Multibody System Dynamics

, Volume 45, Issue 3, pp 273–292 | Cite as

Contact tracking algorithms in case of the omni-directional wheel rolling on the horizontal surface

  • Ivan I. KosenkoEmail author
  • Sergey Y. Stepanov
  • Kirill V. Gerasimov


An omni-wheel is defined as a wheel having rollers along its rim. Vehicles with omni-wheels are able to maneuver in any direction. For modeling the dynamics of omni-wheels we use general formalisms, previously developed by the authors for the multibody dynamics description in the framework of the object-oriented dynamical modeling language Modelica. Such an omni-wheel model, which is a class component, can be built into a vehicle model of any type. The axes of the rollers are usually set along the rim of the wheel either (a) parallel to the mid-plane of the wheel or (b) at some angle to this plane. Case (a) is the simplest one and the floor–roller contact tracking algorithm provides the fastest dynamical model. The more flexible case (b) consumes longer computation time. At the same time the suggested implementation of the case (b) turns out to be more efficient as compared with the approach based on the general formulas of contact problems. As an example, here these algorithms are combined with the simplest and fastest point-contact model, which runs regularly in the process of motion simulation. The proposed algorithms demonstrate the reliability and a nonimpact method of transferring contact point from one roller to another in the process of rolling the wheel. The implementation of these algorithms is described and computational experiments for numerical verification of the model are presented.


Omni wheel Contact tracking Unilateral constraint Contact detection Roller inclination Model of friction 



The investigation was performed at MAI under financial support provided by RSF, project 14-21-00068.


  1. 1.
    Ilon, B.E.: Wheels for a course stable selfpropelling vehicle movable in any desired direction on the ground or some other base. US Patents and Trademarks office, Patent 3,876,255 (1975) Google Scholar
  2. 2.
    Blumrich, J.F.: Omnidirectional wheel. Technical report. US Patents and Trademarks office, Patent 3,789,947 (1974) Google Scholar
  3. 3.
    Campion, G., Bastin, G., d’Andréa-Novel, B.: Structural properties and classification of kinematic and dynamic models of wheeled mobile robots. IEEE Trans. Robot. Autom. 12, 47–62 (1996) CrossRefGoogle Scholar
  4. 4.
    Zobova, A.A., Tatarinov, Ya.V.: The dynamics of an omni-mobile vehicle. J. Appl. Math. Mech. 73, 8–15 (2009) MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Kálmán, V.: Controlled braking for omnidirectional wheels. Int. J. Control Sci. Eng. 3, 48–57 (2013) Google Scholar
  6. 6.
    Tobolár, J., Herrmann, F., Bünte, T.: Object-oriented modelling and control of vehicles with omni-directional wheels. In: Computational Mechanics (2009) Google Scholar
  7. 7.
    Kosenko, I.I.: Physically oriented approach to construct multibody system dynamics models using modelica language. In: Proc. of Multibody 2007, Multibody Dynamics 2007. An ECCOMAS Thematic Conference. Politecnico di Milano, Milano, Italy (2007), 20 pp. Google Scholar
  8. 8.
    Awrejcewicz, J.: Nonlinear Dynamics of a Wheeled Vehicle. Springer, Berlin (2005) zbMATHGoogle Scholar
  9. 9.
    Leine, R.I., van de Wouw, N.: Stability and Convergence of Mechanical Systems with Unilateral Constraints. Springer, Berlin (2008) CrossRefzbMATHGoogle Scholar
  10. 10.
    Awrejcewicz, J., Kudra, G., Lamarque, C.-H.: Dynamics investigation of three coupled rods with a horizontal barrier. Meccanica 38, 687–698 (2003) MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Awrejcewicz, J., Kudra, G., Lamarque, C.-H.: Investigation of triple pendulum with impacts using fundamental solution matrices. Int. J. Bifurc. Chaos 14, 4191–4213 (2004) MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Awrejcewicz, J., Kudra, G.: The piston-connecting Rod–Crankshaft system as a triple physical pendulum with impacts. Int. J. Bifurc. Chaos 15, 2207–2226 (2005) CrossRefGoogle Scholar
  13. 13.
    Kossenko, I.I.: Implementation of unilateral multibody dynamics on modelica. In: Proceedings of the 4th International Modelica Conference, Hamburg–Harburg, Germany, March 7–8, 2005, pp. 13–23 (2005) Google Scholar
  14. 14.
    Kudra, G., Awrejcewicz, J.: Tangens hyperbolicus approximations of the spatial model of friction coupled with rolling resistance. Int. J. Bifurc. Chaos 21, 2905–2917 (2011) CrossRefzbMATHGoogle Scholar
  15. 15.
    Kudra, G., Awrejcewicz, J.: Bifurcational dynamics of a two-dimensional stick–slip system. Differ. Equ. Dyn. Syst. 20, 301–322 (2012) MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kosenko, I.I., Aleksandrov, E.B.: Implementation of the Contensou–Erismann tangent forces model in the Hertz contact problem. Multibody Syst. Dyn. 24, 281–301 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Novozhilov, I.V.: Fractional Analysis: Methods of Motion Decomposition. Birkhauser, Boston (1997) zbMATHGoogle Scholar
  18. 18.
    Kosenko, I.I.: Integration of the equations of the rotational motion of a rigid body in the quaternion algebra. The Euler case. J. Appl. Math. Mech. 62, 193–200 (1998) MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Borisov, A.V., Kilin, A.A., Mamaev, I.S.: Dynamics and control of an omniwheel vehicle. Regul. Chaotic Dyn. 20, 153–172 (2015) MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Moscow Aviation Institute (National Research University)MoscowRussia
  2. 2.Dorodnicyn Computing Centre of Russian Academy of SciencesMoscowRussia
  3. 3.Lomonosov Moscow State UniversityMoscowRussia

Personalised recommendations