Geodesic
Qualitative Analysis of the Dynamics of a Trailed
Russian journal of nonlinear dynamics, Tome 17 (2021) no. 4, pp. 437-451.

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

This article examines the dynamics of the movement of a wheeled vehicle consisting of two links (trolleys). The trolleys are articulated by a frame. One wheel pair is fixed on each link. Periodic excitation is created in the system due to the movement of a pair of masses along the axis of the first trolley. The center of mass of the second link coincides with the geometric center of the wheelset. The center of mass of the first link can be shifted along the axis relative to the geometric center of the wheelset. The movement of point masses does not change the center of mass of the trolley itself. Based on the joint solution of the Lagrange equations of motion with undetermined multipliers and time derivatives of nonholonomic coupling equations, a reduced system of differential equations is obtained, which is generally nonautonomous. A qualitative analysis of the dynamics of the system is carried out in the absence of periodic excitation and in the presence of periodic excitation. The article proves the boundedness of the solutions of the system under study, which gives the boundedness of the linear and angular velocities of the driving link of the articulated wheeled vehicle. Based on the numerical solution of the equations of motion, graphs of the desired mechanical parameters and the trajectory of motion are constructed. In the case of an unbiased center of mass, the solutions of the system can be periodic, quasi-periodic and asymptotic. In the case of a displaced center of mass, the system has asymptotic dynamics and the mobile transport system goes into rectilinear uniform motion.
Keywords: trailed wheeled vehicle, nonholonomic problem, qualitative analysis, periodic excitation, time-dependent dynamic system, stability. 
@article{ND_2021_17_4_a5,
     author = {E. A. Mikishanina},
     title = {Qualitative {Analysis} of the {Dynamics} of a {Trailed}},
     journal = {Russian journal of nonlinear dynamics},
     pages = {437--451},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ND_2021_17_4_a5/}
}
TY  - JOUR
AU  - E. A. Mikishanina
TI  - Qualitative Analysis of the Dynamics of a Trailed
JO  - Russian journal of nonlinear dynamics
PY  - 2021
SP  - 437
EP  - 451
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2021_17_4_a5/
LA  - en
ID  - ND_2021_17_4_a5
ER  - 
%0 Journal Article
%A E. A. Mikishanina
%T Qualitative Analysis of the Dynamics of a Trailed
%J Russian journal of nonlinear dynamics
%D 2021
%P 437-451
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2021_17_4_a5/
%G en
%F ND_2021_17_4_a5
E. A. Mikishanina. Qualitative Analysis of the Dynamics of a Trailed. Russian journal of nonlinear dynamics, Tome 17 (2021) no. 4, pp. 437-451. http://geodesic.mathdoc.fr/item/ND_2021_17_4_a5/

[1] Borisov, A. V., Kilin, A. A., and Mamaev, I. S., “Invariant Submanifolds of Genus $5$ and a Cantor Staircase in the Nonholonomic Model of a Snakeboard”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 29:3 (2019), 1930008, 19 pp. | DOI | MR | Zbl

[2] Pavlovsky, V. E. and Petrovskaya, N. V., Investigation of the Dynamics of Movement of the Chain “Robopoezd”: Methods of Planning of Movement, Preprint No. 121, KIAM, Moscow, 2005, 31 pp. (Russian)

[3] Bravo-Doddoli, A. and García-Naranjo, L. C., “The Dynamics of an Articulated $n$-Trailer Vehicle”, Regul. Chaotic Dyn., 20:5 (2015), 497–517 | DOI | MR | Zbl

[4] Bizyaev, I. A., Borisov, A. V., and Mamaev, I. S., “Exotic Dynamics of Nonholonomic Roller Racer with Periodic Control”, Regul. Chaotic Dyn., 23:7–8 (2018), 983–994 | DOI | MR | Zbl

[5] de Wit, C. C., NDoudi-Likoho, A. D., and Micaelli, A., “Nonlinear Control for a Train-Like Vehicle”, Int. J. Robot. Res., 16:3 (1997), 300–319 | DOI

[6] Yu, W., Chuy, O. Y., Collins, E. G., and Hollis, P., “Analysis and Experimental Verification for Dynamic Modeling of a Skid-Steered Wheeled Vehicle”, IEEE Trans. on Robotics, 26:2 (2010), 340–353 | DOI

[7] Rocard, Y., L'instabilité en mécanique: Automobiles, avions, ponts suspendus, Masson, Paris, 1954, 239 pp.

[8] Stückler, B., “Über die Differentialgleichungen für die Bewegung eines idealisierten Kraftwagens”, Arch. Appl. Mech., 20:5 (1952), 337–356

[9] Stückler, B., “Über die Berechnung der an rollenden Fahrzeugen wirkenden Haftreibungen”, Arch. Appl. Mech., 23:4 (1955), 279–287

[10] Lobas, L. G., Nonholonomic Models of Vehicles, Naukova Dumka, Kiev, 1986, 232 pp. (Russian) | MR | Zbl

[11] Martynyuk, A. A., Lobas, L. G., and Nikitina, N. V., Dynamics and Stability of the Movement of Wheeled Transport Vehicles, Tekhnika, Kiev, 1981, 224 pp. (Russian)

[12] Krishnaprasad, P. S. and Tsakiris, D. P., “Oscillations, $\mathop{\rm SE}(2)$-Snakes and Motion Control: A Study of the Roller Racer”, Dyn. Syst., 16:4 (2001), 347–397 | DOI | MR | Zbl

[13] Khalil, H. K., Nonlinear Systems, 3rd ed., Prentice Hall, Upper Saddle River, N.J., 2002, 750 pp. | Zbl

[14] Bakhvalov, N. S., Zhidkov, N. P., and Kobelkov, G. M., Numerical Methods, 6th ed., Binom, Moscow, 2008, 636 pp. (Russian) | MR

[15] Tilbury, D., Murray, R. M., and Sastry, S. Sh., “Trajectory Generation for the $n$-Trailer Problem Using Goursat Normal Form”, IEEE Trans. Automat. Control, 40:5 (1995), 802–819 | DOI | MR | Zbl

[16] Alipour, K., Robat, A., and Tarvirdizadeh, B., “Dynamics Modeling and Sliding Mode Control of Tractor-Trailer Wheeled Mobile Robots Subject to Wheels Slip”, Mech. Mach. Theory, 138 (2019), 16–37 | DOI

[17] Borisov, A. V., Mikishanina, E. A., and Sokolov, S. V., “Dynamics of Multi-Link Uncontrolled Wheeled Vehicle”, Russ. J. Math. Phys., 27:4 (2020), 433–445 | DOI | MR | Zbl

[18] Mikishanina, E. A., “Dynamics of a Controlled Articulated $n$-Trailer Wheeled Vehicle”, Russian J. Nonlinear Dyn., 17:1 (2021), 39–48 | MR | Zbl

[19] Bizyaev, I. A., Borisov, A. V., and Kuznetsov, S. P., “The Chaplygin Sleigh with Friction Moving due to Periodic Oscillations of an Internal Mass”, Nonlinear Dyn., 95:1 (2019), 699–714 | DOI

[20] Bizyaev, I. A., “A Chaplygin Sleigh with a Moving Point Mass”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017), 583–589 (Russian) | DOI | MR | Zbl

[21] Bloch, A. M., Nonholonomic Mechanics and Control, Interdiscip. Appl. Math., 24, 2nd ed., Springer, New York, 2015, xxi+565 pp. | DOI | MR | Zbl

[22] Yefremov, K. S., Ivanova, T. B., Kilin, A. A., and Karavaev, Yu. L., “Theoretical and Experimental Investigation of the Controlled Motion of the Roller Racer”, Proc. of the IEEE Internat. Conf. “Nonlinearity, Information and Robotics” (Innopolis, Russia, 2020), 5 pp.

[23] Bizyaev, I. A., “The Inertial Motion of a Roller Racer”, Regul. Chaotic Dyn., 22:3 (2017), 239–247 | DOI | MR | Zbl

[24] Borisov, A. V., Kilin, A. A., Mamaev, I. S., and Bizyaev, I. A., Selected Problems of Nonholonomic Mechanics, R Dynamics, Institute of Computer Science, Izhevsk, 2016, 882 pp. (Russian) | MR

[25] Borisov, A. V. and Mamaev, I. S., “An Inhomogeneous Chaplygin Sleigh”, Regul. Chaotic Dyn., 22:4 (2017), 435–447 | DOI | MR | Zbl

[26] Bizyaev, I. A., Borisov, A. V., and Mamaev, I. S., “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975 | DOI | MR | Zbl