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IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS 1
Adaptive Fuzzy Tracking Control of Flexible-Joint
Robots With Full-State Constraints
Wei Sun, Shun-Feng Su , Fellow, IEEE,JianweiXia , and Van-Truong Nguyen , Student Member, IEEE
Abstract—This paper reports our study on adaptive fuzzy
tracking control for flexible-joint robots with full state con-
straints. In the control design, fuzzy systems are adopted
to identify the totally unknown nonlinear functions and can
properly avoid burdensome computations. The tan-type barrier
Lyapunov functions are used to deal with state constraints so that
even without state constraints, the controller is still valid. By com-
bining the method of backstepping design with adaptive fuzzy
control approaches, a novel simpler controller is successfully con-
structed to ensure that the output tracking errors converge to
a sufficiently small neighborhood of the origin, while the con-
straints on the system states will not be violated during operation.
Finally, comparison simulations are presented to demonstrate the
effectiveness of the proposed control schemes.
Index Terms—Adaptive fuzzy tracking control, barrier
Lyapunov functions (BLFs), flexible-joint (FJ) robots, full state
constraints.
I. INTRODUCTION
I
N THE past decades, tracking control of the flexible-joint
(FJ) robots have attracted much attention on the field of
control theory and engineering [1]–[3]. The joint flexibility is
usually caused by harmonic drives, shaft windup, and bearing
deformation. Neglecting this property in control design may
lead to oscillation and the whole system crash. Therefore, con-
siderable efforts have been made to guarantee stability and
robustness for FJ robots. For example, adaptive fuzzy con-
trol approaches are proposed in [4] and [5]. By employing
the Lyapunov–Krasovskii functional and backstepping design
technique, robust control schemes are developed in [6] and [7].
Manuscript received May 1, 2018; revised July 4, 2018; accepted September
11, 2018. This work was supported in part by the National Natural Science
Foundation of China under Grant 61603170 and Grant 61573177, in part by
the National Science Council, Taiwan, under Grant NSC 101-2221-E-011-
077-MY3, and in part by the Center for Cyber-Physical System Innovation
from the Featured Areas Research Center Program within the Framework of
the Higher Education Sprout Project by the Ministry of Education in Taiwan.
This paper was recommended by Associate Editor Q. Ge. (Corresponding
author: Shun-Feng Su.)
W. Sun and J. Xia are with the School of Mathematics Science, Liaocheng
University, Liaocheng 252000, China (e-mail: sunw8617@163.com;
njustxjw@126.com).
S.-F. Su is with the Department of Electrical Engineering, National
Taiwan University of Science and Technology, Taipei 106, Taiwan (e-mail:
sfsu@mail.ntust.edu.tw).
V.-T. Nguyen is with the Department of Mechanical Engineering, National
Taiwan University of Science and Technology, Taipei 106, Taiwan, and also
with the Department of Mechanical Engineering, Hanoi University of Industry,
Hanoi 159999, Vietnam (e-mail: nguyenvantruong@haui.edu.vn).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TSMC.2018.2870642
Based on online gravity compensation, [8] presents a posi-
tion control scheme. Liu and Wu [9] investigated the tracking
control for a stochastic FJ joint robot model. A stable neu-
ral network-based observer for an FJ manipulator is presented
in [10]. In addition, by using an adaptive dynamic surface and
a self-recurrent wavelet neural network, a robust control for
an uncertain FJ robot is proposed in [11].Basedonadistur-
bance observer, [12] proposes a robust PD control scheme for
FJ robots, and so on. Although the aforementioned approaches
have nice results on the tracking control of FJ robots, those
approaches are not able to cope with the tracking control
problem when there are state constraints.
Constraints are widespread in most physical systems, such
as physical stoppages, saturation, and safety specifications.
Many methods have been proposed to guarantee the stability
for various kinds of systems with the state or output con-
straints. With the aid of barrier Lyapunov function (BLF),
an adaptive control scheme is developed in [13] for stochas-
tic nonlinear systems with unknown parameters and full state
constraints. For a class of nonlinear strict-feedback systems
with time-varying state constraints, a BLF-based backstep-
ping is given in [14] to prevent the states from violating
of the constraints. By the dynamic surface control, back-
stepping designs are constructed in [15] and [16] for pure
feedback nonlinear systems with full state constraints. The
finite-time adaptive tracking control is presented in [17]for
strict-feedback nonlinear systems with full-state constraints.
Adaptive neural network control for uncertain n-link robots
with full-state constraints is designed in [18]. A control algo-
rithm is presented in [19] for a class of stochastic nonlinear
systems with constraint requirement on the system output.
The studies in [20]–[27] and the references therein also
report several control strategies for the systems with input
constraints.
Being universal approximators, fuzzy systems or neural
networks have usually been applied to identify unknown
uncertainty terms required in control design. Lots of out-
standing results have been obtained for various systems, like
single-input and single-output nonlinear systems [28]–[31],
multiinput and multioutput nonlinear systems [32], [33],
and interconnected large-scale systems [34]–[36], and so
on. Similar to aforementioned literatures, fuzzy systems are
adopted to identify unknown nonlinear functions in this paper.
In fact, by taking into account some internal or external
factors, such as electric motor aging, currents or hardware
limitations, the states of FJ robots system may be sub-
jected by some constraints. The existing approaches proposed
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