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.

References

References
1.
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
.
2.
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
.
3.
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
.
4.
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
.
5.
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
.
6.
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
.
7.
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
.
8.
Lewis
,
F. L.
,
1996
, “
Neural Network Control of Robot Manipulators
,”
IEEE Expert
,
11
(
3
), pp.
64
75
.
9.
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
.
10.
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
.
11.
Shang
,
W.
, and
Cong
,
S.
,
2009
, “
Nonlinear Computed Torque Control for a High-Speed Planar Parallel Manipulator
,”
Mechatronics
,
19
(
6
), pp.
987
992
.
12.
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
.
13.
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
.
14.
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
.
15.
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
.
16.
Slotine
,
J. J. E.
, and
Li
,
W.
,
1987
, “
On the Adaptive Control of Robot Manipulators
,”
Int. J. Rob. Res.
,
6
(
3
), pp.
49
59
.
17.
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
.
18.
Utkin
,
V. I.
,
2013
,
Sliding Modes in Control and Optimization
,
Springer Science & Business Media
, Moscow, Russia.
19.
Slotine
,
J. J. E.
, and
Li
,
W.
,
1991
,
Applied Nonlinear Control
,
Prentice Hall
,
Englewood Cliffs, NJ
.
20.
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
.
21.
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
.
22.
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
.
23.
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
.
24.
Zeinali
,
M.
, and
Notash
,
L.
,
2010
, “
Adaptive Sliding Mode Control With Uncertainty Estimator for Robot Manipulators
,”
Mech. Mach. Theory
,
45
(
1
), pp.
80
90
.
25.
Xu
,
Q.
,
2015
, “
Piezoelectric Nanopositioning Control Using Second-Order Discrete-Time Terminal Sliding-Mode Strategy
,”
IEEE Trans. Ind. Electron.
,
62
(
12
), pp.
7738
7748
.
26.
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
.
27.
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.
28.
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
.
29.
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
.
30.
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
.
31.
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
.
32.
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
.
33.
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
.
34.
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
.
35.
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
.
36.
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
.
37.
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
.
38.
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
.
39.
Xu
,
Q.
,
2016
, “
Digital Integral Terminal Sliding Mode Predictive Control of Piezoelectric-Driven Motion System
,”
IEEE Trans. Ind. Electron.
,
63
(
6
), pp.
3976
3984
.
40.
Feng
,
Y.
,
Yu
,
X.
, and
Man
,
Z.
,
2002
, “
Non-Singular Terminal Sliding Mode Control of Rigid Manipulators
,”
Automatica
,
38
(
12
), pp.
2159
2167
.
41.
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
.
42.
Feng
,
Y.
,
Han
,
F.
, and
Yu
,
X.
,
2014
, “
Chattering Free Full-Order Sliding-Mode Control
,”
Automatica
,
50
(
4
), pp.
1310
1314
.
43.
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).
44.
Moreno
,
J. A.
, and
Osorio
,
M.
,
2012
, “
Strict Lyapunov Functions for the Super-Twisting Algorithm
,”
IEEE Trans. Autom. Control
,
57
(
4
), pp.
1035
1040
.
45.
Hung
,
J. Y.
,
Gao
,
W.
, and
Hung
,
J. C.
,
1993
, “
Variable Structure Control: A Survey
,”
IEEE Trans. Ind. Electron.
,
40
(
1
), pp.
2
22
.
46.
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
.
47.
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
.
48.
Polyakov
,
A.
, and
Fridman
,
L.
,
2014
, “
Stability Notions and Lyapunov Functions for Sliding Mode Control Systems
,”
J. Franklin Inst.
,
351
(
4
), pp.
1831
1865
.
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