WO2018131778A1

WO2018131778A1 - Method for generating motion profile by using s-curve, and computing device

Info

Publication number: WO2018131778A1
Application number: PCT/KR2017/012030
Authority: WO
Inventors: 배상진
Original assignee: 한화테크윈주식회사
Priority date: 2017-01-10
Filing date: 2017-10-27
Publication date: 2018-07-19
Also published as: KR20180082115A; CN110023856B; CN110023856A

Abstract

The present embodiment provides a method for generating a motion profile by using an S-curve, and a computing device therefor. A method for generating a motion profile by using an S-curve according to an embodiment of the present invention comprises the steps of: under one or more restrictions, calculating a time of each of an acceleration section, a maximum acceleration section, a maximum velocity section, a deceleration section, and a maximum deceleration section; applying the calculated time and a jerk to a polynomial defined for each section to generate a motion profile; and generating a superimposed motion profile having two or more consecutive motion profiles in which a final velocity of a previous motion is an initial velocity of a subsequent motion.

Description

Motion profile generation method and computing device using S-curve

The present embodiment relates to a method for generating a motion profile using an S-curve and a computing device therefor.

Recently, the introduction of robots for manufacturing in small, precision assembly and processing processes has been actively made around the automotive and semiconductor industries. Incoming motor control mounted on the robot's joints uses an S-curve velocity profile that limits the trapezoidal or jerk values as a reference signal to generate point to point motion. Since the movement time and the moving pattern of the robot are determined by the generated profile, it is important to generate a profile for high speed low vibration motion.

Embodiments of the present invention provide a method of generating a motion profile having any limited jerk value, generating an asymmetric speed profile with any constant as the initial and ending speeds, and superimposing two or more motions.

Motion profile generation method using the S-curve according to an embodiment of the present invention, under one or more constraints, calculating the time of each of the acceleration section, the maximum acceleration section, the maximum speed section, the deceleration section and the maximum deceleration section; Generating a motion profile by applying the calculated time and jerk to a polynomial defined for each section; And generating an overlapping motion profile in which two or more motion profiles, the final velocity of the previous motion as the initial velocity of the next motion, are continuous.

The initial speed and the final speed may be any constant.

The calculating of time may include calculating time of each section by a corresponding polynomial according to a comparison result with a moving distance to a target position, a first threshold distance, and a second threshold distance longer than the first threshold distance. can do.

If the moving distance is less than the first critical distance,

The time of each interval is calculated by the polynomial of

Here, Ta may be a time of the maximum acceleration section, Tv may be a time of the maximum speed section, Td may be a time of the maximum deceleration section, Tja may be a time of the acceleration section, and Tjd may be a time of the deceleration section.

If the moving distance is between the first critical distance and the second critical distance,

The time of each interval is calculated by the polynomial of

Here, Ta may be a time of the maximum acceleration section, Td may be a time of the maximum deceleration section, Tja may be a time of the acceleration section, and Tjd may be a time of the deceleration section.

If the moving distance is greater than the second critical distance,

The time of each interval is calculated by the polynomial of

Here, Ta is the time of the maximum acceleration section, Tv is the time of the maximum speed section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section,

Tja satisfying the maximum acceleration in Tja may be Tja *, and Tjd satisfying the maximum deceleration in Tjd may be Tjd *.

The one or more constraints may include a first constraint (C1), which is an equivalent constraint of a starting position and an ending position, a second constraint (C2), which is a constraint that the value of velocity does not cross zero, and a jerk at any point in time, It may include a third constraint (C3) is a constraint that the acceleration, the speed is within any limit value.

The time calculating step may include calculating a time of each section by a nonlinear program technique for finding a solution that minimizes an objective function using the time of each section as a parameter.

Computing device according to an embodiment of the present invention, under one or more constraints, the pre-processing unit for calculating the time of each of the acceleration section, the maximum acceleration section, the maximum speed section, the deceleration section and the maximum deceleration section; And generating a motion profile by applying the calculated time and jerk to a polynomial defined for each section, and generating a superimposed motion profile in which two or more motion profiles in which the final velocity of the previous motion is the initial velocity of the next motion are generated. It includes;

The initial speed and the final speed may be any constant.

The preprocessor may calculate the time of each section by a corresponding polynomial according to a comparison result of the movement distance to the target position, the first critical distance, and the second critical distance longer than the first critical distance.

The preprocessing unit, if the movement distance is less than the first critical distance,

Calculate the time of each interval by the polynomial of

The preprocessing unit, if the movement distance is between the first critical distance and the second critical distance,

Calculate the time of each interval by the polynomial of

The preprocessing unit, if the movement distance is greater than the second critical distance,

Calculate the time of each interval by the polynomial of

The preprocessing unit may calculate the time of each section by a nonlinear program technique for finding a solution that minimizes the objective function using the time of each section as a parameter.

According to the present embodiment, a motion profile capable of moving to an optimal time while satisfying a constraint condition may be generated.

1 illustrates a computing device for generating a motion profile according to an embodiment of the present invention.

2 is an example of a position profile (a), a velocity profile (b) and an acceleration profile (c) generated according to one embodiment of the invention.

3 is an example of generating a motion profile by calculating the time for each section by comparing the critical distance and the target position according to an embodiment of the present invention.

4 is an example in which a motion profile is generated by calculating time for each section by nonlinear programming according to an embodiment of the present invention.

5 and 6 are flowcharts schematically illustrating a method of generating a motion profile according to an embodiment of the present invention.

7 is an example of an overlapping motion profile superimposing two motion profiles according to an embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

Referring to FIG. 1, the computing device 10 may generate a motion profile for controlling a motor or the like. Computing device 10 may be implemented in various numbers of hardware or / and software configurations that perform particular functions. For example, computing device 10 may refer to a data processing device embedded in hardware that has physically structured circuitry to perform functions represented by code or instructions contained within a program.

The computing device 10 may include a preprocessor 20 and a profile generator 40. The computing device 10 may be connected to the display 60 and the input device 80 by wire or wirelessly.

The preprocessor 20 may calculate an optimal time for each section of the motion profile. A detailed description of the time calculation method for each section will be described later. The optimum time may be a minimum time that minimizes the moving distance of the section.

The profile generator 40 may generate a motion profile using a polynomial defined for each section. The motion profile may include a position profile, a velocity profile and an acceleration profile.

When the optimum time for each section is calculated, the profile generator 40 may calculate the acceleration, speed, and position of each section by applying time and jerk to the polynomial defined in each section. In one embodiment, the profile generator 40 may calculate the acceleration by integrating the jerk, calculate the speed by integrating the acceleration, and calculate the position by integrating the speed.

The profile generator 40 may generate an overlapping motion profile connecting two or more motions. The profile generator 40 sets the final speed Vf of the previous motion to the initial speed Vi of the next motion in order to generate the overlapping motion profile. The final speed Vf and the initial speed Vi can be any constant. The constant may contain zero.

Existing trapezoidal or S-curve velocity profiles can generate asymmetric velocity profiles with different acceleration and deceleration times, but limit the velocity of the starting and destination points to zero, so that the end of the previous motion ( After the velocity: 0) you have to generate the next motion.

Embodiments of the present invention can generate a motion profile including constraints that limit the initial and end speeds to arbitrary constants, and can reduce operation time and increase productivity by superimposing two motion profiles without stationary motion.

The display 60 may be connected to the computing device 10 by wire or wirelessly, and may process an image output from the computing device 10 to provide to the user. The display 50 may include a liquid crystal display panel (LCD), an organic light emitting display panel (OLED), an electrophoretic display panel (EPD), or the like. The display 60 may be provided in the form of a touch screen to receive an input through a user's touch and operate as a user input interface.

The input device 80 is connected to the computing device 10 by wire or wirelessly to generate input data for controlling the computing device 10. The input device 80 may include a key pad, a dome switch, a touch pad, a mouse, a remote controller, a jog wheel, a jog switch, and the like.

The motion profile according to an embodiment of the present invention may include an acceleration step for accelerating from an initial initial speed to a maximum speed, a constant velocity step following the acceleration step, and a deceleration step for decelerating to a final speed in succession with the constant speed step. Can be.

All sections from the start to the end of the motion profile can be divided into seven sections, T0 to T7. Here, the sections T0 to T3 correspond to the acceleration stage, the sections T3 to T4 correspond to the constant speed stage, and the sections T4 to T7 correspond to the deceleration stage.

The acceleration stage may be divided into an acceleration section including a T0 to T1 and a T2 to T3 section and a maximum acceleration section, which is a T1 to T2 section operating at the maximum acceleration. The constant speed step may include a maximum speed section that is a T3 to T4 section operating at constant speed at the maximum speed. The deceleration step may be divided into a deceleration section including a T4 to T5 and a T6 to T7 section and a maximum deceleration section that is a T5 to T6 section that operates at the maximum deceleration. As can be seen in the velocity profile b, the initial velocity v (T0) and final velocity v (T7) can be non-zero values.

The initial velocity and slope of the acceleration section in the velocity profile b may be different from the final velocity and slope of the deceleration section, so that an asymmetric S-curve velocity profile can be generated.

Hereinafter, the time calculation method for each section of the preprocessor 20 will be described.

Constraints for calculating the time of the motion profile according to an embodiment of the present invention are as follows.

Constraints C1 are equality constraints of the starting position and the ending position. The starting position is the origin (0) and the ending position is the target position (Pf). Since the moving distance is from the origin to the target position, the target position becomes the moving distance. The initial velocity Vi at the starting position and the final velocity Vf at the ending position may each be any constant. Any constant may contain zero. The acceleration at the start and end positions is zero.

Constraint C2 is a constraint that the velocity value does not cross over velocity zero. That is, in each of the acceleration section and the deceleration section, the speed does not change from a negative value to a positive value or from a positive value to a negative value, and has a negative value or a positive value.

Constraints C3 are constraints that jerk (j, jerk), acceleration (a), and speed (v) are within arbitrary limits at any time point T0? T? In the acceleration stage, the jerk is equal to or less than the first jerk limit value Ja and the acceleration is equal to or less than the maximum acceleration Am. In the deceleration step, the jerk is below the second limit value Jd and the deceleration is below the maximum deceleration Dm. In all sections, the speed is below the maximum speed (Vm).

The first jerk limit value Ja and the second jerk limit value Jd may be determined by the following equations (1) and (2), respectively.

Here, β is a constant set by the user and may indicate a smoothness of the motion profile, and may be set to a value greater than 0 and less than or equal to 1. β can generate an S-curve velocity profile in which the time between the acceleration and deceleration sections is asymmetric.

The first jerk limit value Ja may be calculated by the maximum acceleration Am, the maximum speed Vm, the final speed Vf, and βa. The second jerk limit value Jd may be calculated by the maximum deceleration Dm, the maximum speed Vm, the final speed Vf, and βd.

Since the motion profile depends on time and movement distance, the motion profile generation method according to the embodiment of the present invention is classified into three cases of short distance, medium distance, and long distance according to the movement distance. Separate.

The shorter distance has shorter travel distance (Pf),

) And speed (

) Is characterized by not reaching the maximum acceleration (Am), the maximum deceleration (Dm), the maximum speed (Vm). The moving distance Pf of the intermediate distance is the acceleration (

) Reaches maximum acceleration (Am) and maximum deceleration (Dm), but speed (

) Does not reach the maximum speed (Vm). The long distance travel distance (Pf) is long enough that the acceleration (

) And speed (

) Is characterized by reaching the maximum acceleration Am, the maximum deceleration Dm, and the maximum speed Vm.

The preprocessor 20 compares the moving distance (ie, the target position Pf) with the first threshold value Pshort and the second threshold value Pmedium, and corresponds to the movement distance Pf among the short distance, the medium distance, and the long distance. The time for each section can be calculated using a polynomial defined according to the case.

The preprocessing unit 20 may calculate the first threshold value Pshort and the second threshold value Pmedium by the following equations (3) and (4), respectively.

If the moving distance Pf satisfies the condition of the following equation (5), that is, if the moving distance Pf is less than or equal to the first threshold value Pshort (Pf ≦ Pshort), the moving distance Pf ) Can be determined to belong to a short distance.

If the moving distance Pf satisfies Equation (5), the preprocessor 20 may calculate time for each section as shown in Equation (6).

Here, Ta is the time in the T1 ~ T2 section, Tv is the time in the T3 ~ T4 section, Td is the time in the T5 ~ T6 section, Tja is the time in each of the T0 ~ T1 and T2 ~ T3 section, Tjd is T4 ~ T5 and T6 Time of each of the ~ T7 section is shown.

In the short-range case, the T1 to T2, T3 to T4, and T5 to T6 sections are omitted, and the times of the T0 to T1 and T2 to T3 sections (Tja) and the T4 to T5 sections and the T6 to T7 sections, respectively. (Tjd) can be calculated using the numerical solution of nonlinear equations. In this case, Tja and Tjd may be calculated as a solution by applying Newton's Method to equations f1 and f2. Since the numerical solution of the nonlinear equation and the Newton method are used for obtaining a solution, a detailed description thereof will be omitted.

If the moving distance Pf satisfies equation (7), that is, if the moving distance Pf is between the first threshold value Pshort and the second threshold value (Pshort <Pf ≦ Pmedium), It may be determined that the movement distance Pf belongs to the intermediate distance.

If the moving distance Pf satisfies Equation (7), the preprocessor 20 may calculate time for each section as shown in Equation (8).

In the medium distance case, the sections T3 to T4 are omitted, and the time to accelerate to the slope of the first jerk limit value Ja in the sections T0 to T1 and T2 to T3 respectively to reach the maximum acceleration Am is calculated. The time to reach the maximum deceleration Dm by accelerating with the slope of the second jerk limit value Jd in the intervals T˜T5 and T6˜T7 is calculated. In this case, the area of the jerk during the sections T0 to T1 and the period T2 to T3 is equal to the maximum acceleration (Am), respectively, and the areas of the jerk for the sections T4 to T5 and T6 to T7 are the maximum deceleration (Dm) and same. In the constraint of C3

= Tja to Tja * satisfying Am, and

= Tjd satisfying Dm is expressed as Tjd *.

The time in each of the T1 to T2 sections and the T5 to T6 sections can be calculated using the numerical solution of the nonlinear equation. At this time, Ta and Td can be calculated as a solution by applying Newton's Method to equations f1 and f2.

When the moving distance Pf satisfies Equation (9), that is, when the moving distance Pf is greater than the second threshold value Pmedium (Pf> Pmedium), the preprocessor 20 determines that the moving distance Pf belongs to the long distance. Can be.

If the moving distance Pf satisfies Equation (9), the preprocessor 20 may calculate time for each section as shown in Equation (10).

The acceleration phase includes a section that accelerates and accelerates to the maximum acceleration and a maximum acceleration, and the deceleration section includes a section that decelerates with the maximum deceleration and a section that decelerates with the maximum deceleration.

In the case of the long-distance case, as in the medium-distance case, the time for accelerating with the slope of the first jerk limit value Ja and reaching the maximum acceleration Am in each of the T0 to T1 sections and the T2 to T3 sections is calculated, and the T4 to T5 sections are calculated. And a time for accelerating with the slope of the second jerk limit value Jd in the period T6 to T7 to reach the maximum deceleration Dm, respectively. In this case, the area of the jerk during the sections T0 to T1 and the period T2 to T3 is equal to the maximum acceleration (Am), respectively, and the areas of the jerk for the sections T4 to T5 and T6 to T7 are the maximum deceleration (Dm) and same. In the constraint of C3

= Tja to Tja * satisfying Am, and

= Tjd satisfying Dm is expressed as Tjd *.

The acceleration area is equal to the maximum speed during the time T0 to T3 of the acceleration phase and the time T4 to T7 of the deceleration phase. In the constraint of C3

Satisfying Ta *,

Td that satisfies is expressed as Td *.

As described above, the preprocessing unit 20 may determine the threshold distance, compare it with the movement distance according to the target position, and calculate the optimum time for each section by the polynomial corresponding to the case determined according to the comparison result.

In another embodiment, the preprocessor 20 may calculate the optimal time for each section using a nonlinear programming technique. The nonlinear programming technique uses a constrained optimization technique such as (11). Since the nonlinear programming technique using the limited optimization technique is well known, a detailed description thereof will be omitted.

The objective function f (Tn) for minimizing time uses integral time-squared as shown in Eq. (12).

An inequality constraint h (Tn) is a condition that is within an arbitrary limit value such as C3, and an equality constraint g (Tn) is a condition indicating that the g function is zero at the end of each time period, as in C1. The summer condition (l) of the optimization variable is 0, and the summer condition (u) is calculated when the above-mentioned moving distance is long.

Use

The preprocessor 20 may calculate the optimal time for each section by finding a solution that minimizes a predetermined objective function under a predetermined constraint.

3 is an example of generating a motion profile by calculating the time for each section by comparing the critical distance and the target position according to an embodiment of the present invention. 4 is an example in which a motion profile is generated by calculating time for each section by nonlinear programming according to an embodiment of the present invention. 3 and 4 are motion profiles for any initial and final velocity other than zero. (a) is a position profile, (b) is a velocity profile, and (c) is an acceleration profile. Referring to FIGS. 3 and 4, it can be seen that the motion profiles of the two methods yield similar results.

5 is a flowchart schematically illustrating a motion profile generation method according to an embodiment of the present invention. The method of generating a motion profile according to an embodiment of the present invention may be performed by the computing device 10 shown in FIG. 1. In the following, detailed descriptions of contents overlapping with those described above will be omitted.

Referring to FIG. 5, the computing device 10 may receive a constraint for generating a motion profile according to an embodiment of the present invention (S31). The computing device 10 may receive a predetermined constraint condition according to a method of calculating an optimal time.

The computing device 10 may calculate the optimal time for each section of the motion profile under the constraint condition (S33). The computing device 10 may calculate an optimal time for each section by a polynomial corresponding to a case determined according to a result of comparing the critical distance and the moving distance. Alternatively, the computing device 10 may calculate the optimal time for each section using a nonlinear programming technique.

The computing device 10 may generate a motion profile based on the optimal time and jerk of each section (S35). The computing device 10 calculates the acceleration a (t) by integrating the jerks j (t) of each section, and calculates the speed v (t) by integrating the acceleration a (t). , The velocity v (t) may be integrated to calculate the position p (t).

The computing device 10 may generate an overlapping motion profile that overlaps two or more motion profiles. The computing device 10 may set the final speed Vf of the previous motion to the initial speed Vi of the next motion to generate an overlapping motion profile.

6 is a flowchart schematically illustrating a method of calculating an optimum time for each section of FIG. 5. 6 illustrates an example of calculating an optimum time for each section by a polynomial corresponding to a case determined according to a comparison result of a critical distance and a moving distance.

Referring to FIG. 6, the computing device 10 may receive the constraints C1 to C3 for generating the motion profile according to an embodiment of the present invention and calculate the optimal time for each section of the motion profile under the constraint. have.

Constraint C1 is an equivalent constraint between the starting position and the ending position. Constraint C2 is a constraint that the velocity value does not cross velocity zero. Constraints C3 are constraints that jerk j, acceleration a, and speed v are within arbitrary limit values Ja, Jd, Am, Dm, Vm at any time point T0 ≦ t ≦ T7.

The computing device 10 may calculate the limit value Ja of the jerk in the acceleration section and the limit value Jd of the jerk in the deceleration section by equations (1) and (2) (S331).

The computing device 10 calculates the first threshold value Pshort and the second threshold value Pmedium as shown in equations (3) and (4), and sets the target position Pf as the first threshold value Pshort and It may be compared with a second threshold value (Pmedium) (S332, S334).

If the target position Pf is less than or equal to the first threshold value Pshort (S332), the computing device 10 determines that the movement distance Pf from the origin to the target position belongs to a short distance, and the nonlinearity of Equation (6) is determined. The time for each section may be calculated using a numerical solution of the equation (S333). The section may include an acceleration section, a maximum acceleration section, a maximum speed section, a deceleration section and a maximum deceleration section.

If the target position Pf is greater than the first threshold Pshort and is less than or equal to the second threshold Pmedium (S334), the computing device 10 indicates that the movement distance Pf from the origin to the target position belongs to the intermediate distance. After the determination, the time for each section may be calculated using the numerical solution of the nonlinear equation (8) (S335).

When the target position Pf is greater than the second threshold value Pmedium (S334), the computing device 10 determines that the movement distance Pf from the origin to the target position belongs to a long distance, as shown in Equation (10). The time for each section may be calculated (S336).

The computing device 10 determines the time of the sections T0 to T1 and T2 to T3 by the time Tja of the acceleration section, and determines the time of the sections of T1 to T2 by the time of the maximum acceleration section Ta, The time of the T3 to T4 section is determined by the time Tv of the speed section, the time of the T4 to T5 and T6 to T7 sections is determined by the time Tjd of the deceleration section, and the time Td of the maximum deceleration section. By the time of the section T5 ~ T6 can be determined (S337).

The computing device 10 may generate a motion profile and an overlapping motion profile based on the optimal time and jerk of each section, as shown in FIG. 5.

7 is an example of an overlapping motion profile superimposing two motion profiles according to an embodiment of the present invention. (a) is a position profile, (b) is a velocity profile, and (c) is an acceleration profile.

Referring to FIG. 7, the final speed when motion 1 ends is a non-zero value, and motion 2 subsequent to motion 1 sets the final speed of motion 1 as the initial speed. Therefore, motion 1 decelerates to a final speed of zero, and motion 2 does not need to accelerate from zero, thereby reducing the time.

That is, the exemplary embodiment of the present invention sets the final speed Vf of the previous motion to the initial speed Vi of the next motion, thereby reducing the operation time by overlapping two or more successive motion profiles without stopping, thereby optimizing time. Can be moved to increase productivity.

In addition, in the embodiment of the present invention, the final velocity Vf and the initial velocity Vi of the motion profile may be set to any constant other than zero, so that the final velocity Vf does not need to be decelerated to zero. Can be reduced.

In addition, the embodiment of the present invention can have a value different from the initial speed and the slope of the acceleration section and the final speed and the slope of the deceleration section to generate an asymmetric S-curve profile, and thus is effective for vibration reduction even in motion overlapping. .

Although the present invention has been described with reference to one embodiment shown in the accompanying drawings, it is merely an example, and those skilled in the art may realize various modifications and equivalent other embodiments therefrom. I can understand. Accordingly, the true scope of protection of the invention should be defined only by the appended claims.

Claims

Calculating, under one or more constraints, each time of the acceleration section, the maximum acceleration section, the maximum speed section, the deceleration section and the maximum deceleration section;

Generating a motion profile by applying the calculated time and jerk to a polynomial defined for each section; And

And generating an overlapping motion profile in which two or more motion profiles having the final speed of the previous motion as the initial speed of the next motion are successive.
The method of claim 1,

Wherein the initial speed and the final speed are arbitrary constants.
The method of claim 1, wherein the time calculation step,

Comprising a step of calculating the time of each section by the corresponding polynomial according to the comparison result of the moving distance to the target position and the first critical distance and the second critical distance longer than the first threshold distance; Motion profile generation method using
The method of claim 3,

If the moving distance is less than the first critical distance,

The time of each interval is calculated by the polynomial of

Here, Ta is the time of the maximum acceleration section, Tv is the time of the maximum speed section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section, the motion profile generation method using the S-curve. .
The method of claim 3,

If the moving distance is between the first critical distance and the second critical distance,

The time of each interval is calculated by the polynomial of

Here, Ta is the time of the maximum acceleration section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section, motion profile generation method using the S-curve.
The method of claim 3,

If the moving distance is greater than the second critical distance,

The time of each interval is calculated by the polynomial of

Here, Ta is the time of the maximum acceleration section, Tv is the time of the maximum speed section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section,

Tja that satisfies the maximum acceleration in Tja is Tja *,

Tjd satisfying the maximum deceleration in Tjd is Tjd *,

Motion profile generation method using S-curve.
The method of claim 1, wherein the one or more constraints are:

The first constraint C1, which is an equivalent constraint of the starting position and the end position, the second constraint C2, which is a constraint that the value of velocity does not cross zero, and the jerk, acceleration, and velocity at any point in time. And a third constraint (C3) which is a constraint present within the value.
The method of claim 1, wherein the time calculation step,

And calculating a time of each section by a nonlinear program technique for finding a solution that minimizes an objective function using the time of each section as a parameter.
Pre-processing unit for calculating the time of each of the acceleration section, the maximum acceleration section, the maximum speed section, the deceleration section and the maximum deceleration section under one or more constraints; And

A profile generation unit generating a motion profile by applying the calculated time and jerk to a polynomial defined for each section, and generating a superimposed motion profile in which two or more motion profiles, the final velocity of the previous motion as the initial velocity of the next motion, are consecutive. Computing device for generating a motion profile using the S-curve comprising a.
The method of claim 9,

And the initial speed and the final speed are arbitrary constants.
The method of claim 9, wherein the pretreatment unit,

And calculating a time of each section by a corresponding polynomial according to a comparison result of a movement distance to a target position, a first threshold distance, and a second threshold distance longer than the first threshold distance.
The method of claim 11, wherein the preprocessing unit,

If the moving distance is less than the first critical distance,

Calculate the time of each interval by the polynomial of

Here, Ta is the time of the maximum acceleration section, Tv is the time of the maximum speed section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section, computing device for generating a motion profile.
The method of claim 11, wherein the preprocessing unit,

If the moving distance is between the first critical distance and the second critical distance,

Calculate the time of each interval by the polynomial of

Here, Ta is the time of the maximum acceleration section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section, computing device for generating a motion profile.
The method of claim 11, wherein the preprocessing unit,

If the moving distance is greater than the second critical distance,

Calculate the time of each interval by the polynomial of

Here, Ta is the time of the maximum acceleration section, Tv is the time of the maximum speed section, Td is the time of the maximum deceleration section, Tja is the time of the acceleration section, Tjd is the time of the deceleration section,

Tja that satisfies the maximum acceleration in Tja is Tja *,

Tjd satisfying the maximum deceleration in Tjd is Tjd *,

Computing device for motion profile generation.
The method of claim 11, wherein the one or more constraints are:

The first constraint C1, which is an equivalent constraint of the starting position and the end position, the second constraint C2, which is a constraint that the value of velocity does not cross zero, and the jerk, acceleration, and velocity at any point in time. And a third constraint (C3) which is a constraint present within the value.
The method of claim 11, wherein the preprocessing unit,

Calculating a time of each section by a nonlinear program technique for finding a solution that minimizes an objective function using the time of each section as a parameter.