0
Research Papers

A New Finite Time Control Solution for Robotic Manipulators Based on Nonsingular Fast Terminal Sliding Variables and the Adaptive Super-Twisting Scheme

[+] Author and Article Information
Vo Anh Tuan

School of Electrical Engineering,
University of Ulsan,
93 Daehak-ro, Nam-gu,
Ulsan 680-749, South Korea
e-mail: voanhtuan2204@gmail.com

Hee-Jun Kang

School of Electrical Engineering,
University of Ulsan,
93 Daehak-ro, Nam-gu,
Ulsan 680-749, South Korea
e-mail: hjkang@ulsan.ac.kr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 14, 2018; final manuscript received December 6, 2018; published online January 11, 2019. Assoc. Editor: Tsuyoshi Inoue.

J. Comput. Nonlinear Dynam 14(3), 031002 (Jan 11, 2019) (10 pages) Paper No: CND-18-1101; doi: 10.1115/1.4042293 History: Received September 14, 2018; Revised December 06, 2018

In this study, a new finite time control method is suggested for robotic manipulators based on nonsingular fast terminal sliding variables and the adaptive super-twisting method. First, to avoid the singularity drawback and achieve the finite time convergence of positional errors with a fast transient response rate, nonsingular fast terminal sliding variables are constructed in the position errors' state space. Next, adaptive tuning laws based on the super-twisting scheme are presented for the switching control law of terminal sliding mode control (TSMC) so that a continuous control law is extended to reject the effects of chattering behavior. Finally, a new finite time control method ensures that sliding motion will take place, regardless of the effects of the perturbations and uncertainties on the robot system. Accordingly, the stabilization and robustness of the suggested control system can be guaranteed with high-precision performance. The robustness issue and the finite time convergence of the suggested system are totally confirmed by the Lyapunov stability principle. In simulation studies, the experimental results exhibit the effectiveness and viability of our proposed scheme for joint position tracking control of a 3DOF PUMA560 robot.

FIGURES IN THIS ARTICLE
<>
Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.

References

Yang, C. , Huang, Q. , Jiang, H. , Peter, O. O. , and Han, J. , 2010, “ PD Control With Gravity Compensation for Hydraulic 6-DOF Parallel Manipulator,” Mech. Mach. Theory, 45(4), pp. 666–677. [CrossRef]
Ouyang, P. R. , Zhang, W. J. , and Wu, F. X. , 2002, “ Nonlinear PD Control for Trajectory Tracking With Consideration of the Design for Control Methodology,” IEEE International Conference on Robotics and Automation (ICRA'02), Washington, DC, May 11–15, pp. 4126–4131.
Ouyang, P. R. , Zhang, W. J. , and Gupta, M. M. , 2006, “ An Adaptive Switching Learning Control Method for Trajectory Tracking of Robot Manipulators,” Mechatronics, 16(1), pp. 51–61. [CrossRef]
Yu, W. , and Rosen, J. , 2013, “ Neural PID Control of Robot Manipulators With Application to an Upper Limb Exoskeleton,” IEEE Trans. Cybern., 43(2), pp. 673–684. [CrossRef] [PubMed]
Su, Y. , Muller, P. C. , and Zheng, C. , 2010, “ Global Asymptotic Saturated PID Control for Robot Manipulators,” IEEE Trans. Control Syst. Technol., 18(6), pp. 1280–1288.
Guo, Y. , and Woo, P. Y. , 2003, “ An Adaptive Fuzzy Sliding Mode Controller for Robotic Manipulators,” IEEE Trans. Syst., Man, Cybern.-Part A, 33(2), pp. 149–159. [CrossRef]
Vo, A. T. , Kang, H. J. , and Le, T. D. , 2018, “ An Adaptive Fuzzy Terminal Sliding Mode Control Methodology for Uncertain Nonlinear Second-Order Systems,” International Conference on Intelligent Computing, Wuhan, China, Aug. 15–18, pp. 123–135.
Lewis, F. L. , 1996, “ Neural Network Control of Robot Manipulators,” IEEE Expert, 11(3), pp. 64–75. [CrossRef]
Kim, Y. H. , and Lewis, F. L. , 1999, “ Neural Network Output Feedback Control of Robot Manipulators,” IEEE Trans. Rob. Autom., 15(2), pp. 301–309. [CrossRef]
Vo, A. T. , Kang, H. J. , and Nguyen, V. C. , 2017, “ An Output Feedback Tracking Control Based on Neural Sliding Mode and High Order Sliding Mode Observer,” Tenth International Conference on Human System Interactions (HSI), Ulsan, South Korea, July 17–19, pp. 161–165.
Shang, W. , and Cong, S. , 2009, “ Nonlinear Computed Torque Control for a High-Speed Planar Parallel Manipulator,” Mechatronics, 19(6), pp. 987–992. [CrossRef]
Van, M. , Kang, H. J. , Suh, Y. S. , and Shin, K. S. , 2013, “ A Robust Fault Diagnosis and Accommodation Scheme for Robot Manipulators,” Int. J. Control, Autom. Syst., 11(2), pp. 377–388. [CrossRef]
Le, T. D. , Kang, H. J. , Suh, Y. S. , and Ro, Y. S. , 2013, “ An Online Self-Gain Tuning Method Using Neural Networks for Nonlinear PD Computed Torque Controller of a 2-dof Parallel Manipulator,” Neurocomputing, 116, pp. 53–61. [CrossRef]
Lin, F. , and Brandt, R. D. , 1998, “ An Optimal Control Approach to Robust Control of Robot Manipulators,” IEEE Trans. Rob. Autom., 14(1), pp. 69–77. [CrossRef]
Fujimoto, K. , and Sugie, T. , 2003, “ Iterative Learning Control of Hamiltonian Systems: I/O Based Optimal Control Approach,” IEEE Trans. Autom. Control, 48(10), pp. 1756–1761. [CrossRef]
Slotine, J. J. E. , and Li, W. , 1987, “ On the Adaptive Control of Robot Manipulators,” Int. J. Rob. Res., 6(3), pp. 49–59. [CrossRef]
Jin, M. , Kang, S. H. , Chang, P. H. , and Lee, J. , 2017, “ Robust Control of Robot Manipulators Using Inclusive and Enhanced Time Delay Control,” IEEE/ASME Trans. Mechatronics, 22(5), pp. 2141–2152. [CrossRef]
Utkin, V. I. , 2013, Sliding Modes in Control and Optimization, Springer Science & Business Media, Moscow, Russia.
Slotine, J. J. E. , and Li, W. , 1991, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, NJ.
Young, K. D. , Utkin, V. I. , and Ozguner, U. , 1996, “ A Control Engineer's Guide to Sliding Mode Control,” IEEE International Workshop on Variable Structure Systems (VSS'96), Tokyo, Japan, Dec. 5–6, p. 1.
Shang, W. W. , Cong, S. , and Jiang, S. L. , 2010, “ Dynamic Model Based Nonlinear Tracking Control of a Planar Parallel Manipulator,” Nonlinear Dyn., 60(4), pp. 597–606. [CrossRef]
Yang, Z. Y. , Huang, T. , Xu, X. , and Cooper, J. E. , 2007, “ Variable Structure Control of High-Speed Parallel Manipulator Considering the Mechatronics Coupling Model,” Int. J. Adv. Manuf. Technol., 34(9–10), pp. 1037–1051. [CrossRef]
Qi, Z. , McInroy, J. E. , and Jafari, F. , 2007, “ Trajectory Tracking With Parallel Robots Using Low Chattering, Fuzzy Sliding Mode Controller,” J. Intell. Rob. Syst., 48(3), pp. 333–356. [CrossRef]
Zeinali, M. , and Notash, L. , 2010, “ Adaptive Sliding Mode Control With Uncertainty Estimator for Robot Manipulators,” Mech. Mach. Theory, 45(1), pp. 80–90. [CrossRef]
Xu, Q. , 2015, “ Piezoelectric Nanopositioning Control Using Second-Order Discrete-Time Terminal Sliding-Mode Strategy,” IEEE Trans. Ind. Electron., 62(12), pp. 7738–7748. [CrossRef]
Wang, H. , Man, Z. , Kong, H. , Zhao, Y. , Yu, M. , Cao, Z. , Zheng, J. , and Do, M. T. , 2016, “ Design and Implementation of Adaptive Terminal Sliding-Mode Control on a Steer-by-Wire Equipped Road Vehicle,” IEEE Trans. Ind. Electron., 63(9), pp. 5774–5785. [CrossRef]
Chen, G. , Song, Y. , and Guan, Y. , 2016, “ Terminal Sliding Mode-Based Consensus Tracking Control for Networked Uncertain Mechanical Systems on Digraphs,” IEEE Trans. Neural Networks Learn. Syst., 29(3), pp. 749–756.
Solis, C. U. , Clempner, J. B. , and Poznyak, A. S. , 2017, “ Fast Terminal Sliding-Mode Control With an Integral Filter Applied to a Van Der Pol Oscillator,” IEEE Trans. Ind. Electron., 64(7), pp. 5622–5628. [CrossRef]
Madani, T. , Daachi, B. , and Djouani, K. , 2017, “ Modular-Controller-Design-Based Fast Terminal Sliding Mode for Articulated Exoskeleton Systems,” IEEE Trans. Control Syst. Technol., 25(3), pp. 1133–1140. [CrossRef]
Wang, Y. , Gu, L. , Xu, Y. , and Cao, X. , 2016, “ Practical Tracking Control of Robot Manipulators With Continuous Fractional-Order Nonsingular Terminal Sliding Mode,” IEEE Trans. Ind. Electron., 63(10), pp. 6194–6204. [CrossRef]
Lin, C. K. , 2006, “ Nonsingular Terminal Sliding Mode Control of Robot Manipulators Using Fuzzy Wavelet Networks,” IEEE Trans. Fuzzy Syst., 14(6), pp. 849–859. [CrossRef]
Chen, S. Y. , and Lin, F. J. , 2011, “ Robust Nonsingular Terminal Sliding-Mode Control for Nonlinear Magnetic Bearing System,” IEEE Trans. Control Syst. Technol., 19(3), pp. 636–643. [CrossRef]
Xu, S. S. D. , Chen, C. C. , and Wu, Z. L. , 2015, “ Study of Nonsingular Fast Terminal Sliding-Mode Fault-Tolerant Control,” IEEE Trans. Ind. Electron., 62(6), pp. 3906–3913.
Zheng, J. , Wang, H. , Man, Z. , Jin, J. , and Fu, M. , 2015, “ Robust Motion Control of a Linear Motor Positioner Using Fast Nonsingular Terminal Sliding Mode,” IEEE/ASME Trans. Mechatronics, 20(4), pp. 1743–1752. [CrossRef]
Van, M. , Ge, S. S. , and Ren, H. , 2017, “ Finite Time Fault Tolerant Control for Robot Manipulators Using Time Delay Estimation and Continuous Nonsingular Fast Terminal Sliding Mode Control,” IEEE Tran. Cybern., 47(7), pp. 1681–1693. [CrossRef]
Cui, R. , Chen, L. , Yang, C. , and Chen, M. , 2017, “ Extended State Observer-Based Integral Sliding Mode Control for an Underwater Robot With Unknown Disturbances and Uncertain Nonlinearities,” IEEE Trans. Ind. Electron., 64(8), pp. 6785–6795. [CrossRef]
Lee, J. , Chang, P. H. , and Jin, M. , 2017, “ Adaptive Integral Sliding Mode Control With Time-Delay Estimation for Robot Manipulators,” IEEE Trans. Ind. Electron., 64(8), pp. 6796–6804. [CrossRef]
Xu, Q. , 2017, “ Continuous Integral Terminal Third-Order Sliding Mode Motion Control for Piezoelectric Nanopositioning System,” IEEE/ASME Trans. Mechatronics, 22(4), pp. 1828–1838. [CrossRef]
Xu, Q. , 2016, “ Digital Integral Terminal Sliding Mode Predictive Control of Piezoelectric-Driven Motion System,” IEEE Trans. Ind. Electron., 63(6), pp. 3976–3984. [CrossRef]
Feng, Y. , Yu, X. , and Man, Z. , 2002, “ Non-Singular Terminal Sliding Mode Control of Rigid Manipulators,” Automatica, 38(12), pp. 2159–2167. [CrossRef]
Yu, S. , Yu, X. , Shirinzadeh, B. , and Man, Z. , 2005, “ Continuous Finite-Time Control for Robotic Manipulators With Terminal Sliding Mode,” Automatica, 41(11), pp. 1957–1964. [CrossRef]
Feng, Y. , Han, F. , and Yu, X. , 2014, “ Chattering Free Full-Order Sliding-Mode Control,” Automatica, 50(4), pp. 1310–1314. [CrossRef]
Van, M. , Mavrovouniotis, M. , and Ge, S. S. , 2018, “ An Adaptive Backstepping Nonsingular Fast Terminal Sliding Mode Control for Robust Fault Tolerant Control of Robot Manipulators,” IEEE Trans. Syst., Man, Cybern. Syst., (epub).
Moreno, J. A. , and Osorio, M. , 2012, “ Strict Lyapunov Functions for the Super-Twisting Algorithm,” IEEE Trans. Autom. Control, 57(4), pp. 1035–1040. [CrossRef]
Hung, J. Y. , Gao, W. , and Hung, J. C. , 1993, “ Variable Structure Control: A Survey,” IEEE Trans. Ind. Electron., 40(1), pp. 2–22. [CrossRef]
Laghrouche, S. , Liu, J. , Ahmed, F. S. , Harmouche, M. , and Wack, M. , 2015, “ Adaptive Second-Order Sliding Mode Observer-Based Fault Reconstruction for PEM Fuel Cell Air-Feed System,” IEEE Trans. Control Syst. Technol., 23(3), pp. 1098–1109. [CrossRef]
Armstrong, B. , Khatib, O. , and Burdick, J. , 1986, “ The Explicit Dynamic Model and Inertial Parameters of the PUMA 560 Arm,” IEEE International Conference on Robotics and Automation (ICRA '86), San Francisco, CA, Apr. 7–10, pp. 510–518.
Polyakov, A. , and Fridman, L. , 2014, “ Stability Notions and Lyapunov Functions for Sliding Mode Control Systems,” J. Franklin Inst., 351(4), pp. 1831–1865. [CrossRef]

Figures

Grahic Jump Location
Fig. 4

Control input signals: (a) at joint 1, (b) at joint 2, and (c) at joint 3

Grahic Jump Location
Fig. 3

Tracking errors: (a) at joint 1, (b) at joint 2, and (c) at joint 3

Grahic Jump Location
Fig. 2

Tracking positions: (a) at joint 1, (b) at joint 2, and (c) at joint 3

Grahic Jump Location
Fig. 1

Three degrees-of-freedom PUMA560 robot manipulator

Grahic Jump Location
Fig. 5

Sliding variables: (a) at joint 1, (b) at joint 2, and (c) at joint 3

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In