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Research Papers

Comparison of Semirecursive and Subsystem Synthesis Algorithms for the Efficient Simulation of Multibody Systems

[+] Author and Article Information
Alfonso Callejo

Centre for Intelligent Machines,
McGill University,
Montréal, QC H3A 0E9, Canada
e-mail: acallejo@cim.mcgill.ca

Yongjun Pan

INSIA,
Universidad Politécnica de Madrid,
Madrid 28031, Spain
e-mail: yongjun.pan@alumnos.upm.es

José L. Ricón

INSIA,
Universidad Politécnica de Madrid,
Madrid 28031, Spain
e-mail: jl.ricon@alumnos.upm.es

József Kövecses

Centre for Intelligent Machines,
McGill University,
Montréal, QC H3A 0E9, Canada
e-mail: jozsef.kovecses@mcgill.ca

Javier García de Jalón

INSIA,
Universidad Politécnica de Madrid,
Madrid 28031, Spain
e-mail: javier.garciadejalon@upm.es

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received August 15, 2016; final manuscript received September 27, 2016; published online November 22, 2016. Assoc. Editor: Paramsothy Jayakumar.

J. Comput. Nonlinear Dynam 12(1), 011020 (Nov 22, 2016) (11 pages) Paper No: CND-16-1383; doi: 10.1115/1.4034870 History: Received August 15, 2016; Revised September 27, 2016

A great variety of formulations exist for the numerical simulation of rigid-body systems, particularly of medium-large systems such as vehicles. Topological formulations, which are considered to be the most efficient ones, are often cumbersome and not necessarily easy to implement. As a consequence, there is a lack of comparative evidence to support the performance of these formulations. In this paper, we present and compare three state-of-the-art topological formulations for multibody dynamics: generalized semirecursive, double-step semirecursive, and subsystem synthesis methods. We analyze the background, underlying principles, numerical efficiency, and accuracy of these formulations in a systematic way. A 28-degree-of-freedom, open-loop rover model and a 16-degree-of-freedom, closed-loop sedan car model are selected as study cases. Insight on the key aspects toward performance is provided.

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References

Schiehlen, W. , 2014, “ History of Benchmark Problems in Multibody Dynamics,” Multibody Dynamics: Computational Methods and Applications, Springer, Cham, Switzerland, pp. 357–368.
Pàmies-Vilà, R. , Font-Llagunes, J. M. , Lugrís, U. , Alonso, F. J. , and Cuadrado, J. , 2015, “ A Computational Benchmark for 2D Gait Analysis Problems,” New Trends in Mechanism and Machine Science, Springer, Cham, Switzerland, pp. 689–697.
González, M. , Dopico, D. , Lugrís, U. , and Cuadrado, J. , 2006, “ A Benchmarking System for MBS Simulation Software: Problem Standardization and Performance Measurement,” Multibody Syst. Dyn., 16(2), pp. 179–190. [CrossRef]
Walker, M. W. , and Orin, D. E. , 1982, “ Efficient Dynamic Computer Simulation of Robotic Mechanisms,” ASME J. Dyn. Syst., Meas., Control, 104(3), pp. 205–211. [CrossRef]
Jerkovsky, W. , 1978, “ The Structure of Multibody Dynamics Equations,” J. Guid. Control Dyn., 1(3), pp. 173–182. [CrossRef]
Avello, A. , Jiménez, J. , Bayo, E. , and García de Jalón, J. , 1993, “ A Simple and Highly Parallelizable Method for Real-Time Dynamic Simulation Based on Velocity Transformations,” Comput. Methods Appl. Mech. Eng., 107(3), pp. 313–339. [CrossRef]
Featherstone, R. , 1983, “ The Calculation of Robot Dynamics Using Articulated-Body Inertias,” Int. J. Rob. Res., 2(1), pp. 13–30. [CrossRef]
Stelzle, W. , Kecskeméthy, A. , and Hiller, M. , 1995, “ A Comparative Study of Recursive Methods,” Arch. Appl. Mech., 66(1), pp. 9–19. [CrossRef]
Bae, D.-S. , and Haug, E. J. , 1987, “ A Recursive Formulation for Constrained Mechanical System Dynamics: Part II. Closed Loop Systems,” J. Struct. Mech., 15(4), pp. 481–506.
García de Jalón, J. , and Bayo, E. , 1994, Kinematic and Dynamic Simulation of Multibody Systems: The Real-Time Challenge, Springer, New York.
García de Jalón, J. , Callejo, A. , and Hidalgo, A. F. , 2012, “ Efficient Solution of Maggi's Equations,” ASME J. Comput. Nonlinear Dyn., 7(2), p. 021003. [CrossRef]
Kim, S. , and Vanderploeg, M. , 1986, “ A General and Efficient Method for Dynamic Analysis of Mechanical Systems Using Velocity Transformations,” ASME J. Mech. Des., 108(2), pp. 176–182.
Negrut, D. , Serban, R. , and Potra, F. A. , 1997, “ A Topology-Based Approach to Exploiting Sparsity in Multibody Dynamics: Joint Formulation,” J. Struct. Mech., 25(2), pp. 221–241.
Bae, D. , Han, J. , and Yoo, H. , 1999, “ A Generalized Recursive Formulation for Constrained Mechanical System Dynamics,” Mech. Struct. Mach., 27(3), pp. 293–315. [CrossRef]
Bae, D. , Han, J. , and Choi, J. , 2000, “ An Implementation Method for Constrained Flexible Multibody Dynamics Using a Virtual Body and Joint,” Multibody Syst. Dyn., 4(4), pp. 297–315. [CrossRef]
Bae, D. , Lee, J. , Cho, H. , and Yae, H. , 2000, “ An Explicit Integration Method for Realtime Simulation of Multibody Vehicle Models,” Comput. Methods Appl. Mech. Eng., 187(1–2), pp. 337–350. [CrossRef]
Bae, D. , Cho, H. , Lee, S. , and Moon, W. , 2001, “ Recursive Formulas for Design Sensitivity Analysis of Mechanical Systems,” Comput. Methods Appl. Mech. Eng., 190(29–30), pp. 3865–3879. [CrossRef]
Bae, D. S. , Han, J. M. , Choi, J. H. , and Yang, S. M. , 2001, “ A Generalized Recursive Formulation for Constrained Flexible Multibody Dynamics,” Int. J. Numer. Methods Eng., 50(8), pp. 1841–1859. [CrossRef]
Ricón, J. L. , 2014, “ Implementación de la formulación implícita semi-recursiva de Bae para la simulación en tiempo real de sistemas multicuerpo,” Master's thesis, ETSII—Technical University of Madrid, Madrid, Spain.
Yen, J. , Haug, E. J. , and Potra, F. A. , 1990, “ Numerical Method for Constrained Equations of Motion in Mechanical Systems Dynamics,” Center for Simulation and Design Optimization, University of Iowa, Iowa City, IA, Technical Report No. R-92.
Funes, F. J. , and García de Jalón, J. , 2016, “ An Efficient Dynamic Formulation for Solving Rigid and Flexible Multibody Systems Based on Semirecursive Method and Implicit Integration,” ASME J. Comput. Nonlinear Dyn., 11(5), p. 051001. [CrossRef]
Rodríguez, J. I. , Jiménez, J. M. , Funes, F. J. , and García de Jalón, J. , 2004, “ Recursive and Residual Algorithms for the Efficient Numerical Integration of Multi-Body Systems,” Multibody Syst. Dyn., 11(4), pp. 295–320. [CrossRef]
García de Jalón, J. , Álvarez, E. , de Ribera, F. A. , Rodríguez, I. , and Funes, F. J. , 2005, “ A Fast and Simple Semi-Recursive Formulation for Multi-Rigid-Body Systems,” Advances in Computational Multibody Systems (Computational Methods in Applied Sciences, Vol. 2), J. Ambrósio , ed., Springer, Dordrecht, The Netherlands, pp. 1–23.
Jerkovsky, W. , 1978, “ The Structure of Multibody Dynamic Equations,” J. Guid. Control Dyn., 1(3), pp. 173–182. [CrossRef]
Wittenburg, J. , 1977, Dynamics of Systems of Rigid Bodies, B. G. Teubner, Stuttgart, Germany.
von Schwerin, R. , 1999, Multibody System Simulation, Numerical Methods, Algorithms and Software, Springer, Berlin.
Kurdila, A. , Papastavridis, J. G. , and Kamat, M. P. , 1990, “ Role of Maggi's Equations in Computational Methods for Constrained Multibody Systems,” J. Guid. Control Dyn., 13(1), pp. 113–120. [CrossRef]
Papastavridis, J. G. , 1990, “ Maggi's Equations of Motion and the Determination of Constraint Reactions,” J. Guid. Control Dyn., 13(2), pp. 213–220. [CrossRef]
Wampler, C. , Buffinton, K. , and Shu-hui, J. , 1985, “ Formulation of Equations of Motion for Systems Subject to Constraints,” ASME J. Appl. Mech., 52(2), pp. 465–470. [CrossRef]
Laulusa, A. , and Bauchau, O. A. , 2007, “ Review of Classical Approaches for Constraint Enforcement in Multibody Systems,” ASME J. Comput. Nonlinear Dyn., 3(1), p. 011004. [CrossRef]
Serban, R. , and Haug, E. , 2000, “ Globally Independent Coordinates for Real-Time Vehicle Simulation,” ASME J. Mech. Des., 122(4), pp. 575–582. [CrossRef]
Kim, S.-S. , 2002, “ A Subsystem Synthesis Method for Efficient Vehicle Multibody Dynamics,” Multibody Syst. Dyn., 7(2), pp. 189–207. [CrossRef]
Kim, S.-S. , and Wang, J.-H. , 2005, “ Subsystem Synthesis Methods With Independent Coordinates for Real-Time Multibody Dynamics,” J. Mech. Sci. Technol., 19(1), pp. 312–319. [CrossRef]
Kim, S.-S. , and Jeong, W. , 2007, “ Subsystem Synthesis Method With Approximate Function Approach for a Real-Time Multibody Vehicle Model,” Multibody Syst. Dyn., 17(2–3), pp. 141–156. [CrossRef]
Pacejka, H. B. , 2012, Tyre and Vehicle Dynamics, Elsevier/Butterworth-Heinemann, Oxford, UK.

Figures

Grahic Jump Location
Fig. 1

Kinematic relationship between two connected bodies

Grahic Jump Location
Fig. 2

Structure of RdTMΣRd (dependent-coordinate form)

Grahic Jump Location
Fig. 3

Structure of RzTRdTMΣRdRz (independent-coordinate form)

Grahic Jump Location
Fig. 4

Exploration rover: multibody model

Grahic Jump Location
Fig. 5

Sedan vehicle: multibody model

Grahic Jump Location
Fig. 6

Rover: system topology

Grahic Jump Location
Fig. 7

Sedan vehicle: system topology

Grahic Jump Location
Fig. 8

X-, Y-, and Z-displacements of the rover chassis

Grahic Jump Location
Fig. 9

X-, Y-, and Z-displacements of the sedan chassis

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