Abstract
The dynamics of a symmetrical vehicle with omniwheels, moving along a fixed, absolutely rough horizontal plane, is considered, making the following assumptions: the mass of each roller is nonzero, there is a point contact between the rollers and the plane, and there is no slip. The equations of motion composed with the use of the Maxima symbolic computation system, contain additional terms, proportional to the axial moment of inertia of the roller and depending on angles of rotation of the wheels. The mass of the rollers is taken into account in those phases of motion when there is no change of rollers at the contact. The mass of rollers is considered to be negligible when wheels change from one roller to another. It is shown that a set of motions, existing in the inertialess model (i.e., the model that does not take into account mass of rollers), disappears, as well as its linear first integral. The main types of motion for a symmetrical three-wheeled vehicle, obtained by a numerical integration of equations of motion, are compared with results obtained on the basis of the inertialess model.
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References
Gfrerrer, A., Geometry and kinematics of the Mecanum wheel, Comput. Aided Geom. Des., 2008, vol. 25, pp. 784–791.
Zobova, A.A. and Tatarinov, Ya.V., Motion dynamics for a vehicle with three ring wheels: Mathematical aspects, in Mobil’nye roboty i mekhatronnye sistemy (Mobile Robots and Mechatronic Systems), Moscow: Moscow State Univ., 2006, pp. 61–67.
Martynenko, Yu.G. and Formal’skii, A.M., On the motion of a mobile robot with roller-carrying wheels, J. Comput. Syst. Sci. Int., 2007, vol. 46, no. 6, pp. 976–983.
Zobova, A.A. and Tatarinov, Ya.V., Free and controlled motions of an omni-wheel vehicle, Moscow Univ. Mech. Bull., 2008, vol. 63, no. 6, pp. 146–151.
Zobova, A.A. and Tatarinov, Ya.V., The dynamics of an omni-mobile vehicle, J. Appl. Math. Mech. (Engl. Transl.), 2009, vol. 73, no. 1, pp. 8–15.
Martynenko, Yu.G., Stability of steady motions of a mobile robot with roller-carrying wheels and a displaced center of mass, J. Appl. Math. Mech. (Engl. Transl.), 2010, vol. 74, no. 4, pp. 436–442.
Borisov, A.V., Kilin, A.A., and Mamaev, I.S., An omni-wheel vehicle on a plane and a sphere, Rus. J. Nonlinear Dyn., 2011, vol. 7, no. 4, pp. 785–801.
Williams, R.L., Carter, B.E., Gallina, P., and Rosati, G., Dynamic model with slip for wheeled omnidirectional robots, IEEE Trans. Rob. Autom., 2002, vol. 18, no. 3, pp. 285–293.
Ashmore, M. and Barnes, N., Omni-drive robot motion on curved paths: the fastest path between two points is not a straight-line, in Lecture Notes in Computer Science, Berlin, Heidelberg: Springer, 2002, pp. 226–236.
Tobolar, J., Herrmann, F., and Bunte, T., Object-oriented modelling and control of vehicles with omni-directional wheels, Proc. Conference “Computational Mechanics,” Hrad Nectiny, 2009.
Kosenko, I. and Gerasimov, K., Physically oriented simulation of the omni-vehicle dynamics, Rus. J. Nonlinear Dyn., 2016, vol. 12, no. 2, pp. 251–262.
Tatarinov, Ya.V., Classical mechanics equations in new form, Vestn. Mosk. Univ., Ser. 1: Mat., Mech., 2003, no. 3, pp. 67–76.
Zobova, A.A., Application of laconic forms of the equations of motion in the dynamics of nonholonomic mobile robots, Rus. J. Nonlinear Dyn., 2011, vol. 7, no. 4, pp. 771–783.
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Original Russian Text © K.V. Gerasimov, A.A. Zobova, 2018, published in Prikladnaya Matematika i Mekhanika, 2018, Vol. 82, No. 4, pp. 427–440.
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Gerasimov, K.V., Zobova, A.A. On the Motion of a Symmetrical Vehicle with Omniwheels with Massive Rollers. Mech. Solids 53 (Suppl 2), 32–42 (2018). https://doi.org/10.3103/S0025654418050060
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DOI: https://doi.org/10.3103/S0025654418050060