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Tracking Control of Electrically Driven Robots Using a Model-free Observer

Published online by Cambridge University Press:  18 December 2018

Alireza Izadbakhsh Open the ORCID record for Alireza Izadbakhsh [Opens in a new window] ,
Saeed Khorashadizadeh  and
Payam Kheirkhahan Open the ORCID record for Payam Kheirkhahan [Opens in a new window]
Alireza Izadbakhsh*
Affiliation:
Department of Electrical Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran E-mail: kheirkhahan_payam@hotmail.com
Saeed Khorashadizadeh
Affiliation:
Faculty of Electrical and Computer Engineering, University of Birjand, 615/97175 Birjand, Iran E-mail: s.khorashadizadeh@birjand.ac.ir
Payam Kheirkhahan
Affiliation:
Department of Electrical Engineering, Garmsar Branch, Islamic Azad University, Garmsar, Iran E-mail: kheirkhahan_payam@hotmail.com
*
*Corresponding author. E-mail: izadbakhsh_alireza@hotmail.com
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Summary

This paper presents a robust tracking controller for electrically driven robots, without the need for velocity measurements of joint variables. Many observers require the system dynamics or nominal models, while a model-free observer is presented in this paper. The novelty of this paper is presenting a new observer–controller structure based on function approximation techniques and Stone–Weierstrass theorem using differential equations. In fact, it is assumed that the lumped uncertainty can be modeled by linear differential equations. Then, using Stone–Weierstrass theorem, it is verified that these differential equations are universal approximators. The advantage of proposed approach in comparison with previous related works is simplicity and reducing the dimensions of regressor matrices without the need for any information of the systems’ dynamic. Simulation results on a 6-degrees of freedom robot manipulator driven by geared permanent magnet DC motors indicate the satisfactory performance of the proposed method in overcoming uncertainties and reducing the tracking error. To evaluate the performance of proposed controller in practical implementations, experimental results on an SCARA manipulator are presented.

Keywords

Cable driven parallel manipulatorDifferential equationsElectrically driven robotObserver-based controlRedundant robotRobust controlUniversal approximator
Type
Articles
Information
Robotica , Volume 37 , Issue 4 , April 2019 , pp. 729 - 755
Copyright
Copyright © Cambridge University Press 2018 

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References

Van Den Berg, J., Abbeel, P. and Goldberg, K., “LQG-MP: Optimized path planning for robots with motion uncertainty and imperfect state information,” Int. J. Rob. Res. 30, 895–913 (2011).10.1177/0278364911406562CrossRefGoogle Scholar
Berenson, D., Abbeel, P. and Goldberg, K., “A robot path planning framework that learns from experience,” Rob. Autom. IEEE Int. Conf. 3671–3678 (2012).Google Scholar
Schulman, J., Duan, Y., Ho, J., Lee, A., Awwal, I., Bradlow, H., Pan, J., Patil, S., Goldberg, K. and Abbeel, P., “Motion planning with sequential convex optimization and convex collision checking,” Int. J. Rob. Res. 33, 1251–1270 (2014).10.1177/0278364914528132CrossRefGoogle Scholar
Srivastava, S., Fang, E., Riano, L., Chitnis, R., Russell, S. and Abbeel, P., “Combined task and motion planning through an extensible planner-independent interface layer,” IEEE Int. Conf. Rob. Autom. 639–646 (2014).Google Scholar
Abbeel, P., Dolgov, D., Ng, A. Y. and Thrun, S., “Apprenticeship learning formotion planning with application to parking lot navigation,” IEEE/RSJ Int. Conf. Intell. Rob. Syst. 1083–1090 (2008).Google Scholar
Shang, Y., “Resilient multiscale coordination control against adversarial nodes,” Energies 11, 1–17 (2018). doi:10.3390/en11071844CrossRefGoogle Scholar
Schulman, J., Ho, J., Lee, A. X., Awwal, I., Bradlow, H. and Abbeel, P., “Finding locally optimal, collision-free trajectories with sequential convex optimization,” Rob. Sci. Syst. 9, 1–10 (2013).Google Scholar
Ham, W. C., “Adaptive control based on explicit model of robot manipulators,” IEEE Trans. Autom. Control 38, 654–658 (1993).Google Scholar
Izadbakhsh, A. and Kheirkhahan, P., “On the voltage-based control of robot manipulators revisited,” Int. J. Control Autom. Syst. 16(4), 1887–1894 (2018).10.1007/s12555-017-0035-0CrossRefGoogle Scholar
Wang, L. X., A Course in Fuzzy Systems and Control, Englewood Cliffs (Prentice-Hall, NJ, 1996).Google Scholar
Guzmán, S. P., Valenzuela, J. M. and Santibanez, V., “Adaptive neural network motion control of manipulators with experimental evaluations,” Sci. World J. 1–13 (2014). doi:10.1155/2014/694706CrossRefGoogle Scholar
Wang, L., Chai, T. and Zhai, L., “Neural network based terminal sliding-mode control of robotic manipulators including actuator dynamics,” IEEE Trans. Ind. Electron. 56, 3296–3304 (2009).10.1109/TIE.2008.2011350CrossRefGoogle Scholar
Peng, J., Wang, J. and Wang, Y., “Neural network based robust hybrid control for robotic system: An H 8 approach,” Nonlinear Dyn. 65, 421–431 (2011).10.1007/s11071-010-9902-4CrossRefGoogle Scholar
Fallah Ghavidel, H. and Akbarzadeh Kalat, A., “Observer-based hybrid adaptive fuzzy control for affine and nonaffine uncertain nonlinear systems,” Neural Comput. Appl. 30, 1187–1202 (2018).10.1007/s00521-016-2732-7CrossRefGoogle Scholar
Wai, R. J. and Muthusamy, R., “Fuzzy-neural-network inherited sliding-mode control for robot manipulator including actuator dynamics,” IEEE Trans. Neural Networks Learn. Syst. 24, 274–287 (2013).Google ScholarPubMed
Izadbakhsh, A. and Kheirkhahan, P., “An alternative stability proof for “Adaptive Type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots”,” J. Vibr. Control. doi:10.1177/1077546318802694Google Scholar
Pan, Y. and Er, M. J., “Enhanced adaptive fuzzy control with optimal approximation error convergence,” IEEE Trans. Fuzzy Syst. 21, 1123–1132 (2013).10.1109/TFUZZ.2013.2244899CrossRefGoogle Scholar
Khorashadizadeh, S. and Fateh, M. M., “Robust task-space control of robot manipulators using Legendre polynomials for uncertainty estimation,” Nonlinear Dyn. 79, 1151–1161 (2015).10.1007/s11071-014-1730-5CrossRefGoogle Scholar
Izadbakhsh, A., “Robust control design for rigid-link flexible-joint electrically driven robot subjected to constraint: theory and experimental verification,” Nonlinear Dyn. 85, 751–765 (2016).10.1007/s11071-016-2720-6CrossRefGoogle Scholar
Izadbakhsh, A., “FAT-based robust adaptive control of electrically driven robots without velocity measurements,” Nonlinear Dyn. 89, 289–304 (2017).10.1007/s11071-017-3454-9CrossRefGoogle Scholar
Gole, N., Gole, A., Barra, K. and Bouktir, T., “Observer-based adaptive control of robot manipulators: Fuzzy systems approach,” Appl. Soft Comput. 8, 778–787 (2008).10.1016/j.asoc.2007.05.011CrossRefGoogle Scholar
Talole, S. E., Kolhe, J. P. and Phadke, S. B., “Extended-state-observer-based control of flexible-joint system with experimental validation,” IEEE Trans. Ind. Electron. 57, 1411–1419 (2010).10.1109/TIE.2009.2029528CrossRefGoogle Scholar
Wei, X. and Guo, L., “Composite disturbance-observer-based control and terminal sliding mode control for non-linear systems with disturbances,” Int. J. Control 82, 1082–1098 (2009).10.1080/00207170802455339CrossRefGoogle Scholar
Alvarez, J., Rosas, D. and Pena, J., “Analog implementation of a robust control strategy for mechanical systems,” IEEE Trans. Ind. Electron. 56, 3377–3385 (2009).10.1109/TIE.2009.2020706CrossRefGoogle Scholar
Sira-Ramírez, H., López-Uribe, C. andVelasco-Villa, M., “Linear observer-based active disturbance rejection control of the omnidirectional mobile robot,” Asian J. Control 15, 51–63 (2013).10.1002/asjc.523CrossRefGoogle Scholar
Cui, R., Chen, L., Yang, C. and Chen, M., “Extended state observer-based integral sliding mode control for an underwater robot with unknown disturbances and uncertain nonlinearities,” IEEE Trans. Ind. Electron. 64(8), 6785–6795 (2017).10.1109/TIE.2017.2694410CrossRefGoogle Scholar
Peng, Z. and Wang, J., “Output-feedback path-following control of autonomous underwater vehicles based on an extended state observer and projection neural networks,” IEEE Trans. Syst. Man Cybern. Syst. 48(4), 535–544 (2018).10.1109/TSMC.2017.2697447CrossRefGoogle Scholar
Zhao, L., Li, Q., Liu, B. and Cheng, H., “Trajectory tracking control of a one degree of freedom manipulator based on a switched sliding mode controller with a novel extended state observer framework,” IEEE Trans. Syst. Man Cybern. Syst. 1–9 (2018).Google Scholar
Wang, H., Li, S., Lan, Q., Zhao, Z. and Zhou, X., “Continuous terminal sliding mode control with extended state observer for PMSM speed regulation system,” Trans. Inst. Meas. Control 39(8), 1195–1204 (2017).10.1177/0142331216630361CrossRefGoogle Scholar
Wang, S., Ren, X., Na, J. and Zeng, T., “Extended-state-observer-based funnel control for nonlinear servomechanisms with prescribed tracking performance,” IEEE Trans. Autom. Sci. Eng. 14(1), 98–108 (2017).10.1109/TASE.2016.2618010CrossRefGoogle Scholar
Peng, Z. and Wang, J., “Output-feedback path-following control of autonomous underwater vehicles based on an extended state observer and projection neural networks,” IEEE Trans. Syst. Man Cybern. Syst. 48(4), 535–544 (2018).10.1109/TSMC.2017.2697447CrossRefGoogle Scholar
Muller, P. C. and Ackermann, J., “Nichtlineare regelung von elastischen robotern,” In: VDI-Berichte 598, Steuerung und Regelung von Roboter (Springer-Verlag, Berlin, Germany, 1986) pp. 321–333.Google Scholar
Nakao, M., Ohnishi, K. and Miyachi, K., “Robust decentralized joint control based on interference estimation,” IEEE Int. Conf. Rob. Autom. 4, 326–333 (1987).Google Scholar
Kemf, C. J. and Kobayashi, S., “Disturbance observer and feedforward design for a high-speed direct-drive positioning table,” IEEE Trans. Contr. Syst. Technol. 7, 513–526 (1999).10.1109/87.784416CrossRefGoogle Scholar
Huang, Y. H. and Messner, W., “A novel disturbance observer design for magnetic hard drive servo system with rotary actuator,” IEEE Trans. Magn. 4, 1892–1894 (1998).10.1109/20.706734CrossRefGoogle Scholar
Ishikawa, J. and Tomizuka, M., “Pivot friction compensation using an accelerometer and a disturbance observer for hard disk,” IEEE/ASME Trans. Mechatron. 3, 194–201 (1998).10.1109/3516.712115CrossRefGoogle Scholar
Mohammadi, A., Tavakoli, M., Marquez, H. J. and Hashemzadeh, F., “Nonlinear disturbance observer design for robotic manipulators,” Control Eng. Pract. 21, 253–267 (2013).10.1016/j.conengprac.2012.10.008CrossRefGoogle Scholar
Li, Z., Su, C. Y., Wang, L., Chen, Z. and Chai, T., “Nonlinear disturbance observer-based control design for a robotic exoskeleton incorporating fuzzy approximation,” IEEE Trans. Ind. Electron. 62(9), 5763–5775 (2015).10.1109/TIE.2015.2447498CrossRefGoogle Scholar
Chu, Z., Cui, J. and Sun, F., “Fuzzy adaptive disturbance-observer-based robust tracking control of electrically driven free-floating space manipulator,” IEEE Syst. J. 8, 343–352 (2014).10.1109/JSYST.2012.2220171CrossRefGoogle Scholar
Chen, W. H., Yang, J., Guo, L. and Li, S., “Disturbance-observer-based control and related methods—An overview,” IEEE Trans. Ind. Electron. 63, 1083–1095 (2016).10.1109/TIE.2015.2478397CrossRefGoogle Scholar
Tong, S. and Li, Y., “Observer-based fuzzy adaptive control for strict-feedback nonlinear systems,” Fuzzy Sets Syst. 160, 1749–1764 (2009).10.1016/j.fss.2008.09.004CrossRefGoogle Scholar
Cheah, C. C., Liu, C. and Slotine, J. J. E., “Adaptive Jacobian tracking control of robots with uncertainties in kinematic, dynamic and actuator models,” IEEE Trans. Autom. Control 51, 1024–1029 (2006).10.1109/TAC.2006.876943CrossRefGoogle Scholar
Izadbakhsh, A., “A note on the “nonlinear control of electrical flexible-joint robots”,” Nonlinear Dyn. 89, 2753–2767 (2017).10.1007/s11071-017-3623-xCrossRefGoogle Scholar
Izadbakhsh, A., “Robust adaptive control of voltage saturated flexible joint robots with experimental evaluations,” AUT J. Model. Simul. 50(1), 31–38 (2018).Google Scholar
Chen, W. H., “Disturbance observer based control for nonlinear systems,” IEEE/ASME Trans. Mechatron. 9, 706–710 (2004).10.1109/TMECH.2004.839034CrossRefGoogle Scholar
Spong, M. W., Hutchinson, S. and Vidyasagar, M., Robot Modelling and Control (Wiley, Hoboken, 2006).Google Scholar
Izadbakhsh, A. and Fateh, M. M., “Real-time robust adaptive control of robots subjected to actuator voltage constraint,” Nonlinear Dyn. 78, 1999–2014 (2014).10.1007/s11071-014-1574-zCrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Robust task-space control of robot manipulators using differential equations for uncertainty estimation,” Robotica 35(9), 1923–1938 (2017).10.1017/S0263574716000588CrossRefGoogle Scholar
Qu, Z. and Dawson, D. M., Robust Tracking Control of Robot Manipulators (IEEE Press, Inc., New York, 1996).Google Scholar
Izadbakhsh, A. and Rafiei, S. M. R., “Endpoint perfect tracking control of robots - A robust non inversionbased approach,” Int. J. Control Autom. Syst. 7, 888–898 (2009).10.1007/s12555-009-0603-zCrossRefGoogle Scholar
Izadbakhsh, A., Akbarzadeh Kalat, A., Fateh, M. M. and Rafiei, S. M. R., “A robust anti-windup control design for electrically driven robots–Theory and experiment,” Int. J. Control Autom. Syst. 9, 1005–1012 (2011).10.1007/s12555-011-0524-5CrossRefGoogle Scholar
Izadbakhsh, A. and Khorashadizadeh, S., “Robust impedance control of robot manipulators using differential equations as universal approximator,” Int. J. Control. 91(10), 2170–2186 (2018).10.1080/00207179.2017.1336669CrossRefGoogle Scholar
Izadbakhsh, A., “Closed-Form Dynamic Model of PUMA560 Robot Arm,” Proceedings of the 4th International Conference on Autonomous Robots and Agents (2009) pp. 675–680.Google Scholar
Corke, P., “The unimation puma servo system,” CSIRO Div. Manuf. Technol. MTM-226, 1–54 (1994).Google Scholar
Corke, P. and Armstrong-Helouvry, B., “A search for consensus among model parameters reported for the PUMA560 robot,” IEEE Int. Conf. Rob. Autom. 2, 1608–1613 (1994).Google Scholar
Pratap, B. and Purwar, S., “Real-time implementation of neuro adaptive observer-based robust backstepping controller for twin rotor control system,” J. Control Autom. Electr. Syst. 25, 137–150 (2014).10.1007/s40313-013-0098-yCrossRefGoogle Scholar
Purwar, S., Kar, I. N. and Jha, A. N., “Adaptive output feedback tracking control of robot manipulators using position measurements only,” Expert Syst. Appl. 34, 2789–2798 (2008).10.1016/j.eswa.2007.05.030CrossRefGoogle Scholar
Patra, J. C. and Kot, A. C., “Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks,” IEEE Trans. Syst. Man Cybern. Part B 32, 505–511 (2002).10.1109/TSMCB.2002.1018769CrossRefGoogle ScholarPubMed
Jabbari Asl, H. and Janabi-sharifi, F., “Adaptive neural network control of cable-driven parallel robots with input saturation,” Eng. Appl. Artif. Intell. 65, 252–260 (2017).10.1016/j.engappai.2017.05.011CrossRefGoogle Scholar
Jabbari Asl, H. and Yoon, J., “Robust trajectory tracking control of cable-driven parallel robots,” Nonlinear Dyn. 89(4), 2769–2784 (2017).10.1007/s11071-017-3624-9CrossRefGoogle Scholar
Shang, Y., “On the delayed scaled consensus problems,” Appl. Sci. 7(7), 713 (2017).10.3390/app7070713CrossRefGoogle Scholar