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A non-iterative implicit integration method using a HHT-α integrator for real-time analysis of multibody systems

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Abstract

This paper proposes a non-iterative implicit integration method for real-time analysis of multibody systems. Although the implicit Euler integrator is widely used for real-time simulations, we use a HHT-α integrator to improve the accuracy of the solution. For a noniterative procedure, the HHT-α integral formula was reformed and applied to the linearized equations of motion for multibody systems. A stability analysis of the HHT-α integrator was carried out to determine whether the proposed integrator has absolute stability. Numerical simulations with stiff linear systems that represent a highly damped system and a highly oscillatory system were also carried out to evaluate the performance of the proposed integrator. For non-linear multibody systems, the performance of the proposed integrator was also evaluated with a double pendulum example. Through the double pendulum multibody simulations, we confirmed the accuracy and stability characteristics of the proposed integration method by comparison of the conventional HHT-α integrator with the iterative method and the implicit Euler integrator, which is widely used in real-time applications.

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Authors and Affiliations

  1. Department of Mechatronics Engineering, Chungnam National University, #99, Daehak-ro, Yuseong-gu, Daejeon, 34134, Korea

    Myoungho Kim & Sung-Soo Kim

  2. Intelligent Robotics Research Center, Korea Electronics Technology Institute, #655, Pyeongcheon-ro, Wonmi-gu, Bucheon-si, Gyeonggi-do, 14502, Korea

    Hajun Song

Authors
  1. Myoungho Kim
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  2. Hajun Song
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  3. Sung-Soo Kim
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Corresponding author

Correspondence to Sung-Soo Kim.

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Recommended by Associate Editor Kyoung-Su Park

Myoungho Kim received his master’s degree in Mechatronics Engineering from Chungnam National University, Korea at 2013. He is currently studying Ph.D. at the Department of Mechatronics Engineering, Chungnam National University and the Korea Atomic Energy Research Institute. His research interests are multibody dynamics and control for robot systems.

Hajun Song graduated from the Dept. of Mechatronics Engineering at Chungnam National University, Korea in 2015. He received his master’s degree in Mechatronics Engineering from Chungnam National University in 2018. His research interests are real-time applications of multibody dynamics and modeling.

Sung-Soo Kim received his Ph.D. degree in Mechanical Engineering from University of Iowa, U.S.A., in 1988. He is currently a Professor of the Mechatronics Engineering Department at Chungnam National University, Daejeon, Korea. His research interests are real-time multibody dynamics and its application to automotive systems and robot systems.

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Kim, M., Song, H. & Kim, SS. A non-iterative implicit integration method using a HHT-α integrator for real-time analysis of multibody systems. J Mech Sci Technol 33, 1087–1096 (2019). https://doi.org/10.1007/s12206-019-0208-2

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  • DOI: https://doi.org/10.1007/s12206-019-0208-2

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