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An Improvement of Trajectory Tracking Accuracy of Automatic Sewing Robot System by Variable Gain Learning Control
Budapest, Hungary, August 27-30, 2018 12th IFAC Symposium on Robot Control Budapest, Hungary, August 27-30, 2018 12th IFAC Symposium on Robot Control Available online at www.sciencedirect.com 12th IFAC Symposium on Robot Control Budapest, Hungary, August 27-30, 2018 Budapest, Hungary, August 27-30, 2018
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IFAC PapersOnLine 51-22 (2018) 1–6 An Improvement of Trajectory Tracking Accuracy of An Sewing Improvement Trajectory Tracking Accuracy ofControl Automatic Robot of System by Variable Gain Learning An Improvement of Trajectory Tracking Accuracy ofControl Automatic Robot of System by Variable Gain Learning An Sewing Improvement Trajectory Tracking Accuracy of TakashiRobot Yoshimi*, Kenta Takezawa* and Motoki Automatic Sewing System by Variable GainHirayama** Learning Control Automatic Sewing Robot System by Variable Gain Learning Control Takashi Yoshimi*, Kenta Takezawa* and Motoki Hirayama**
* Shibaura Institute of Technology, Tokyo, 135-8548 Japan Takashi Yoshimi*, Kenta Takezawa* and Motoki Hirayama** Takashi Yoshimi*, Kenta Takezawa* and Motoki Hirayama** (e-mail: [email protected]). * Shibaura Institute of Technology, 135-8548 Japan Tokyo,Tokyo, ** JUKI Corporation, 206-8551 Japan Japan * Shibaura Institute of Technology, Tokyo, 135-8548 (e-mail: [email protected]). * Shibaura Institute of Technology, Tokyo, 135-8548 Japan (e-mail: [email protected]) (e-mail: [email protected]). ** JUKI Corporation, Tokyo, 206-8551 Japan [email protected]). ** (e-mail: JUKI Corporation, Tokyo, 206-8551 Japan (e-mail: [email protected]) ** JUKI Corporation, Tokyo, 206-8551 Japan (e-mail: [email protected]) (e-mail: [email protected]) Abstract: In the sewing factory, non-routine tasks, especially curved surface sewing of threedimensionalInproducts are stillfactory, executed manually by human workers, curved because surface it is difficult to handle the Abstract: the sewing non-routine tasks, especially sewing of threesewing parts precisely by the automatic machine. Then, we are developing an automatic sewing robot Abstract: In the sewing factory, non-routine tasks, especially curved surface sewing of threedimensional products are still executed manually by human workers, because it is difficult to handle the Abstract: Inproducts the sewing factory, non-routine tasks, especially surface sewing of surface threetheir sewing. We evaluated the developed robotwe system andcurved confirmed that the curved system for dimensional are still executed manually by human workers, because it is difficult to handle the sewing parts precisely by the automatic machine. Then, are developing an automatic sewing robot dimensional products are still executed manually by human workers, because it is difficult to handle the sewing motion is executed smoothly with low feeding speed. But, the trajectory tracking accuracy sewing for parts precisely automatic Then, are developing an automatic sewingsurface robot their sewing.by Wetheevaluated themachine. developed robotwe system and confirmed that the curved system sewing parts precisely by the automatic machine. Then, we are developing an automatic sewing robot becomes bad when the feeding speed is high. Then, we applied learning control method to our their sewing. We evaluated developed robot speed. system But, and confirmed that the curvedaccuracy surface system sewing for motion is executed smoothly the with low feeding the trajectory tracking their sewing. Wethe evaluated developed robot system and confirmed surface system and confirmed trajectory tracking accuracy is improved sufficiently bythe thiscurved method even sewing for motion is executed smoothly with lowThen, feeding speed. But, the trajectory tracking accuracy becomes bad when thethat feeding speed the is high. we applied learning controlthat method to our robot sewing motion is executed smoothly with low feeding speed. But, the trajectory tracking accuracy the sewing parts feeding speed is equal to human workers. However, we need much time to find suitable becomes bad when the feeding speed is high. Then, we applied learning control method to our robot system and confirmed that the trajectory tracking accuracy is improved sufficiently by this method even becomes bad when thethat feeding is high. we aapplied learning control method to robot learning gains forfeeding getting the result. So, weThen, propose gain learning which system and confirmed thegood trajectory accuracy isvariable improved by this method even the sewing parts speed isspeed equal totracking human workers. However, wesufficiently need muchcontrol time tomethod findour suitable system and confirmed that the trajectory tracking accuracy is improved sufficiently by this method even finds suitable learning gains automatically based on the trajectory tracking error of the robot arm. Finally, the sewing parts feeding speed is equal to human workers. However, we need much time to find suitable learning gains for getting the good result. So, we propose a variable gain learning control method which the sewing parts feeding speed is equal to human workers. However, we need much time to find suitable we confirmed that the enough trajectory tracking accuracy is achieved by the proposed method without learning gainslearning for getting theautomatically good result. So, weon propose a variable gain learning control which finds suitable gains based the trajectory tracking error of the robotmethod arm. Finally, learning gains for getting theautomatically good result.tracking So, weon propose a isvariable gain control method which much time andlearning effort. finds suitable based the trajectory tracking error of the robot arm. Finally, we confirmed that the gains enough trajectory accuracy achieved bylearning the proposed method without finds suitable learning gains automatically based on the trajectory tracking error of the robot arm. Finally, we confirmed that the enough trajectory tracking accuracy is achieved by the proposed method without much time and effort. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Three-dimensional object, Curved surface sewing, Non-routine Trajectory tracking we confirmed the enough trajectory tracking accuracy is achieved by task, the proposed method without much time andthat effort. accuracy, control,Curved Variable gain, sewing, Automatic sewing robot much time and effort.Learning object, Keywords: Three-dimensional surface Non-routine task,system Trajectory tracking Keywords: accuracy, Three-dimensional surface sewing, Non-routine task,system Trajectory tracking Learning object, control,Curved Variable gain, Automatic sewing robot Keywords: accuracy, Three-dimensional surface Non-routine task,system Trajectory tracking Learning object, control,Curved Variable gain, sewing, Automatic sewing robot controllingsewing the robot arm. The target task is set to the curved Learning control, Variable gain, Automatic robot system 1.accuracy, INTRODUCTION surface sewing of three-dimensional products shown in controlling the robot arm. The target task is setlike to the curved 1. INTRODUCTION Fig.1. Recently, production process automation is proceeded in surface controlling the robot arm. The target task is setlike to the curved sewing of three-dimensional products shown in 1. INTRODUCTION controlling the robot arm. The target task is setlike to the curved many factories for quality stabilization, productivity surface sewing of three-dimensional products shown in Fig.1. 1. INTRODUCTION Recently, production process automation is proceeded in surface We evaluated automatic sewinglike robot system sewingthe of developed three-dimensional products shown in improvement and labor shortage resolution. In the sewing Fig.1. Recently, production process automation is proceeded in many factories for quality stabilization, productivity Fig.1. and evaluated confirmedthe that the curved surfacesewing sewingrobot motion of We developed automatic system Recently, production process automation is proceeded in factory, factories many dedicated are used for routine many quality improvement and for labor machines shortage stabilization, resolution. In productivity the sewing sewing We three-dimensional products isautomatic executed smoothly with low developed system confirmedthe that the curved surfacesewing sewingrobot motion of many factories quality stabilization, tasks button or pocket sewing, so productivity on sewing [1][2]. and evaluated improvement and for labor shortage resolution. In the factory,like many dedicated machines are usedand for routine We evaluated the developed automatic sewing robot system sewing parts feeding speed. But, we found that the trajectory and confirmed that the curved surface sewing motion of three-dimensional products is executed smoothly with low improvement and labor shortage resolution. In the sewing However, non-routine sewing tasks, especially curved surface factory,like many dedicated machines are usedand for routine tasks button or pocket sewing, so on sewing [1][2]. tracking and confirmed that the curved surface sewing motion of accuracy becomes bad along with the increase in three-dimensional products is executed smoothly with low factory, many dedicated machines areespecially used for routine sewing sewing of three-dimensional products, are difficult their sewing parts feeding speed. But, we found that the trajectory tasks like button or sewing pocket sewing, and so onfor [1][2]. However, non-routine tasks, curved surface three-dimensional products is So, executed smoothly with low sewing parts feeding feeding speed.But, wefound have to the improve the sewing parts speed. we that trajectory tasks like button or sewing pocket sewing, anddifficult so on [1][2]. tracking accuracy becomes bad along with the increase in automation, and they are stillproducts, executed manually byfor human However, tasks, especially curved surface sewing of non-routine three-dimensional are their trajectory sewing parts feeding speed. trajectory tracking accuracy of we the developed automatic tracking accuracy becomes bad along withthat thethe increase in sewing parts feeding speed.But, So, wefound have to improve the However, non-routine sewing tasks, especially curved surface workers. Because, material of sewing parts such as cloth or sewing of three-dimensional difficultbyfor their sewing automation, and they are stillproducts, executed are manually human tracking accuracy becomes bad along with the increase in robot system in the level of equivalent sewing parts sewing parts feeding speed. So, we have to improve the trajectory tracking accuracy of the developed automatic sewing of products, difficultbyso, for their leather is three-dimensional soft, its is easilyare changed, it is automation, and and they areshape still manually human sewing parts feeding speed. So, we have to improve the workers. Because, material of executed sewing parts such as cloth or trajectory feeding speed to human workers for its practical use. tracking of of theequivalent developed automatic systemaccuracy in the level sewing parts automation, are still executed manually bycloth human difficult for and the they automatic machine toparts set such the sewing line sewing robot workers. of sewing accuracy offor the developed automatic tracking leather isBecause, soft, andmaterial its shape is easily changed,as so, it or is trajectory in the level of equivalent sewing parts sewing robot system feeding speed to human workers its practical use. workers. Because, material of sewing parts such as cloth or along actual edge accurately handle theso, sewing tracking accuracy methodsparts for leathertheisfor soft, and its shape is easily changed, itline is Some difficult the parts automatic machine toandset the sewing sewingtrajectory robot in workers the levelfor ofimprovement equivalent sewing feeding speed system to human its practical use. leather is soft, and its shape is easily changed, so, it is parts in three dimensions. This kind of work is executed by robot manipulators based on their repetitive motion trials are difficult the parts automatic machine toandsethandle the sewing line Some along thefor actual edge accurately the sewing feedingtrajectory speed to tracking human workers forimprovement its practical use. accuracy methods for difficult for the automatic machine toand sethandle the sewing line skilled workers, but training of workers needs much and by several researchers [3]-[12]. Then, wetrials applied along the actual parts edge This accurately thetime sewing parts in three dimensions. kind of work is executed by proposed Some manipulators trajectory tracking accuracy improvement methods for robot based on their repetitive motion are alongand the partstraining accurately handle thetime sewing cost, aactual variation inedge taskThis quality depending on and the Some trajectory tracking accuracy improvement methods for control method to our developed automatic sewing parts in three dimensions. kindoccurs ofand work is executed by learning skilled workers, but of workers needs much robot manipulators based on their repetitive motion trials are proposed by several researchers [3]-[12]. Then, we applied parts inworkers, three dimensions. kindwe of needs work is executed by degree of worker’s skill.This Then, are developing an proposed robot system manipulators based on their repetitive motion trials are to improve the trajectory tracking accuracy. We skilled but training workers much time by several researchers [3]-[12]. Then, we applied cost, and a variation in task of quality occurs depending on and the learning control method to our developed automatic sewing skilledand workers, but training of workers much time and automatic sewing robot for needs non-routine threeproposed by experiments several researchers [3]-[12]. we applied some evaluate the Then, effectiveness of cost, inskill. tasksystem quality occurs depending on the degree ofa variation worker’s Then, we are developing an made learning control method totoour developed automatic sewing robot system to improve the trajectory tracking accuracy. We cost, and a variation in task quality occurs depending on the dimensional products sewing to stabilize quality and improve control method to our developed automatic sewing learning control method with some learning gains and finally degree of worker’s skill. Then, we are developing an automatic sewing robot system for non-routine three- made robot system to improve thetotrajectory accuracy. We some experiments evaluate tracking the effectiveness of degree of sewing worker’s skill. system Then, we are developing an made productivity. robot system to improve thetotrajectory tracking accuracy. We automatic for quality non-routine threedimensional productsrobot sewing to stabilize and improve some experiments evaluate the effectiveness of learning control method with some learning gains and finally automatic sewing for quality non-routine three- made some experiments to evaluate the effectiveness of dimensional productsrobot sewingsystem to stabilize and improve productivity. learning control method with some learning gains and finally Our automatic sewing robottosystem non-routine dimensional products sewing stabilizeexecutes quality and improve learning control method with some learning gains and finally productivity. sewing tasks bysewing movingrobot the grasped sewing parts on the productivity. Our automatic system executes non-routine sewing machine. It is executed with two-step process. Our automatic system executes non-routine sewing tasks bysewing movingrobot the grasped sewing parts onFirst, the Our automatic sewing robot system executes non-routine the system generates a desired sewing trajectory by tasks by Itmoving the grasped sewingprocess. parts onFirst, the sewing machine. is executed with two-step sewing tasks by moving the grasped sewing parts on the measuring the actual parts edge line using a later sensor, then sewing machine. It is executed with two-step the system generates a desired sewing process. trajectoryFirst, by sewing machine. Itparts isparts executed with two-step process. First, moves the sewing along theline generated trajectory the system aedge desired sewing trajectory by measuring the generates actual using a sewing later sensor, then the the system afor desired sewing trajectory by on sewing machine executing the sewing taskthen measuring the generates actual parts edge using a sewing later sensor, Fig. 1. Sewing of three-dimensional products moves the sewing parts along theline generated trajectory measuring the actual parts edge line using a later sensor, then moves the sewing parts along the generated sewing trajectory on the sewing machine for executing the sewing task by Fig. 1. Sewing of three-dimensional products moves sewing parts along the generated on the the sewing machine for executing the sewing sewingtrajectory task by 1 Copyright © 2018 IFAC Fig. 1. Sewing of three-dimensional products on the sewing for executing the ofsewing taskControl) by Hosting byFig. 2405-8963 © 2018, machine IFAC (International Federation Automatic Elsevier Ltd. All reserved. 1. Sewing ofrights three-dimensional products Copyright 2018 responsibility IFAC 1 Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 1 10.1016/j.ifacol.2018.11.509 Copyright © 2018 IFAC 1
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confirmed that the trajectory tracking accuracy becomes sufficiently good even the sewing parts feeding speed is equal to human workers. However, we had much time to find suitable learning gains for getting this good result. So, we propose a variable gain learning control method which finds suitable learning gains automatically based on the trajectory tracking error of the robot arm.
Feed in g D ista n ce [m m ]
Fig. 3. Generated sewing trajectory Feed in g D ista n ce [m m ]
In this paper, our developed automatic sewing robot system and its sewing process is described. And the results of applying learning control method to our developed system for trajectory tracking accuracy improvement is introduced. Then, our proposed variable gain learning control method for automatic finding of suitable learning gains is explained. The effectiveness of our proposed method is also confirmed through experiments and shown in the paper.
D esired
Fig. 4. Trajectory tracking result (Feeding speed: 5.0 mm/s) measured point and detects the parts edge line at a constant cycle. Then, the system generates a desired sewing trajectory which is several mm inside from the parts edge line. The generated sewing trajectory is shown in Fig. 3.
2. AUTOMATIC SEWING ROBOT SYSTEM AND ITS SEWING PROCESS
In the second step, the robot arm moves the grasped sewing parts on the sewing machine and executes the sewing task by feeding the tip of the sewing machine needle along the generated sewing trajectory. Here, the right robot arm feeds the grasped sewing parts in the Y axis direction at the sewing point and moves in the X axis direction to follow the grasped sewing parts along the desired trajectory. The trajectory tracking result of the developed system with 5.0[mm/s] feeding speed which is equal to the parts edge line measurement speed is shown in Fig. 4. From this result, we confirmed that the developed system can execute the sewing task motion with good tracking accuracy to the generated desired trajectory.
2.1 Developed Automatic Sewing Robot System A schematic diagram of our developed automatic sewing robot system is shown in Fig. 2. This system moves the grasped sewing parts on the sewing machine to execute the sewing task along the generated sewing trajectory. We used dual robot arm system which is constructed by two 7 degrees of freedom articulated type manipulators (Mitsubishi Heavy Industries Ltd., PA10-7C). The sewing parts of threedimensional product is grasped by the right arm using the prepared fixture, and the laser sensor (Optex FA Co. Ltd., LS-100CN) for measuring the edge of sewing parts is fixed on the left arm. The sewing machine is a Post-bed, 1-needle, Unison-feed, Lockstitch Machine (JUKI Corporation, PLC2710-7), and it moves synchronously with the robot. Its automatic feeding mechanism is removed because the robot arm feeds the grasped sewing parts. The coordinate system of the developed robot system is also shown in Fig. 2.
3. IMPROVEMENT OF TRAJECTORY TRACKING ACCURACY BY LEARNING CONTROL 3.1 Applying Learning Control to Our Developed System for Trajectory Tracking Accuracy Improvement
2.2 Sewing Process of the Automatic Sewing Robot System
In the previous chapter, we confirmed that our developed system can execute the sewing task motion with good tracking accuracy to the generated desired trajectory when the robot arm moves the grasped sewing parts on the sewing machine with 5.0[mm/s] feeding speed which is equal to the parts edge line measurement speed. This feeding speed is low compared to the required sewing parts feeding speed which is an equivalent level to human workers. Then, we confirmed the trajectory tracking result of the developed system with 46.7[mm/s] feeding speed which is equal to the human workers feeding speed. The result of this experiment is shown in Fig. 5. From this result, we confirmed that the trajectory tracking accuracy became very bad when the
This system executes the sewing task with two-step process. In the first step, the actual parts edge line is detected by measuring the distance from the sensor to the parts surface by using a laser sensor. Here, the right robot arm feeds the grasped sewing parts only in the Y axis direction at the Left Arm Lase r Se n sor
Tra cked Resu lt
Se w in g M ach in e N e e d le
Rig h t Arm Sew in g Parts
Feed in g D ista n ce [m m ]
Fixtu re Sew in g M ach in e
D esired
Fig. 2. A schematic diagram of our developed automatic sewing robot system
Tra cked Resu lt
Fig. 5. Trajectory tracking result (Feeding speed: 46.7 mm/s) 2
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sewing parts feeding speed is high. So, we found that we have to improve the trajectory tracking accuracy of the developed automatic sewing robot system in the level of equivalent sewing parts feeding speed to human workers. This trajectory tracking error seems to occur due to the control delay of the robot arm to the desired trajectory, then we considered to apply learning control method to our developed system for its trajectory tracking accuracy improvement.
Feed in g D ista n ce [m m ]
D esired
Here,
Tra cked Resu lt 3rd 1st 2n d Tria l Tria l Tria l
(a) X axis direction
Feed in g D ista n ce [m m ]
Learning control is a feedforward system input modification method based on the tracking errors occurred in the repetition of the trial motion. It has some advantages that it can modify the tracking error occurred by the time delay or reproducible disturbances without robot dynamic parameters. We used the following learning control method. Its block diagram is shown in Fig. 6.
𝑢𝑢 𝑘𝑘+1 𝑡𝑡 = 𝑢𝑢 𝑘𝑘 𝑡𝑡 + 𝑒𝑒𝑘𝑘 (𝑡𝑡)
3
D esired
Tra cked Resu lt 1st 2n d Tria l Tria l
3rd Tria l
(b) Y axis direction Feed in g D ista n ce [m m ]
( 1)
D esired
Tra cked Resu lt 1st 2n d Tria l Tria l
3rd Tria l
(c) Z axis direction Fig. 7. Trajectory tracking result of learning control by equation (1) (From 1st to 3rd trials)
𝑘𝑘 ≥ 1 : Trial number, t : Time, 𝑢𝑢 𝑘𝑘 : Desired input vector in the kth trial, 𝑒𝑒𝑘𝑘 = 𝑦𝑦𝑑𝑑 − 𝑦𝑦𝑘𝑘 : Position error vector in the kth trial, 𝑦𝑦𝑑𝑑 : Desired Position vector, 𝑦𝑦𝑘𝑘 : Measured position vector in the kth trial.
Feed in g D ista n ce [m m ]
U n kn ow n D yn a m ics D esired
5th Tria l
Tra cked Resu lt 20th 10th Tria l Tria l
(a) X axis direction
Feed in g D ista n ce [m m ]
Fig. 6. Block diagram of the learning control method
D esired
Tra cked Resu lt 5th 10th Tria l Tria l
20th Tria l
(b) Y axis direction
This method calculates the next desired input vector from the current position error vector. By modifying the desired input vector using equation (1) repeatedly, the trajectory tracking error of the robot arm decreases gradually. We applied the equation (1) to generate the desired input vector in the task coordinate system (X, Y, Z direction) of the robot arm.
Feed in g D ista n ce [m m ]
D esired
5th Tria l
Tra cked Resu lt 20th 10th Tria l Tria l
(c) Z axis direction Fig. 8. Trajectory tracking result of learning control by equation (1) (At 5ts, 10th and 20th trials)
3.2 Results of Applying Learning Control to Our Developed System
E rror M ea n Sq u a re[m m ]
We applied learning control method described in the previous section to our developed automatic sewing robot system and confirmed its effectiveness to improve the trajectory tracking accuracy of the robot arm through experiments. The results of the experiments are shown from Fig. 7 to Fig. 10. Fig.7 shows the results of trajectory tracking from 1st to 3rd trials using learning control method by equation (1). Here, desired positions in Y axis and Z axis are set to constant. From these results, we can recognize that the trajectory tracking accuracies become good according to the increase of trial times. However, the trajectory tracking error in X axis remains in the result of 3rd trial, and the robot arm is not moving along the desired trajectory, precisely. Fig.8 shows the results of trajectory tracking at 5th, 10th and 20th trials
X a xis
Y a xis Z a xis
Tria l N u m b er k[tim es]
Fig. 9. Error mean square transition of the trajectory tracking by learning control of equation (1) 3
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Table 1. Learning gains of experiments by equation (2)
Feed in g D ista n ce [m m ]
Case Case Case Case D esired
1 2 3 4
X axis Gain 0.5 0.4 0.3 0.25
Y axis Gain 1.0 0.8 0.6 0.5
Z axis Gain 0.25 0.2 0.15 0.0625
4th Tria l Tra cked Resu lt
E rro r M e an Sq u are [m m ]
(a) X axis direction
Feed in g D ista n ce [m m ] D esired
4th Tria l Tra cked Resu lt
(b) Y axis direction
X axis Y axis Z axis
Trial N u m b e r k[tim e s] Feed in g D ista n ce [m m ] D esired
(a) Case 1, Learning gain = (0.5, 1.0, 0.25)
4th Tria l Tra cked Resu lt
Erro r M e an Sq u are [m m ]
(c) Z axis direction Fig. 10. Trajectory tracking result of learning control by equation (1) (At 4th trial) using learning control method by equation (1). From these results, we find that the trajectory tracking accuracies in X axis and Y axis become good, but the accuracy in Z axis becomes bad at the 10th trial. And, the trajectory tracking errors in all axes increase at the 20th trial. Fig.9 shows the error mean square transition of the trajectory tracking by learning control of equation (1). From this graph, we can recognize that the result of 4th trial is the best for trajectory tracking, and it becomes bad according to the increase of trial times. Fig.10 shows the results of trajectory tracking at the 4th trial which is the best result using learning control method by equation (1). The error mean square of the trajectory tracking in X axis direction at the 4th trial is 0.24[mm], and the required accuracy is 0.15[mm]. So, we found that we cannot meet the required accuracy under this condition.
X axis Y axis Z axis
Trial N u m b e r k[tim e s]
E rro r M e an Sq u are [m m ]
(b) Case 2, Learning gain = (0.4, 0.8, 0.2)
X axis Y axis Z axis
3.3 Improvement of Learning Control by Gain Adjustment Trial N u m b e r k[tim e s]
From the results shown in the previous section, we confirmed that the trajectory tracking accuracy becomes good using learning control method by equation (1) in the early stage. However, the trajectory tracking error starts increasing after decreasing according to the increase of trial times by this method. This phenomenon seems to occur because the learning gain of all directions is not suitable and too big for the reduction of trajectory tracking errors. So, we used the following learning control method instead of equation (1).
𝑢𝑢 𝑘𝑘+1 𝑡𝑡 = 𝑢𝑢 𝑘𝑘 𝑡𝑡 + 𝛬𝛬𝑒𝑒𝑘𝑘 (𝑡𝑡) Here,
E rro r M e an Sq u are [m m ]
(c) Case 3, Learning gain = (0.3, 0.6, 0.15)
X axis Y axis Z axis
( 2)
𝑘𝑘 ≥ 1 : Trial number, t : Time, Λ : Learning gain 𝑢𝑢 𝑘𝑘 : Desired input vector in the kth trial, 𝑒𝑒𝑘𝑘 = 𝑦𝑦𝑑𝑑 − 𝑦𝑦𝑘𝑘 : Position error vector in the kth trial, 𝑦𝑦𝑑𝑑 : Desired Position vector, 𝑦𝑦𝑘𝑘 : Measured position vector in the kth trial.
Trial N u m b e r k[tim e s]
(d) Case 4, Learning gain = (0.25, 0.5, 0.0625) Fig. 11. Error mean square transition of the trajectory tracking by learning control of equation (2) 4
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To define the suitable learning gain in equation (2), we considered to use the gains in constant ratio of X, Y, Z directions. Its ratio is defined from the increasing ratio of the error mean square of the trajectory tracking experiment shown in Fig. 9, so we set the constant ratio as: X : Y : Z = 1/2 : 1/1 : 1/4
Feed in g D ista n ce [m m ]
D esired
(3)
Feed in g D ista n ce [m m ] D esired
Feed in g D ista n ce [m m ] D esired
Erro r M e an Sq u are [m m ]
X a xis Y a xis Z a xis
Trial N u m b e r k[tim e s]
Fig. 13. Error mean square transition of the trajectory tracking by variable gain learning control
( 4) Le arn in g Gain
Λ𝑘𝑘
30th Tria l Tra cked Resu lt
(c) Z axis direction Fig. 12. Trajectory tracking result of learning control by equation (2) (At 30th trial in Case 4)
In the previous section, we confirmed the effectiveness of the learning control method by equation (2) using the learning gains in constant ratio of X, Y, Z directions shown in Table 1. However, the definition of the learning gains is based on the trial and error, so we have to make much experiments and need much time to define them. To reduce the time and effort to define the learning gains, we considered the method to change the learning gains in every trials based on the change of trajectory tracking error of the robot arm. Then, we propose a variable gain learning control method which calculate learning gains based on the following equation. 𝐸𝐸𝑀𝑀𝑆𝑆1
30th Tria l Tra cked Resu lt
(b) Y axis direction
3.4 The Proposal of Variable Gain Learning Control Method
𝐸𝐸𝑀𝑀𝑆𝑆 𝑘𝑘
30th Tria l Tra cked Resu lt
(a) X axis direction
Then, we made experiments to confirm the effectiveness of the learning control method by equation (2) under the learning gains by the ratio of (3) shown in Table 1. Fig.11 shows the error mean square transition of the trajectory tracking of learning control by equation (2) under the learning gains shown in Table 1. From these results, we recognized that the learning control by equation (2) is effective for reducing the trajectory tracking errors by using the gains in constant ratio of X, Y, Z directions shown in Table 1. We found that the best learning gains for reducing trajectory tracking errors are that of case 4 at the 30th trial. Fig. 12 shows the results of trajectory tracking at this condition. The error mean square of the trajectory tracking in X axis direction of this case is 0.13[mm], then we understood that we could meet the required accuracy (=0.15[mm]) under this condition. But, the gains in case 4 is very small, so we needed much time to realize enough trajectory tracking accuracy.
Λ𝑘𝑘 +1 =
5
Here, Λ1 = Λ2 = 1 𝑘𝑘 ≥ 2 : Trial number, 𝐸𝐸𝑀𝑀𝑆𝑆𝑘𝑘 : Error mean square at the kth trial. The learning gains Λ is calculated by the equation (4) from the third trial. This equation calculates the learning gains from the ratio of first and present error mean squares, so the learning gains become small according to the decrease of trajectory tracking errors. By using this method of equations (2) and (4), we can find suitable learning gains automatically based on the trajectory tracking error of the robot arm.
X a xis Y a xis Z a xis
Trial N u m b e r k[tim e s]
Fig. 14. Learning gains transition of the trajectory tracking by variable gain learning control and (4) is effective for reducing the trajectory tracking errors and the suitable learning gains are calculated automatically. The smallest trajectory tracking error is achieved at the 30th trial. Fig. 15 shows the results of trajectory tracking at the 30th trial of the variable gain learning control. The error mean square of the trajectory tracking in X axis direction of this case is 0.15[mm], then we understood that we could meet the required accuracy (=0.15[mm]) and realized enough
We made experiments to confirm the effectiveness of the proposed variable gain learning control method. Fig.13 shows the error mean square transition, and Fig.14 shows the learning gains transition of the trajectory tracking by variable gain learning control. From these results, we can recognize that the variable gain learning control method by equation (2) 5
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REFERENCES
Feed in g D ista n ce [m m ]
D esired
[1] JUKI Corporation Webpage, “Computer-controlled, High-speed, Lockstitch, Button Sewing System” : http://www.juki.co.jp/industrial_e/products_e/apparel_e/ cat10/lk1903bnseries.html [2] JUKI Corporation Webpage, “Automatic Pocket Setter” : http://www.juki.co.jp/industrial_e/products_e/apparel_e/ cat90/ap876.html [3] M.Uchiyama: “Formation of High-Speed Motion Pattern of a Mechanical Arm by Trial”, Trans. of the Society of Instrument and Control Engineers, Vol.14, No.6, pp.706-712, 1978 (in Japanese). [4] T.Inoue, M.Nakano, T.Kubo, S.Matsumoto and H.Baba: “High Accuracy Control of a Proton Synchrotron Magnet Power Supply”, IFAC Proceedings, Vol.14, Issue 2, pp.3137-3142, 1981. [5] S.Arimoto, S.Kawamura and F.Miyazaki: “Bettering Operation of Robots by Learning”, Journal of Robotic Systems, Vol.1, No.2, pp.123-140, 1984. [6] S.Arimoto, S.Kawamura and F.Miyazaki: “Can Mechanical Robots Learn by Themselves?”, Proc. of the 2nd International Symposium of Robotic Research, Kyoto, Japan, August, 1984. [7] S.Arimoto, S.Kawamura and F.Miyazaki: “Bettering Operation of Dynamic Systems by Learning: A New Control Theory for Servomechanism or Mechatronics Systems”, Proc. of the 23rd IEEE CDC, Las Vegas, Nevada, December, 1984. [8] S.Kawamura, F.Miyazaki and S.Arimoto: “Iterative Learning Control for Robotic Systems”, Proc. of IECON’84, Tokyo, Japan, October, 1984. [9] S.Arimoto, S.Kawamura and F.Miyazaki: “Learning Control Theory for Dynamical Systems”, Proc. of the 24th IEEE CDC, Fort Lauderdale, Florida, December, 1985. [10] T.Mita and E.Kato: “Iterative control and its application to motion control of robot arm - A direct approach to servo-problems”, Proc. of the 24th IEEE Conference on Decision and Control, 1985. [11] S.Kawamura, T.Yoshimi, F.Miyazaki and S.Arimoto: “Technical Issues in Learning Control for Robot Motions”, Proc. of the 1987 International Conference on Advanced Robotics (ICAR'87), pp.513-524, 1987. [12] T.Omata, S.Hara and M.Nakano: “Nonlinear repetitive control with application to trajectory control of manipulators”, Journal of Field Robotics, Vol.4, No.5, pp.631-652, 1987.
30th Tria l Tra cked Resu lt
(a) X axis direction
Feed in g D ista n ce [m m ] D esired
30th Tria l Tra cked Resu lt
(b) Y axis direction
Feed in g D ista n ce [m m ] D esired
30th Tria l Tra cked Resu lt
(c) Z axis direction Fig. 15. Trajectory tracking result of variable gain learning control method (At 30th trial) trajectory tracking accuracy without much time by this method. 4. CONCLUSIONS We have developed an automatic sewing robot system for non-routine three-dimensional products sewing. We evaluated the developed robot system and confirmed that the trajectory tracking accuracy of the curved surface sewing motion of three-dimensional products becomes bad when the feeding speed is high. Then, we applied learning control method to our robot system to improve the trajectory tracking accuracy and confirmed that the accuracy is improved sufficiently by the method even the sewing parts feeding speed is equal to human workers. And, to decrease the time to find suitable learning gains for the good result, we proposed a variable gain learning control method which finds suitable learning gains automatically based on the trajectory tracking error of the robot arm. Finally, we confirmed that the enough trajectory tracking accuracy is achieved by the proposed learning control method without much time and effort through experiments. We will improve the completeness of the proposed method to the practical use level in near future.
6
ScienceDirect
IFAC PapersOnLine 51-22 (2018) 1–6 An Improvement of Trajectory Tracking Accuracy of An Sewing Improvement Trajectory Tracking Accuracy ofControl Automatic Robot of System by Variable Gain Learning An Improvement of Trajectory Tracking Accuracy ofControl Automatic Robot of System by Variable Gain Learning An Sewing Improvement Trajectory Tracking Accuracy of TakashiRobot Yoshimi*, Kenta Takezawa* and Motoki Automatic Sewing System by Variable GainHirayama** Learning Control Automatic Sewing Robot System by Variable Gain Learning Control Takashi Yoshimi*, Kenta Takezawa* and Motoki Hirayama**
* Shibaura Institute of Technology, Tokyo, 135-8548 Japan Takashi Yoshimi*, Kenta Takezawa* and Motoki Hirayama** Takashi Yoshimi*, Kenta Takezawa* and Motoki Hirayama** (e-mail: [email protected]). * Shibaura Institute of Technology, 135-8548 Japan Tokyo,Tokyo, ** JUKI Corporation, 206-8551 Japan Japan * Shibaura Institute of Technology, Tokyo, 135-8548 (e-mail: [email protected]). * Shibaura Institute of Technology, Tokyo, 135-8548 Japan (e-mail: [email protected]) (e-mail: [email protected]). ** JUKI Corporation, Tokyo, 206-8551 Japan [email protected]). ** (e-mail: JUKI Corporation, Tokyo, 206-8551 Japan (e-mail: [email protected]) ** JUKI Corporation, Tokyo, 206-8551 Japan (e-mail: [email protected]) (e-mail: [email protected]) Abstract: In the sewing factory, non-routine tasks, especially curved surface sewing of threedimensionalInproducts are stillfactory, executed manually by human workers, curved because surface it is difficult to handle the Abstract: the sewing non-routine tasks, especially sewing of threesewing parts precisely by the automatic machine. Then, we are developing an automatic sewing robot Abstract: In the sewing factory, non-routine tasks, especially curved surface sewing of threedimensional products are still executed manually by human workers, because it is difficult to handle the Abstract: Inproducts the sewing factory, non-routine tasks, especially surface sewing of surface threetheir sewing. We evaluated the developed robotwe system andcurved confirmed that the curved system for dimensional are still executed manually by human workers, because it is difficult to handle the sewing parts precisely by the automatic machine. Then, are developing an automatic sewing robot dimensional products are still executed manually by human workers, because it is difficult to handle the sewing motion is executed smoothly with low feeding speed. But, the trajectory tracking accuracy sewing for parts precisely automatic Then, are developing an automatic sewingsurface robot their sewing.by Wetheevaluated themachine. developed robotwe system and confirmed that the curved system sewing parts precisely by the automatic machine. Then, we are developing an automatic sewing robot becomes bad when the feeding speed is high. Then, we applied learning control method to our their sewing. We evaluated developed robot speed. system But, and confirmed that the curvedaccuracy surface system sewing for motion is executed smoothly the with low feeding the trajectory tracking their sewing. Wethe evaluated developed robot system and confirmed surface system and confirmed trajectory tracking accuracy is improved sufficiently bythe thiscurved method even sewing for motion is executed smoothly with lowThen, feeding speed. But, the trajectory tracking accuracy becomes bad when thethat feeding speed the is high. we applied learning controlthat method to our robot sewing motion is executed smoothly with low feeding speed. But, the trajectory tracking accuracy the sewing parts feeding speed is equal to human workers. However, we need much time to find suitable becomes bad when the feeding speed is high. Then, we applied learning control method to our robot system and confirmed that the trajectory tracking accuracy is improved sufficiently by this method even becomes bad when thethat feeding is high. we aapplied learning control method to robot learning gains forfeeding getting the result. So, weThen, propose gain learning which system and confirmed thegood trajectory accuracy isvariable improved by this method even the sewing parts speed isspeed equal totracking human workers. However, wesufficiently need muchcontrol time tomethod findour suitable system and confirmed that the trajectory tracking accuracy is improved sufficiently by this method even finds suitable learning gains automatically based on the trajectory tracking error of the robot arm. Finally, the sewing parts feeding speed is equal to human workers. However, we need much time to find suitable learning gains for getting the good result. So, we propose a variable gain learning control method which the sewing parts feeding speed is equal to human workers. However, we need much time to find suitable we confirmed that the enough trajectory tracking accuracy is achieved by the proposed method without learning gainslearning for getting theautomatically good result. So, weon propose a variable gain learning control which finds suitable gains based the trajectory tracking error of the robotmethod arm. Finally, learning gains for getting theautomatically good result.tracking So, weon propose a isvariable gain control method which much time andlearning effort. finds suitable based the trajectory tracking error of the robot arm. Finally, we confirmed that the gains enough trajectory accuracy achieved bylearning the proposed method without finds suitable learning gains automatically based on the trajectory tracking error of the robot arm. Finally, we confirmed that the enough trajectory tracking accuracy is achieved by the proposed method without much time and effort. © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Keywords: Three-dimensional object, Curved surface sewing, Non-routine Trajectory tracking we confirmed the enough trajectory tracking accuracy is achieved by task, the proposed method without much time andthat effort. accuracy, control,Curved Variable gain, sewing, Automatic sewing robot much time and effort.Learning object, Keywords: Three-dimensional surface Non-routine task,system Trajectory tracking Keywords: accuracy, Three-dimensional surface sewing, Non-routine task,system Trajectory tracking Learning object, control,Curved Variable gain, Automatic sewing robot Keywords: accuracy, Three-dimensional surface Non-routine task,system Trajectory tracking Learning object, control,Curved Variable gain, sewing, Automatic sewing robot controllingsewing the robot arm. The target task is set to the curved Learning control, Variable gain, Automatic robot system 1.accuracy, INTRODUCTION surface sewing of three-dimensional products shown in controlling the robot arm. The target task is setlike to the curved 1. INTRODUCTION Fig.1. Recently, production process automation is proceeded in surface controlling the robot arm. The target task is setlike to the curved sewing of three-dimensional products shown in 1. INTRODUCTION controlling the robot arm. The target task is setlike to the curved many factories for quality stabilization, productivity surface sewing of three-dimensional products shown in Fig.1. 1. INTRODUCTION Recently, production process automation is proceeded in surface We evaluated automatic sewinglike robot system sewingthe of developed three-dimensional products shown in improvement and labor shortage resolution. In the sewing Fig.1. Recently, production process automation is proceeded in many factories for quality stabilization, productivity Fig.1. and evaluated confirmedthe that the curved surfacesewing sewingrobot motion of We developed automatic system Recently, production process automation is proceeded in factory, factories many dedicated are used for routine many quality improvement and for labor machines shortage stabilization, resolution. In productivity the sewing sewing We three-dimensional products isautomatic executed smoothly with low developed system confirmedthe that the curved surfacesewing sewingrobot motion of many factories quality stabilization, tasks button or pocket sewing, so productivity on sewing [1][2]. and evaluated improvement and for labor shortage resolution. In the factory,like many dedicated machines are usedand for routine We evaluated the developed automatic sewing robot system sewing parts feeding speed. But, we found that the trajectory and confirmed that the curved surface sewing motion of three-dimensional products is executed smoothly with low improvement and labor shortage resolution. In the sewing However, non-routine sewing tasks, especially curved surface factory,like many dedicated machines are usedand for routine tasks button or pocket sewing, so on sewing [1][2]. tracking and confirmed that the curved surface sewing motion of accuracy becomes bad along with the increase in three-dimensional products is executed smoothly with low factory, many dedicated machines areespecially used for routine sewing sewing of three-dimensional products, are difficult their sewing parts feeding speed. But, we found that the trajectory tasks like button or sewing pocket sewing, and so onfor [1][2]. However, non-routine tasks, curved surface three-dimensional products is So, executed smoothly with low sewing parts feeding feeding speed.But, wefound have to the improve the sewing parts speed. we that trajectory tasks like button or sewing pocket sewing, anddifficult so on [1][2]. tracking accuracy becomes bad along with the increase in automation, and they are stillproducts, executed manually byfor human However, tasks, especially curved surface sewing of non-routine three-dimensional are their trajectory sewing parts feeding speed. trajectory tracking accuracy of we the developed automatic tracking accuracy becomes bad along withthat thethe increase in sewing parts feeding speed.But, So, wefound have to improve the However, non-routine sewing tasks, especially curved surface workers. Because, material of sewing parts such as cloth or sewing of three-dimensional difficultbyfor their sewing automation, and they are stillproducts, executed are manually human tracking accuracy becomes bad along with the increase in robot system in the level of equivalent sewing parts sewing parts feeding speed. So, we have to improve the trajectory tracking accuracy of the developed automatic sewing of products, difficultbyso, for their leather is three-dimensional soft, its is easilyare changed, it is automation, and and they areshape still manually human sewing parts feeding speed. So, we have to improve the workers. Because, material of executed sewing parts such as cloth or trajectory feeding speed to human workers for its practical use. tracking of of theequivalent developed automatic systemaccuracy in the level sewing parts automation, are still executed manually bycloth human difficult for and the they automatic machine toparts set such the sewing line sewing robot workers. of sewing accuracy offor the developed automatic tracking leather isBecause, soft, andmaterial its shape is easily changed,as so, it or is trajectory in the level of equivalent sewing parts sewing robot system feeding speed to human workers its practical use. workers. Because, material of sewing parts such as cloth or along actual edge accurately handle theso, sewing tracking accuracy methodsparts for leathertheisfor soft, and its shape is easily changed, itline is Some difficult the parts automatic machine toandset the sewing sewingtrajectory robot in workers the levelfor ofimprovement equivalent sewing feeding speed system to human its practical use. leather is soft, and its shape is easily changed, so, it is parts in three dimensions. This kind of work is executed by robot manipulators based on their repetitive motion trials are difficult the parts automatic machine toandsethandle the sewing line Some along thefor actual edge accurately the sewing feedingtrajectory speed to tracking human workers forimprovement its practical use. accuracy methods for difficult for the automatic machine toand sethandle the sewing line skilled workers, but training of workers needs much and by several researchers [3]-[12]. Then, wetrials applied along the actual parts edge This accurately thetime sewing parts in three dimensions. kind of work is executed by proposed Some manipulators trajectory tracking accuracy improvement methods for robot based on their repetitive motion are alongand the partstraining accurately handle thetime sewing cost, aactual variation inedge taskThis quality depending on and the Some trajectory tracking accuracy improvement methods for control method to our developed automatic sewing parts in three dimensions. kindoccurs ofand work is executed by learning skilled workers, but of workers needs much robot manipulators based on their repetitive motion trials are proposed by several researchers [3]-[12]. Then, we applied parts inworkers, three dimensions. kindwe of needs work is executed by degree of worker’s skill.This Then, are developing an proposed robot system manipulators based on their repetitive motion trials are to improve the trajectory tracking accuracy. We skilled but training workers much time by several researchers [3]-[12]. Then, we applied cost, and a variation in task of quality occurs depending on and the learning control method to our developed automatic sewing skilledand workers, but training of workers much time and automatic sewing robot for needs non-routine threeproposed by experiments several researchers [3]-[12]. we applied some evaluate the Then, effectiveness of cost, inskill. tasksystem quality occurs depending on the degree ofa variation worker’s Then, we are developing an made learning control method totoour developed automatic sewing robot system to improve the trajectory tracking accuracy. We cost, and a variation in task quality occurs depending on the dimensional products sewing to stabilize quality and improve control method to our developed automatic sewing learning control method with some learning gains and finally degree of worker’s skill. Then, we are developing an automatic sewing robot system for non-routine three- made robot system to improve thetotrajectory accuracy. We some experiments evaluate tracking the effectiveness of degree of sewing worker’s skill. system Then, we are developing an made productivity. robot system to improve thetotrajectory tracking accuracy. We automatic for quality non-routine threedimensional productsrobot sewing to stabilize and improve some experiments evaluate the effectiveness of learning control method with some learning gains and finally automatic sewing for quality non-routine three- made some experiments to evaluate the effectiveness of dimensional productsrobot sewingsystem to stabilize and improve productivity. learning control method with some learning gains and finally Our automatic sewing robottosystem non-routine dimensional products sewing stabilizeexecutes quality and improve learning control method with some learning gains and finally productivity. sewing tasks bysewing movingrobot the grasped sewing parts on the productivity. Our automatic system executes non-routine sewing machine. It is executed with two-step process. Our automatic system executes non-routine sewing tasks bysewing movingrobot the grasped sewing parts onFirst, the Our automatic sewing robot system executes non-routine the system generates a desired sewing trajectory by tasks by Itmoving the grasped sewingprocess. parts onFirst, the sewing machine. is executed with two-step sewing tasks by moving the grasped sewing parts on the measuring the actual parts edge line using a later sensor, then sewing machine. It is executed with two-step the system generates a desired sewing process. trajectoryFirst, by sewing machine. Itparts isparts executed with two-step process. First, moves the sewing along theline generated trajectory the system aedge desired sewing trajectory by measuring the generates actual using a sewing later sensor, then the the system afor desired sewing trajectory by on sewing machine executing the sewing taskthen measuring the generates actual parts edge using a sewing later sensor, Fig. 1. Sewing of three-dimensional products moves the sewing parts along theline generated trajectory measuring the actual parts edge line using a later sensor, then moves the sewing parts along the generated sewing trajectory on the sewing machine for executing the sewing task by Fig. 1. Sewing of three-dimensional products moves sewing parts along the generated on the the sewing machine for executing the sewing sewingtrajectory task by 1 Copyright © 2018 IFAC Fig. 1. Sewing of three-dimensional products on the sewing for executing the ofsewing taskControl) by Hosting byFig. 2405-8963 © 2018, machine IFAC (International Federation Automatic Elsevier Ltd. All reserved. 1. Sewing ofrights three-dimensional products Copyright 2018 responsibility IFAC 1 Control. Peer review©under of International Federation of Automatic Copyright © 2018 IFAC 1 10.1016/j.ifacol.2018.11.509 Copyright © 2018 IFAC 1
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confirmed that the trajectory tracking accuracy becomes sufficiently good even the sewing parts feeding speed is equal to human workers. However, we had much time to find suitable learning gains for getting this good result. So, we propose a variable gain learning control method which finds suitable learning gains automatically based on the trajectory tracking error of the robot arm.
Feed in g D ista n ce [m m ]
Fig. 3. Generated sewing trajectory Feed in g D ista n ce [m m ]
In this paper, our developed automatic sewing robot system and its sewing process is described. And the results of applying learning control method to our developed system for trajectory tracking accuracy improvement is introduced. Then, our proposed variable gain learning control method for automatic finding of suitable learning gains is explained. The effectiveness of our proposed method is also confirmed through experiments and shown in the paper.
D esired
Fig. 4. Trajectory tracking result (Feeding speed: 5.0 mm/s) measured point and detects the parts edge line at a constant cycle. Then, the system generates a desired sewing trajectory which is several mm inside from the parts edge line. The generated sewing trajectory is shown in Fig. 3.
2. AUTOMATIC SEWING ROBOT SYSTEM AND ITS SEWING PROCESS
In the second step, the robot arm moves the grasped sewing parts on the sewing machine and executes the sewing task by feeding the tip of the sewing machine needle along the generated sewing trajectory. Here, the right robot arm feeds the grasped sewing parts in the Y axis direction at the sewing point and moves in the X axis direction to follow the grasped sewing parts along the desired trajectory. The trajectory tracking result of the developed system with 5.0[mm/s] feeding speed which is equal to the parts edge line measurement speed is shown in Fig. 4. From this result, we confirmed that the developed system can execute the sewing task motion with good tracking accuracy to the generated desired trajectory.
2.1 Developed Automatic Sewing Robot System A schematic diagram of our developed automatic sewing robot system is shown in Fig. 2. This system moves the grasped sewing parts on the sewing machine to execute the sewing task along the generated sewing trajectory. We used dual robot arm system which is constructed by two 7 degrees of freedom articulated type manipulators (Mitsubishi Heavy Industries Ltd., PA10-7C). The sewing parts of threedimensional product is grasped by the right arm using the prepared fixture, and the laser sensor (Optex FA Co. Ltd., LS-100CN) for measuring the edge of sewing parts is fixed on the left arm. The sewing machine is a Post-bed, 1-needle, Unison-feed, Lockstitch Machine (JUKI Corporation, PLC2710-7), and it moves synchronously with the robot. Its automatic feeding mechanism is removed because the robot arm feeds the grasped sewing parts. The coordinate system of the developed robot system is also shown in Fig. 2.
3. IMPROVEMENT OF TRAJECTORY TRACKING ACCURACY BY LEARNING CONTROL 3.1 Applying Learning Control to Our Developed System for Trajectory Tracking Accuracy Improvement
2.2 Sewing Process of the Automatic Sewing Robot System
In the previous chapter, we confirmed that our developed system can execute the sewing task motion with good tracking accuracy to the generated desired trajectory when the robot arm moves the grasped sewing parts on the sewing machine with 5.0[mm/s] feeding speed which is equal to the parts edge line measurement speed. This feeding speed is low compared to the required sewing parts feeding speed which is an equivalent level to human workers. Then, we confirmed the trajectory tracking result of the developed system with 46.7[mm/s] feeding speed which is equal to the human workers feeding speed. The result of this experiment is shown in Fig. 5. From this result, we confirmed that the trajectory tracking accuracy became very bad when the
This system executes the sewing task with two-step process. In the first step, the actual parts edge line is detected by measuring the distance from the sensor to the parts surface by using a laser sensor. Here, the right robot arm feeds the grasped sewing parts only in the Y axis direction at the Left Arm Lase r Se n sor
Tra cked Resu lt
Se w in g M ach in e N e e d le
Rig h t Arm Sew in g Parts
Feed in g D ista n ce [m m ]
Fixtu re Sew in g M ach in e
D esired
Fig. 2. A schematic diagram of our developed automatic sewing robot system
Tra cked Resu lt
Fig. 5. Trajectory tracking result (Feeding speed: 46.7 mm/s) 2
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sewing parts feeding speed is high. So, we found that we have to improve the trajectory tracking accuracy of the developed automatic sewing robot system in the level of equivalent sewing parts feeding speed to human workers. This trajectory tracking error seems to occur due to the control delay of the robot arm to the desired trajectory, then we considered to apply learning control method to our developed system for its trajectory tracking accuracy improvement.
Feed in g D ista n ce [m m ]
D esired
Here,
Tra cked Resu lt 3rd 1st 2n d Tria l Tria l Tria l
(a) X axis direction
Feed in g D ista n ce [m m ]
Learning control is a feedforward system input modification method based on the tracking errors occurred in the repetition of the trial motion. It has some advantages that it can modify the tracking error occurred by the time delay or reproducible disturbances without robot dynamic parameters. We used the following learning control method. Its block diagram is shown in Fig. 6.
𝑢𝑢 𝑘𝑘+1 𝑡𝑡 = 𝑢𝑢 𝑘𝑘 𝑡𝑡 + 𝑒𝑒𝑘𝑘 (𝑡𝑡)
3
D esired
Tra cked Resu lt 1st 2n d Tria l Tria l
3rd Tria l
(b) Y axis direction Feed in g D ista n ce [m m ]
( 1)
D esired
Tra cked Resu lt 1st 2n d Tria l Tria l
3rd Tria l
(c) Z axis direction Fig. 7. Trajectory tracking result of learning control by equation (1) (From 1st to 3rd trials)
𝑘𝑘 ≥ 1 : Trial number, t : Time, 𝑢𝑢 𝑘𝑘 : Desired input vector in the kth trial, 𝑒𝑒𝑘𝑘 = 𝑦𝑦𝑑𝑑 − 𝑦𝑦𝑘𝑘 : Position error vector in the kth trial, 𝑦𝑦𝑑𝑑 : Desired Position vector, 𝑦𝑦𝑘𝑘 : Measured position vector in the kth trial.
Feed in g D ista n ce [m m ]
U n kn ow n D yn a m ics D esired
5th Tria l
Tra cked Resu lt 20th 10th Tria l Tria l
(a) X axis direction
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Fig. 6. Block diagram of the learning control method
D esired
Tra cked Resu lt 5th 10th Tria l Tria l
20th Tria l
(b) Y axis direction
This method calculates the next desired input vector from the current position error vector. By modifying the desired input vector using equation (1) repeatedly, the trajectory tracking error of the robot arm decreases gradually. We applied the equation (1) to generate the desired input vector in the task coordinate system (X, Y, Z direction) of the robot arm.
Feed in g D ista n ce [m m ]
D esired
5th Tria l
Tra cked Resu lt 20th 10th Tria l Tria l
(c) Z axis direction Fig. 8. Trajectory tracking result of learning control by equation (1) (At 5ts, 10th and 20th trials)
3.2 Results of Applying Learning Control to Our Developed System
E rror M ea n Sq u a re[m m ]
We applied learning control method described in the previous section to our developed automatic sewing robot system and confirmed its effectiveness to improve the trajectory tracking accuracy of the robot arm through experiments. The results of the experiments are shown from Fig. 7 to Fig. 10. Fig.7 shows the results of trajectory tracking from 1st to 3rd trials using learning control method by equation (1). Here, desired positions in Y axis and Z axis are set to constant. From these results, we can recognize that the trajectory tracking accuracies become good according to the increase of trial times. However, the trajectory tracking error in X axis remains in the result of 3rd trial, and the robot arm is not moving along the desired trajectory, precisely. Fig.8 shows the results of trajectory tracking at 5th, 10th and 20th trials
X a xis
Y a xis Z a xis
Tria l N u m b er k[tim es]
Fig. 9. Error mean square transition of the trajectory tracking by learning control of equation (1) 3
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Table 1. Learning gains of experiments by equation (2)
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Case Case Case Case D esired
1 2 3 4
X axis Gain 0.5 0.4 0.3 0.25
Y axis Gain 1.0 0.8 0.6 0.5
Z axis Gain 0.25 0.2 0.15 0.0625
4th Tria l Tra cked Resu lt
E rro r M e an Sq u are [m m ]
(a) X axis direction
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4th Tria l Tra cked Resu lt
(b) Y axis direction
X axis Y axis Z axis
Trial N u m b e r k[tim e s] Feed in g D ista n ce [m m ] D esired
(a) Case 1, Learning gain = (0.5, 1.0, 0.25)
4th Tria l Tra cked Resu lt
Erro r M e an Sq u are [m m ]
(c) Z axis direction Fig. 10. Trajectory tracking result of learning control by equation (1) (At 4th trial) using learning control method by equation (1). From these results, we find that the trajectory tracking accuracies in X axis and Y axis become good, but the accuracy in Z axis becomes bad at the 10th trial. And, the trajectory tracking errors in all axes increase at the 20th trial. Fig.9 shows the error mean square transition of the trajectory tracking by learning control of equation (1). From this graph, we can recognize that the result of 4th trial is the best for trajectory tracking, and it becomes bad according to the increase of trial times. Fig.10 shows the results of trajectory tracking at the 4th trial which is the best result using learning control method by equation (1). The error mean square of the trajectory tracking in X axis direction at the 4th trial is 0.24[mm], and the required accuracy is 0.15[mm]. So, we found that we cannot meet the required accuracy under this condition.
X axis Y axis Z axis
Trial N u m b e r k[tim e s]
E rro r M e an Sq u are [m m ]
(b) Case 2, Learning gain = (0.4, 0.8, 0.2)
X axis Y axis Z axis
3.3 Improvement of Learning Control by Gain Adjustment Trial N u m b e r k[tim e s]
From the results shown in the previous section, we confirmed that the trajectory tracking accuracy becomes good using learning control method by equation (1) in the early stage. However, the trajectory tracking error starts increasing after decreasing according to the increase of trial times by this method. This phenomenon seems to occur because the learning gain of all directions is not suitable and too big for the reduction of trajectory tracking errors. So, we used the following learning control method instead of equation (1).
𝑢𝑢 𝑘𝑘+1 𝑡𝑡 = 𝑢𝑢 𝑘𝑘 𝑡𝑡 + 𝛬𝛬𝑒𝑒𝑘𝑘 (𝑡𝑡) Here,
E rro r M e an Sq u are [m m ]
(c) Case 3, Learning gain = (0.3, 0.6, 0.15)
X axis Y axis Z axis
( 2)
𝑘𝑘 ≥ 1 : Trial number, t : Time, Λ : Learning gain 𝑢𝑢 𝑘𝑘 : Desired input vector in the kth trial, 𝑒𝑒𝑘𝑘 = 𝑦𝑦𝑑𝑑 − 𝑦𝑦𝑘𝑘 : Position error vector in the kth trial, 𝑦𝑦𝑑𝑑 : Desired Position vector, 𝑦𝑦𝑘𝑘 : Measured position vector in the kth trial.
Trial N u m b e r k[tim e s]
(d) Case 4, Learning gain = (0.25, 0.5, 0.0625) Fig. 11. Error mean square transition of the trajectory tracking by learning control of equation (2) 4
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To define the suitable learning gain in equation (2), we considered to use the gains in constant ratio of X, Y, Z directions. Its ratio is defined from the increasing ratio of the error mean square of the trajectory tracking experiment shown in Fig. 9, so we set the constant ratio as: X : Y : Z = 1/2 : 1/1 : 1/4
Feed in g D ista n ce [m m ]
D esired
(3)
Feed in g D ista n ce [m m ] D esired
Feed in g D ista n ce [m m ] D esired
Erro r M e an Sq u are [m m ]
X a xis Y a xis Z a xis
Trial N u m b e r k[tim e s]
Fig. 13. Error mean square transition of the trajectory tracking by variable gain learning control
( 4) Le arn in g Gain
Λ𝑘𝑘
30th Tria l Tra cked Resu lt
(c) Z axis direction Fig. 12. Trajectory tracking result of learning control by equation (2) (At 30th trial in Case 4)
In the previous section, we confirmed the effectiveness of the learning control method by equation (2) using the learning gains in constant ratio of X, Y, Z directions shown in Table 1. However, the definition of the learning gains is based on the trial and error, so we have to make much experiments and need much time to define them. To reduce the time and effort to define the learning gains, we considered the method to change the learning gains in every trials based on the change of trajectory tracking error of the robot arm. Then, we propose a variable gain learning control method which calculate learning gains based on the following equation. 𝐸𝐸𝑀𝑀𝑆𝑆1
30th Tria l Tra cked Resu lt
(b) Y axis direction
3.4 The Proposal of Variable Gain Learning Control Method
𝐸𝐸𝑀𝑀𝑆𝑆 𝑘𝑘
30th Tria l Tra cked Resu lt
(a) X axis direction
Then, we made experiments to confirm the effectiveness of the learning control method by equation (2) under the learning gains by the ratio of (3) shown in Table 1. Fig.11 shows the error mean square transition of the trajectory tracking of learning control by equation (2) under the learning gains shown in Table 1. From these results, we recognized that the learning control by equation (2) is effective for reducing the trajectory tracking errors by using the gains in constant ratio of X, Y, Z directions shown in Table 1. We found that the best learning gains for reducing trajectory tracking errors are that of case 4 at the 30th trial. Fig. 12 shows the results of trajectory tracking at this condition. The error mean square of the trajectory tracking in X axis direction of this case is 0.13[mm], then we understood that we could meet the required accuracy (=0.15[mm]) under this condition. But, the gains in case 4 is very small, so we needed much time to realize enough trajectory tracking accuracy.
Λ𝑘𝑘 +1 =
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Here, Λ1 = Λ2 = 1 𝑘𝑘 ≥ 2 : Trial number, 𝐸𝐸𝑀𝑀𝑆𝑆𝑘𝑘 : Error mean square at the kth trial. The learning gains Λ is calculated by the equation (4) from the third trial. This equation calculates the learning gains from the ratio of first and present error mean squares, so the learning gains become small according to the decrease of trajectory tracking errors. By using this method of equations (2) and (4), we can find suitable learning gains automatically based on the trajectory tracking error of the robot arm.
X a xis Y a xis Z a xis
Trial N u m b e r k[tim e s]
Fig. 14. Learning gains transition of the trajectory tracking by variable gain learning control and (4) is effective for reducing the trajectory tracking errors and the suitable learning gains are calculated automatically. The smallest trajectory tracking error is achieved at the 30th trial. Fig. 15 shows the results of trajectory tracking at the 30th trial of the variable gain learning control. The error mean square of the trajectory tracking in X axis direction of this case is 0.15[mm], then we understood that we could meet the required accuracy (=0.15[mm]) and realized enough
We made experiments to confirm the effectiveness of the proposed variable gain learning control method. Fig.13 shows the error mean square transition, and Fig.14 shows the learning gains transition of the trajectory tracking by variable gain learning control. From these results, we can recognize that the variable gain learning control method by equation (2) 5
IFAC SYROCO 2018 6 Budapest, Hungary, August 27-30, 2018
Takashi Yoshimi et al. / IFAC PapersOnLine 51-22 (2018) 1–6
REFERENCES
Feed in g D ista n ce [m m ]
D esired
[1] JUKI Corporation Webpage, “Computer-controlled, High-speed, Lockstitch, Button Sewing System” : http://www.juki.co.jp/industrial_e/products_e/apparel_e/ cat10/lk1903bnseries.html [2] JUKI Corporation Webpage, “Automatic Pocket Setter
30th Tria l Tra cked Resu lt
(a) X axis direction
Feed in g D ista n ce [m m ] D esired
30th Tria l Tra cked Resu lt
(b) Y axis direction
Feed in g D ista n ce [m m ] D esired
30th Tria l Tra cked Resu lt
(c) Z axis direction Fig. 15. Trajectory tracking result of variable gain learning control method (At 30th trial) trajectory tracking accuracy without much time by this method. 4. CONCLUSIONS We have developed an automatic sewing robot system for non-routine three-dimensional products sewing. We evaluated the developed robot system and confirmed that the trajectory tracking accuracy of the curved surface sewing motion of three-dimensional products becomes bad when the feeding speed is high. Then, we applied learning control method to our robot system to improve the trajectory tracking accuracy and confirmed that the accuracy is improved sufficiently by the method even the sewing parts feeding speed is equal to human workers. And, to decrease the time to find suitable learning gains for the good result, we proposed a variable gain learning control method which finds suitable learning gains automatically based on the trajectory tracking error of the robot arm. Finally, we confirmed that the enough trajectory tracking accuracy is achieved by the proposed learning control method without much time and effort through experiments. We will improve the completeness of the proposed method to the practical use level in near future.
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