Statistical Analysis Methods and Applications of Errors in Robot Motion Control Experiments
Research Article
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Statistical Analysis Methods and Applications of Errors in Robot Motion Control Experiments

Xiwen Liang 1*
1 The University of Hong Kong
*Corresponding author: 20293420@hkuspace.hku.hk
Published on 14 October 2025
Journal Cover
TNS Vol.142
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-80590-305-5
ISBN (Online): 978-1-80590-306-2
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Abstract

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.

Keywords:

robot motion control, error statistical analysis, mathematical modeling, error handling, multi-source error compensation

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Liang,X. (2025). Statistical Analysis Methods and Applications of Errors in Robot Motion Control Experiments. Theoretical and Natural Science,142,1-8.

References

[1]. Meggiolaro M, Dubowsky S. Statistical analysis of positioning errors for robotic manipulators. IEEE Transactions on Robotics and Automation, 2003, 19(4): 601-613.

[2]. Wu P, Yang D. Statistical Tolerance Analysis for Serial Manipulators. Mechanism and Machine Theory, 2018, 126: 235-251.

[3]. Gouttefarde R, Lamaury J. Non-Gaussian Error Modeling for Cable-Driven Parallel Robots. IEEE Transactions on Robotics, 2022, 38(2): 1024-1038.

[4]. Schröer K, Albright S. Stochastic Modeling of Robotic Assembly Tasks for Error Prediction [J]. Journal of Manufacturing Systems, 2017, 44: 152-163.

[5]. Lee T, Park H. Bayesian Network for Robotic Error Diagnosis. IEEE Transactions on Industrial Informatics, 2019, 15(7): 4012-4021.

[6]. Lee T, Park H. Multi-source Error Fusion and State Estimation for Industrial Robots Based on Bayesian Network. International Journal of Precision Engineering and Manufacturing, 2020, 21(3): 543-554.

[7]. Li B, Tian W, Zhang C, et al. Positioning Error Compensation of an Industrial Robot Using Neural Networks and Experimental Study. Journal of Intelligent Manufacturing, 2022, 33(5): 1389-1405.

[8]. Wu L, Ren H, Li P. Data-Driven Statistical Framework for Calibration. IEEE Transactions on Industrial Electronics, 2021, 68(8): 7256-7265.

[9]. Chen Y, Yang W. Federated Learning for Multi-Robot Error Compensation. Robotics and Autonomous Systems, 2023, 162: 104389.

[10]. Meggiolaro M, Dubowsky S. Comparative Study of Monte Carlo Simulation for Nonlinear Error Propagation in Robotic Manipulators. ASME Journal of Mechanical Design, 2003, 125(3): 487-494.

[11]. Wu P, Yang D. Sensitivity Analysis of Manufacturing Tolerances in Serial Manipulators via Taylor Series Expansion. Precision Engineering, 2018, 54: 182-191.

[12]. Chen Y, Yang W. Bandwidth Requirements Analysis for Federated Learning-Based Multi-Robot Error Compensation. IEEE Internet of Things Journal, 2023, 10(12): 10689-10700.

[13]. Chen M, Zhang L. Generalization Ability Evaluation of Deep Learning Models for Collaborative Robot Error Compensation. Neural Computing and Applications, 2020, 32(18): 14567-14580.

[14]. Nakamura K, Ando S. Quantum-Inspired Sampling for High-Dimensional Error Spaces. Physical Review Applied, 2023, 19(5): 054023.

[15]. Levin M, Kriegman S. Biohybrid Error Correction Using Living Neural Networks. Science Robotics, 2023, 8(82): eabq4641.

References

[1]. Meggiolaro M, Dubowsky S. Statistical analysis of positioning errors for robotic manipulators. IEEE Transactions on Robotics and Automation, 2003, 19(4): 601-613.

[2]. Wu P, Yang D. Statistical Tolerance Analysis for Serial Manipulators. Mechanism and Machine Theory, 2018, 126: 235-251.

[3]. Gouttefarde R, Lamaury J. Non-Gaussian Error Modeling for Cable-Driven Parallel Robots. IEEE Transactions on Robotics, 2022, 38(2): 1024-1038.

[4]. Schröer K, Albright S. Stochastic Modeling of Robotic Assembly Tasks for Error Prediction [J]. Journal of Manufacturing Systems, 2017, 44: 152-163.

[5]. Lee T, Park H. Bayesian Network for Robotic Error Diagnosis. IEEE Transactions on Industrial Informatics, 2019, 15(7): 4012-4021.

[6]. Lee T, Park H. Multi-source Error Fusion and State Estimation for Industrial Robots Based on Bayesian Network. International Journal of Precision Engineering and Manufacturing, 2020, 21(3): 543-554.

[7]. Li B, Tian W, Zhang C, et al. Positioning Error Compensation of an Industrial Robot Using Neural Networks and Experimental Study. Journal of Intelligent Manufacturing, 2022, 33(5): 1389-1405.

[8]. Wu L, Ren H, Li P. Data-Driven Statistical Framework for Calibration. IEEE Transactions on Industrial Electronics, 2021, 68(8): 7256-7265.

[9]. Chen Y, Yang W. Federated Learning for Multi-Robot Error Compensation. Robotics and Autonomous Systems, 2023, 162: 104389.

[10]. Meggiolaro M, Dubowsky S. Comparative Study of Monte Carlo Simulation for Nonlinear Error Propagation in Robotic Manipulators. ASME Journal of Mechanical Design, 2003, 125(3): 487-494.

[11]. Wu P, Yang D. Sensitivity Analysis of Manufacturing Tolerances in Serial Manipulators via Taylor Series Expansion. Precision Engineering, 2018, 54: 182-191.

[12]. Chen Y, Yang W. Bandwidth Requirements Analysis for Federated Learning-Based Multi-Robot Error Compensation. IEEE Internet of Things Journal, 2023, 10(12): 10689-10700.

[13]. Chen M, Zhang L. Generalization Ability Evaluation of Deep Learning Models for Collaborative Robot Error Compensation. Neural Computing and Applications, 2020, 32(18): 14567-14580.

[14]. Nakamura K, Ando S. Quantum-Inspired Sampling for High-Dimensional Error Spaces. Physical Review Applied, 2023, 19(5): 054023.

[15]. Levin M, Kriegman S. Biohybrid Error Correction Using Living Neural Networks. Science Robotics, 2023, 8(82): eabq4641.

Cite this article

Liang,X. (2025). Statistical Analysis Methods and Applications of Errors in Robot Motion Control Experiments. Theoretical and Natural Science,142,1-8.

Data availability

The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

About volume

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)
Editor: Marwan Omar, Shuxia Zhao
Conference website: https://www.confapmm.org/dalian.html
Conference date: 27 September 2025
Series: Theoretical and Natural Science
Volume number: Vol.142
ISSN: 2753-8818(Print) / 2753-8826(Online)

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