CN112506143A - High-quality processing quintic polynomial speed planning method based on S-shaped curve - Google Patents

High-quality processing quintic polynomial speed planning method based on S-shaped curve Download PDF

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CN112506143A
CN112506143A CN202011418004.3A CN202011418004A CN112506143A CN 112506143 A CN112506143 A CN 112506143A CN 202011418004 A CN202011418004 A CN 202011418004A CN 112506143 A CN112506143 A CN 112506143A
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acceleration
interpolation
speed
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deceleration
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盖荣丽
杜晓燕
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Dalian University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/416—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control of velocity, acceleration or deceleration
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
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Abstract

The invention discloses a high-quality processing quintic polynomial speed planning method based on an S-shaped curve. Judging the reverse maximum acceleration-AmaxAnd maximum acceleration AmaxCan not be reached. Then, the whole acceleration and deceleration process is segmented to respectively obtain a fifth-order polynomial equation of each segment. And recording the interpolated parameters and the interpolated distance in the rapid interpolation process. Data obtained by fast interpolation is recorded in an acceleration and deceleration array and then applied to real-time interpolation. The method can achieve the continuous change of the speed, the acceleration and the jerk in the moving process of the machine tool cutter, controls the speed, the acceleration and the jerk in an ideal range, has small error and greatly improved precision, and realizes high flexibilityAnd (4) controlling the acceleration and deceleration.

Description

High-quality processing quintic polynomial speed planning method based on S-shaped curve
Technical Field
The invention relates to the field of numerical control machine tool machining, in particular to a high-quality machining fifth-order polynomial speed planning method based on an S-shaped curve.
Background
Under the rapid development of science and technology in the society nowadays, the field of numerical control machine tools is developing towards the direction of high speed, high precision, intellectualization and openness. Whether continuous and smooth change of the feeding speed and improvement of the flexibility of the system can be ensured in high-speed precision machining has a great influence on the actual machining quality, and acceleration and deceleration control is particularly important at this time. The acceleration and deceleration control algorithm is used for controlling and planning the speed, the acceleration, the jerk and the like in the machining path. The good acceleration and deceleration control algorithm has important influence on the processing efficiency and quality of the numerical control machine tool. Therefore, the search for a good acceleration and deceleration control algorithm has important significance on high quality, high speed and high precision required in the numerical control machine tool machining.
The most used acceleration and deceleration control methods in the machining of the numerical control machine tool at present mainly comprise a linear acceleration and deceleration control method, an exponential acceleration and deceleration control method, an S-curve acceleration and deceleration control method, a sine function square curve acceleration and deceleration control method and the like. The acceleration and deceleration control methods have respective advantages and disadvantages. For example, although the linear acceleration and deceleration control method cannot guarantee the continuity of a curve in the acceleration and deceleration process, if the acceleration suddenly changes, the linear acceleration and deceleration control method may have a great influence on a machine tool, but the formula is easy to understand, the implementation method is simple, and the linear acceleration and deceleration control method is the earliest used acceleration and deceleration control method. In contrast, the exponential acceleration and deceleration control method has better continuity, stronger stability during experiment, and ideal overall effect compared with a linear acceleration and deceleration control algorithm. However, the exponential acceleration and deceleration control method comprises a large amount of exponential calculation, is complex and difficult to realize, and has sudden change of the acceleration. The S-curve acceleration and deceleration control method can ensure the flexibility of the system, in the acceleration and deceleration process, the whole process is divided into seven sections, and each section is calculated respectively, so that the stability and the precision are improved, but the method is complex, the calculation amount is large, and the program is difficult to realize. The sine square curve acceleration and deceleration method is improved on the basis of other methods, and the continuity of curves such as speed and the like is realized, but the speed curve in the method is not smooth enough, and large errors of a system can be caused, so that unnecessary loss is caused to a final result.
Disclosure of Invention
Aiming at the defects and shortcomings of the existing numerical control machine tool machining acceleration and deceleration motion process, the application provides a high-quality machining quintic polynomial speed planning method based on an S-shaped curve, the method can ensure the continuous change of speed, acceleration and acceleration, the machining flexibility is improved, the error is reduced, and the precision is obviously improved.
In order to achieve the purpose, the technical scheme of the application is as follows: the high-quality processing quintic polynomial speed planning method based on the S-shaped curve comprises the following steps:
fast interpolating a curve to be processed to obtain a feeding speed in an acceleration and deceleration process, and recording a starting point of acceleration/deceleration and an extreme point of the speed in the acceleration and deceleration process;
judging whether the maximum acceleration and the maximum reverse acceleration can be reached according to the extreme point of the speed in the acceleration and deceleration process;
segmenting the acceleration and deceleration process and obtaining a quintic polynomial equation corresponding to each segment;
recording interpolation distances traveled by the maximum acceleration and the maximum reverse acceleration, and recording interpolation parameters in the process in an acceleration and deceleration array for real-time interpolation;
and carrying out real-time interpolation through the information in the acceleration and deceleration array and the interpolation parameters.
Further, the feed interpolation speed of the fast interpolation is as follows:
Figure BDA0002820866130000021
wherein v ismaxIs the maximum velocity, xiIs the interpolation parameter corresponding to the current interpolation point, ve(xi) The velocity within the specified range for the current system is calculated by the following formula:
Figure BDA0002820866130000031
wherein T is a system interpolation period, betaiIs the radius of curvature, HmaxThe maximum chord height error specified for the system.
Further, the starting point of acceleration refers to a point at which the speed starts to increase gradually within a range of a prescribed condition; let x beaFor an interpolation point at which acceleration starts, the velocity v at this interpolation pointaThe following conditions need to be satisfied:
va≥va-1,va＜va+1
wherein v isa-1For interpolation of point xa-1At the corresponding interpolation speed, va+1For interpolation of point xa+1The corresponding interpolation speed is processed;
the starting point of deceleration is a point at which the speed starts to decrease gradually within a range of a predetermined condition; let x bebAt the interpolation point where deceleration starts, the velocity v at the interpolation pointbThe following conditions need to be satisfied:
vb＜vb+1,vb≥vb-1
wherein v isb+1For interpolation of point xb+1At the corresponding interpolation speed, vb-1For interpolation of point xb-1The corresponding interpolation speed is obtained.
Further, the maximum speed value is the speed at the moment when the speed reaches the maximum within the system constraint range in the acceleration process; interpolation point x to maximum speedmAt a maximum velocity vmThe following conditions are satisfied:
vm＞vm-1,vm＞vm+1
wherein v ism-1For interpolation of point xm-1At a corresponding speed, vm+1For interpolation of point xm+1The corresponding speed;
the speed minimum value is the speed at the moment when the speed reaches the minimum within the system constraint range in the acceleration process; interpolation point x to minimum speednMinimum velocity v ofnThe following conditions are satisfied:
vn＜vn-1,vn＜vn+1
wherein v isn-1For interpolation of point xn-1At a corresponding speed, vn+1For interpolation of point xn+1At the corresponding speed.
Further, whether or not the maximum acceleration A can be reachedmaxAccording to
Figure BDA0002820866130000032
And
Figure BDA0002820866130000033
judging the size of the product:
if it is
Figure BDA0002820866130000041
Is greater than
Figure BDA0002820866130000042
The maximum acceleration a can be reachedmaxThe acceleration process at this moment is a jerk section, a uniform acceleration section and a deceleration and acceleration section;
if it is
Figure BDA0002820866130000043
Is equal to
Figure BDA0002820866130000044
The maximum acceleration a may still be reachedmaxThe acceleration process at this moment is an acceleration adding section and an acceleration reducing section;
if it is
Figure BDA0002820866130000045
Is less than
Figure BDA0002820866130000046
The maximum acceleration a cannot be reachedmaxWhen the acceleration process comprises an acceleration adding section and an acceleration reducing section;
wherein, JmaxIs the maximum jerk, vj，viRespectively the initial speed and the end speed of the acceleration and deceleration process;
the process of determining whether the minimum acceleration can be reached is the same as the above process of determining whether the maximum acceleration can be reached.
Further, the fifth order polynomial velocity equation is:
v(t)＝a0+a1t+a2t2+a3t3+a4t4+a5t5
wherein t is the time of the movement; a is0、a1、a2、a3、a4、a5Respectively the coefficient of the time of the movement.
Further, the fifth order polynomial displacement equation is:
Figure BDA0002820866130000047
wherein S is0Is the initial displacement, t is the time of the movement; a is0、a1、a2、a3、a4、a5Respectively the coefficient of the time of the movement.
Further, the interpolation distance traveled to achieve the maximum acceleration and the maximum reverse acceleration refers to the theoretical path length of acceleration/deceleration between two interpolation points within the range of system-specified conditions.
As a further step, searching interpolation parameters forward, and recording the speed of the current interpolation point; specifying the interpolation parameter to be found as xkFind xkThen, x is obtainedkHas an interpolation path of lk(ii) a If it is satisfied at xjInterpolation distance of points and xkIf the difference of the interpolation distances is not less than S, x iskThe correct interpolation point; namely, it is
lj-lk≥S
Wherein S is an interpolation distance of acceleration/deceleration;
continuously comparing the current interpolation point with the specified interpolation point, if x is satisfiedi≤xkThen x is obviousiThe point is the starting point of the acceleration section; if x appearsi＞xkCase, then xkIs the starting point of the acceleration section; the velocity size of the starting point is recorded.
As a further specific process, the real-time interpolation is as follows:
comparing whether the current interpolation parameter is in the range of the acceleration and deceleration starting parameter, if the current interpolation parameter is not in the range of the acceleration and deceleration starting parameter, keeping the system moving at a constant speed; if the current interpolation parameter is in the initial parameter range of acceleration and deceleration, fast interpolation is firstly carried out to obtain the real-time speed of the current interpolation parameter, and then real-time interpolation is carried out; if the speed is reduced to the minimum value in advance in the deceleration process, the machine tool is kept to move at a constant speed in order to avoid shaking of the machine tool.
Compared with the existing method, the method has the advantages that: the speed curve is a quintic curve, the acceleration curve is a quartic curve, and the jerk curve is a cubic curve; the speed, the acceleration and the jerk all realize continuous change in the moving process of the cutter, so that the good smoothness and stability are ensured, sudden change is avoided, and unnecessary loss caused by machine tool shaking due to discontinuity is effectively avoided. The high-flexibility quintic polynomial method adopted by the invention has the advantages of small error and high precision.
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FIG. 1 is a flow chart of a high quality process quintic polynomial velocity planning method of the present application;
FIG. 2 is a graph of velocity, acceleration and jerk of a fifth order polynomial containing a uniform acceleration section of an acceleration section;
FIG. 3 is a graph of velocity, acceleration and jerk of a fifth order polynomial of an acceleration section without a uniform acceleration section;
FIG. 4 is a graph of velocity, acceleration and jerk of a fifth order polynomial containing a uniform deceleration section of the deceleration section;
FIG. 5 is a graph of a fifth order polynomial of the deceleration section without velocity, acceleration and jerk of the uniform deceleration section;
FIG. 6 is a graph of curvature calculated using chordal height error;
FIG. 7 is a processed NURBS graph;
FIG. 8 is a graph of fifth order polynomial velocity;
FIG. 9 is a graph of a fifth order polynomial acceleration curve;
FIG. 10 is a graph of a fifth order polynomial jerk;
FIG. 11 is a graph of a fifth order polynomial error plot.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples: the present application is further described by taking this as an example.
The method of the invention is executed with simulation verification at the computer end, runs in Dev-C + +. lnk, uses C language to program, and realizes drawing in Matlab2016 edition. The spline curve used was an "inverted 8" NURBS curve, as shown in fig. 7.
The interpolation parameters of the system are as follows:
the simulated programming speed F is 0.5 m/s.
Maximum acceleration of Amax＝0.005m/s2。
Maximum jerk is Jmax＝0.0006m/s2。
Maximum error limit is Hmax＝0.0005mm。
The interpolation period T is 2 ms.
The method is suitable for the movement of a machining tool of a numerical control system, and the interpolation and speed planning are carried out on a curve to be machined, and a flow chart is shown in figure 1. The method comprises the following specific steps:
firstly, rapidly interpolating a curve to be processed: and obtaining the feeding speed in the acceleration and deceleration process, recording the starting point of acceleration/deceleration and the speed extreme point in the acceleration and deceleration process. Judging whether the maximum acceleration and the maximum reverse acceleration can be reached or not according to the speed extreme point, segmenting the whole acceleration and deceleration process and solving a quintic polynomial equation corresponding to each segment; recording interpolation distances traveled by the maximum acceleration and the maximum reverse acceleration, and recording interpolation parameters in the process in an acceleration and deceleration array for real-time interpolation; and performing real-time interpolation according to the information, interpolation parameters and the like in the acceleration and deceleration array obtained in the rapid interpolation.
The fast interpolation steps are:
firstly, the feed interpolation speed is obtained through the following formula:
Figure BDA0002820866130000071
wherein v ismaxIs the maximum velocity, xiIs the interpolation parameter corresponding to the current interpolation point, ve(xi) Speed within the specified range for the current systemDegree, calculated by the following formula:
Figure BDA0002820866130000072
wherein T is a system interpolation period, betaiIs the radius of curvature, HmaxThe maximum chord height error specified for the system.
The start of acceleration/deceleration is then recorded.
The starting point of acceleration is a point at which the speed starts to increase gradually within a predetermined range of conditions. Let x beaFor an interpolation point at which acceleration starts, the velocity v at this interpolation pointaThe following conditions need to be satisfied:
va≥va-1,va＜va+1
wherein v isa-1For interpolation of point xa-1At the corresponding interpolation speed, va+1For interpolation of point xa+1The corresponding interpolation speed is obtained.
The start point of deceleration is a point at which the speed starts to decrease gradually within a range of a predetermined condition. Let x bebAt the interpolation point where deceleration starts, the velocity v at the interpolation pointbThe following conditions need to be satisfied:
vb＜vb+1,vb≥vb-1
wherein v isb+1For interpolation of point xb+1At the corresponding interpolation speed, vb-1For interpolation of point xb-1The corresponding interpolation speed is obtained.
The maximum and minimum speed values are determined.
The speed maximum is the speed at the moment when the speed reaches the maximum within the constraints of the system during acceleration. The speed minimum refers to the speed at the moment when the speed reaches the minimum within the constraints of the system during acceleration.
The invention solves the problem of machine tool shaking caused by discontinuous unsmooth speed, acceleration, jerk and the like in the traditional algorithm. The velocity curve adopts a fifth-order polynomial curve, the acceleration curve conducts first-order derivation on the velocity curve to obtain a fourth-order polynomial curve, and the acceleration curve conducts derivation on the acceleration curve to obtain a third-order polynomial velocity curve. The invention ensures the continuous change of speed, acceleration and jerk. And carrying out segmented processing on the whole acceleration and deceleration process according to the judgment of whether the maximum acceleration can be reached, wherein the specific speed planning steps are as follows:
1) and judging whether the maximum acceleration can be reached. The specific method comprises the following steps:
according to
Figure BDA0002820866130000081
And
Figure BDA0002820866130000082
judging the size of the product:
if it is
Figure BDA0002820866130000083
Is greater than
Figure BDA0002820866130000084
The maximum acceleration AmaxThe acceleration process at the moment can be a jerk section, a uniform acceleration section and a deceleration and acceleration section.
If it is
Figure BDA0002820866130000085
Is equal to
Figure BDA0002820866130000086
At this time, the maximum acceleration AmaxStill, the acceleration process can be achieved, but the acceleration process does not contain a uniform acceleration section, and is divided into an acceleration increasing section and an acceleration decreasing section.
If it is
Figure BDA0002820866130000087
Is less than
Figure BDA0002820866130000088
At this time, the maximum acceleration AmaxCannot be achieved. The acceleration process includes an acceleration segment and a deceleration segment.
The deceleration process is the same as the acceleration process.
2) Introducing a fifth-order polynomial velocity equation into each section, wherein the velocity equation is as follows:
v(t)＝a0+a1t+a2t2+a3t3+a4t4+a5t5
the acceleration equation is obtained by performing a derivation on the velocity equation, and the acceleration equation is as follows:
a(t)＝a1+2a2t+3a3t2+4a4t3+5a5t4
the jerk equation is derived once more from the acceleration equation as follows:
j(t)＝2a2+6a3t+12a4t2+20a5t3
solving each acceleration and deceleration section by adopting an undetermined coefficient method according to the equation to obtain the following equation: if the acceleration stage is divided into three sections, as shown in fig. 2, the equations of the sections are as follows:
an acceleration section:
Figure BDA0002820866130000091
a uniform acceleration section:
Figure BDA0002820866130000092
a deceleration and acceleration section:
Figure BDA0002820866130000093
wherein the content of the first and second substances,
Figure BDA0002820866130000094
vs,verespectively the starting speed and the ending speed of the acceleration and deceleration section.
If the acceleration phase is divided into two segments, as shown in fig. 3, the equations for each segment are as follows:
an acceleration section:
Figure BDA0002820866130000095
a deceleration and acceleration section:
Figure BDA0002820866130000096
if the deceleration section is divided into three sections, as shown in fig. 4, the velocity equation of each section at this time is as follows:
an acceleration and deceleration section:
Figure BDA0002820866130000097
a uniform deceleration section:
Figure BDA0002820866130000101
a speed reduction section:
Figure BDA0002820866130000102
if the deceleration section is divided into two sections, as shown in fig. 5, the velocity equation of each section is as follows:
an acceleration and deceleration section:
Figure BDA0002820866130000103
a speed reduction section:
Figure BDA0002820866130000104
3) and a displacement equation is introduced, so that the theoretical acceleration and deceleration distance can be conveniently calculated.
The fifth order polynomial displacement equation is:
Figure BDA0002820866130000105
4) and judging that the acceleration and deceleration section is divided into a plurality of sections, and if the acceleration section is divided into three sections, namely an acceleration adding section, an acceleration homogenizing section and an acceleration reducing section, judging the distance of the theoretical acceleration section, namely the sum of the three sections. If the acceleration section comprises only two sections: and adding an acceleration section and subtracting the acceleration section, wherein the theoretical acceleration section distance is the sum of the two sections. The deceleration section works in the same way.
5) And searching interpolation parameters forward, and recording the speed of the current interpolation point. Specifying the interpolation parameter to be found as xkFind xkThen, x is obtainedkHas an interpolation path of lk. If it is satisfied at xjInterpolation distance of points and xkIf the difference of the interpolation distances is not less than S, x iskIs the correct interpolation point. I.e. |j-lkAnd the S is the interpolation distance of acceleration/deceleration.
Continuously comparing the current interpolation point with the specified interpolation point, if x is satisfiedi≤xkThen x is obviousiThe point is the starting point of the acceleration segment. If x appearsi＞xkCase, then xkIs the starting point of the acceleration segment. The velocity size of the starting point is recorded.
When the rapid interpolation, namely the preprocessing stage is finished, an acceleration and deceleration stage array can be obtained to store the interpolation information of the rapid interpolation stage. After the rapid interpolation is finished, performing real-time interpolation, and specifically comprising the following steps of: and comparing whether the current interpolation parameter is in the range of the acceleration and deceleration starting parameter, and if the current interpolation parameter is not in the range of the acceleration and deceleration starting parameter, keeping the system to do uniform motion. If the current interpolation parameter is in the initial parameter range of acceleration and deceleration, fast interpolation is firstly carried out to obtain the real-time speed of the current interpolation parameter, and then real-time interpolation is carried out. If the speed is reduced to the minimum value in advance in the deceleration process, the machine tool is kept to move at a constant speed in order to avoid shaking of the machine tool.
The fast and real-time interpolation of the NURBS curve shown in fig. 7 was performed using a quintic polynomial velocity planning algorithm, and the results are shown in fig. 8-11. The following conclusions are reached by analyzing fig. 8-11:
the method has stronger continuity. The speed curve is a quintic curve, the acceleration curve is a quartic curve, and the jerk curve is a cubic curve. The speed, the acceleration and the jerk all realize continuous change in the moving process of the cutter. The method ensures good smoothness and stability, does not generate sudden change, and effectively avoids unnecessary loss caused by machine tool shaking due to discontinuity.
The invention has high precision. The high-flexibility quintic polynomial method adopted by the invention has the advantages of small error, high flexibility and obviously improved precision compared with other speed planning algorithms.
The invention meets the requirement of the numerical control machine tool system on precision, controls the speed, the acceleration, the jerk and the error within the ideal range, and meets the processing requirement of the system.
The above description is only for the purpose of creating a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.

Claims (10)

1. The high-quality processing quintic polynomial speed planning method based on the S-shaped curve is characterized by comprising the following steps of:
fast interpolating a curve to be processed to obtain a feeding speed in an acceleration and deceleration process, and recording a starting point of acceleration/deceleration and an extreme point of the speed in the acceleration and deceleration process;
judging whether the maximum acceleration and the maximum reverse acceleration can be reached according to the extreme point of the speed in the acceleration and deceleration process;
segmenting the acceleration and deceleration process and obtaining a quintic polynomial equation corresponding to each segment;
recording interpolation distances traveled by the maximum acceleration and the maximum reverse acceleration, and recording interpolation parameters in the process in an acceleration and deceleration array for real-time interpolation;
and carrying out real-time interpolation through the information in the acceleration and deceleration array and the interpolation parameters.
2. The sigmoidal curve-based quintic polynomial speed planning method of claim 1 wherein the fast interpolation feed interpolation speed is:
Figure FDA0002820866120000011
wherein v ismaxIs the maximum velocity, xiIs the interpolation parameter corresponding to the current interpolation point, ve(xi) The velocity within the specified range for the current system is calculated by the following formula:
Figure FDA0002820866120000012
wherein T is a system interpolation period, betaiIs the radius of curvature, HmaxThe maximum chord height error specified for the system.
3. The sigmoid curve-based quintic polynomial velocity planning method of claim 1, wherein the starting point of acceleration is the point at which the velocity starts to increase gradually within a specified condition; let x beaFor an interpolation point at which acceleration starts, the velocity v at this interpolation pointaThe following conditions need to be satisfied:
va≥va-1,va＜va+1
wherein v isa-1For interpolation of point xa-1At the corresponding interpolation speed, va+1For interpolation of point xa+1The corresponding interpolation speed is processed;
the starting point of deceleration is a point at which the speed starts to decrease gradually within a range of a predetermined condition; let x bebAt the interpolation point where deceleration starts, the velocity v at the interpolation pointbThe following conditions need to be satisfied:
vb＜vb+1,vb≥vb-1
wherein v isb+1For interpolation of point xb+1At the corresponding interpolation speed, vb-1For interpolation of point xb-1The corresponding interpolation speed is obtained.
4. The sigmoidal curve-based quintic velocity planning method of claim 1, wherein the velocity maxima is the velocity at which the velocity reaches the maximum time within the system constraints during acceleration; interpolation point x to maximum speedmAt a maximum velocity vmThe following conditions are satisfied:
vm＞vm-1,vm＞vm+1
wherein v ism-1For interpolation of point xm-1At a corresponding speed, vm+1For interpolation of point xm+1The corresponding speed;
the speed minimum value is the speed at the moment when the speed reaches the minimum within the system constraint range in the acceleration process; interpolation point x to minimum speednMinimum velocity v ofnThe following conditions are satisfied:
vn＜vn-1,vn＜vn+1
wherein v isn-1For interpolation of point xn-1At a corresponding speed, vn+1For interpolation of point xn+1At the corresponding speed.
5. The sigmoidal curve-based high quality process quintic polynomial velocity planning method of claim 1, wherein the maximum acceleration A can be reachedmaxAccording to
Figure FDA0002820866120000021
And
Figure FDA0002820866120000022
judging the size of the product:
if it is
Figure FDA0002820866120000023
Is greater than
Figure FDA0002820866120000024
The maximum acceleration a can be reachedmaxThe acceleration process at this moment is a jerk section, a uniform acceleration section and a deceleration and acceleration section;
if it is
Figure FDA0002820866120000025
Is equal to
Figure FDA0002820866120000026
The maximum acceleration a may still be reachedmaxThe acceleration process at this moment is an acceleration adding section and an acceleration reducing section;
if it is
Figure FDA0002820866120000031
Is less than
Figure FDA0002820866120000032
The maximum acceleration a cannot be reachedmaxWhen the acceleration process comprises an acceleration adding section and an acceleration reducing section;
wherein, JmaxIs the maximum jerk, vj，viRespectively the initial speed and the end speed of the acceleration and deceleration process;
the process of determining whether the minimum acceleration can be reached is the same as the above process of determining whether the maximum acceleration can be reached.
6. The sigmoidal curve-based quintic velocity planning method of claim 1, wherein the quintic polynomial velocity equation is:
v(t)＝a0+a1t+a2t2+a3t3+a4t4+a5t5
wherein t is the time of the movement; a is0、a1、a2、a3、a4、a5Respectively the coefficient of the time of the movement.
7. The sigmoidal curve-based quintic velocity planning method for high quality processing according to claim 1, wherein the quintic polynomial displacement equation is:
Figure FDA0002820866120000033
wherein S is0Is the initial displacement, t is the time of the movement; a is0、a1、a2、a3、a4、a5Respectively the coefficient of the time of the movement.
8. The sigmoidal curve-based quintic polynomial velocity planning method of claim 1, wherein the interpolation distance traveled to achieve maximum acceleration and maximum reverse acceleration is the theoretical path length of acceleration/deceleration between two interpolation points within the system-specified condition range.
9. The sigmoidal curve-based high-quality processing quintic polynomial velocity planning method of claim 8, wherein interpolation parameters are found forward while recording the velocity of the current interpolation point; specifying the interpolation parameter to be found as xkFind xkThen, x is obtainedkHas an interpolation path of lk(ii) a If it is satisfied at xjInterpolation distance of points and xkIf the difference of the interpolation distances is not less than S, x iskThe correct interpolation point; namely, it is
lj-lk≥S
Wherein S is an interpolation distance of acceleration/deceleration;
continuously comparing the current interpolation point with the specified interpolation point, if x is satisfiedi≤xkThen x is obviousiThe point is the starting point of the acceleration section; if x appearsi＞xkCase, then xkIs the starting point of the acceleration section; the velocity size of the starting point is recorded.
10. The sigmoidal curve-based high-quality processing quintic polynomial speed planning method of claim 1, wherein the real-time interpolation specifically comprises the following steps:
comparing whether the current interpolation parameter is in the range of the acceleration and deceleration starting parameter, if the current interpolation parameter is not in the range of the acceleration and deceleration starting parameter, keeping the system moving at a constant speed; if the current interpolation parameter is in the initial parameter range of acceleration and deceleration, fast interpolation is firstly carried out to obtain the real-time speed of the current interpolation parameter, and then real-time interpolation is carried out; if the speed is reduced to the minimum value in advance in the deceleration process, the machine tool is kept to move at a constant speed in order to avoid shaking of the machine tool.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113534789A (en) * 2021-05-18 2021-10-22 杭州壹悟科技有限公司 Real-time planning method and device for cubic polynomial speed curve of mobile robot
CN113970905A (en) * 2021-10-26 2022-01-25 广东工业大学 Arbitrary-order S-shaped curve motion planning method for high-precision motion platform control

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103801981A (en) * 2012-11-14 2014-05-21 中国科学院沈阳计算技术研究所有限公司 Quartic polynomial speed planning algorithm for spline interpolation

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103801981A (en) * 2012-11-14 2014-05-21 中国科学院沈阳计算技术研究所有限公司 Quartic polynomial speed planning algorithm for spline interpolation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
CHEN J H: "An S-curve Acceleration/Deceleration Design for CNC Machine Tools Using Quintic Feedrate Function", COMPUTER-AIDED DESIGN AND APPLICATIONS, pages 583 - 592 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113534789A (en) * 2021-05-18 2021-10-22 杭州壹悟科技有限公司 Real-time planning method and device for cubic polynomial speed curve of mobile robot
CN113534789B (en) * 2021-05-18 2024-04-05 杭州壹悟科技有限公司 Method and device for real-time planning of three-time polynomial speed curve of mobile robot
CN113970905A (en) * 2021-10-26 2022-01-25 广东工业大学 Arbitrary-order S-shaped curve motion planning method for high-precision motion platform control
CN113970905B (en) * 2021-10-26 2023-07-18 广东工业大学 Arbitrary-order S-shaped curve motion planning method for high-precision motion platform control

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