Multibody System Dynamics

, Volume 26, Issue 1, pp 1–14 | Cite as

Smooth velocity approximation for constrained systems in real-time simulation

  • Bernhard Burgermeister
  • Martin Arnold
  • Alexander Eichberger
Article

Abstract

The rapidly increasing complexity of multi-body system models in applications like vehicle dynamics, robotics and bio-mechanics requires qualitative new solution methods to slash computing times for the dynamical simulation.

Detailed multi-body systems are designed for accurate off-line simulation. For real-time applications or efficient long-term simulations simplified models are used (Rill, G.: J. Braz. Soc. Mech. Sci. XIX(2):192–206 (1997)). In contrast to pure numerical model reduction techniques (Antoulas, A.C.: Approximation of large-scale dynamical systems (2005) and Fehr, J., Eberhard, P.: J. Comput. Nonlinear Dyn. 5:031005 (2010)), the presented quasi-static solution method is based on analytical model reduction combined with adapted numerical methods for evaluating and solving the (reduced) equations of motion efficiently and focuses on accelerated computation of the low frequency parts of the solution of the nonlinear equations of motion by smoothing out the velocities of fast moving low-mass bodies. The high frequency parts are eliminated by neglecting some of the inertia forces and torques. This reduces numerical stiffness and allows larger step-sizes for the time integration.

The efficient and real-time capable combination with existing highly efficient algorithms for multi-body dynamics (\(\mathcal{O}(N)\) multi-body formalisms) requires appropriate integration methods that are adapted to the special structure of the multi-body formalism and solve the nonlinear constraints with a small, limited number of calculation steps.

Keywords

Model reduction Equations of motion Quasi-static Multi-body formalism 

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References

  1. 1.
    Antoulas, A.C.: Approximation of Large-Scale Dynamical Systems. SIAM, Philadelphia (2005) CrossRefMATHGoogle Scholar
  2. 2.
    Arnold, M., Burgermeister, B., Eichberger, A.: Linearly implicit time integration methods in real-time applications: DAEs and stiff ODEs. Multibody Syst. Dyn. 17, 99–117 (2007) MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Arnold, M., Strehmel, K., Weiner, R.: Half-explicit Runge–Kutta methods for semi-explicit differential-algebraic equations of index 1. Numer. Math. 64, 409–431 (1993) MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Brandl, H., Johanni, R., Otter, M.: A very efficient algorithm for the simulation of robots and similar multibody systems without inversion of the mass matrix. In: Proc. of the IFAC/IFIP/IMACS International Symposium on Theory of Robots, Vienna (1986) Google Scholar
  5. 5.
    Burgermeister, B., Arnold, M., Esterl, B.: DAE time integration for real-time applications in multi-body dynamics. Z. Angew. Math. Mech. 86, 759–771 (2006) MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Burgermeister, B.: Linear-implizite Zeitintegrationsverfahren für differentiell-algebraische Systeme in der Mehrkörperdynamik. In: Fortschritt-Berichte VDI Reihe vol. 20, Nr. 431. VDI-Verlag, Düsseldorf (2010) Google Scholar
  7. 7.
    Eichberger, A., Rulka, W.: Process save reduction by macro joint approach: The key to real time and efficient vehicle simulation. Veh. Syst. Dyn. 41, 401–413 (2004) CrossRefGoogle Scholar
  8. 8.
    Fehr, J., Eberhard, P.: Error-controlled model reduction in flexible multibody dynamics. J. Comput. Nonlinear Dyn. 5, 031005 (2010) CrossRefGoogle Scholar
  9. 9.
    Hairer, E., Wanner, G.: Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems, 2nd edn. Springer, Berlin (1996) CrossRefMATHGoogle Scholar
  10. 10.
    Petzold, L.R.: A description of DASSL: A differential/algebraic system solver. Technical Report SAND82–8637, Sandia National Laboratories Livermore (1982) Google Scholar
  11. 11.
    Rill, G.: Vehicle modelling for real time applications. J. Braz. Soc. Mech. Sci. XIX(2), 192–206 (1997) Google Scholar
  12. 12.
    Roberson, R.E., Schwertassek, R.: Dynamics of Multibody Systems. Springer, Berlin (1988) CrossRefMATHGoogle Scholar
  13. 13.
    Rulka, W.: SIMPACK—A computer program for simulation of large-motion multibody systems. In: Schiehlen, W.O. (ed.) Multibody Systems Handbook. Springer, Berlin (1990) Google Scholar
  14. 14.
    Rulka, W.: Effiziente Simulation der Dynamik mechatronischer Systeme für industrielle Anwendungen. PhD thesis, Vienna University of Technology, Department of Mechanical Engineering (1998) Google Scholar
  15. 15.
    Rulka, W., Pankiewicz, E.: MBS approach to generate equations of motions for HiL-simulations in vehicle dynamics. Multibody Syst. Dyn. 14, 367–386 (2005) CrossRefMATHGoogle Scholar
  16. 16.
    Shampine, L.F., Gear, C.W.: A user’s view of solving stiff ordinary differential equations. SIAM Rev. 21, 1–17 (1979) MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Wade, H.L.: Basic and Advanced Regulatory Control: System Design and Application, 2nd edn. ISA, USA (2004) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Bernhard Burgermeister
    • 1
  • Martin Arnold
    • 2
  • Alexander Eichberger
    • 1
  1. 1.SIMPACK AGGilchingGermany
  2. 2.NWF II-Institute of MathematicsMartin Luther University Halle-WittenbergHalle (Saale)Germany

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