Variation of the Newton-Rhapson algorithm that copes with noise, with some illustrative applications such as robotics

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.

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