according to small curvature radius district interpolated point sets of speeds and curvature situation of change ^m(u _i)={ u _iMin (V ^m(u _i))

With adjacent velocity characteristic point nurbs curve is carried out segmentation, obtains sectional curve:

L _m={(C ^m(u _i),C ^m+1(u _i+1))}

Adopt self-adaptation Simpson method to calculate sectional curve length, obtain four-tuple { u _s, u _e, v _i, S _iThe segment of curve data of expression, these data comprise the information of segment of curve head and the tail endpoint parameter, speed of feed, segment of curve length; The segment of curve data are written in the fifo queue of FPGA by the ARM9 embedded system by bus;

2) smart interpolation

FPGA reads segment of curve data in the fifo queue, adopts S type acceleration and deceleration method to carry out acceleration and deceleration and processes, and generates in real time the interpolated point coordinate according to the nurbs curve definition;

Peripheral circuit with the signal controlling port of pulsed quantity formal output to motor, is realized motor servo control with each feed shaft component motion.

2. a kind of nurbs curve subsection interpolation method based on ARM9 embedded system and FPGA according to claim 1, it is characterized in that system extracts small curvature radius district velocity characteristic point according to small curvature radius district interpolated point sets of speeds and curvature situation of change, concrete steps are:

The pre-interpolation spot speed set in described small curvature radius district is:

V ^m(u _i)={v|v(u _i)<F}

Wherein:

Be m small curve radius district initial parameters;

Adopt greedy algorithm that the small curvature radius district is scanned, extract the minimum speed interpolated point in small curvature radius district, be specially:

Step1 velocity characteristic point initialization: make unique point speed of feed V _f=F, parameter U _f=1;

Step2 interpolated point calculation of parameter: by parameters u _i, speed of feed V (u _i) according to the second Taylor series formula calculating parameter u _I+1

The Step3 sensitive spot is judged: calculate string C (u according to the approximate error of interpolation model of circular arc _i) C (u _i+ 1) bow high level error ER _iIf, ER _iGreater than longbow high level error restriction δ _Max, then dynamically adjust speed of feed V (u _i), this moment C (u _i) be sensitive spot, carry out Step4; If ER _iLess than or equal to longbow high level error restriction δ _Max, when curved scanning finishes, carry out Step5; Otherwise, carry out Step2;

Step4 velocity characteristic point detects: if V _fU _f, then current sensitive spot is new velocity characteristic point, makes V _f=V (u _i), U _f=u _i, carry out Step2; If V _f≤ U _f, pre-interpolated point C (u _i) be small curvature radius district velocity characteristic point, when curved scanning finishes, carry out Step5; Otherwise, continue to detect next small curvature radius district velocity characteristic point, carry out Step1;

The Step5 algorithm finishes: obtain the set of nurbs curve velocity characteristic point

C ^m(u _i)={u _i|min(V ^m(u _i))}

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