Vehicle Escape Dynamics on an Arbitrarily Curved Surface

  • Levi H. ManringEmail author
  • Brian P. Mann
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


This paper derives a planar model for a vehicle on an arbitrarily curved surface. The goal is to investigate different strategies that may be used to free a vehicle from a ditch. More specifically, extricating a modern vehicle typically requires someone to get behind the vehicle and assist in pushing it out of the ditch. Due to human limitations in power output, the individual learns to rhythmically time their push, or applied force, to build momentum and achieve escape.

Numerical simulations were used to explore different strategies, or forcing functions, on this system. For example, this paper considers forcing the system at its linear natural frequency and a forcing strategy more akin to human behavior. Comparisons are made to determine the safest and most efficient strategy to achieve an escape. This paper will show the effectiveness of human intuition in pushing a vehicle out of a ditch.


Vehicle dynamics Nonlinear dynamical system Unknown terrain Arbitrary surface Escape 



The research is funded by Army Research Lab Grant W911NF-17-2-0047.


  1. 1.
    Sharp, R.S., Peng, H.: Vehicle dynamics applications of optimal control theory. Veh. Syst. Dyn. 49(7), 1073–1111 (2011)CrossRefGoogle Scholar
  2. 2.
    Yang, S., Lu, Y., Li, S.: An overview on vehicle dynamics. Int. J. Dynam. Control. 1(4), 385–395 (2013)CrossRefGoogle Scholar
  3. 3.
    Schiehlen, W.: Benchmark problems from vehicle dynamics. J. Mech. Sci. Technol. 29(7), 2601–2606 (2015)CrossRefGoogle Scholar
  4. 4.
    Leoro, J., Krutitskiy, S., Tarasov, A., Borovkov, A., Aleshin, M., Kylavin, O.: Vehicle dynamics prediction module. Mater. Phys. Mech. 34(1), 82–89 (2017)Google Scholar
  5. 5.
    He, Z., Ji, X.: Nonlinear robust control of integrated vehicle dynamics. Veh. Syst. Dyn. 50(2), 247–280 (2012)CrossRefGoogle Scholar
  6. 6.
    Wang, J., Longoria, R.G.: Coordinated and reconfigurable vehicle dynamics control. IEEE Trans. Control Syst. Technol. 17(3), 723–732 (2009)CrossRefGoogle Scholar
  7. 7.
    Mashadi, B., Gowdini, M.: Vehicle dynamics control by using an active gyroscopic device. J. Dyn. Syst. Meas. Control. 137(12), 121007 (2015)CrossRefGoogle Scholar
  8. 8.
    Velardocchia, M.: Control systems integration for enhanced vehicle dynamics. Open Mech. Eng. J. 7(1), 58–69 (2013)CrossRefGoogle Scholar
  9. 9.
    Ferrara, A., Incremona, G.P., Regolin, E.: Optimization-based adaptive sliding mode control with application to vehicle dynamics control. Int. J. Robust Nonlinear Control. (2018).
  10. 10.
    Lopez, A., Moriano, C., Olazagoitia, J.L., Paez, F.J.: Fast computing on vehicle dynamics using Chebyshev series expansions. IEEE/ASME Trans. Mechatronics. 20(5), 2563–2574 (2015)CrossRefGoogle Scholar
  11. 11.
    Yavin, Y.: Modelling of the motion of a cart on a smooth rigid surface. Math. Comput. Model. 36(4–5), 525–533 (2002)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Yavin, Y.: Modelling and control of the motion of a cart moving on a plane with a time-dependent inclination. Math. Comput. Model. 37(3–4), 293–299 (2003)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Chatzis, M.N., Smyth, A.W.: Three-dimensional dynamics of a rigid body with wheels on a moving base. J. Eng. Mech. 139(4), 496–511 (2013)CrossRefGoogle Scholar
  14. 14.
    Virgin, L.N., Lyman, T.C., Davis, R.B.: Nonlinear dynamics of a ball rolling on a surface. Am. J. Phys. 78(3), 250–257 (2010)CrossRefGoogle Scholar
  15. 15.
    Nimbarte, A.D., Sun, Y., Jaridi, M., Hsiao, H.: Biomechanical loading of the shoulder complex and lumbosacral joints during dynamic cart pushing task. Appl. Ergon. 44(5), 841–849 (2013)CrossRefGoogle Scholar
  16. 16.
    Hoozemans, M.J.M., Slaghuis, W., Faber, G.S., van Dieën, J.H.: Cart pushing: the effects of magnitude and direction of the exerted push force, and of trunk inclination on low back loading. Int. J. Ind. Ergon. 37(11–12), 832–844 (Nov 2007)CrossRefGoogle Scholar
  17. 17.
    Glitsch, U., Ottersbach, H.J., Ellegast, R., Schaub, K., Franz, G., Jäger, M.: Physical workload of flight attendants when pushing and pulling trolleys aboard aircraft. Int. J. Ind. Ergon. 37(11–12), 845–854 (2007)CrossRefGoogle Scholar
  18. 18.
    Ciriello, V.M., Maikala, R.V., Dempsey, P.G., OBrien, N.V.: Cart pushing capabilities for males and females: an update. Proc. Hum. Factors Ergonomics Soc. Annu. Meet. 53(14), 897–901 (2009)CrossRefGoogle Scholar
  19. 19.
    Berning, J.M., Adams, K.J., Climstein, M., Stamford, B.A.: Metabolic demands of “junkyard” training: pushing and pulling a motor vehicle. J. Strength Cond. Res. 21(3), 853 (2007)Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 2020

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Materials SciencePratt School of Engineering, Duke UniversityDurhamUSA

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