This paper presents H∞ adaptive tracking control of uncertain robotic manipulator with unknown external disturbances and input time-varying delays. The new adaptive scheme is proposed for trajectory tracking, while H∞ performance is used to attenuate the effect of external disturbances. Firstly, a delay-dependent sufficient condition with input delay and the proposed adaptive controller are developed for the uncertain robotic manipulator, such that the resulting closed-loop system is robustly asymptotically stable. Secondly, a sufficient condition for the H∞ disturbance attenuation performance of the closed-loop system is derived, consequently, the system is robustly asymptotically stable. In the end, two examples are presented to verify the effectiveness of the proposed method.
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L. Jin, S. Li, H. M. La, X. Zhang, and B. Hu, “Dynamic task allocation in multi-robot coordination for moving target tracking: a distributed approach,” Automatica, vol. 100, pp. 75–81, February 2019.
S. Ahmed, H. P. Wang, and Y. Tian, “Robust adaptive fractional-order terminal sliding mode control for lower-limb exoskeleton,” Asian Journal of Control, vol. 21, no. 1, pp. 473–482, January 2019.
S. Ahmed, H. P. Wang, and Y. Tian, “Fault tolerant control using fractional-order terminal sliding mode control for robotic manipulators,” Studies in Informatics and Control, vol. 27, no. 1, pp. 55–64, March 2018.
E. Rouhani and A. Erfanian, “A finite-time adaptive fuzzy terminal sliding mode control for uncertain nonlinear systems,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1938–50, August 2018.
Y. Wang, J. Chen, F. Yan, K. Zhu, and B. Chen, “Adaptive super-twisting fractional-order nonsingular terminal sliding mode control of cable-driven manipulators. ISA Trans., vol. 86, pp. 163–180, March 2019.
V. T. Yen, W. Y. Nan, and C. P Van, “Robust adaptive sliding mode neural networks control for industrial robot manipulators,” International Journal of Control, Automation and Systems, pp. 1–10, March 2019.
Y. Wang, F. Yan, J. Chen, F. Ju, and B. Chen, “A new adaptive time-delay control scheme for cable-driven manipulators,” IEEE Trans. on Industrial Informatics, 2018. DOI: https://doi.org/10.1109/TII.2018.2876605
X. M. Wang, B. Niu, G. Q. Wu, J. Q. Li, P. Y. Duan, and D. Yang, “Adaptive RBF neural network based design strategy for non-Strict feedback nonlinear systems by using integral Lyapunov functions,” IEEE Access, vol. 6, pp.75076–75085, 2018.
Y. Wang, B. Li, F. Yan, and B. Chen, “Practical adaptive fractional-order nonsingular terminal sliding mode control for a cable-driven manipulator,” International Journal of Robust and Nonlinear Control, vol. 29, no. 5, pp. 1396–1417, 2018.
S. Ahmed, H. P. Wang, and Y. Tian, “Adaptive high-order terminal sliding mode control based on time delay estimation for the robotic manipulators with backlash hysteresis,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, 2019. DOI: https://doi.org/10.1109/TSMC.2019.2895588
W. He, H. Huang, and S. S. Ge, “Adaptive neural network control of a robotic manipulator with time-varying output constraints,” IEEE Trans. on Cybernetics, vol. 47, no. 10, pp.3136–3147, October 2017.
W. He and Y. Dong, “Adaptive fuzzy neural network control for a constrained robot using impedance learning,” IEEE Trans. on Neural Networks and Learning Systems, vol. 29, no. 4, pp.1174–1186, April 2018.
V. T. Yen, W. Y. Nan, C. P. Van, N. X. Quynh, and V. H. Thich, “Robust adaptive sliding mode control for industrial robot manipulator using fuzzy wavelet neural networks,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2930–2941, December 2017.
E. Lavretsky and K. Wise, Robust and Adaptive Control: With Aerospace Applcations, Springer-Verlag, London, 2013.
N. T. Binh, N. A. Tung, D. P. Nam, and N. H. Quang, “An adaptive backstepping trajectory tracking control of a tractor trailer wheeled mobile robot,” International Journal of Control, Automation and Systems, vol. 17 pp. 1–9, Feberaury 2019.
Y. H. Joo, L. Q. Tien, and P. X. Duong, “Adaptive neural network second-order sliding mode control of dual arm robots,” International Journal of Control, Automation and Systems, vol. 15, no. 6, pp. 2883–2891, December 2017.
K. Jiang, B. Niu, J. Q. Li, P. Duan, J. Wang, and D. Yang, “Adaptive neural controller design scheme of nonlinear delayed systems with completely unknown nonlinearities and non-strict-feedback structure,” IEEE Access, vol. 6, pp. 66418–66427, 2018.
S. Ahmed, H. P. Wang, and Y. Tian, “Model-free control using time delay estimation and fractional-order nonsingular fast terminal sliding mode for uncertain lower-limb exoskeleton,” Journal of Vibration and Control, vol. 24, no. 22, pp. 5273–5290, November 2018.
S. Ahmed, H. P. Wang, and Y. Tian, “Modification to model reference adaptive control of 5-link exoskeleton with gravity compensation,” Proc. of IEEE Chinese Control Conf., pp. 6115–6120, 2016.
K. Y. Chen, “Robust optimal adaptive sliding mode control with the disturbance observer for a manipulator robot system,” International Journal of Control, Automation and Systems, vol. 16, no. 4, pp. 1701–1715, August 2018.
T. S. Wu, M. Karkoub, H. Wang, H. S. Chen, and T. H. Chen, “Robust tracking control of MIMO underactuated nonlinear systems with dead-zone band and delayed uncertainty using an adaptive fuzzy control,” IEEE Trans. on Fuzzy Systems, vol. 25, no. 4, pp. 1–13, August 2017.
B. Niu, D. Wang, N. D. Alotaibi, and F. E. Alsaadi, “Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: An average dwell-time method,” IEEE Trans. on Neural Networks and Learning Systems, pp. 1–12, August 2018.
B. Niu, H. Li, Z. Zhang, J. Li, T. Hayat, and F. E. Alsaadi, “Adaptive neural-network-based dynamic surface control for stochastic interconnected nonlinear nonstrict-feedback systems with dead zone,” IEEE Trans. on Systems, Man, and Cybernetics: Systems, pp. 1–13, September 2018.
X. Wang, R. S. Niu, C. Chen, and J. Zhao, “H∞ switched adaptive control for a class of robot manipulators,” Trans. of the Institute of Measurement and Control, vol. 36, no. 3, pp. 347–353, May 2014.
I. Ghous and Z. Xiang, “Robust state feedback H∞ control for uncertain 2-D continuous state delayed systems in the Roesser model,” Multidimensional Systems and Signal Processing, vol. 27, no. 2, pp. 297–319, April 2016.
G. Zames, “Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses,” IEEE Trans. on Automatic Control, vol. 26, no. 2, pp. 301–320, April 1981.
Z. Duan, I. Ghous, J. Akhtar, K. Ali, and M. H. Jeffery, “Robust L2 −L∞ filter design for uncertain 2-D continuous nonlinear delayed systems with saturation,” IEEE Access, vol. 6, pp. 73647–73658, 2018.
H. Yazici, R. Guclu, I. B. Kucukdemiral, and M. A. Parlakci, “Robust delay-dependent H∞ control for uncertain structural systems with actuator delay,” Journal of Dynamic Systems, Measurement, and Control, vol. 134, no. 3, pp. 031013, May 2012.
S. Xu and J. Lam, “A survey of linear matrix inequality techniques in stability analysis of delay systems,” International Journal of Systems Science, vol. 3, no. 12, pp. 1095–1113, December 2008.
I. Sharifi, H. A. Talebi, and M. Motaharifar, “Robust output feedback controller design for time-delayed teleoperation: experimental results,” Asian Journal of Control, vol. 19, no. 2, pp. 625–635, March 2017.
A. Shahdi and S. Sirouspour, “Adaptive/robust control for time-delay teleoperation,” IEEE Trans. on Robotics, vol. 25, no. 1, pp. 196–205, February 2009.
I. Buzurovic, D. L. Debeljkovic, V. Misic, and G. Simeunovic, “Stability of the robotic system with time delay in open kinematic chain configuration,” Acta Polytechnica Hungarica, vol. 11, no. 8, pp. 51–74, January 2014.
Y. C. Liu and N. Chopra, “Gravity-compensation-driven position regulation for robotic systems under input/output delays,” IEEE Trans. on Control Systems Technology, vol. 22, no. 3, pp. 995–1005, May 2014.
Y. Kang, Z. Li, X. Cao, and D. Zhai, “Robust control of motion/force for robotic manipulators with random time delays,” IEEE Trans. on Control Systems Technology, vol. 21, no. 5, pp. 1708–1718, September 2013.
S. Bahrami and M. Namvar, “Motion tracking in robotic manipulators in presence of delay in measurements,” Proc. of IEEE International Conf. on Robotics and Automation, pp. 3884–3889, 2010.
G. C. Streuding and G. Chen, “Stability analysis of controlled multiple-link robotic manipulator systems with time delays,” Mathematical and Computer Modelling, vol. 27, no. 1, pp. 53–74, January 1998.
H. Du, F. Naghdy, and D. A. Stirling, “Fuzzy stability control of robotic manipulator with input delays,” Proc. of International Conf. on Robotics and Biomimetics, Tianjin, China, pp. 955–960, 2010.
Recommended by Associate Editor Yingmin Jia under the direction of Editor Fumitoshi Matsuno. This work is partially supported by the National Natural Science Foundation of China (61773212), by International Science & Technology Cooperation Program of China (2015DFA01710), by the Natural Science Foundation of Jiangsu Province (BK20170094), and by the 11th Jiangsu Province Six talent peaks of high level talents (2014_ZBZZ_005).
Saim Ahmed received his M.E degree in Industrial Control and Automation from Hamdard University, Pakistan, in 2013. He is currently pursuing a Ph.D. degree in control science and engineering from Nanjing University of Science and Technology, China in 2019. His research interests include the theory and applications of adaptive control, sliding mode control, time delay control, robotic exoskeleton and manipulators, nonlinearities and its compensation.
Haoping Wang received the Ph.D. degree in Automatic Control from Lille University of Science and Technology (LUST), France, in 2008. He is currently a Professor at Automation School, Deputy Director of Sino French Engineering School, Nanjing University of Science and Technology, China. He was research fellows at MIS Laboratory of Picardie University and at LAGIS of LUST, France. His research interests include the theory and applications of hybrid systems, visual servo control, observation design.
Muhammad Shamrrooz Aslam received the B.Sc. and M.S. degrees in electronics and electrical engineering from COM-SATS University, Abbottabad and Attock campus, Pakistan, in 2009 and 2013, respectively. He is currently pursuing a Ph.D. degree in control science and engineering with the School of Automation, Nanjing University of Science and Technology, China. His research interests include fuzzy systems, time-delay systems and network control systems.
Imran Ghous received his B.Sc. and M.Sc. degrees in Electrical Engineering from University of Engineering and Technology, Taxila, Pakistan, in 2011 and 2013 respectively. He completed his Ph.D. degree in Control Science and Engineering from Nanjing University of Science and Technology, P. R. China in 2016. He is currently serving as an Assistant Professor at the Department of Electrical and Computer Engineering, COMSATS University, Pakistan. His research interests mainly include 2-D systems, switched systems, and positive systems etc.
Irfan Qaisar received the BE (Electronics) degree from Dawood University of Engineering and Technology, Pakistan, in 2013. He is studying for his Master degree from Nanjing University of Science and Technology, P. R. China. His research interests include Multi-agent Systems, and Networked Control systems.
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Ahmed, S., Wang, H., Aslam, M.S. et al. Robust Adaptive Control of Robotic Manipulator with Input Time-varying Delay. Int. J. Control Autom. Syst. 17, 2193–2202 (2019). https://doi.org/10.1007/s12555-018-0767-5
- Adaptive tracking control
- H∞ analysis
- robotic manipulator
- time varying delay