 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10482 |
| In Russian (ÏÌÌ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.A. Zobova and Ya.V. Tatarinov, "The dynamics of an omni-mobile vehicle," J. Appl. Math. Mech. 73 (1), 8-15 (2009) |
| Year |
2009 |
Volume |
73 |
Issue |
1 |
Pages |
8-15 |
| Title |
The dynamics of an omni-mobile vehicle |
| Author(s) |
A.A. Zobova (Moscow, Russia, azobova@mail.ru)
Ya.V. Tatarinov (Moscow, Russia) |
| Abstract |
The motion of an omni-mobile vehicle on a horizontal plane is considered. The wheels are modelled by absolutely rigid discs. Slippage in a certain direction, which makes a constant non- zero angle with the plane of a disc, is possible at the contact point of a wheel and the plane, and the planes of the discs are fixed with respect to the platform of the vehicle. The dynamic equations of motion are obtained for vehicles of this type with an arbitrary number and arrangement of the wheels. A complete qualitative description of the inertial motion of a vehicle is given (there are no control actions and it is assumed that there is no friction in the axes). The result is presented in the form of a phase portrait of the system. The motion of a vehicle is then considered in the case when control moments are applied to the axes of the wheels. The stability and branching of a certain class of steady motions of the vehicle are investigated. The domain of parameters is separated out where Andronov-Hopf bifurcation occurs with the formation of unstable limit cycles. |
| References |
| 1. | R.L. Williams II, B.E. Carter, P. Gallina and G. Rosati, Dynamic model with slip for wheeled omni-directional robots, IEEE Trans Robotics and Automation 18 (3) (2002), pp. 285–293. |
| 2. | M. Ashmore and N. Barnes, Omni-drive robot motion on curved paths: the fastest path between two points is not a straight line, Proc. 15th Australian Joint Conf. on Artificial Intelligence (2002), pp. 225–236. |
| 3. | Yu.G. Martynenko and A.M. Formal'skii, The motion of a mobile robot with roller-carrying wheels, Izv Ross Akad Nauk Theory and Control Systems 6 (2007), pp. 142–149. |
| 4. | Ya.V Tatarinov, The equations of classical mechanics in a new form, Vestnik MGU Ser 1 Matematika Mekhanika 3 (2003), pp. 67–76. |
| 5. | Tatarinov Ya.V. The Equations of Classical Mechanics in Concise Forms. Moscow: Izd Tsentra Prikladnykh Issledovanii pri Mekhaniko-Matematicheskom Fakul’tete MGU (Publishing House of the Centre for Applied Research at the Mechanical-Mathematical Faculty of MGU); 2005. |
| 6. | V.M. Budanov and Ye.A. Devyanin, The motion of wheeled robots, Prikl Mat Mekh 67 (2) (2003), pp. 244–255. |
| 7. | A.V. Karapetyan and M.A. Salmina, Poincaré-Chetayev and Andronov-Hopf bifurcations in the dynamics of a three-wheeled robot, Vestnik MGU Ser 1 Matematika Mekhanika 2 (2006), pp. 56–59. |
| 8. | N.N. Bautin, The Behaviour of Dynamical Systems Close to the Boundaries of the Instability Domain, Nauka, Moscow (1984). |
|
| Received |
15 January 2008 |
| Link to Fulltext |
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