阅读说明：本技术 一种快速规划6阶s型运动曲线的方法 (Method for rapidly planning 6-order S-shaped motion curve ) 是由 董杰楚 徐亦新 王飞 王志超 黄少强 于 2020-06-10 设计创作，主要内容包括：本发明公开一种快速规划6阶S型运动曲线的方法,通过已知的运动参数距离L<Sub>d</Sub>、启动速度V<Sub>s</Sub>、结束速度V<Sub>e</Sub>、最大加加速J<Sub>m</Sub>、最大允许速度V<Sub>m</Sub>将待规划的S型速度曲线分为H(Head)加速阶段、B(Body)匀速阶段、T(Tail)减速阶段三种分段；对H与T段使用5阶贝塞尔曲线的方法来规划6阶S型速度曲线,同时设计了一种前向差分的计算法来提升计算效率；最后对速度曲线进行等间隔采样,分别设计了脉冲和总线型控制器的位置数据更新计算方法。(The invention discloses a method for rapidly planning a 6-order S-shaped motion curve, which is implemented by using a known motion parameter distance L d Starting speed V s End velocity V e Maximum acceleration J m Maximum allowable speed V m Dividing an S-shaped speed curve to be planned into three segments, namely an H (head) acceleration stage, a B (body) constant speed stage and a T (Tail) deceleration stage; planning a 6-order S-shaped speed curve by using a 5-order Bezier curve method for H and T sections, and simultaneously designing a forward difference calculation method to improve the calculation efficiency; and finally, sampling the speed curve at equal intervals, and designing position data updating and calculating methods of the pulse controller and the bus controller respectively.)

1. A method for rapidly planning a 6-order S-shaped motion curve is characterized by comprising the following steps:

step 1, inputting motion curve parameters to be planned: length of track L_dStarting speed V_sEnd velocity V_eMaximum acceleration J_mMaximum allowable speed V_m；

Step 2, use J_mAnd V_mAs a constraint, calculate V_s、V_e、L_dThe relation between them is that the motion curve to be planned is divided into acceleration stage, uniform speed stage and deceleration stage, in which the acceleration stage is recorded as H-segment, uniformThe speed stage is marked as a B section, the speed reduction stage is marked as a T section, the motion state section condition which can appear on the S-shaped curve to be planned is one of the sections of H, T, B, BT, HB, HT and HBT, and the motion state combination on the S-shaped curve to be planned is judged;

step 3, planning a speed curve by using a 5-order Bezier curve for the motion curves of the existing H section and the T section;

and 4, sampling the speed curve planned in the third step at equal intervals, equally dividing the speed curve into N parts, wherein the time interval of each part is h, and calculating the discrete V value on the speed curve in a forward difference mode.

2. The method of claim 1, wherein the initial velocity V of a segment of the sigmoid motion curve is known_iAnd end velocity V_fThe moving distance L can be calculated_xThe concrete formula is as follows;

the initial speed V of a certain section on the S-shaped motion curve is known_iAnd a moving distance L_xCalculating the final velocity V of the segment_fThe concrete formula is as follows;

through the calculation of the formulas (1) and (2), the motion state segmentation combination on the S-shaped curve to be planned can be judged, and the specific method is as follows:

step 2.1 if V_s＝V_eIf so, the segment is in a uniform motion state process and is segmented B, the step II is ended, otherwise, the step 2.2 is started;

step 2.2 reaction of V_sAnd V_eSubstituting formula (1) to obtain the actual movement distance L during the speed variation_cEntering step 2.2.1;

step 2.2.1 if L_c≥L_dAnd V is_s<V_eIn time, it shows that the speed can be driven from V only by actually running a longer distance_sChange into V_eAnd then V is_sAnd less than V_eThen at a set distance L_dThe acceleration motion is always performed, the acceleration motion is in an H-segment mode, and the actual final speed V of the segment can be calculated by the formula (2)_cEntering the step three, otherwise entering the step 2.2.2;

step 2.2.2 if L_c≥L_dAnd V is_s>V_eIn time, it shows that the speed can be driven from V only by actually running a longer distance_sChange into V_eAnd then V is_sIs greater than V_eThen at a set distance L_dThe speed is always reduced and divided into T sections, and the actual final speed V of the section can be calculated by the formula (2)_cEntering the step three, otherwise entering the step 2.2.3;

step 2.2.3 if L_c<L_dAnd V is_m＝V_sWill V_sAnd V_eSubstituting formula (1) to obtain the distance L of movement in a deceleration state_tAnd when L is_t<L_dIf yes, the BT segment is segmented, namely the BT segment is in a constant speed-first deceleration motion mode, the step three is carried out, and if not, the step 2.2.4 is carried out;

step 2.2.4 if L_c<L_dWill V_sAnd V_mSubstituting formula (1) to obtain the acceleration distance L_hIf L is_h<L_dAnd V is_m＝V_eIf the motion mode is the HB section mode, namely the section is an acceleration mode and a uniform motion mode, the step III is carried out, otherwise, the step 2.2.5 is carried out;

step 2.2.5 if L_c<L_dWill V_sAnd V_mSubstituting formula (1) to obtain the moving distance L in the acceleration state_hWill V_mAnd V_eSubstituting formula (1) to obtain the distance L of movement in a deceleration state_tGo to step 2.2.5.1;

step 2.2.5.1 if L_d<(L_h+L_t) Segmenting HT, namely, the curve of the segment is accelerated first and then enters a deceleration motion mode immediately, and entering the step three, and if not, the stepStep 2.2.5.2 is entered;

step 2.2.5.2 if L_d>(L_h+L_t) And (4) segmenting the HBT, accelerating the curve, then entering a constant speed, finally decelerating, and entering the step three.

3. The method for rapidly planning the 6 th-order S-shaped motion curve according to claim 1, wherein for the motion curves of the H segment and the T segment existing in the step three, a 5 th-order Bezier curve is used for planning the speed curve, and the specific method is as follows:

general expressions according to bezier curves:deriving a velocity profile expression generated from a bezier curve of order 5:

V(t)＝P₀B₀(t)+P₁B₁(t)+P₂B₂(t)+P₃B₃(t)+P₄B₄(t)+P₅B₅(t) (3)

where t is 0-1, V (t) is the speed, P₀～P₅Is a Bessel control point, B₀(t)～B₅(t) is a bernstein polynomial;

therefore, equation (3) can also be written as:

V(t)＝At⁵+Bt⁴+Ct³+Dt²+Et+F (4)

wherein the coefficients A-F can be expressed as follows:

A＝-P₀+5P₁-10P₂+10P₃-5P₄+P₅

B＝5P₀-20P₁+30P₂-20P₃+5P₄

C＝-10P₀+30P₁-30P₂+10P₃

D＝10P₀-20P₁+10P₂

E＝-5P₀+5P₁

F＝P₀

h segmentOr acceleration and acceleration at two end points of the speed curve of the T section are zero, and the initial speed of the speed curve of the H section or the T section is marked as V_iThe last speed is denoted as V_fSetting a differential calculation initial phase P₀＝P₁＝P₂＝V_i，P₀、P₁And P₂Are all equal to the initial speed V_i，P₃＝P₄＝P₅＝V_f，P₃、P₄And P₅Are all equal to the final speed V_f；

Simplified A-F coefficient expression

A＝-6V_i+6V_f

B＝15V_i-15V_f

C＝-10V_i+10V_f

D＝0

E＝0

F＝V_i

Substituting coefficients A to F into formula (4), wherein the expression of the H-segment or T-segment speed curve is as follows:

V(t)＝(-6V_i+6V_f)t⁵+(15V_i-15V_f)Bt⁴+(-10V_i+10V_f)t³+V_i(5)。

4. the method for rapidly planning a 6 th-order S-shaped motion curve according to claim 3, wherein in the fourth step, the specific method for calculating the discrete V value on the velocity curve by using the forward difference method is as follows:

the calculation of the speed curve is designed as a forward difference mode:

V＝V+F₅

F₅＝F₅+F₄

F₄＝F₄+F₃

F₃＝F₃+F₂

F₂＝F₂+F₁

wherein F₁～F₅Calculating the difference;

the initial value calculation method of the forward difference algorithm comprises the following steps: equally dividing the speed curve into N parts according to time, wherein N is an integer, and the interval of each part is h, and then respectively calculating the initial value of the differential expression by using the following formula:

F₃(t₀)＝255Ah⁵+48Bh⁴+6Ch³

F₂(t₀)＝300Ah⁵+24Bh⁴

F₁(t₀)＝120Ah⁵

and (3) substituting the calculated initial value into a differential mode to carry out N-1 times of iterative calculation to obtain a complete 6-order speed curve, wherein each iterative calculation can calculate a real-time speed V.

5. A method for fast planning a 6 th order sigmoid motion curve according to claim 2,

solving for the final velocity V in equation (2)_fThe calculation of the power of 3 is used in the process, the calculation result is further approximated by a Newton-Laverson method,

0 equation is constructed for equation (2),

to facilitate the calculation of the equation to, Z (V)_f)＝((V_f-V_i)³)/L_x ²-J_m；

To Z (V)_f) Find at V_fThe derivative of (a):

use ofAnd (4) performing iterative calculation to approximate a true value, wherein n is an integer.

Technical Field

The invention relates to precision motion control, and is particularly suitable for high-speed and stable speed curve planning required by motion control.

Background

In the automation equipment with the motion unit, the motion unit of the equipment is prevented from generating impact, step loss, oscillation and overtravel in the processes of motion starting, stopping and speed changing so as to ensure the stability of the whole equipment under the condition of high-speed motion. The control signal output to the motion driver needs to be subjected to fine process planning, common motion process planning comprises two types of trapezoidal curves and S-shaped curves, the trapezoidal curves are small in calculation amount and easy to realize, and moment impact exists due to the fact that the acceleration track does not have a smooth process, and the motion process planning is rarely applied in engineering. The S-shaped curve is added with acceleration control, so that the sudden change of the moment can be effectively reduced, the moment output of the motor can be better controlled, the system can achieve higher acceleration and control precision, meanwhile, the mechanical impact is reduced, and the reliability of the equipment is improved.

The S curve is divided on the derivation order of the position curve according to the control fineness, 1 order Velocity, 2 order accumulation, 3 order Jerk,4 order Snap,5 order crack and 6 order Pop are formed, the track planning algorithm is more complex when the order is higher, the control effect is better, most commercial motion controllers in the market are controlled by 3 order curves at present, special equipment of part special industries can achieve 4 order curves, the S curve is calculated by using a traditional method and depends on very detailed segmentation, for example, the S curve of 4 order needs to be divided into 14 segments for calculation, the segmentation condition is complicated, the trajectory analysis is very complicated, errors are easy to generate in practical use, the requirement on realized hardware is very high, and the curve of 6 order belongs to the technology which is difficult to realize by using the traditional method.

Disclosure of Invention

Aiming at the problem that the planning of the current 6-order S-shaped motion curve is difficult to reliably realize, the invention provides a method for quickly planning the 6-order S-shaped motion curve, which is a method for realizing the planning of the 6-order motion curve based on the Bezier curve sampled at equal intervals and is easy for multi-platform realization and transplantation.

The invention discloses a method for rapidly planning a 6-order S-shaped motion curve, which comprises the following steps:

step 1, inputting motion curve parameters to be planned: length of track L_dStarting speed V_sEnd velocity V_eMaximum acceleration J_mMaximum allowable speed V_m。

Step 2, use J_mAnd V_mAs a constraint, calculate V_s、V_e、L_dRelation between, the fortune to be plannedThe dynamic curve is divided into an acceleration stage, a constant speed stage and a deceleration stage, wherein the acceleration stage is marked as an H section, the constant speed stage is marked as a B section, the deceleration stage is marked as a T section, the motion state segmentation condition which can appear on the S-shaped curve to be planned is one of HBT, HB, BT, HT, H, T and B, and the motion state combination on the S-shaped curve to be planned is judged;

step 3, planning a speed curve by using a 5-order Bezier curve for the motion curves of the existing H section and the T section;

and 4, sampling the speed curve planned in the third step at equal intervals, equally dividing the speed curve into N parts, wherein the time interval of each part is h, and calculating the discrete V value on the speed curve by adopting a forward difference mode, so that the 6-order control curve can be realized on different hardware platforms.

Has the advantages that:

according to the method for rapidly planning the 6-order S-shaped motion curve, the Bezier curve method of forward difference calculation is adopted, so that the calculation amount of the algorithm is reduced, and multiple platforms can be realized; the idea that a multi-stage motion control curve is divided into multiple sections in the traditional method and segmented execution is carried out by using numerous condition judgment is abandoned, the motion curve is divided into three types of acceleration, constant speed and deceleration by adopting simple classification or a combination of the three types, the speed curve is directly planned in the acceleration or deceleration process, the planning stage is simple and visual, and the robustness of the algorithm is greatly improved.

Drawings

FIG. 1 is a flowchart illustrating the overall steps of the present invention.

FIG. 2 is a flow chart of the present invention for determining the combination of the segments on the curve

Detailed Description

In order to make the technical solutions of the present invention better understood, the following description of the present invention in the course of its use is set forth without departing from the scope of the present invention, and the description in this section is only exemplary and explanatory and should not be construed as limiting the scope of the present invention in any way

The technical scheme adopted by the invention comprises the following steps:

the method comprises the following steps: for inputting curves to be plannedParameter, track length L_dStarting speed V_sEnd velocity V_eMaximum acceleration J_mMaximum allowable speed V_m。

Step two: use of J_mAnd V_mAs a constraint, calculate V_s、V_e、L_dThe relationship between; and segmenting the S-shaped curve to be planned according to the motion state, namely an acceleration stage, a constant speed stage and a deceleration stage, wherein the acceleration stage is marked as an H segment, the constant speed stage is marked as a B segment, the deceleration stage is marked as a T segment, the motion state combination condition which can appear on the S-shaped curve to be planned is one of HBT, HB, BT, HT, H, T and B, and the motion state combination on the S-shaped curve to be planned is judged.

Step three: for the motion curve with H segment and T segment, a 5 th order Bezier curve is used for planning the speed curve.

Step four: equally sampling the speed curve planned in the third step, equally dividing the speed curve into N parts, equally dividing the time interval of each part into h, adjusting the sampling interval according to the fine degree required to be controlled, calculating the Bezier curve by using a forward difference mode, correspondingly using a linear Pop as the speed plan to correspond to an S-shaped motion curve, namely 6-stage control, and realizing 6-stage control curves on different hardware platforms, wherein the hardware platform refers to a hardware scheme of a pulse type controller and a bus type controller

In the second step, the motion state segmentation combination on the S-shaped curve to be planned is judged according to the following formula:

according to the input initial speed V_iAnd end velocity V_fCalculating the moving distance L_xThe formula (2);

according to initial velocity V_iAnd a moving distance L_xCalculating the final velocity V_fThe formula (2);

the specific plunging process is as follows, using a fixed plus acceleration J during plunging_m；

The expression for the movement time T is:

the expression of the inflection point acceleration As of the concave-convex position of the S curve is As follows:

the expression of the acceleration change rate Ar is:

the expression for the distance of movement Lx is:

the reduction of the carry-in variables yields:

the final velocity V is simplified from the formula (1)_f：

Last velocity V_fThe calculation of the power of 3 is used, calculation errors can be brought in the calculation in a system with limited resources, and a Newton-Laverson method is used for further approximating the calculation result.

0 equation is constructed from the derivation process above,convenient calculation conversion into Z (V)_f)＝((V_f-V_i)³)/L_x ²-J_m。

Derivative at x for Z (x):

use ofAnd (3) performing iterative computation to approach a true value, wherein n is an integer, and performing twice iteration by using Newton-Laverson in a system with limited resources to achieve available computation precision.

Judging the motion state segmentation combination on the S-shaped curve to be planned, specifically as follows;

step 2.1, if V_s＝V_eIf so, the segment is in a constant-speed motion state process and is in a B-segment mode, the step II is ended, the curve planning step is exited, and otherwise, the step 2.2 is entered.

Step 2.2 if V_s≠V_eWill V_sAnd V_eSubstituting formula (1) to obtain the actual movement distance L during the speed variation_c：

Step 2.2.1, if L_c≥L_dAnd V is_s<V_eWhen the speed is changed from Vs to Ve, the speed is changed from Vs to Ve by indicating that the speed needs to be actually moved for a longer distance, and when Vs is smaller than Ve, the speed is changed for a set distance L_dThe inner part always makes acceleration movement, which is in an H-section mode, and the actual final speed V of the section can be calculated by the formula (2)_c，

And step three is entered, otherwise, step 2.2.2 is entered.

Step 2.2.1, if L_c≥L_dAnd V is_s>V_eWhen the speed is changed from Vs to Ve, the speed is changed from Vs to Ve by indicating that the speed needs to be actually moved for a longer distance, and when Vs is larger than Ve, the speed is changed for a set distance L_dThe inside of the cylinder is always in deceleration motion and is a T section, and the T section can be calculated by a formula (2)Actual end velocity V of the segment_cAnd entering a step three, otherwise, entering a step 2.2.3.

Step 2.2.3, if L_c<L_dAnd V is_m＝V_sWill V_sAnd V_eSubstituting formula (1) to obtain the distance L of movement in a deceleration state_t. And when L is_t<L_dWhen it is, it is BT segmented, i.e. the segment is first V_sIs at a constant speed and a uniform movement distance L_bFollowed by a deceleration movement, wherein L_b＝L_d-L_t. And step three, planning a speed curve of the T section in the BT section, otherwise, entering step 2.2.4.

Step 2.2.4, if L_c<L_dWill V_sAnd V_mSubstituting formula (1) to obtain the acceleration distance L_hIf L is_h<L_dAnd V is_m＝V_eIn HB segment mode, i.e. the segment is accelerated to V first_mThen, the reaction is performed again with V_mIs moved at a speed of (1). And step three, planning a speed curve of the H section in the HB section, and otherwise, entering step 2.2.5.

Step 2.2.5, if L_c<L_dWill V_sAnd V_mSubstituting formula (1) to obtain the moving distance L in the acceleration state_hWill V_mAnd V_eSubstituting formula (1) to obtain the distance L of movement in a deceleration state_t(ii) a Proceed to step 2.2.5.1

Step 2.2.5.1, if L_d<(L_h+L_t) Segmenting HT, namely, the curve of the segment is accelerated first, then immediately entering a deceleration motion mode, entering a step three, and otherwise, entering a step 2.2.5.2;

step 2.2.5.2, when L is_d>(L_h+L_t) When the HBT is segmented, the curve is accelerated, then enters a constant speed and is decelerated finally, and the movement distance in the middle constant speed state is L_b＝L_d-(L_h+L_t) And entering the step three.

In the step 3, the 5 th order Bezier curve is calculated by adopting a forward difference method, and the algorithm calculation derivation process comprises the following steps:

general expressions according to bezier curves:deriving a velocity profile expression generated from a bezier curve of order 5:

V(t)＝P₀B₀(t)+P₁B₁(t)+P₂B₂(t)+P₃B₃(t)+P₄B₄(t)+P₅B₅(t) (3)

where t is 0-1, V (t) is the speed, P₀～P₅Is a Bessel control point;

wherein B is₀(t)～B₅(t) is a Bernstein polynomial

B₀(t)＝(1-t)⁵＝-t⁵+5t⁴-10t³+10t²-5t+1

B₁(t)＝5(1-t)⁴×t＝5t⁵-20t⁴+30t³-20t²+5t

B₂(t)＝10(1-t)³×t²＝-10t⁵+30t⁴-30t³+10t²

B₃(t)＝10(1-t)²×t³＝10t⁵-20t⁴+10t³

B₄(t)＝5(1-t)×t⁴＝-5t⁵+5t⁴

B₅(t)＝t⁵

The velocity profile according to equation (3) can be expressed as:

V(t)＝At⁵+Bt⁴+Ct³+Dt²+Et+F

wherein the coefficients A-F can be expressed as follows:

A＝-P₀+5P₁-10P₂+10P₃-5P₄+P₅

B＝5P₀-20P₁+30P₂-20P₃+5P₄

C＝-10P₀+30P₁-30P₂+10P₃

D＝10P₀-20P₁+10P₂

E＝-5P₀+5P₁

F＝P₀

acceleration and acceleration at two end points of the motion curve of the H section and the T section are both zero, the initial speed of the speed curve of the H section or the T section is recorded as Vi, the final speed is recorded as Vf, and a difference calculation initial stage P is set₀＝P₁＝P₂＝V_iP0, P1 and P2 are all equal to the initial velocity V_i，P₃＝P₄＝P₅＝V_fP3, P4, and P5 are all equal to the terminal velocity Vf.

Simplified A-F coefficient expression

A＝-6V_i+6V_f

B＝15V_i-15V_f

C＝-10V_i+10V_f

D＝0

E＝0

F＝V_i

The velocity profile can be expressed as:

V(t)＝(-6V_i+6V_f)t⁵+(15V_i-15V_f)Bt⁴+(-10V_i+10V_f)t³+V_i

forward Difference Algorithm Condition, assuming Slave velocity Slave V_i～V_fAre divided into N steps and step lengthDifferential expression F₁～F₅Is started.

Under the existing initial condition, using the formula as shown to iterate and calculate for N times

V＝V+F₅

F₅＝F₅+F₄

F₄＝F₄+F₃

F₃＝F₃+F₂

F₂＝F₂+F₁

I.e. the discrete V values of the entire speed curve can be calculated.

Initial value calculation derivation: to facilitate the expression of the intermediate coefficient iterative transformation process, a is set to a, B is set to B, C is set to C, D is set to D, E is set to E, and F is set to F;

F₅(t)＝at⁵+bt⁴+ct³+dt²+et+f

F₅(t+h)-F₅(t)

＝(5ah)t⁴+(10ah²+4bh)t³+(10ah³+6bh²+3ch)t²

+(5ah⁴+4bh³+3ch²+2dh)t+ah⁵+bh⁴+ch³+dh²+eh

set by derivation of the previous step

a＝5Ah,b＝10Ah²+4Bh，c＝10Ah³+6Bh²+3Ch；

d＝5Ah⁴+4Bh³+3Ch²+2Dh

F₄(t)＝at⁴+bt³+ct²+dt+e

F₄(t+h)-F₄(t)

＝(20ah²)t³+(60ah³+12bh²)t³+(70ah⁴+24bh³+6ch²)t

+30ah⁵+14bh⁴+6ch³+2dh²

Set by derivation of the previous step

a＝20Ah²,b＝60Ah³+12Bh²,c＝70Ah⁴+24Bh³+6Ch²

F₃(t)＝at³+bt²+ct+d

F₃(t+h)-F₃(t)＝(60ah³)t²+(180ah⁴+24bh³)t+150ah⁵+36bh⁴+6ch³

Set by derivation of the previous step

a＝60Ah³,b＝180Ah⁴+24Bh³

F₂(t)＝at²+bt+c

F₂(t+h)-F₂(t)＝(120ah⁴)t+240ah⁵+24bh⁴

Set by derivation of the previous step

a＝120Ah⁴

F₁(t)＝at+b

F₁(t+h)-F₁(t)＝120ah⁵

Since we divide the speed curve equally by h, each speed point represents the speed in this segment, then the initial time point in the initial value calculationWhile the number of iterations becomes N-1, bringing into the initial time point t₀Calculating an initial value of the difference calculation:

F₃(t₀)＝255Ah⁵+48Bh⁴+6Ch³

F₂(t₀)＝300Ah⁵+24Bh⁴

F₁(t₀)＝120Ah⁵

in the step 4, sampling is carried out at equal intervals, the sampling interval is h defined in the step three, and the number of segments is N-1.

Pulse type controller using frequency at each speed update pointDuration of outputh, until the iteration is finished, the control output can be finished;

and the bus type controller outputs V (t + h) which is V (t) + F5 at each speed updating point until iteration is completed, so that control output can be completed, wherein V (t + h) is a control position required to be output by motion control.

The following description of the speed planning is given for possible combinations of the movement states that can occur on the sigmoid curve to be planned.

Knowing the length L of the trajectory of the curve to be planned_dStarting speed V_sEnd velocity V_eMaximum acceleration J_mMaximum allowable speed V_mAfter the judgment in the step 2;

if the segment is a B segment curve after judgment, the B segment does not need to be subjected to speed curve transformation because the B segment is a constant-speed motion segment, the B segment speed curve is a constant value, and the speed value V of the B segment is V_s＝V_e(ii) a Completing the operation curve planning;

if the segment is the H-segment curve after judgment, the speed of the segment curve is from V_sAccelerating to the actual final speed V_cFrom the equation (2), the actual final velocity V can be found_cValue of (A)In which the velocity can be planned from V by step 3 of the invention_sTo the actual final speed V_cThe velocity profile of (a) on which V can be calculated by step 4 of the present invention_sTo V_cDiscrete speed values are obtained, and operation curve planning is completed;

if the section is a T-section curve after judgment, the speed of the section of curve is from V_sDecelerating to the actual final speed V_cWherein the velocity can be programmed from V by step 3 of the invention_sTo the actual final speed V_cThe velocity profile of (a) on which V can be calculated by step 4 of the present invention_sTo V_cDiscrete speed values are obtained, and operation curve planning is completed;

if the section is a BT piecewise curve after judgment, the section of curve isThe speed is initially held at V_sThen from V_sIs decelerated to V_eCalculating the speed of the T subsection part by adopting the methods of the steps 3 and 4 in the invention to complete the planning of the operation curve;

if the section is HB piecewise curve after judgment, the speed of the curve is from V_sAccelerating to maximum allowable speed V_mThen at a speed V_mThe movement is always uniform. Wherein the slave speed V is planned by step 3 of the invention_sTo the maximum allowable speed V_mThe velocity variation curve between, V on which can be calculated by step 4 of the present invention_sTo V_mDiscrete speed values are obtained, and operation curve planning is completed;

if the segment is a HT segmented curve after judgment, the speed of the segment is from V_sAccelerate to V_mThen from V_mIs decelerated to V_eCalculating the speed of the H and T sections by adopting the methods of the step 3 and the step 4 in the invention to complete the planning of the operation curve;

if the segment is HBT segment curve after judgment, the speed of the segment curve is from V_sAccelerate to V_mThen enter B segment by V_mRun at uniform speed L_bLength back into T segment from V_mIs decelerated to V_eAnd calculating the speed of the H and T sections by adopting the methods of the steps 3 and 4 in the invention to finish the planning of the operation curve.