Abstract
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.
Similar content being viewed by others
References
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)
Blumrich, J.F.: Omnidirectional wheel. Technical report. US Patents and Trademarks office, Patent 3,789,947 (1974)
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)
Zobova, A.A., Tatarinov, Ya.V.: The dynamics of an omni-mobile vehicle. J. Appl. Math. Mech. 73, 8–15 (2009)
Kálmán, V.: Controlled braking for omnidirectional wheels. Int. J. Control Sci. Eng. 3, 48–57 (2013)
Tobolár, J., Herrmann, F., Bünte, T.: Object-oriented modelling and control of vehicles with omni-directional wheels. In: Computational Mechanics (2009)
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.
Awrejcewicz, J.: Nonlinear Dynamics of a Wheeled Vehicle. Springer, Berlin (2005)
Leine, R.I., van de Wouw, N.: Stability and Convergence of Mechanical Systems with Unilateral Constraints. Springer, Berlin (2008)
Awrejcewicz, J., Kudra, G., Lamarque, C.-H.: Dynamics investigation of three coupled rods with a horizontal barrier. Meccanica 38, 687–698 (2003)
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)
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)
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)
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)
Kudra, G., Awrejcewicz, J.: Bifurcational dynamics of a two-dimensional stick–slip system. Differ. Equ. Dyn. Syst. 20, 301–322 (2012)
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)
Novozhilov, I.V.: Fractional Analysis: Methods of Motion Decomposition. Birkhauser, Boston (1997)
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)
Borisov, A.V., Kilin, A.A., Mamaev, I.S.: Dynamics and control of an omniwheel vehicle. Regul. Chaotic Dyn. 20, 153–172 (2015)
Acknowledgements
The investigation was performed at MAI under financial support provided by RSF, project 14-21-00068.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kosenko, I.I., Stepanov, S.Y. & Gerasimov, K.V. Contact tracking algorithms in case of the omni-directional wheel rolling on the horizontal surface. Multibody Syst Dyn 45, 273–292 (2019). https://doi.org/10.1007/s11044-018-09649-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11044-018-09649-x