A Modified Structured Spectral HS Method for Nonlinear Least Squares Problems and Applications in Robot Arm Control

Rabiu Bashir Yunus (), Nooraini Zainuddin, Hanita Daud, Ramani Kannan, Samsul Ariffin Abdul Karim and Mahmoud Muhammad Yahaya
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Rabiu Bashir Yunus: Department of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
Nooraini Zainuddin: Department of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
Hanita Daud: Department of Fundamental and Applied Sciences, Faculty of Science and Information Technology, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
Ramani Kannan: Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Bandar Seri Iskandar 32610, Perak Darul Ridzuan, Malaysia
Samsul Ariffin Abdul Karim: Software Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Sabah, Malaysia
Mahmoud Muhammad Yahaya: Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand

Mathematics, 2023, vol. 11, issue 14, 1-17

Abstract: This paper proposes a modification to the Hestenes-Stiefel (HS) method by devising a spectral parameter using a modified secant relation to solve nonlinear least-squares problems. Notably, in the implementation, the proposed method differs from existing approaches, in that it does not require a safeguarding strategy and its Hessian matrix is positive and definite throughout the iteration process. Numerical experiments are conducted on a range of test problems, with 120 instances to demonstrate the efficacy of the proposed algorithm by comparing it with existing techniques in the literature. However, the results obtained validate the effectiveness of the proposed method in terms of the standard metrics of comparison. Additionally, the proposed approach is applied to address motion-control problems in a robotic model, resulting in favorable outcomes in terms of the robot’s motion characteristics.

Keywords: conjugate gradient; iterative algorithm; nonlinear least-squares; secant equation; robotic model; quasi-Newton (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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