Geodesic
Robust trajectory tracking control of omni-mobile robot with slipping of the wheels
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 1, pp. 13-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we consider the problem of constructing a robust controller to track the trajectory of a mobile robot with three omni-wheels moving on a horizontal surface. A dynamic model of the robot has been constructed such that the center of mass of the circular platform is offset from its geometric center and the wheel slippage occurs during braking. The motion control of the wheeled robot is carried out by using three independent DC motors. The torques developed by the engines are linear with respect to voltage supplied to the engine and to angular velocity of the rotor. Basing on the Lyapunov function method we construct a bounded controller without velocity measurement that solves the robust trajectory tracking problem. This means that for all initial deviations the robot's trajectory falls into a given neighborhood of the tracked trajectory after some time and remains there forever. Theorem on an ultimate boundedness of a closed system is proved. The results of numerical simulation are presented confirming the effectiveness of the proposed controller.
Keywords: wheeled mobile robot, omni-wheel, slipping, trajectory tracking control, Lyapunov function, dynamical model. 
@article{SVMO_2019_21_1_a0,
     author = {A. S. Andreev and O. A. Peregudova},
     title = {Robust trajectory tracking control of omni-mobile robot with slipping of the wheels},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {13--23},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2019_21_1_a0/}
}
TY  - JOUR
AU  - A. S. Andreev
AU  - O. A. Peregudova
TI  - Robust trajectory tracking control of omni-mobile robot with slipping of the wheels
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2019
SP  - 13
EP  - 23
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2019_21_1_a0/
LA  - ru
ID  - SVMO_2019_21_1_a0
ER  - 
%0 Journal Article
%A A. S. Andreev
%A O. A. Peregudova
%T Robust trajectory tracking control of omni-mobile robot with slipping of the wheels
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2019
%P 13-23
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2019_21_1_a0/
%G ru
%F SVMO_2019_21_1_a0
A. S. Andreev; O. A. Peregudova. Robust trajectory tracking control of omni-mobile robot with slipping of the wheels. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 21 (2019) no. 1, pp. 13-23. http://geodesic.mathdoc.fr/item/SVMO_2019_21_1_a0/

[1] Yu. G. Martynenko, A. M. Formalskii, “On the motion of a mobile robot with roller-carrying wheels”, Journal of Computer and Systems Sciences International, 46:6 (2007), 976–983 (In Russ.) | Zbl

[2] Ju. G. Martynenko, “Stability of steady motions of mobile robot with omniwheels and displacement of the center of mass”, Journal of Applied Mathematics and Mechanics, 74:4 (2010), 436–442 (In Russ.) | Zbl

[3] A. A. Zobova, Ja. V. Tatarinov, “The dynamics of an omni-mobile vehicle”, Journal of Applied Mathematics and Mechanics, 73:1 (2009), 8–15 (In Russ.) | MR | Zbl

[4] A. A. Zobova, K. V. Gerasimov, “The movement of a symmetric carriage on omni-wheels with massive rollers”, Applied Mathematics and Mechanics, 82:4 (2018), 427–440 (In Russ.)

[5] A. V. Borisov, A. A. Kilin, I. S. Mamaev, “An omni-wheel vehicle on a plane and a sphere”, Nonlinear Dynamics and Mobile Robotics, 1:1 (2013), 33 (In Russ.)

[6] Ju. L. Karavaev, S. A. Trefilov, “Deviation based discrete control algorithm for omni-wheeled mobile robot”, Nelineynaya Dinamika, 9:1 (2013), 91–100 (In Russ.) | MR

[7] A. A. Kilin, Ju. L. Karavaev, A. V. Klekovkin, “Kinematic control of a high manoeuvrable mobile spherical robot with internal omni-wheeled platform”, Nelineynaya Dinamika, 10:1 (2014), 113–126 (In Russ.) | Zbl

[8] A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Dynamics and control of an omniwheel vehicle”, Regular and Chaotic Dynamics, 20 (2015), 153–-172 | DOI | MR | Zbl

[9] Y. Liu, J. J. Zhu, R. L. Williams, J. Wu, “Omni-directional mobile robot controller based on trajectory linearization”, Robotics and Autonomous Systems, 56 (2008), 461–479 | DOI

[10] H. C. Huang, C. C. Tsai, “Adaptive trajectory tracking and stabilization for omnidirectional mobile robot with dynamic effect and uncertainties”, Proc. of the 17th World Congress The International Federation of Automatic Control (Seoul, Korea, July 6–11, 2008), 2008, 5383–5388

[11] A. S. Andreyev, O. A. Peregudova, “The motion control of a wheeled mobile robot”, Journal of Applied Mathematics and Mechanics, 79:4 (2015), 316–324 | DOI

[12] A. S. Andreyev, O. A. Peregudova, “Nonlinear controllers in the regulation problem of the robots”, IFAC Papers-OnLine, 51:4 (2018), 7–12 | DOI

[13] S. J. C. Lins Barreto, A. G. Scolari Conceicao, C. E. T. Dorea, L. Martinez, E. R. De Pieri, “Design and implementation of model-predictive control with friction compensation on an omnidirectional mobile robot”, IEEE-ASME Transactions on Mechatronics, 19:2 (2014), 467–476 | DOI

[14] Y. Huang, Q. Cao, C. Leng, “The path-tracking controller based on dynamic model with slip for one four-wheeled OMR”, Industrial Robot: An International Journal, 37:2 (2010), 193–201 | DOI

[15] D. Stonier, S.-H. Cho, S.-L. Choi, N.-S. Kuppuswamy, J.-H. Kim, “Nonlinera slip dynamics for a omniwheel mobile robot platform”, IEEE International Conference on Robotics and Automation (Roma, Italy, April 10–14, 2007), 2007, 2367–2372 | DOI