Citation: Amiri, M.S.; Ramli, R.
Utilisation of Initialised Observation
Scheme for Multi-Joint Robotic Arm
in Lyapunov-Based Adaptive Control
Strategy. Mathematics 2022, 10, 3126.
https://doi.org/10.3390/
math10173126
Academic Editors: Shuai Li, Dechao
Chen, Vasilios N. Katsikis, Predrag
Stanimirovi´c, Dunhui Xiao and
Mohammed Aquil Mirza
Received: 28 July 2022
Accepted: 18 August 2022
Published: 31 August 2022
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Article
Utilisation of Initialised Observation Scheme for Multi-Joint
Robotic Arm in Lyapunov-Based Adaptive Control Strategy
Mohammad Soleimani Amiri and Rizauddin Ramli *
Department of Mechanical and Manufacturing Engineering, Faculty of Engineering and Built Environment,
Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
* Correspondence: rizauddin@ukm.edu.my
Abstract:
In this paper, we present a modelling, dynamic analysis, and controller tuning comparison
for a five-degree-of-freedom (DoF) multi-joint robotic arm based on the Lyapunov-based Adaptive
Controller (LAC). In most pick-and-place applications of robotic arms, it is essential to control the
end-effector trajectory to reach a precise target position. The kinematic solution of the 5-DoF robotic
arm has been determined by the Lagrangian technique, and the mathematical model of each joint
has been obtained in the range of motion condition. The Proportional-Integral-Derivative (PID)
control parameters of the LAC have been determined by the Lyapunov stability approach and are
initialised by four observation methods based on the obtained transfer function. The effectiveness of
the initialised controller’s parameters is compared by a unit step response as the desired input of
the controller system. As a result, the average error (AE) for Ziegler–Nichols is 6.6%, 83%, and 53%
lower than for Pettit & Carr, Chau, and Bucz. The performance of LAC for the robotic arm model
is validated in a virtual 3D model under a robot operating system environment. The results of root
mean square error by LAC are 0.021 (rad) and 0.025 (rad) for joint 1 and joint 2, respectively, which
indicate the efficiency of the proposed LAC strategy in reaching the predetermined trajectory and the
potential of minimizing the controller tuning complexity.
Keywords:
multi-joint robotic arm; Proportional-Integral-Derivative; controller tuning; Lyapunov
approach
MSC: 93C40
1. Introduction
The advancements in robotic and autonomous systems involve various types of robots
in our daily lives and in industry [
1
]. Therefore, the multi-joint robotic arm represents
an essential role in the automotive, agriculture, and bio-medical sectors because of its
satisfactory performance, flexibility, and accuracy [2–4].
The robotic arm is one of the most common types of robots that is used in several
industrial applications [
5
]. For example, Xie et al. [
6
] developed an obstacle avoidance and
path planning algorithm for a multi-joint manipulator equipped with a spacecraft based on
forward and backward inverse kinematics. Pavlovcic et al. [
7
] utilised a six-degree-of-freedom
(DoF) robotic arm for simultaneous laser profilometry and hand–eye calibration in an
industrial application. In another study, Jeong et al. [
8
] presented brain–machine interfaces
for robotic arm applications. They developed an electroencephalogram, worn by humans
to acquire signals for implementation as desire tracking for a robotic arm.
Proportional-Integral-Derivative (PID) is one of the classical controllers, and it has been
widely used in different industries due to its simplicity, flexibility, adequate results
[9,10]
,
ease of implementation, and excellent performance [
11
]. In order to increase the precision
and robustness of the controller, its parameters are tuned by various methods, such as
classical observation and optimisation techniques [
12
,
13
]. Belkadi et al. [
14
] presented a
Mathematics 2022, 10, 3126. https://doi.org/10.3390/math10173126 https://www.mdpi.com/journal/mathematics
