Advertisement

Accurate real-time truck simulation via semirecursive formulation and Adams–Bashforth–Moulton algorithm

  • Yongjun PanEmail author
  • Yansong He
  • Aki Mikkola
Research Paper
  • 18 Downloads

Abstract

In this paper, a tailored four-step Adams–Bashforth–Moulton (ABM) algorithm is applied to a semirecursive formulation to perform a real-time simulation of a semitrailer truck. In the ABM algorithm, each integration step involves two function evaluations, namely predictor and corrector. This is fundamentally different when compared to the classic fourth-order Runge–Kutta (RK) integrator approach that contains four function evaluations. A semitrailer truck under investigation is modeled in term of a semirecursive method and simulated by using the presented ABM algorithm. The results show that the four-step ABM method can reduce CPU time almost 50% for solving the truck dynamics with very similar accuracy, in comparison to the fourth-order RK method. The presented ABM algorithm could be used in the semirecursive formulation to carry out accurate real-time simulation of medium-large vehicle systems.

Keywords

Numerical algorithm Semirecursive formulation Vehicle dynamics Computational efficiency 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant 11702039) and the Fundamental Research Funds for the Central Universities of China (Grant 106112017CDJXY330002). We also thank Javier García de Jalón for the seminal idea.

References

  1. 1.
    Rahikainen, J., Mikkola, A., Sopanen, J., et al.: Combined semi-recursive formulation and lumped fluid method for monolithic simulation of multibody and hydraulic dynamics. Multibody Syst. Dyn. 44(3), 293–311 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Abbas, M.A., Milman, R., Mikael, J.: Obstacle avoidance in real time with nonlinear model predictive control of autonomous vehicles. Can. J. Electric. Comput. Eng. 40, 12–22 (2017)Google Scholar
  3. 3.
    Verma, R., Vecchio, D.D., Fathy, H.K.: Development of a scaled vehicle with longitudinal dynamics of an HMMWV for an ITS testbed. IEEE/ASME Trans. Mech. 13, 46–57 (2008)CrossRefGoogle Scholar
  4. 4.
    Li, X., Sun, Z., Cao, D., et al.: Real-time trajectory planning for autonomous urban driving: framework, algorithms, and verifications. IEEE/ASME Trans. Mech. 21, 740–753 (2016)CrossRefGoogle Scholar
  5. 5.
    Ding, J., Guo, K.: Development of a generalised equivalent estimation approach for multi-axle vehicle handling dynamics. Veh. Syst. Dyn. 54, 20–57 (2016)CrossRefGoogle Scholar
  6. 6.
    Zhang, H., Wang, J.: Vehicle lateral dynamics control through AFS/DYC and robust gain-scheduling approach. IEEE Trans. Veh. Technol. 65, 489–494 (2016)CrossRefGoogle Scholar
  7. 7.
    Boada, B.L., Boada, M.J.L., Diaz, V.: Vehicle sideslip angle measurement based on sensor data fusion using an integrated ANFIS and an Unscented Kalman Filter algorithm. Mech. Syst. Signal Process. 72, 832–845 (2016)CrossRefGoogle Scholar
  8. 8.
    Rulka, W., Pankiewicz, E.: MBS approach to generate equations of motions for HiL-simulations in vehicle dynamics. Multibody Syst. Dyn. 14, 367–386 (2005)CrossRefGoogle Scholar
  9. 9.
    Marques, F., Souto, A.P., Flores, P.: On the constraints violation in forward dynamics of multibody systems. Multibody Syst. Dyn. 39, 385–419 (2017)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Pan, Y., de Jalón, J.G.: Iterative refinement of accelerations in real-time vehicle dynamics. J. Comput. Nonlinear Dyn. 13, 011009 (2018)CrossRefGoogle Scholar
  11. 11.
    Shabana, A.A.: Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dyn. 16, 293–306 (1998)MathSciNetCrossRefGoogle Scholar
  12. 12.
    García de Jalón, J., Bayo, E.: Kinematic and Dynamic Simulation of Multibody Systems: The Real Time Challenge. Springer, New York (1994)CrossRefGoogle Scholar
  13. 13.
    von Schwerin, R.: Multibody System Simulation, Numerical Methods, Algorithms and Software. Springer, New York (1999)CrossRefGoogle Scholar
  14. 14.
    Shi, J., Liu, Z., Hong, J.: Multibody dynamic analysis using a rotation-free shell element with corotational frame. Acta Mech. Sin. 34(4), 769–780 (2018)MathSciNetCrossRefGoogle Scholar
  15. 15.
    García de Jalón, J., Álvarez, E., de Ribera, F.A., et al.: A fast and simple semi-recursive formulation for multi-rigid-body systems. In: Ambrsio, J.A.C. (ed.) Advances in Computational Multibody Systems. Computational Methods in Applied Sciences, 2nd edn. Springer, Dordrecht (2005)Google Scholar
  16. 16.
    Bae, D.S., Han, J.M., Choi, J.H., et al.: A generalized recursive formulation for constrained flexible multibody dynamics. Int. J. Numer. Methods Eng. 50, 1841–1859 (2001)CrossRefGoogle Scholar
  17. 17.
    Callejo, A., Pan, Y., Ricón, J.L., et al.: Comparison of semirecursive and subsystem synthesis algorithms for the efficient simulation of multibody systems. J. Comput. Nonlinear Dyn. 12, 011020 (2017)CrossRefGoogle Scholar
  18. 18.
    Kim, S.S.: A subsystem synthesis method for efficient vehicle multibody dynamics. Multibody Syst. Dyn. 7, 189–207 (2002)CrossRefGoogle Scholar
  19. 19.
    Kang, H.C., Kim, S.S., Lee, C.H.: Parallel processing with the subsystem synthesis method for efficient vehicle analysis. J. Mech. Sci. Technol. 29, 2663–2669 (2015)CrossRefGoogle Scholar
  20. 20.
    Cuadrado, J., Dopico, D., Gonzalez, M., et al.: A combined penalty and recursive real-time formulation for multibody dynamics. J. Mech. Des. 126, 602–608 (2004)CrossRefGoogle Scholar
  21. 21.
    Lee, J.K., Kang, J.S., Bae, D.S.: An efficient real-time vehicle simulation method using a chassis-based kinematic formulation. Proc. Inst. Mech. Eng. Part D J. Autom. Eng. 228, 272–284 (2014)CrossRefGoogle Scholar
  22. 22.
    Hidalgo, A.F., de Jalón, J.: Real-time dynamic simulations of large road vehicles using dense, sparse, and parallelization techniques. J. Comput. Nonlinear Dyn. 10, 031005 (2015)CrossRefGoogle Scholar
  23. 23.
    Zhang, H., Xing, Y.: A three-parameter single-step time integration method for structural dynamic analysis. Acta Mech. Sin. (2018).  https://doi.org/10.1007/s10409-018-0775-y
  24. 24.
    Pan, Y., Callejo, A., Bueno, J.L., et al.: Efficient and accurate modeling of rigid rods. Multibody Syst. Dyn. 40, 23–42 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Rodríguez, J.I., Jiménez, J.M., Funes, F.J., et al.: Recursive and residual algorithms for the efficient numerical integration of multi-body systems. Multibody Syst. Dyn. 11, 295–320 (2004)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Jerkovsky, W.: The structure of multibody dynamic equations. J. Guid. Control Dyn. 1, 173–182 (1978)CrossRefGoogle Scholar
  27. 27.
    Aniszewska, D.: Multiplicative Runge–Kutta methods. Nonlinear Dyn. 50, 265–272 (2007)CrossRefGoogle Scholar
  28. 28.
    Diethelm, K., Ford, N.J., Freed, A.D.: A predictor–corrector approach for the numerical solution of fractional differential equations. Nonlinear Dyn. 29, 3–22 (2002)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Misirli, E., Gurefe, Y.: Multiplicative Adams–Bashforth–Moulton methods. Numer. Algorithms 57, 425–439 (2011)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Peinado, J., Ibánez, J., Arias, E., et al.: Adams–Bashforth and Adams–Moulton methods for solving differential Riccati equations. Comput. Math. Appl. 60, 3032–3045 (2010)MathSciNetCrossRefGoogle Scholar
  31. 31.
    Zhao, B., Zhang, B.: Comparison of different order Adams–Bashforth methods in an atmospheric general circulation model. Acta Meteorol. Sin. 25, 754–764 (2011)CrossRefGoogle Scholar
  32. 32.
    Zayernouri, M., Matzavinos, A.: Fractional Adams–Bashforth/Moulton methods: an application to the fractional Keller–Segel chemotaxis system. J. Comput. Phys. 317, 1–14 (2016)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Pacejka, H.B.: Tyre and Vehicle Dynamics. Elsevier Butterworth-Heinemann, Oxford (2012)Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Automotive EngineeringChongqing UniversityChongqingChina
  2. 2.Department of Mechanical EngineeringLappeenranta University of TechnologyLappeenrantaFinland

Personalised recommendations