Abstract
This paper proposes an iterative learning controller (ILC) under the alignment condition for trajectory tracking of a parallel Delta robot, that performs various repetitive tasks for palletization. Motivated by the high cadence of our application that leads to significant coupling effects, where the traditional PD/PID fail to satisfy the requirements performances. A PD-type ILC is combined with a PD controller in order to enhance the performance through iterations during the whole operation interval. The traditional resetting condition is replaced by the practical alignment condition, then the convergence of the tracking error is derived based on the Lyapunov’s theory. We definitely point out that the position and velocity errors decrease as the number of iterations increases. Experiments are carried out to demonstrate the effectiveness of the proposed controller.
Zusammenfassung
In diesem Beitrag wird ein iterativ lernender Regler für die Trajektorienverfolgung eines parallelen Delta-Roboters unter Gleichlaufbedingungen vorgeschlagen, der verschiedene wiederkehrende Palettierungsaufgaben ausführt. Durch den schnellen, zu signifikanten Kopplungen führenden, Rhythmus dieser Anwendung erwiesen sich übliche PD/PID-Regelungen als ungeeignet, um die Güteforderungen zu erfüllen. Um die Güte der Regelung über den gesamten Betriebszyklus zu steigern, wird eine iterativ lernende Regelung mit einem PD-Regler kombiniert. Die übliche Rücksetzbedingung wird zunächst durch die praktische Annäherungsbedingung ersetzt, anschließend wird die Konvergenz des Folgefehlers auf Basis der Ljapunow-Theorie gezeigt. Es statt Eindeutig wird gezeigt, dass der Positions- und Geschwindigkeitsfehler mit der Zahl der Iterationen abnimmt. Anhand von Experimenten wird die Tauglichkeit der vorgeschlagenen Regelung demonstriert.
About the authors
Chems Eddine Boudjedir received the engineer degree in Automatic Control from Ecole Nationale Polytechnique of Algeria in 2015. He is pursuing his PhD in the Automatic department of Ecole Nationale Polytechnique (ENP), Algiers, Algeria. His research interests include iterative learning control, time-delay control and robotics.
Mohamed Bouri graduated in Electrical Engineering in 1992 and obtained his PhD degree in 1997 in Industrial Automation at INSA LYON, France. He joined EPFL, Ecole Polytechnique Federal de Lausanne in 1997 and since 2005, he is a group leader of Rehabilitation and Assistive Robotics in the LSRO and lecturer of Robotics and Industrial Robotics. He is mainly active in the field of robot control, automation and robot design for medical and industrial applications. He has strong references with the development of many industrialized robots such as Hita machine (Willemein Macodel), Delta Direct Drive (Bosch Packaging Technology), MotionMaker and WalkTrainer (Swortec), 5 Axis Polishing Delta (Unitechnnologies).
Prof. Djamel Boukhetala was born in Algeria, on September 24, 1964. He received the Magister degree and the PhD degree in Automatic Control from the Ecole Nationale Polytechnique, Algeria in 1993 and 2002 respectively. From 1996 to 1999 he was the head of the Department of Automatic Control. From 2005 to 2013 he was the Director of the Control Process Laboratory and from 2010 to date he is the Director of Postgraduate Studies and Scientific Research at Ecole Nationale Polytechnique of Algeria. His research interests are decentralized control, non linear control, fuzzy control and artificial neural networks control applied to robotics, industrial process and Smart Grids.
References
1. R. Clavel. “Device for movement and displacing of an element in space”. US Patent, no. 4976582, 1990.Search in Google Scholar
2. R. Clavel. “Conception d’un robot parallèle rapide à 4 degré de liberté”. [Doctoral Thesis]. Swiss Federal Institute of Technology Lausanne (EPFL), 1991.Search in Google Scholar
3. M. Bouri, R. Clavel, M. Y. Zerrouki and W. Maeder. “Towards a new Delta robot: an inverted Delta”. Proc of the international symposium on robotics, Paris, 2004.Search in Google Scholar
4. M. Bouri and R. Clavel. “The Linear Delta: Developments and Applications”. International Symposium on Robotics, Munich, June, 2010.Search in Google Scholar
5. J. Brinker and B. Corves. “A Survey on parallel robots with delta-like architecture”. The 14th IFToMM World Congress, Taipei, Taiwan, Oct. 2015.Search in Google Scholar
6. A. Codourey. “Dynamic modelling and mass matrix evaluation of the delta parallel robot for axes decoupling control”. The International Conference on Intelligent Robots and Systems, vol. 3, pp. 1211–1218, 1996.Search in Google Scholar
7. M. A. Laribi, L. Romdhane and S. Zeghloul. “Analysis and dimensional synthesis of the delta robot for a prescribed workspace”. Mech. Mach. Theory vol. 42, no. 7, pp. 859–870, 2007.10.1016/j.mechmachtheory.2006.06.012Search in Google Scholar
8. P. Prempraneerach. “Delta parallel robot workspace and dynamic trajectory tracking of delta parallel robot”. International Computer Science and Engineering Conference (ICSEC), pp. 469–474, 2014.10.1109/ICSEC.2014.6978242Search in Google Scholar
9. M. Bennehar, A. Chemori, M. Bouri, L. F. Jenni and F. Pierrot. “A new RISE-based adaptive control of PKMs: design, stability analysis and experiments”. International Journal of Control pp. 1–15, 2017.10.1080/00207179.2017.1286536Search in Google Scholar
10. M. Rachedi, B. Hemici and M. Bouri. “Design of an
11. L. Xingguo and L. Ming. “A fuzzy logic controller tuned with pso for delta robot trajectory Control”. Industrial Electronics Society, IECON 2015 – 41st Annual Conference of the IEEE, pp. 4345–4351, Nov. 2015.10.1109/IECON.2015.7392776Search in Google Scholar
12. Y. Huang and Z. Huang. “Neural network based dynamic trajectory tracking of delta parallel robot”. IEEE International Conference on Mechatronics and Automation, August 2–5, Beijing, China, 2015.10.1109/ICMA.2015.7237782Search in Google Scholar
13. C. E. Boudjedir, D. Boukhetala and M. Bouri. “Fuzzy logic iterative learning control for trajectory tracking of parallel kinematic manipulators”. 5th International conference on electrical engineering, Algeria, pp. 1–6, doi: 10.1109/ICEE-B.2017.8192041, 2017.Search in Google Scholar
14. Y. Tang, G. Shen, Z. C. Zhu, X. Li and C. F. Yang. “Time waveform replication for electro-hydraulic shaking table incorporating off-line iterative learning control and modified internal model control”. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 228, no. 9, pp.722–733, 2014.10.1177/0959651814536553Search in Google Scholar
15. C. E. Boudjedir, D. Boukhetala and M. Bouri. “Iterative Learning Control of a Parallel Delta Robot”. ICEECA 2017, Lecture Notes in Electrical Engineering, vol. 522. Springer, Cham, doi: 10.1007/978-3-319-97816-1_6, 2017.Search in Google Scholar
16. H. S. Ahn, Y. Chen and K. L. Moore. “Iterative learning control: brief survey and categorization”. IEEE Trans. Syst. Man. Cy. C– Appl. Rev., vol. 37, no. 6, pp. 1099–1121, Nov. 2007.10.1109/TSMCC.2007.905759Search in Google Scholar
17. A. Tayebi. “Adaptive iterative learning control for robot manipulators”. Automatica, vol. 40, no. 7, pp. 1195–1203, 2004.10.1016/j.automatica.2004.01.026Search in Google Scholar
18. Q. X. Yu, Z. S. Hou and R. H. Chi. “Adaptive Iterative Learning Control for Nonlinear Uncertain Systems with Both State and Input Constraints”. Journal of the Franklin Institute, vol. 353, no. 15, pp. 2279–2289, 2016.10.1016/j.jfranklin.2016.07.007Search in Google Scholar
19. P. R. Ouyang, W. J. Zhang and M. Gupta. “An adaptive switching learning control method for trajectory tracking of robot manipulators”. Mechatronics, vol. 16, no. 1, pp. 51–61. 2006.10.1016/j.mechatronics.2005.08.002Search in Google Scholar
20. F. Bouakrif, D. Boukhetala and F. Boudjema. “Velocity observer-based iterative learning control for robot manipulators”. International Journal of Systems Science, vol. 44, no. 2, pp. 214–222, 2013.10.1080/00207721.2011.600467Search in Google Scholar
21. L. Zhang, W. Chen, J. Liu and C. Wen. “A robust adaptive iterative learning control for trajectory tracking of permanent-magnet spherical actuator”. IEEE Transactions on Industrial Electronics, vol. 63, no. 1, pp. 291–301, 2016.10.1109/TIE.2015.2464186Search in Google Scholar
22. M. Zheng, C. Wang, L. Sun and M. Tomizuka. “Design of arbitrary-order robust iterative learning control based on robust control theory”. Mechatronics vol. 47, pp. 67–76, 2017.10.1016/j.mechatronics.2017.08.009Search in Google Scholar
23. X. Jin, D. Huang and J. X. Xu. “Iterative Learning Control for systems with nonparametric uncertainties under alignment condition”. 51st IEEE Conference on Decision and Control, 10–13, USA, pp. 3942–3947, Dec. 2012.10.1109/CDC.2012.6426998Search in Google Scholar
24. Z. Yang and C. W. Chan. “Conditional iterative learning control for non-linear systems with non-parametric uncertainties under alignment condition”. IET Control Theory Appl, vol. 3, no. 11, pp. 1521–1527. 2009.10.1049/iet-cta.2008.0532Search in Google Scholar
25. T.-Y. Kuc, K. Nam and J. S. Lee. “An Iterative Learning Control of Robot Manipulators”. IEEE Trans. on Robot. Autom, vol. 7, no. 6, 1991.10.1109/70.105392Search in Google Scholar
26. G. Ruvinda and G. Fathi. “PD control of closed- chain mechanical systems: An experimental study”. Proc. of the Fifth IFAC Symposium of Robot Control, France, pp. 79–84, 1997.10.1016/S1474-6670(17)44247-9Search in Google Scholar
27. W. W. Shang, S. Cong, Z. X. Li and S. L. Jiang. “Augmented Nonlinear PD Controller for a Redundantly Actuated Parallel Manipulator”. Advanced Robotics, vol. 23, no. 12–13, pp. 1725–1742, 2009.10.1163/016918609X12496340080490Search in Google Scholar
28. J. Moreno-Valenzuela and V. Santibáñez. “Robust and saturated PI joint velocity control for robot manipulators”. Asian Journal of Control, vol. 15, no. 4, pp. 1–16, 2013.10.1002/asjc.586Search in Google Scholar
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