Volume 142

Published on October 2025

Volume title: Proceedings of CONF-APMM 2025 Symposium: Simulation and Theory of Differential-Integral Equation in Applied Physics

ISBN:978-1-80590-305-5(Print) / 978-1-80590-306-2(Online)
Conference date: 27 September 2025
Editor:Marwan Omar, Shuxia Zhao
Research Article
Published on 14 October 2025 DOI: 10.54254/2753-8818/2025.DL27940
Xiwen Liang
DOI: 10.54254/2753-8818/2025.DL27940

Robot motion control is crucial for high-precision tasks in fields such as industrial manufacturing and surgical operations. However, multi-source errors related to machinery, sensors, environment, and modeling significantly reduce its precision. This paper systematically reviews the statistical analysis methods for such errors in motion control experiments, with a focus on introducing the mathematical modeling and handling strategies of errors. For modeling, it analyzes probability-based error propagation models such as covariance analysis-least squares, Monte Carlo simulation, Taylor series expansion, and non-Gaussian modeling to quantify the transmission of uncertainties in the kinematic chain, as well as spatiotemporal correlation models such as Markov chain integrated stochastic frameworks and multi-source error Bayesian networks to capture the error dynamics coupled with time and space. For processing, it explores three technical directions: first, real-time filtering and state estimation, which includes statistical process control and Bayesian network fusion; second, parameter identification and system calibration, including genetic particle swarm optimization-neural network and Bayesian optimization-random forest; third, robust control and adaptive strategies, including deep learning, dynamic compensation, and federated learning, among others. It compares the applicability of methods. For example, the Monte Carlo method is used for offline nonlinear analysis but has a large computational load; federated learning is used for rapid multi-robot convergence but has high bandwidth requirements to guide selection, and looks forward to future research directions, such as improving robustness in extreme environments.

Show more
View pdf
Liang,X. (2025). Statistical Analysis Methods and Applications of Errors in Robot Motion Control Experiments. Theoretical and Natural Science,142,1-8.
Export citation
Research Article
Published on 14 October 2025 DOI: 10.54254/2753-8818/2025.DL27731
Muyao Wang
DOI: 10.54254/2753-8818/2025.DL27731

This paper explores Lagrange’s Theorem, a foundational result in abstract algebra that establishes a connection between the orders of a group and its subgroups. Initially introduced by Joseph Lagrange in the 18th century, the theorem asserts that the order of any subgroup divides the order of the entire group. This investigation begins with essential concepts of group theory, including cosets and bijections, leading to a rigorous proof of Lagrange’s Theorem. The paper also highlights significant implications of the theorem, such as its role in deriving Wilson’s Theorem and Fermat’s Little Theorem, both of which proves pivotal in algebraic theory. Furthermore, the applications of Lagrange’s Theorem in modern cryptography, particularly in the RSA public-key cryptosystem, are discussed, illustrating its relevance in contemporary mathematical practices. Despite its profound impact, there is no guarantee of the existence of subgroups for every divisor by the theorem, a limitation addressed by Sylow’s Theorem. This paper concludes by emphasizing the enduring significance of Lagrange’s Theorem in linking abstract algebra to practical applications and suggests avenues for future research in Galois theory and advanced cryptographic methods.

Show more
View pdf
Wang,M. (2025). The Proof of Lagrange Theorem and Its Applications. Theoretical and Natural Science,142,9-13.
Export citation