KR20170044987A - Trajectory generating method for jerk limited - Google Patents
Trajectory generating method for jerk limited Download PDFInfo
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- KR20170044987A KR20170044987A KR1020150144778A KR20150144778A KR20170044987A KR 20170044987 A KR20170044987 A KR 20170044987A KR 1020150144778 A KR1020150144778 A KR 1020150144778A KR 20150144778 A KR20150144778 A KR 20150144778A KR 20170044987 A KR20170044987 A KR 20170044987A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1628—Programme controls characterised by the control loop
- B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1661—Programme controls characterised by programming, planning systems for manipulators characterised by task planning, object-oriented languages
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- Mechanical Engineering (AREA)
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Abstract
The present invention relates to a locus generating method with limited jerk, and more particularly, to a jerk-limited locus generating method that can control operation even in a low-cost processor by limiting the jerk to a threshold value or less while requiring a small amount of calculation.
In the present invention, the target position, velocity, acceleration, and jerk are calculated by setting the initial position to the final position as three sections including an acceleration section, a constant-speed section, and a deceleration section, It is possible to reduce the amount of calculation compared to the conventional trajectory generation technique and to minimize the occurrence of vibration in the section where the acceleration is changed to limit the wear and damage of the joint by limiting the trajectory of acceleration and the trajectory of jerk below the jerk threshold value. .
Description
The present invention relates to a locus generating method with limited jerk, and more particularly, to a jerk-limited locus generating method that can control operation even in a low-cost processor by limiting the jerk to a threshold value or less while requiring a small amount of calculation.
Generally, in a dynamic system including a robot and a machining machine, an actuator or a motor that performs a linear or linear motion is provided in a joint, and after generating a work locus in a target work space using a locus generator, This allows the joints to operate flexibly.
This trajectory generator reflects the maximum velocity and maximum acceleration of the dynamic system and creates a trajectory for the joint to operate from the initial position to the final position. Also, among the conventional trajectory generation techniques, a trapezoidal velocity profile is most commonly used.
On the other hand, the conventional trapezoidal profile is easy to generate due to simple formulas and can be moved quickly, but has a characteristic in which the acceleration is rapidly changed, so that there is a problem that vibration occurs in a region where acceleration is rapidly changed when the joint operates.
That is, when the trajectory is generated using the conventional trapezoidal profile, jerk represented by the differential value of the acceleration is not limited, vibration occurs in the section where the acceleration changes, and wear and damage of the dynamic system .
Also, a jerk-limited trajectory technique has been developed to limit the jerk by changing the acceleration over time. In this case, one trajectory is divided into eight sections, and the position, velocity, acceleration and jerk Therefore, complex formulas are required and the amount of calculation is increased.
That is, an expensive processor having a high processing speed is required to process a large amount of computation, thereby increasing the economic cost.
Therefore, it is possible to generate trajectory with limited jerk, minimize wear and damage caused by vibration, improve trajectory tracking accuracy and follow-up speed, and have a small calculation amount to enable operation control even in a low- The development of a trajectory generation technique is required.
SUMMARY OF THE INVENTION The present invention has been made in view of the above problems, and it is an object of the present invention to provide a jerk-limited trajectory generation method which can limit jerk below a threshold value and require a relatively small amount of calculation as compared with a conventional trajectory generation technique. have.
The objects of the present invention are not limited to the above-mentioned objects, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.
According to another aspect of the present invention, there is provided a trajectory generation method performed by a trajectory generator, the method comprising the steps of: (1) receiving a final position to be moved from an initial position, , A constant velocity section and a deceleration section; (2) the locus generator receives an acceleration threshold value and a jerk threshold value for the acceleration section and the deceleration section; (3) The trajectory generator calculates a trajectory of a target position, a velocity, an acceleration, and a jerk for each section using a sinusoidal-based equation, wherein the trajectory of acceleration and jerk is equal to or less than the acceleration threshold value and the jerk threshold value Limiting step; And (4) generating the final trajectory of the calculated trajectories by the trajectory generator.
In a preferred embodiment, in the step (3), the locus generator generates a locus such that a velocity change in the acceleration section and the deceleration section is increased or decreased in an S-curve shape.
In a preferred embodiment, in the third step, the locus generator generates a locus such that acceleration changes in the acceleration period and the deceleration period are increased or decreased in waveforms of a positive half sine wave and a negative half sine wave, respectively.
In a preferred embodiment, in the third step, the locus generator generates a locus such that the jerk changes in the acceleration section and the deceleration section are increased or decreased in a sinusoidal waveform shape symmetrical to each other.
In a preferred embodiment, in the step (3), the locus generator calculates a target position in the acceleration section using the following equation.
[Mathematical Expression]
Here, A 1 is the acceleration in the acceleration period, t 1 is the time of the acceleration period, J limit is the jerk threshold, v max is the maximum velocity, and v i is the initial velocity.
In a preferred embodiment, in the step (3), the locus generator calculates a target position in the constant velocity section using the following equation.
[Mathematical Expression]
Here, A 1 is the acceleration in the acceleration section, t 1 is the time of the acceleration section, v i is the initial velocity, and v max is the maximum velocity.
In a preferred embodiment, in the step (3), the locus generator calculates a target position in the deceleration section using the following equation.
[Mathematical Expression]
Where A 3 is the acceleration of the deceleration section, t 3 is the time of the deceleration section, A 1 is the acceleration of the acceleration section, t 1 is the time of the acceleration section, v i is the initial velocity, t 2 is the time of the constant velocity section, v max is the maximum velocity, J limit is the jerk threshold, v f is the final velocity, and x d is the final position.
In a preferred embodiment, in the step (3), the locus generator calculates a velocity trajectory for each section by using a velocity calculation equation that differentiates the equation for each section, and calculates the velocity trajectory by using the differential acceleration formula And a jerk trajectory for each section is calculated by using the jerk calculation equation obtained by differentiating the acceleration calculation equation.
According to the above-mentioned problem solving means, the present invention sets three sections including an acceleration section, a constant velocity section and a deceleration section from an initial position to a final position, and sets a target position, a velocity, an acceleration and a jerk Therefore, it is possible to reduce the amount of calculation as compared with the conventional trajectory generation technique.
That is, since the present invention can control the operation even in a low-cost processor having a low processing speed, the economic cost can be minimized.
Further, since the trajectory of the acceleration and the trajectory of the jerk can be limited below the acceleration threshold value and the jerk threshold inputted by the user, the trajectory of the target position, velocity, acceleration and jerk for each section can be generated, It is possible to minimize the occurrence of vibration in the generated section to prevent wear and damage of the joint.
BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a diagram for explaining a locus generating method according to an embodiment of the present invention; FIG.
2 is a view for explaining a position locus according to an embodiment of the present invention;
3 is a view for explaining a speed trajectory according to an embodiment of the present invention;
4 is a view for explaining an acceleration trajectory according to an embodiment of the present invention;
5 is a view for explaining a jerk trajectory according to an embodiment of the present invention.
It should be understood that the specific details of the invention are set forth in the following description to provide a more thorough understanding of the present invention and that the present invention may be readily practiced without these specific details, It will be clear to those who have knowledge.
Hereinafter, preferred embodiments according to the present invention will be described in detail with reference to FIGS. 1 to 5, and a description will be given centering on parts necessary for understanding the operation and operation according to the present invention.
FIG. 1 is a view for explaining a locus generating method according to an embodiment of the present invention. FIG. 2 is a view for explaining a locus trajectory according to an embodiment of the present invention. FIG. 4 is a view for explaining an acceleration trajectory according to an embodiment of the present invention, and FIG. 5 is a view for explaining a jerk trajectory according to an embodiment of the present invention .
1 to 5, a trajectory generating method according to an embodiment of the present invention performed in a trajectory generator will be described. Here, the locus generator is provided in a dynamic system including a robot and a machining machine, and may be for generating a locus for the joint of the dynamic system to operate from an initial position to a final position.
First, when the final position to be moved is input from the initial position, the locus generator divides the initial position to the final position into three sections including an acceleration section, a constant-speed section, and a deceleration section (S110).
Also, the locus generator may receive a measurement of initial position and speed from a sensor provided in the joint, for example, an encoder, and the maximum speed according to the performance of the dynamic system itself is preset.
Meanwhile, if the distance between the initial position and the final position is short and can not be divided into three sections, the locus generator may set only two sections including the acceleration section and the constant velocity section, or may set only the acceleration section.
Next, a threshold value for the acceleration and jerk to be limited in generating the trajectory of the joint is input (S120).
At this time, the locus generator receives the acceleration threshold value and the jerk threshold value in the acceleration period and the deceleration period as a user input, or the acceleration threshold value and jerk threshold value stored in the database or the like may be input. Here, the acceleration threshold value and the jerk threshold value may be stored as values derived by experiments or simulations in advance.
Next, the locus generator calculates the locus of the target position, velocity, acceleration, and jerk for each section (S130).
At this time, the locus generator limits the trajectory of acceleration and jerk to the acceleration threshold value and the jerk threshold value for each section, and calculates the target position, velocity, acceleration and jerk of each section using a trigonometric function- The trajectory is calculated.
For example, the locus generator may calculate a target position in the acceleration section using Equation 1 below.
[Equation 1]
Where P (t) is the target position in the acceleration section, A, B and C are constants for locus generation, and a is a function of time.
Also, the locus generator calculates a velocity locus in the acceleration region using a velocity calculation formula differentiated from Equation (1), calculates an acceleration locus in the acceleration region using an acceleration calculation formula obtained by differentiating the velocity calculation formula, The jerk trajectory in the acceleration section can be calculated using the jerk calculation equation that differentiates the acceleration calculation equation.
Substantially, the locus generator calculates the target position for the acceleration section by applying Equation (1) to Equation (2) below.
&Quot; (2) "
Here, A 1 is an acceleration in the acceleration section, t 1 is a time of the acceleration section, and A 1 and T 1 are calculated from the following equations (3) and (4), respectively.
&Quot; (3) "
&Quot; (4) "
Where J limit is the jerk threshold, v max is the maximum velocity, and v i is the initial velocity.
Also, the locus generator may calculate the velocity trajectory in the acceleration section using Equation (5) below, which is differentiated from Equation (2).
&Quot; (5) "
Here, A 1 is the acceleration in the acceleration section, t 1 is the time in the acceleration section, and can be calculated from Equations (3) and (4), respectively.
Also, the locus generator may calculate an acceleration locus in the acceleration region using Equation (6) below, which is obtained by differentiating Equation (5).
&Quot; (6) "
Here, A 1 is the acceleration in the acceleration period and can be calculated from the above-described Equation (3). Further, the acceleration trajectory A (t) in the acceleration section is limited to the acceleration threshold value or less.
Also, the locus generator may calculate the jerk trajectory in the acceleration period using Equation (7) below, which is differentiated from Equation (6).
&Quot; (7) "
Here, A 1 is an acceleration in the acceleration period, t 1 is a time period of the acceleration period, and is calculated from Equations (3) and (4). Further, the jerk trajectory J (t) in the acceleration section is limited to the jerk threshold value or less.
Therefore, the locus generator can generate the velocity locus such that the velocity change is increased or decreased in the S-curve shape in the acceleration region, and the acceleration locus can be generated so as to increase or decrease in the form of the positive half- A jerk trajectory can be generated so as to increase or decrease in the form of a sinusoidal waveform.
Also, the maximum value in the case of the acceleration trajectory is limited to be equal to or less than the acceleration threshold value, and in the case of the jerk trajectory, the maximum value is limited below the jerk threshold value.
Also, the locus generator may calculate a target position in the constant velocity section using Equation (8) below.
&Quot; (8) "
Where P (t) is the target position in the constant velocity section, D is the target position in the acceleration section, and v max is the maximum velocity.
Also, the locus generator can calculate the velocity trajectory in the constant velocity section using the equation (8). In addition, since there is no change in the acceleration in the constant velocity section, the acceleration locus and the jerk locus can be calculated as zero.
Substantially, the locus generator calculates the target position for the constant velocity section by applying Equation (8) to Equation (9) below.
&Quot; (9) "
Here, A 1 is the acceleration in the acceleration period, t 1 is the time of the acceleration period, respectively, and is calculated from Equations (3) and (4), v i is the initial velocity and v max is the maximum velocity .
Also, the locus generator may calculate the velocity trajectory in the constant velocity section using Equation (10) below, which is obtained by differentiating Equation (9).
&Quot; (10) "
Where v max is the maximum speed.
Therefore, the locus generator can generate a velocity trajectory having a constant maximum speed without increasing or decreasing the velocity change, the acceleration change, and the jerk change in the constant velocity section.
Also, the locus generator may calculate a target position in the deceleration section using Equation (11) below.
&Quot; (11) "
Where P (t) is the target position in the deceleration section, E, F and G are constants for locus generation,? Is a function of time and H is the target position in the constant velocity section.
Also, the locus generator calculates a speed trajectory in the deceleration section using a speed calculation equation differentiated from Equation (11), calculates an acceleration trajectory in the deceleration section using an acceleration calculation formula differentiated from the speed calculation expression, The jerk trajectory in the deceleration section can be calculated using the jerk calculation equation that differentiates the acceleration calculation equation.
Substantially, the locus generator calculates the target position for the deceleration section by applying Equation (11) to Equation (12) below.
&Quot; (12) "
Where A 3 is the acceleration of the deceleration section, t 3 is the time of the deceleration section, A 1 is the acceleration of the acceleration section, t 1 is the time of the acceleration section, v i is the initial velocity, t 2 is the time of the constant velocity section, and v max is the maximum velocity.
In addition, A 1 and T 1 are calculated from the above-described equations (3) and (4), respectively, and A 3 and T 3 can be calculated from the following equations (13) and (14), respectively.
&Quot; (13) "
&Quot; (14) "
Where J limit is the jerk threshold, v max is the maximum velocity, and v f is the final velocity. In the case of t 2 , it can be calculated from the following equation (15).
&Quot; (15) "
Here, v max is the maximum velocity, x d is the final position, A 1 is the acceleration of the acceleration section, t 1 is the time of the acceleration section, v i is the initial velocity and A 3 is the velocity of the deceleration section the acceleration, t 3 is the time of the deceleration stage. Further, A 1 and T 1 are respectively calculated from the above-mentioned equations (3) and (4), and A 3 and T 3 can be respectively calculated from the above-mentioned equations (13) and (14).
Also, the locus generator calculates a velocity trajectory in the deceleration section using Equation (16) below, which is differentiated from Equation (12).
&Quot; (16) "
Here, A 3 is the acceleration of the deceleration section, t 3 is the time of the deceleration section, and v max is the maximum velocity. Further, A 3 and T 3 are respectively calculated from the above-described equations (13) and (14).
Also, the locus generator calculates an acceleration locus in the deceleration section using Equation (17) below, which is differentiated from Equation (16).
&Quot; (17) "
Here, A 3 is the acceleration of the deceleration section, t 3 is the time of the deceleration section, and A 3 and T 3 can be calculated from the above-described equations (13) and (14), respectively.
Also, the locus generator calculates the jerk trajectory in the deceleration section using the following Equation (18), which is differentiated from Equation (17).
&Quot; (18) "
Here, A 3 is the acceleration of the deceleration section, t 3 is the time of the deceleration section, and A 3 and T 3 are calculated from the above-described equations (13) and (14), respectively.
Accordingly, the locus generator can generate a velocity locus such that the velocity change is increased or decreased in the S-curve form in the deceleration region, the acceleration change is increased or decreased in the form of a negative half-sine sign and the maximum acceleration locus is limited below the acceleration threshold value In case of jerk change, jerk trajectory can be generated in the form of a sinusoidal waveform and limited to below the jerk threshold value. At this time, the jerk trajectory of the deceleration section and the jerk trajectory of the acceleration section may be generated symmetrically with respect to each other.
Next, the locus generator generates a final locus of the calculated loci (S140).
That is, as shown in FIG. 2, the locus generator calculates the final time t (t) including the time t 1 of the acceleration section, the time t 2 of the constant velocity section and the time t 3 of the deceleration section f ), a position locus for moving from the initial position to the final position.
Also, as shown in FIG. 3, the locus generator may generate a speed trajectory in which the speed variation in the acceleration section and the deceleration section is increased or decreased in the S-curve form.
Also, as shown in FIG. 4, the locus generator may generate acceleration trajectories in which acceleration changes in the acceleration period and the deceleration period are increased or decreased in the form of a positive half sine waveform and a negative half sine waveform, respectively. At this time, the maximum value of the acceleration in the acceleration section and the deceleration section is limited to 2000 (mm / s / s), which is an acceleration threshold value.
Also, as shown in FIG. 5, the locus generator may generate a jerk trajectory in which the jerk changes in the acceleration period and the deceleration period are increased or decreased in a sinusoidal waveform symmetrical to each other. At this time, the maximum value of the jerk in the acceleration section and the deceleration section may be limited to within the jerk threshold value of 50000 (mm / s / s / s).
While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the invention.
Claims (8)
(1) The locus generator receives a final position to move from an initial position, and sets the initial position to a final position by dividing the acceleration region, the constant velocity region, and the deceleration region;
(2) the locus generator receives an acceleration threshold value and a jerk threshold value for the acceleration section and the deceleration section;
(3) The trajectory generator calculates a trajectory of a target position, a velocity, an acceleration, and a jerk of each section using a trigonometric function-based equation, wherein the trajectory of acceleration and jerk is equal to or less than the acceleration threshold value and the jerk threshold value ; And
(4) The trajectory generator generates a final trajectory of the calculated trajectories.
Wherein the trajectory generator generates the trajectory in such a manner that the velocity change in the acceleration section and the deceleration section increases or decreases in the S-curve form in the step (3).
Wherein the trajectory generator generates the trajectory in such a manner that the acceleration changes in the acceleration section and the deceleration section are increased or decreased in waveforms of a positive half sine waveform and a negative half sine waveform, respectively, in the step (3) Generation method.
Wherein the trajectory generator generates the trajectory in such a manner that the jerk changes in the acceleration section and the deceleration section are increased or decreased in a sinusoidal waveform symmetrical to each other in the step (3).
Wherein the trajectory generator in the step (3) calculates a target position in the acceleration section using the following equation.
[Mathematical Expression]
Here, A 1 is the acceleration in the acceleration period, t 1 is the time of the acceleration period, J limit is the jerk threshold, v max is the maximum velocity, and v i is the initial velocity.
Wherein the trajectory generator in the step (3) calculates a target position in the constant velocity section using the following equation.
[Mathematical Expression]
Here, A 1 is the acceleration in the acceleration section, t 1 is the time of the acceleration section, v i is the initial velocity, and v max is the maximum velocity.
Wherein the trajectory generator in the step (3) calculates a target position in the deceleration section using the following equation.
[Mathematical Expression]
Where A 3 is the acceleration of the deceleration section, t 3 is the time of the deceleration section, A 1 is the acceleration of the acceleration section, t 1 is the time of the acceleration section, v i is the initial velocity, t 2 is the time of the constant velocity section, v max is the maximum velocity, J limit is the jerk threshold, v f is the final velocity, and x d is the final position.
In the step (3), the locus generator calculates a velocity trajectory for each section by using a velocity calculation expression that differentiates the equation for each section, and calculates the acceleration trajectory for each section using the differential equation And calculating a jerk trajectory for each section by using the jerk calculation equation for differentiating the acceleration calculation equation.
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|---|---|---|---|---|
| CN107914273A (en) * | 2017-11-08 | 2018-04-17 | 浙江工业大学 | Mechanical arm teaching system based on gesture control |
| CN110000794A (en) * | 2019-05-06 | 2019-07-12 | 江苏集萃智能制造技术研究所有限公司 | A kind of asymmetric speed planning method of clean cut system based on cooperation robot |
| WO2021041223A1 (en) * | 2019-08-23 | 2021-03-04 | Realtime Robotics, Inc. | Motion planning for robots to optimize velocity while maintaining limits on acceleration and jerk |
| CN113043262A (en) * | 2019-12-27 | 2021-06-29 | 沈阳新松机器人自动化股份有限公司 | Method and system for grading speed regulation of manipulator for grabbing object |
| US11292456B2 (en) | 2018-01-12 | 2022-04-05 | Duke University | Apparatus, method and article to facilitate motion planning of an autonomous vehicle in an environment having dynamic objects |
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| CN113043262A (en) * | 2019-12-27 | 2021-06-29 | 沈阳新松机器人自动化股份有限公司 | Method and system for grading speed regulation of manipulator for grabbing object |
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