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

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.