On the motion of a symmetrical vehicle with omniwheels with massive rollers.

*(English. Russian original)*Zbl 07309352
Mech. Solids 53, Suppl. 2, 32-42 (2018); translation from Prikl. Mat. Mekh. 82, No. 4, 427-440 (2018).

Summary: 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.

##### MSC:

70E18 | Motion of a rigid body in contact with a solid surface |

70E55 | Dynamics of multibody systems |

70F25 | Nonholonomic systems related to the dynamics of a system of particles |

##### Keywords:

omniwheel; massive rollers; nonholonomic constraint; laconic form of Ya. V. Tatarinov’s equations of motion
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\textit{K. V. Gerasimov} and \textit{A. A. Zobova}, Mech. Solids 53, 32--42 (2018; Zbl 07309352); translation from Prikl. Mat. Mekh. 82, No. 4, 427--440 (2018)

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##### References:

[1] | Gfrerrer, A., Geometry and kinematics of the Mecanum wheel, Comput. Aided Geom. Des., 25, 784-791 (2008) · Zbl 1172.70301 |

[2] | Zobova, A. A.; Tatarinov, Ya. V., Motion dynamics for a vehicle with three ring wheels: Mathematical aspects, Mobil’nye roboty i mekhatronnye sistemy, 61-67 (2006), Moscow State Univ.: Moscow, Moscow State Univ. |

[3] | Martynenko, Yu. G.; Formal’Skii, A. M., On the motion of a mobile robot with roller-carrying wheels, J. Comput. Syst. Sci. Int., 46, 6, 976-983 (2007) · Zbl 1294.93060 |

[4] | Zobova, A. A.; Tatarinov, Ya. V., Free and controlled motions of an omni-wheel vehicle, Moscow Univ. Mech. Bull., 63, 6, 146-151 (2008) |

[5] | Zobova, A. A.; Tatarinov, Ya. V., The dynamics of an omni-mobile vehicle, J. Appl. Math. Mech. (Engl. Transl.), 73, 1, 8-15 (2009) · Zbl 1189.70020 |

[6] | 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.), 74, 4, 436-442 (2010) · Zbl 1272.70047 |

[7] | Borisov, A. V.; Kilin, A. A.; Mamaev, I. S., An omni-wheel vehicle on a plane and a sphere, Rus. J. Nonlinear Dyn., 7, 4, 785-801 (2011) |

[8] | Williams, R. L.; Carter, B. E.; Gallina, P.; Rosati, G., Dynamic model with slip for wheeled omnidirectional robots, IEEE Trans. Rob. Autom., 18, 3, 285-293 (2002) |

[9] | Ashmore, M.; Barnes, N., Omni-drive robot motion on curved paths: the fastest path between two points is not a straight-line, Lecture Notes in Computer Science, 226-236 (2002), Springer: Berlin, Heidelberg, Springer · Zbl 1032.68774 |

[10] | Tobolar, J.; Herrmann, F.; Bunte, T., Object-oriented modelling and control of vehicles with omni-directional wheels, Proc. Conference “Computational Mechanics,” Hrad Nectiny (2009) |

[11] | Kosenko, I.; Gerasimov, K., Physically oriented simulation of the omni-vehicle dynamics, Rus. J. Nonlinear Dyn., 12, 2, 251-262 (2016) · Zbl 1372.70021 |

[12] | Tatarinov, Ya. V., Classical mechanics equations in new form, Vestn. Mosk. Univ., Ser. 1: Mat., Mech., 3, 67-76 (2003) · Zbl 1101.70305 |

[13] | Zobova, A. A., Application of laconic forms of the equations of motion in the dynamics of nonholonomic mobile robots, Rus. J. Nonlinear Dyn., 7, 4, 771-783 (2011) |

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