KR101640931B1 - automatic PID gain tuning method in articulated robot - Google Patents
automatic PID gain tuning method in articulated robot Download PDFInfo
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- KR101640931B1 KR101640931B1 KR1020160018664A KR20160018664A KR101640931B1 KR 101640931 B1 KR101640931 B1 KR 101640931B1 KR 1020160018664 A KR1020160018664 A KR 1020160018664A KR 20160018664 A KR20160018664 A KR 20160018664A KR 101640931 B1 KR101640931 B1 KR 101640931B1
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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
- G05B11/00—Automatic controllers
- G05B11/01—Automatic controllers electric
- G05B11/36—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential
- G05B11/42—Automatic controllers electric with provision for obtaining particular characteristics, e.g. proportional, integral, differential for obtaining a characteristic which is both proportional and time-dependent, e.g. P.I., P.I.D.
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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
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
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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
- B25J9/1656—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
Abstract
A method for easily and quickly finding the optimal PID gain of a multi-joint robot is disclosed.
According to one aspect of the present invention, a method for automatically tuning a PID gain of a jointed-arm robot is a method for setting a PID gain of a multi-joint robot. The method includes setting a proportional gain, a derivative gain, (A) setting a value; (B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory; (C) comparing the output value and the set value to calculate a figure of merit; (D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit; (E) setting the differential gain found in the step (d) as a new differential gain value; Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit; (G) setting a proportional gain found in the step (f) to a new proportional gain value; (H) repeating the steps (b) and (c) while increasing the integral gain until the predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And (i) setting the integral gain found in the step (h) to a new integral gain value.
Description
The present invention relates to a method of automatically setting a PID gain of a joint articulated robot, and more particularly, to a method of automatically setting all joints of joints by simultaneously moving all joints of the articulated robot.
A robot whose arms have three or more rotating joints is called an articulated robot. A jointed-arm robot is a robot that simulates a human's shoulders, arms, elbows, and wrist joints, and can move in a similar manner to a human motion. Such a jointed-arm robot is fast acting, takes up little space, and has a wide operating range. Therefore, it is widely used for assembling work of factory production equipment and welding.
In order to precisely control the jointed-arm robot, it is necessary to measure the output value, calculate the error by comparing it with a desired setpoint, and calculate the proportional- integral-derivative control is required. In order to perform PID control, the gain should be set to obtain the optimum gain.
However, in the case of setting the PID gain by moving the joints one by one in the articulated robot, it is disadvantageous that it can not be applied to a specific robot which takes a long time and can not move any specific joints. Therefore, there is a need for a gain setting method applicable to all articulated robots.
Also, it may be very difficult to set the gain when there is no expert knowledge of the robot and the PID controller. In order to set the gain, a procedure and an algorithm that can automatically tune the gain are required for a user without expert knowledge. Particularly, when the robot type is not fixed, but a multi-joint robot is constructed by assembling a module type actuator and a link, a method of automatically tuning the gain of each joint is indispensable.
An object of the present invention is to provide a method for easily and quickly finding an optimum PID gain of a jointed-arm robot.
According to one aspect of the present invention, a PID gain tuning method for a jointed-arm robot is a method for setting a PID gain of a jointed-arm robot, which uses proportional gain, derivative gain, and integral gain (A); (B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory; (C) comparing the output value and the set value to calculate a figure of merit; (D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit; (E) setting the differential gain found in the step (d) as a new differential gain value; Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit; (G) setting a proportional gain found in the step (f) to a new proportional gain value; (H) repeating the steps (b) and (c) while increasing the integral gain until the predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And (i) setting the integral gain found in the step (h) to a new integral gain value.
According to another aspect, the PID gain tuning method of the articulated robot is a method of setting the PID gain of the articulated robot, and the initial value of proportional gain, differential gain, and integral gain is set by using the moment of inertia and natural frequency of each arm (A); (B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory; (C) comparing the output value and the set value to calculate a figure of merit; (D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit; (E) setting a value obtained by multiplying the differential gain found in the step (d) by 0.8 as a new differential gain value; Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit; (G) setting a value obtained by multiplying the proportional gain found in the step (f) by 0.8 to a new proportional gain value; (H) repeating the steps (b) and (c) while increasing the integral gain until the predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And (i) setting the integral gain found in the step (h) to a new integral gain value.
According to another aspect, the PID gain tuning method of the articulated robot is a method of setting the PID gain of the articulated robot, and the initial values of proportional gain, differential gain, and integral gain are calculated by using the moment of inertia and natural frequency of each arm (A) setting; (B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory; (C) comparing the output value and the set value to calculate a figure of merit; (D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit; (E) setting a value obtained by multiplying the differential gain found in the step (d) by 0.8 as a new differential gain value; Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit; (G) setting a value obtained by multiplying the proportional gain found in the step (f) by 0.8 to a new proportional gain value; (H) repeating the steps (d) to (g) until a predetermined condition is satisfied, and then finding a differential gain and a proportional gain for minimizing the figure of merit; (I) repeating the steps (b) and (c) while increasing the integral gain until a predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And (j) setting the integral gain found in the step (i) to a new integral gain value.
According to another aspect, the condition may be satisfied when the figure of merit becomes less than the reference value, when the system diverges, when the change value of the figure of merit becomes less than or equal to a predetermined value, or when the predetermined number of repetitions is satisfied.
According to still another aspect, the integral gain value in the step (a) may be zero.
According to another aspect, the initial values of the proportional gain (K p ), differential gain (K v ), and integral gain (K i ) can be set using the following equation.
K p = 1/3 * M ii ? C 2
K v = 2π * K p / ω c
K i = ω c * K p / 2π
M ii is the principal axis moment of inertia corresponding to the i-th axis, and ω c is the natural frequency of each axis
According to the present invention, an accurate value of the PID gain of the articulated robot can be obtained.
Also, the optimum PID gain of the articulated robot can be acquired easily and quickly.
1 is a flowchart of a method for tuning a PID gain of a jointed-arm robot according to an embodiment of the present invention.
2 is a flowchart of a PID gain tuning method of a jointed-arm robot according to another embodiment of the present invention.
The foregoing and further aspects will become apparent through the following examples. In the present specification, corresponding elements in each figure are referred to by the same numerals. In addition, the shape and size of the components can be exaggerated. In the following description, well-known functions or constructions are not described in detail since they would obscure the invention in unnecessary detail.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to various embodiments of the present invention.
In the present invention, not all the joints of the articulated robot are sequentially operated to acquire the PID gain for each joint, but all the joints are operated at once to obtain the optimum PID gain of the whole robot.
1 is a flowchart of a method of automatically tuning a PID gain of a jointed-arm robot according to an embodiment of the present invention.
A method of automatically tuning a PID gain of a multi-joint robot will be described with reference to FIG.
First, the initial values of proportional gain, differential gain, and integral gain are set using the moment of inertia and the natural frequency of each axis (S110).
The initial values of the proportional gain, differential gain, and integral gain are closely related to the performance of the controller and the total time required, so an appropriate value should be set. The initial values of the proportional gain (K p ), differential gain (K v ), and integral gain (K i ) can be set by the following equation.
K p = 1/3 * M ii ? C 2
K v = 2π * K p / ω c
K i = ω c * K p / 2π
Here, M ii is the principal axis moment of inertia corresponding to the i-th axis, and? C is the natural frequency of each axis.
On the other hand, the integration gain (K i ) can be set to 0 as the initial value until the tuning of the PD gain is completed.
Next, PID control is performed using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory (S120).
Here, the target trajectory may be a trajectory of a sinusoidal wave. And the frequency can be set to 1/20 of the robot bandwidth. When the bandwidth of the robot can not be measured or the calculation can not be performed, the bandwidth of the robot can be set to 0.5 Hz, which is 1/20 of the bandwidth of the general industrial robot. The angle is preferably set to about 25 degrees for safety. It is also desirable to set the locus such that the arms rotate in opposite directions to prevent excessive increase in the inertia force.
Next, the performance index is calculated by comparing the output value and the set value (S130). Here, the figure of merit is an index indicating the degree of difference between the output value and the set value, which may be the maximum value of the error value which is the difference between the output value and the set value, or may be the sum of the error values.
Next, steps S120 through S130 are repeated while increasing the differential gain until the condition is satisfied (S140). Then, a differential gain for minimizing the figure of merit is found (S140). Here, the term until the condition is satisfied may mean when the figure of merit is below the reference value, when the system diverges, when the change of the figure of merit becomes less than a predetermined value, or when the predetermined number of iterations is filled. The fact that the system diverges can mean that the figure of merit is degraded. Increasing the derivative gain can, for example, increase the derivative gain value by a factor of two until the gain is ten times the initial setting value. Thus, the differential gain when the figure of merit is the minimum is set as a new differential gain value.
Next, after the differential gain is fixed, the proportional gain is increased until the condition is satisfied, and the proportional gain for minimizing the figure of merit is found (S150) after repeating steps S120 to S130 above. Increasing the proportional gain can be increased to an integer multiple, for example, until the proportional gain value is ten times the initial setting. Thus, the proportional gain when the figure of merit is minimum is set as a new proportional gain value.
Next, the differential gain and the proportional gain are fixed. Then, the integral gain is increased until the condition is satisfied, and the integral gain for minimizing the performance index is found by repeating steps S120 to S130 (S160). Thus, the integral gain when the change in the figure of merit becomes less than or equal to the predetermined reference value can be set as a new integral gain value.
According to the above-described method, the optimum PID gain value according to the shape of the robot can be acquired and recorded, and utilized when controlling the robot in the future.
According to the above-described method, an accurate value of the PID gain of the articulated robot can be obtained. In addition, instead of acquiring the PID gain for each joint by sequentially actuating each joint in the articulated robot, all the joints are operated at once to acquire the PID gain of the whole robot, so that the optimum PID gain of the articulated robot is simple You can get it quickly.
2 is a flowchart of a method of automatically tuning a PID gain of a jointed-arm robot according to another embodiment of the present invention.
Referring to FIG. 2, a method of automatically tuning a PID gain of a jointed-arm robot according to another embodiment will be described.
First, initial values of proportional gain, differential gain, and integral gain are set using the moment of inertia and the natural frequency of each arm (S210).
The initial values of the proportional gain, differential gain, and integral gain are closely related to the performance of the controller and the total time required, so an appropriate value should be set. The initial values of the proportional gain (K p ), differential gain (K v ), and integral gain (K i ) can be set by the following equation.
K p = 1/3 * M ii ? C 2
K v = 2π * K p / ω c
K i = ω c * K p / 2π
Here, M ii is the principal axis moment of inertia corresponding to the i-th axis, and? C is the natural frequency of each axis.
On the other hand, the integration gain (K i ) can be set to 0 as the initial value until the tuning of the PD gain is completed.
Next, PID control is performed using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory (S220).
Here, the target trajectory may be a trajectory of a sinusoidal wave. The frequency can be set to 1/20 of the robot bandwidth. When the bandwidth of the robot can not be measured or can not be calculated, the bandwidth of the robot can be set to 0.5 Hz, which is 1/20 of the bandwidth of the general industrial robot. The angle is preferably set to about 25 degrees for safety. It is also desirable to set the locus such that the arms rotate in opposite directions to prevent excessive increase in the inertia force.
Next, the performance index is calculated by comparing the output value and the set value (S230). Here, the figure of merit is an index indicating the degree of difference between the output value and the set value, which may be the maximum value of the error value which is the difference between the output value and the set value, or may be the sum of the error values.
Next, steps S220 to S230 are repeated while increasing the differential gain until the condition is satisfied (S240). Then, a differential gain for minimizing the figure of merit is found (S240). Here, the term until the condition is satisfied may mean when the figure of merit is below the reference value, when the system diverges, when the change of the figure of merit becomes less than a predetermined value, or when the predetermined number of iterations is filled. The fact that the system diverges can mean that the figure of merit is degraded. Increasing the derivative gain can, for example, increase the derivative gain value by a factor of two until the gain is ten times the initial setting value. Thus, the differential gain when the figure of merit is the minimum is set as a new differential gain value.
Then, a value obtained by multiplying the differential gain when the figure of merit is the minimum is multiplied by 0.8 is set as a new differential gain value (S250).
Next, after the differential gain is fixed, the proportional gain is increased until the condition is satisfied, and the proportional gain for minimizing the figure of merit is found (S260) after repeating steps S120 to S130 above. Increasing the proportional gain may be an integer multiple, for example, until the proportional gain value is 10 times the initial setting value, or it may be increasing by a factor of 0.1 until a constant multiple is reached.
Then, the proportional gain when the figure of merit is the minimum is set as a new proportional gain value (S270).
Then, steps S240 to S270 are repeated until the condition is satisfied, and the differential gain and the integral gain for minimizing the figure of merit are found, and the found differential gain and the integral gain are set to a new differential gain value (S280). The reason why the above steps S240 to S270 are repeated is to increase the accuracy of the PID gain.
Next, the differential gain and the proportional gain are fixed. Thereafter, the integral gain is increased until the condition is satisfied, and the integral gain for minimizing the figure of merit is found by repeating steps S220 to S230 (S90). Thus, the integral gain when the change in the figure of merit becomes less than or equal to the predetermined reference value can be set as a new integral gain value.
According to the above-described method, the optimum PID gain value according to the shape of the robot can be acquired and recorded, and utilized when controlling the robot in the future.
According to the above-described method, a more accurate value of the PID gain of the articulated robot can be obtained.
While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. There will be. Accordingly, the true scope of protection of the present invention should be determined only by the appended claims.
Claims (6)
(A) setting an initial value of a proportional gain, a differential gain, and an integral gain using an inertia moment and a natural frequency of each arm;
(B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory;
(C) comparing the output value and the set value to calculate a figure of merit;
(D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit;
(E) setting the differential gain found in the step (d) as a new differential gain value;
Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit;
(G) setting a proportional gain found in the step (f) to a new proportional gain value;
(H) repeating the steps (b) and (c) while increasing the integral gain until the predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And
(I) setting the integral gain found in the step (h) to a new integral gain value;
Wherein the PID gain of the multi-joint robot is automatically tuned.
(A) setting an initial value of a proportional gain, a differential gain, and an integral gain using an inertia moment and a natural frequency of each arm;
(B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory;
(C) comparing the output value and the set value to calculate a figure of merit;
(D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit;
(E) setting a value obtained by multiplying the differential gain found in the step (d) by 0.8 as a new differential gain value;
Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit;
(G) setting a value obtained by multiplying the proportional gain found in the step (f) by 0.8 to a new proportional gain value;
(H) repeating the steps (b) and (c) while increasing the integral gain until the predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And
(I) setting the integral gain found in the step (h) to a new integral gain value;
Wherein the PID gain of the multi-joint robot is automatically tuned.
(A) setting an initial value of a proportional gain, a differential gain, and an integral gain using an inertia moment and a natural frequency of each arm;
(B) performing PID control using proportional gain, differential gain, and integral gain set so that all the joints of the articulated robot move along the target trajectory;
(C) comparing the output value and the set value to calculate a figure of merit;
(D) repeating the steps (b) and (c) while increasing the differential gain until a predetermined condition is satisfied, and then finding a differential gain to minimize the figure of merit;
(E) setting a value obtained by multiplying the differential gain found in the step (d) by 0.8 as a new differential gain value;
Repeating the steps (b) and (c) while increasing the proportional gain until a predetermined condition is satisfied after fixing the differential gain; (f) searching for a proportional gain that minimizes the figure of merit;
(G) setting a value obtained by multiplying the proportional gain found in the step (f) by 0.8 to a new proportional gain value;
(H) repeating the steps (d) to (g) until a predetermined condition is satisfied, and then finding a differential gain and a proportional gain for minimizing the figure of merit;
(I) repeating the steps (b) and (c) while increasing the integral gain until a predetermined condition is satisfied after fixing the differential gain and the proportional gain, and searching for an integral gain for minimizing the figure of merit; And
(J) setting the integral gain found in the step (i) to a new integral gain value;
Wherein the PID gain of the multi-joint robot is automatically tuned.
Wherein the condition is satisfied when the figure of merit is below the reference value, the system diverges, the change value of the figure of merit falls below a predetermined value, or a predetermined number of repetitions is satisfied.
Wherein the integrated gain value in step (a) is zero.
Wherein the initial values of the proportional gain (K p ), the differential gain (K v ), and the integral gain (K i ) are set using the following mathematical expression.
K p = 1/3 * M ii ? C 2
K v = 2π * K p / ω c
K i = ω c * K p / 2π
M ii is the principal axis moment of inertia corresponding to the i-th axis, and ω c is the natural frequency of each axis
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| KR101849464B1 (en) | 2016-08-26 | 2018-05-31 | 한국로봇융합연구원 | Automatic Tuning Method for PID controllers |
| CN108508870A (en) * | 2018-03-29 | 2018-09-07 | 东南大学 | A kind of method of Drum Water Level Control System for Boiler Performance Evaluation and parameter optimization |
| WO2022220486A1 (en) * | 2021-04-13 | 2022-10-20 | Samsung Electronics Co., Ltd. | Systems and methods for automated tuning of robotics systems |
| US11712804B2 (en) | 2021-03-29 | 2023-08-01 | Samsung Electronics Co., Ltd. | Systems and methods for adaptive robotic motion control |
| US11724390B2 (en) | 2021-03-29 | 2023-08-15 | Samsung Electronics Co., Ltd. | Systems and methods for automated preloading of actuators |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR101849464B1 (en) | 2016-08-26 | 2018-05-31 | 한국로봇융합연구원 | Automatic Tuning Method for PID controllers |
| CN108508870A (en) * | 2018-03-29 | 2018-09-07 | 东南大学 | A kind of method of Drum Water Level Control System for Boiler Performance Evaluation and parameter optimization |
| CN108508870B (en) * | 2018-03-29 | 2021-04-27 | 东南大学 | Method for evaluating performance and optimizing parameters of boiler drum water level control system |
| US11712804B2 (en) | 2021-03-29 | 2023-08-01 | Samsung Electronics Co., Ltd. | Systems and methods for adaptive robotic motion control |
| US11724390B2 (en) | 2021-03-29 | 2023-08-15 | Samsung Electronics Co., Ltd. | Systems and methods for automated preloading of actuators |
| WO2022220486A1 (en) * | 2021-04-13 | 2022-10-20 | Samsung Electronics Co., Ltd. | Systems and methods for automated tuning of robotics systems |
| US11731279B2 (en) | 2021-04-13 | 2023-08-22 | Samsung Electronics Co., Ltd. | Systems and methods for automated tuning of robotics systems |
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