CN104238458A - NURBS curve high-speed prospective interpolation method - Google Patents

Abstract

The invention relates to velocity planning technologies for numerical control systems, in particular to an NURBS curve high-speed prospective interpolation method. The method comprises the steps that on the basis of the curve self-adaptive interpolation technology, S-type velocity planning is adopted, and the kinematics formulas of the jerk, the acceleration, the feedrate and the interpolation distance of a self-adaptive deceleration area in the interpolation process are obtained; a data structure of data stored in a prospective window in the interpolation process is obtained; the prospective window is established, and the minimum value of the prospective window is obtained; the length of the backtracking distance in the prospective process is determined, and expressions of the acceleration and the jerk in the backtracking process are established; a curve is interpolated, and the data in the prospective window are adjusted dynamically after interpolation every time until interpolation is completed. By the adoption of the method, fluctuation of the acceleration and the jerk can be effectively controlled, the processing quality is ensured, the length of the backtracking distance can be accurately determined, the interpolation time is shortened, and the interpolation efficiency is improved.

Description

A kind of nurbs curve is looked forward to the prospect at a high speed interpolating method

Technical field

The present invention relates to the speed planning technology of digital control system, nurbs curve is looked forward to the prospect at a high speed interpolating method specifically.

Background technology

Nurbs curve interpolation technique is the gordian technique of the Open NC System Platform of Based PC.In nurbs curve Interpolation Process, in order to ensure crudy, need by adaptive interpolation, bow high level error to be limited within specialized range, but the acceleration and deceleration demand in adaptive interpolation process may exceed the maximum capacity of lathe, the acceleration produced not only have impact on the crudy of lathe, also can produce vibration to cutter, affect cutter life.Therefore, the acceleration in process is control effectively, most important to raising crudy.

Mostly existing interpolation algorithm is the control realizing acceleration by prediction interpolation, but in existing look-ahead algorithm, after the acceleration of self-adaptation deceleration area or acceleration transfinite, need to carry out interpolation again, and the average velocity of Interpolation Process reduces again, therefore again the arc length of Interpolation Process to parametric line approach more accurate, the backtracking distance determined in algorithm is caused to be longer than the backtracking distance of actual needs, therefore, in the end partly may there is slow running district in Interpolation Process again, cause the interpolation time to increase, interpolation efficiency reduces.

Summary of the invention

For existing common method weak point separately, the technical problem to be solved in the present invention is to provide one and can either control effectively to acceleration, acceleration, accurately can determine again backtracking distance length, to reduce the interpolation time, to improve the method for interpolation efficiency.

The technical scheme that the present invention is adopted for achieving the above object is: a kind of nurbs curve is looked forward to the prospect at a high speed interpolating method, comprises the following steps:

Based on curve self-adapting interpolation technique, adopt S type speed planning, provide the kinematics formula of the acceleration of self-adaptation decelerating area in Interpolation Process, acceleration, speed and interpolation distance;

Provide the data structure of the data that look-ahead window stores in Interpolation Process, set up look-ahead window, provide the minimum value of look-ahead window;

Determine the length recalling distance in prediction process, set up the expression formula of acceleration in trace-back process, acceleration;

Interpolation is carried out to curve, the data after each interpolation in dynamic conditioning look-ahead window, until interpolation terminates.

In described Interpolation Process, the kinematics formula of the acceleration of self-adaptation decelerating area is:

$\mathrm{jerk}=\left\{\begin{array}{c}-J_{\max },t_0\≤t\≤t_1\\ 0,t_1\≤{t\≤t}_2\\ J_{\max },t_2\≤t\≤t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{jerk}=\left\{\begin{array}{c}{-J}_{\max },t_0\≤t\≤t_1\\ J_{\max },t_1\≤t\≤t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

In described Interpolation Process, the kinematics formula of the acceleration of self-adaptation decelerating area is:

$\mathrm{acceleration}=\left\{\begin{array}{c}{-J}_{\max }*(t-t_0),t_0\&le;t<t_1\\ {-A}_{\max },t_1\&le;t<t_2\\ {-A}_{\max }+J_{\max }*(t-t_0),t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{acceleration}=\left\{\begin{array}{c}{-J}_{\max }*(t-t_0),t_0\&le;t<t_1\\ {-A\&prime;}_{\max }+J_{\max }*(t-t_0),t_1\&le;t<t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the acceleration that lathe allows, A' _maxfor the maximum acceleration value that boost phase reaches, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

In described Interpolation Process, the kinematics formula of the speed of self-adaptation decelerating area is:

$\mathrm{feedrate}=\left\{\begin{array}{c}{f}_0-\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_0\&le;t<t_1\\ f_1-A_{\max }*(t-t_0),t_1\&le;{t<t}_2\\ f_2-A_{\max }*(t-t_0)+\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{feedrate}=\left\{\begin{array}{c}{f}_0-\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_0\&le;t<t_1\\ f_2-{A\&prime;}_{\max }*(t-t_0)+\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_1\&le;t<t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, A' _maxfor the maximum acceleration value that boost phase reaches, f ₀, f ₁, f ₂be respectively t ₀, t ₁, t ₂the speed of point, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

In described Interpolation Process, the kinematics formula of the interpolation distance of self-adaptation decelerating area is:

$\mathrm{dis}\tan \mathrm{ce}=\left\{\begin{array}{c}{s}_0+f_0*(t-t_0)-\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_0\&le;t<t_1\\ s_1+f_1*(t-t_0)-\frac{1}{2}{A}_{\max }*{(t-t_0)}^2,t_1\&le;t<t_2\\ s_2+f_2*(t-t_0)-\frac{1}{2}{A}_{\max }*{(t-t_0)}^2+\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{dis}\tan \mathrm{ce}=\left\{\begin{array}{c}{s}_0+f_0*(t-t_0)-\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_0\&le;t<t_1\\ s_2+f_2*(t-t_0)-\frac{1}{2}{A\&prime;}_{\max }*{(t-t_0)}^2+\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_1\&le;t<t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, A' _maxfor the maximum acceleration value that boost phase reaches, f ₀, f ₁, f ₂be respectively t ₀, t ₁, t ₂the speed of point, s ₀, s ₁, s ₂for t ₀, t ₁, t ₂the interpolation distance that point is corresponding, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

Total distance value of the data point stored in described look-ahead window meets formula

$S_{\min }=\left\{\begin{array}{c}\frac{F_c}{2}(\frac{A_{\max }}{J_{\max }}+\frac{F_c}{A_{\max }}),F_c-\frac{A_{\max }}{J_{\max }}>0\\ F_c\sqrt{\frac{F_c}{J_{\max }}},\mathrm{otherwise}\end{array}\right.$

Requirement, and minimum;

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, F _cfor instruction speed, S _minfor recalling the minimum value of distance.

In described trace-back process, the expression formula of acceleration is:

$\mathrm{acceleration}=\left\{\begin{array}{c}{-J}_{\max }*(t-t_0),t_0\&le;t<t_1\\ {-A}_{\max },t_1\&le;t<t_2\\ {-A}_{\max }+J_{\max }*(t-t_0),t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time, $a_m=\frac{F_c^2-{V_{\min }}^2}{S};$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time, F _cfor instruction speed, V _minfor the minimum speed in Interpolation Process, S is backtracking distance.

In described trace-back process, the expression formula of acceleration is:

$j_m=\frac{A_{\max }^2*(F_c+V_{\min })}{V_{\min }^2+2A_{\max }*S-F_c^2}$

Work as t ₁=t ₂time, $j_m=(F_c-V_{\mathrm{mi}n})*{\left(\frac{F_c+V_{\min }}{S}\right)}^2;$

Wherein, A _maxfor the maximal value of the peak acceleration that lathe allows, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, F _cfor instruction speed, V _minfor the minimum speed in Interpolation Process, S is backtracking distance.

Often complete an interpolation, according to form { u, V, a, J, S _step, S _wholethe data of interpolated point are stored in look-ahead window, after each interpolation terminates, adjust the size of look-ahead window, make total distance value of the data point stored in look-ahead window meet formula

$S_{\min }=\left\{\begin{array}{c}\frac{F_c}{2}(\frac{A_{\max }}{J_{\max }}+\frac{F_c}{A_{\max }}),F_c-\frac{A_{\max }}{J_{\max }}>0\\ F_c\sqrt{\frac{F_c}{J_{\max }}},\mathrm{otherwise}\end{array}\right.$

Requirement, and minimum, then proceed prediction, until arrive end point;

Wherein, wherein u represents the parameter value of current interpolated point, and V represents interpolation fast reading, and a represents acceleration, and J represents acceleration, S _stepstore in current interpolation cycle the length of the little straight-line segment passed through, S _step=V*T, S _wholerepresent from first interpolated point to current point process all interpolation cycles in little length of straigh line sum, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, F _cfor instruction speed, S _minfor recalling the minimum value of distance.

The present invention has the following advantages:

1. apply the fluctuation that the inventive method effectively can control acceleration, acceleration, ensure crudy.

2. apply the length that the inventive method accurately can determine to recall distance length, reduce the interpolation time, improve interpolation efficiency.

Accompanying drawing explanation

Fig. 1 has the decelerating area kinematics curve of even acceleration;

Fig. 2 is without the decelerating area kinematics curve of even acceleration;

Fig. 3 look-ahead window;

Fig. 4 starting point determines figure;

Fig. 5 NURBS simulation example;

Speed in Fig. 6 tradition look-ahead algorithm Interpolation Process, acceleration, acceleration;

Speed in Fig. 7 this paper look-ahead algorithm Interpolation Process, acceleration, acceleration figure;

Speed in Fig. 8 this paper look-ahead algorithm Interpolation Process, acceleration, acceleration partial enlarged drawing.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

1., based on curve self-adapting interpolation technique, adopt S type speed planning, provide the kinematics formula of the acceleration of self-adaptation decelerating area in Interpolation Process, acceleration, speed and interpolation distance.Fig. 1 is decelerating area kinematics curve, wherein $T_1=T_3=\frac{A_m}{J_m},$ $T_2=\frac{F-V_{\min }}{A_{\max }}-\frac{A_{\max }}{J_{\max }},$ Its kinematics formula is as shown in table 1.

Table 1

Work as t ₁=t ₂time, formula (1) is set up, as follows:

$\left\{\begin{array}{c}{T}_2=0\\ T_1=T_3=\frac{{A\&prime;}_{\max }}{J_{\max }}\\ {A\&prime;}_{\max }=\sqrt{(F-V_{\min })*J_m},{A\&prime;}_{\max }\&le;A_{\max }\end{array}\right.---\left(1\right)$

Now decelerating area kinematics curve as shown in Figure 2, wherein A' _maxfor the maximum acceleration value that boost phase reaches, corresponding kinematics formula is as shown in table 2.

Table 2

2. provide the data structure of the data that look-ahead window stores in Interpolation Process, set up look-ahead window, provide the minimum value of look-ahead window.

In prediction process, the information that each interpolated point stores is { u, V, a, J, S _step, S _whole, wherein u represents the parameter value of current interpolated point, and V represents interpolation fast reading, and a represents acceleration, and J represents acceleration, S _stepstore in current interpolation cycle the length of the little straight-line segment passed through, S _step=V*T, S _wholerepresent from first interpolated point to current point process all interpolation cycles in little length of straigh line sum.

Fig. 3 is the structure of look-ahead window, and for guaranteeing have enough distances to recall from current point, must store enough interpolated point data in window, total distance of interpolated point record will meet interpolation rate decelerates to minimum value requirement from maximal value.When speed minimum value gets 0, the minimum value expression formula can being recalled distance by table 1 and table 2 is as follows:

$S_{\min }=\left\{\begin{array}{c}\frac{F_c}{2}(\frac{A_{\max }}{J_{\max }}+\frac{F_c}{A_{\max }}),F_c-\frac{A_{\max }}{J_{\max }}>0\\ F_c\sqrt{\frac{F_c}{J_{\max }}},\mathrm{otherwise}\end{array}\right.---\left(2\right)$

In figure 3, along interpolation direction, represent the interpolation distance of i-th+N number of interpolated point record in window, represent the distance of i-th interpolated point record in window, then represent the interpolation distance length when recording in look-ahead window, when there is an interpolated point first, this point meets S'>=S _mintime, look-ahead window is minimum.

3. accurately determine the length recalling distance in prediction process, set up the expression formula of acceleration in trace-back process, acceleration.

In order to determine the starting point of heavily interpolation accurately, as shown in Figure 4, from impact point, adopt the mode of reverse interpolation to carry out speed planning.The information of inverted speed planning institute foundation comprises: the speed of impact point, instruction speed, maximum acceleration value and maximum acceleration value.Need the data message recording interpolated point in reverse Interpolation Process, the information content is identical with prediction process.Often record an interpolated point information in this process, just the information of data point in this some place's information and look-ahead window is compared, until when being incorporated into certain some place, between the u of the u value of this point two adjacent data points in look-ahead window, the speed of this point is also positioned at therebetween simultaneously, and now trace-back process terminates.The interval that these two adjacent data points are formed is referred to as hand over interval, hands over interval starting point to be again the starting point of Interpolation Process.

S in Fig. 4 _minthe deceleration distance needed during the heavily interpolation determined for traditional look-ahead algorithm, S _addfor hangover distance during traditional look-ahead algorithm interpolation, S' _minattach most importance to interpolation time actual needs deceleration distance, S=S'+S' _minfor the deceleration distance that this paper algorithm is determined, wherein S'>=0, in order to reduce the impact of S'>=0 on interpolation efficiency, need again to plan accekeration and acceleration value.When time, need adjustment acceleration value, new acceleration value is $j_m=\frac{A_{\max }^2*(F_c+V_{\min })}{V_{\min }^2+2A_{\max }*S-F_c^2}.$ $F-V_{\min }<\frac{A_{\max }^2}{J_{\max }}$ Time, i.e. t ₁=t ₂time, need to adjust accekeration and acceleration value, result is as follows simultaneously:

$\left\{\begin{array}{c}{j}_m=(F_c-V_{\min })*{\left(\frac{F_c+V_{\min }}{S}\right)}^2\\ a_m=\frac{F_c^2-{V_{\min }}^2}{S}\end{array}\right.---\left(3\right)$

Interpolation is carried out to curve, the data after each interpolation in dynamic conditioning look-ahead window, until interpolation terminates.Often complete an interpolation, according to form { u, V, a, J, S _step, S _wholethe data of interpolated point are stored in look-ahead window.In order to reduce the storage space that window data takies, need the size adjusting look-ahead window after each interpolation terminates, make total distance value of the data point stored in look-ahead window meet the requirement of formula (2), and minimum, then prediction is proceeded, until arrive end point.

4. implementation effect of the present invention:

In order to the performance of verification algorithm, realize algorithm herein by C language, under VC++6.0 environment, test for the nurbs curve shown in Fig. 5.Parameter is as follows:

Reference mark is { 0.15,0.15,0}, { 0,0,0}, { 0,0.3,0}, { 0.15,0.15,0}, { 0.3,0,0}, { 0.3,0.3,0}, { 0.15,0.15,0}.Weight is W={1,1,1,1,1,1,1}, and knot vector is U={0,0,0,0.25,0.5,0.5,0.75,1,1,1}.Interpolation cycle is T=2ms, and instruction speed is F _c=0.2m/s, bow high level error maximal value is 1*10 ^-6m, acceleration maximal value is 0.0004m/s ², acceleration maximal value is 0.00002m/s ³.

Fig. 6 is emulation simulation result, in figure 3.062 seconds, 3.824 seconds, 4.69-4.702 during second, the acceleration value of former algorithm is zero, and corresponding acceleration is zero, and speed is constant, namely interpolation just reached target velocity before arrival impact point, there is slow running district in interpolation, and algorithm, by reverse interpolation, determines the accurate starting point of deceleration area accurately herein, efficiently avoid the appearance in slow running district, result as shown in Figure 7.In fig. 8, former algorithm decelerates to target velocity from instruction speed and has used 0.434 second, and new algorithm has used 0.42 second, and efficiency improves 3.33%.Simulation results show, algorithm can determine the deceleration starting point of adaptive region accurately herein, reduces the interpolation time, improves interpolation efficiency.

Claims (9)

1. nurbs curve is looked forward to the prospect at a high speed an interpolating method, it is characterized in that, comprises the following steps:

Based on curve self-adapting interpolation technique, adopt S type speed planning, provide the kinematics formula of the acceleration of self-adaptation decelerating area in Interpolation Process, acceleration, speed and interpolation distance;

Provide the data structure of the data that look-ahead window stores in Interpolation Process, set up look-ahead window, provide the minimum value of look-ahead window;

Determine the length recalling distance in prediction process, set up the expression formula of acceleration in trace-back process, acceleration;

Interpolation is carried out to curve, the data after each interpolation in dynamic conditioning look-ahead window, until interpolation terminates.

2. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, in described Interpolation Process, the kinematics formula of the acceleration of self-adaptation decelerating area is:

$\mathrm{jerk}=\left\{\begin{array}{c}-J_{\max },t_0\&le;t\&le;t_1\\ 0,t_1\&le;t\&le;t_2\\ J_{\max },t_2\&le;t\&le;t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{jerk}=\left\{\begin{array}{c}{-J}_{\max },t_0\&le;t\&le;t_1\\ J_{\max },t_1\&le;t\&le;t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

3. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, in described Interpolation Process, the kinematics formula of the acceleration of self-adaptation decelerating area is:

$\mathrm{acceleration}=\left\{\begin{array}{c}{-J}_{\max }*(t-t_0),t_0\&le;t<t_1\\ {-A}_{\max },t_1\&le;t<t_2\\ {-A}_{\max }+J_{\max }*(t-t_0),t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{acceleration}=\left\{\begin{array}{c}{-J}_{\max }*(t-t_0),t_0\&le;t<t_1\\ {-A\&prime;}_{\max }+J_{\max }*(t-t_0),t_1\&le;t<t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the acceleration that lathe allows, A' _maxfor the maximum acceleration value that boost phase reaches, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

4. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, in described Interpolation Process, the kinematics formula of the speed of self-adaptation decelerating area is:

$\mathrm{feedrate}=\left\{\begin{array}{c}{f}_0-\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_0\&le;t<t_1\\ f_1-A_{\max }*(t-t_0),t_1\&le;t<t_2\\ f_2-A_{\max }*(t-t_0)+\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{feedrate}=\left\{\begin{array}{c}{f}_0-\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_0\&le;t<t_1\\ f_2-{A\&prime;}_{\max }*(t-t_0)+\frac{1}{2}{J}_{\max }*{(t-t_0)}^2,t_1\&le;t<t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, A' _maxfor the maximum acceleration value that boost phase reaches, f ₀, f ₁, f ₂be respectively t ₀, t ₁, t ₂the speed of point, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

5. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, in described Interpolation Process, the kinematics formula of the interpolation distance of self-adaptation decelerating area is:

$\mathrm{dis}\tan \mathrm{ce}=\left\{\begin{array}{c}{s}_0+f_0*(t-t_0)-\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_0\&le;t<t_1\\ s_1+f_1*(t-t_0)-\frac{1}{2}{A}_{\max }*{(t-t_0)}^2,t_1\&le;t<t_2\\ s_2+f_2*(t-t_0)-\frac{1}{2}{A}_{\max }*{(t-t_0)}^2+\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time,

$\mathrm{dis}\tan \mathrm{ce}=\left\{\begin{array}{c}{s}_0+f_0*(t-t_0)-\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_0\&le;t<t_1\\ s_2+f_2*(t-t_0)-\frac{1}{2}{A\&prime;}_{\max }*{(t-t_0)}^2+\frac{1}{6}{J}_{\max }*{(t-t_0)}^3,t_1\&le;t<t_2\end{array}\right.$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, A' _maxfor the maximum acceleration value that boost phase reaches, f ₀, f ₁, f ₂be respectively t ₀, t ₁, t ₂the speed of point, s ₀, s ₁, s ₂for t ₀, t ₁, t ₂the interpolation distance that point is corresponding, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time.

6. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, total distance value of the data point stored in described look-ahead window meets formula

$S_{\min }=\left\{\begin{array}{c}\frac{F_c}{2}(\frac{A_{\max }}{J_{\max }}+\frac{F_c}{A_{\max }}),F_c-\frac{A_{\max }}{J_{\max }}>0\\ F_c\sqrt{\frac{F_c}{J_{\max }}},\mathrm{otherwise}\end{array}\right.$

Requirement, and minimum;

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, F _cfor instruction speed, S _minfor recalling the minimum value of distance.

7. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, in described trace-back process, the expression formula of acceleration is:

$\mathrm{acceleration}=\left\{\begin{array}{c}{-J}_{\max }*(t-t_0),t_0\&le;t<t_1\\ {-A}_{\max },t_1\&le;t<t_2\\ {-A}_{\max }+J_{\max }*(t-t_0),t_2\&le;t<t_3\end{array}\right.$

Work as t ₁=t ₂time, $a_m=\frac{F_c^2-{V_{\min }}^2}{S};$

Wherein, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, t ₀for slowing down the start time, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, t ₃for slowing down the end time, F _cfor instruction speed, V _minfor the minimum speed in Interpolation Process, S is backtracking distance.

8. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, and it is characterized in that, in described trace-back process, the expression formula of acceleration is:

$j_m=\frac{A_{\max }^2*(F_c+V_{\min })}{V_{\min }^2+2A_{\max }*S-F_c^2}$

Work as t ₁=t ₂time, $j_m=(F_c-V_{\min })*{\left(\frac{F_c+V_{\min }}{S}\right)}^2;$

Wherein, A _maxfor the maximal value of the peak acceleration that lathe allows, t ₁for acceleration reaches the time of maximal value, t ₂for the end time that acceleration maximal value continues, F _cfor instruction speed, V _minfor the minimum speed in Interpolation Process, S is backtracking distance.

9. a kind of nurbs curve according to claim 1 is looked forward to the prospect at a high speed interpolating method, it is characterized in that, often completes an interpolation, according to form { u, V, a, J, S _step, S _wholethe data of interpolated point are stored in look-ahead window, after each interpolation terminates, adjust the size of look-ahead window, make total distance value of the data point stored in look-ahead window meet formula

$S_{\min }=\left\{\begin{array}{c}\frac{F_c}{2}(\frac{A_{\max }}{J_{\max }}+\frac{F_c}{A_{\max }}),F_c-\frac{A_{\max }}{J_{\max }}>0\\ F_c\sqrt{\frac{F_c}{J_{\max }}},\mathrm{otherwise}\end{array}\right.$

Requirement, and minimum, then proceed prediction, until arrive end point;

Wherein, wherein u represents the parameter value of current interpolated point, and V represents interpolation fast reading, and a represents acceleration, and J represents acceleration, S _stepstore in current interpolation cycle the length of the little straight-line segment passed through, S _step=V*T, S _wholerepresent from first interpolated point to current point process all interpolation cycles in little length of straigh line sum, J _maxfor the maximal value of the maximum acceleration that lathe allows, A _maxfor the maximal value of the peak acceleration that lathe allows, F _cfor instruction speed, S _minfor recalling the minimum value of distance.