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Mekhatronika, Avtomatizatsiya, Upravlenie, 2018, vol. 19, no. 5, pp. 327—330
DOI: 10.17587/mau.19.327-330
**Mathematical Model of a Robot with Omni-Wheels Located at the Vertices of the Right Triangle**
**E. Y. Kolesnichenko**, __decstrela@mail.ru__, **V. E. Pavlovsky**, __vlpavl@mail.ru__, Keldysh Institute of Applied Mathematics Russian Academy of Sciences, Moscow, 125047, Russian Federation, **I. A. Orlov,** __i.orlov@imash.ru__, **A. P. Aliseychik**, __aliseychik@imash.ru__, Mechanical Engineering Research Institute of the Russian Academy of Sciences, Moscow, 101990, Russian Federation,** D. A. Gribkov, **__legovas@gmail.com__,** A. V. Podoprosvetov**, __llecxis@gmail.com__, M. V. Lomonosov Moscow State University, Moscow, 119991, Russian Federation
Corresponding author: **Pavlovsky Vladimir E.,** Dr. Sc. in Physics and Mathematics, Professor, Chief Researcher, Head of Laboratory "Intelligence and mechatronics", Keldysh Institute of Applied Mathematics (Russian Academy of Sciences), Moscow, 125047, Russian Federation, e-mail: __vlpavl@mail.ru__, __www.keldysh.ru__
Accepted on August 07, 2017
The article deals with control of a robot with three omni-wheels. The feature of this robot is the triangular platform with a right angle. The steering function is of special interest of the paper. The explicit formulae of moments applied to the wheels are obtained for the robot's movement along a specified trajectory for two particular cases. The first is forward motion, when the robot does not turn during the movement. The second is the tangential movement to the selected curvilinear trajectory, when the robot rotates according to the curvature of the trajectory. The purpose of the study is as follows. A group of described robots can implement a transport system with a different configuration of a common transport platform, for this, the robots connecte by the sides (ribs) of their bodies. In order to form a common platform — for example, a rectangle, or a rhombus, and it is required that the body of the robot agent has a right angle. We note here that, from a general point of view, the problem of connecting triangles to a common given figure (corresponding to transporting thing) is the task of tiling the plane, or part of the plane, with a repeating "pattern" [9], which is also called the tessellation, packing or the problem of parquet (see also [9, 10]). It is known that for triangular tiles this problem has a solution.
**Keywords:** omni-wheels, triangular platform, omni-directional movement, mobile robot, omni-robot control
**Acknowledgements.** This research is supported by RFBR (grants ¹ 15-08-08769-a, ¹ 16-01-00131-a, ¹ 16-08-00880-a, 16-29-04412-ofi_m) and RSF (grant ¹ 16-19-10705).
For citation:
**Kolesnichenko E. Y., Pavlovsky V. E., Orlov I. A., Aliseychik A. P., Gribkov D. A., Podoprosvetov A. V. **Mathematical Model of a Robot with Omni-Wheels Located at the Vertices of the Right Triangle,* Mekhatronika, Avtomatizatsiya, Upravlenie,* 2018, vol. 19, no. 5, pp. 327—330.
DOI: 10.17587/mau.19.327-330
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