D. Fu et al. Modified Newton Integration Algorithm With Noise Tolerance Applied to Robotics, IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 4, pp. 2134-2144 DOI: 10.1109/TSMC.2021.3049386.
Currently, the Newton\u2013Raphson iterative algorithm has been extensively employed in the fields of basic research and engineering. However, when noise components exist in a system, its performance is largely affected. To remedy shortcomings that the conventional computing methods have encountered in a noisy workspace, a novel modified Newton integration (MNI) algorithm is proposed in this article. In addition, the steady-state error of the proposed MNI algorithm is smaller than that of the Newton\u2013Raphson algorithm under a noise-free or noisy workspace. To lay the foundations for the corresponding theoretical analyses, the proposed MNI algorithm is first converted into a homogeneous linear equation with a residual term. Then, the related theoretical analyses are carried out, which indicate that the MNI algorithm possesses noise-tolerance ability under various noisy environments. Finally, multiple computer simulations and physical experiments on robot control applications are performed to verify the feasibility and advantage of the proposed MNI algorithm.