Citation: Raoufi, M.; Habibi, H.;
Yazdani, A.; Wang, H. Robust
Prescribed Trajectory Tracking
Control of a Robot Manipulator
Using Adaptive Finite-Time Sliding
Mode and Extreme Learning
Machine Method. Robotics 2022, 11,
111. https://doi.org/10.3390/
robotics11050111
Academic Editors: Shuai Li,
Dechao Chen, Mohammed
Aquil Mirza, Vasilios N. Katsikis,
Dunhui Xiao and Predrag
S. Stanimirovic
Received: 24 August 2022
Accepted: 13 October 2022
Published: 15 October 2022
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Article
Robust Prescribed Trajectory Tracking Control of a Robot
Manipulator Using Adaptive Finite-Time Sliding Mode and
Extreme Learning Machine Method
Mona Raoufi
1
, Hamed Habibi
2
, Amirmehdi Yazdani
3,
* and Hai Wang
3,
*
1
Department of Electrical Engineering, Hamedan University of Technology, Hamedan 65155, Iran
2
Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg,
L-1855 Luxembourg, Luxembourg
3
College of Science, Health, Engineering and Education, Murdoch University, Perth, WA 6150, Australia
* Correspondence: amirmehdi.yazdani@murdoch.edu.au (A.Y.); hai.wang@murdoch.edu.au (H.W.)
Abstract:
This study aims to provide a robust trajectory tracking controller which guarantees the
prescribed performance of a robot manipulator, both in transient and steady-state modes, experiencing
parametric uncertainties. The main core of the controller is designed based on the adaptive finite-time
sliding mode control (SMC) and extreme learning machine (ELM) methods to collectively estimate
the parametric model uncertainties and enhance the quality of tracking performance. Accordingly,
the global estimation with a fast convergence rate is achieved while the tracking error and the impact
of chattering on the control input are mitigated significantly. Following the control design, the
stability of the overall control system along with the finite-time convergence rate is proved, and the
effectiveness of the proposed method is investigated via extensive simulation studies. The results of
simulations confirm that the prescribed transient and steady-state performances are obtained with
enough accuracy, fast convergence rate, robustness, and smooth control input which are all required
for practical implementation and applications.
Keywords:
robot manipulators; finite-time sliding mode control; model uncertainty; extreme learning
machine; prescribed performance
1. Introduction
Robotic manipulators are extensively being used in different areas such as the manu-
facturing industry, process and mining, automatic surgery, as well as smart agriculture [
1
,
2
].
These robots considerably reduce human effort in complex task operations by adopting
different controllers [
3
–
5
]. Despite the available control technologies in the state-of-the-art,
there are still some gaps and unaddressed challenges in this domain. From the system
modeling perspective, the Lagrange method is commonly used to model rigid-link ma-
nipulators [
6
]. However, these multivariable systems are highly coupled and nonlinear,
meaning that an accurate model representation is hardly obtained for such systems [
7
,
8
].
These issues can accommodate by designing a reliable controller that satisfies precision, fast-
response rate, robustness, and adaptiveness properties by which the uncertain dynamics
and disturbances are handled properly.
In the state-of the-art, the conventional SMC and its developments have been investi-
gated for robotics and nonlinear systems control for several decades. To achieve acceptable
systems performance, in [
9
], a disturbance-observer-based SMC controller is developed
for space manipulators with prescribed performance. Generally, the prescribed perfor-
mance control (PPC) is an approach for ensuring the desired transient and steady-state
system responses. This approach is associated with many challenges such as the time
response and the initial error dependency, which can be developed in various ways [
10
].
Furthermore, additional solutions are required for unpredictable perturbations [
10
]. These
Robotics 2022, 11, 111. https://doi.org/10.3390/robotics11050111 https://www.mdpi.com/journal/robotics
