Previous |  Up |  Next


Title: Smooth super twisting sliding mode based steering control for nonholonomic systems transformable into chained form (English)
Author: Abbasi, Waseem
Author: ur Rehman, Fazal
Author: Shah, Ibrahim
Language: English
Journal: Kybernetika
ISSN: 0023-5954 (print)
ISSN: 1805-949X (online)
Volume: 54
Issue: 3
Year: 2018
Pages: 476-495
Summary lang: English
Category: math
Summary: In this article, a new solution to the steering control problem of nonholonomic systems, which are transformable into chained form is investigated. A smooth super twisting sliding mode control technique is used to steer nonholonomic systems. Firstly, the nonholonomic system is transformed into a chained form system, which is further decomposed into two subsystems. Secondly, the second subsystem is steered to the origin by using smooth super twisting sliding mode control. Finally, the first subsystem is steered to zero using signum function. The proposed method is tested on three nonholonomic systems, which are transformable into chained form; a two-wheel car model, a model of front-wheel car, and a fire truck model. Numerical computer simulations show the effectiveness of the proposed method when applied to chained form nonholonomic systems. (English)
Keyword: nonholonomic mechanical systems
Keyword: chained form
Keyword: steering control
Keyword: smooth super twisting sliding mode control and lyapunov function.
MSC: 70Q05
MSC: 93C85
idZBL: Zbl 06987018
idMR: MR3844828
DOI: 10.14736/kyb-2018-3-0476
Date available: 2018-11-02T10:08:22Z
Last updated: 2020-01-05
Stable URL:
Reference: [1] Abbassi, W., Rehman, F.: Adaptive integral sliding mode stabilization of nonholonomic drift-free systems..Math. Problems Engrg. 2016 (2016), 1-11. MR 3576111, 10.1155/2016/9617283
Reference: [2] Ge, S. sam, Wang, J., Lee, T. heng, Zhou, GY.: Adaptive robust stabilization of dynamic nonholonomic chained systems..J. Field Robotics 18 (2001), 3, 119-133. 10.1002/rob.1010.abs
Reference: [3] Kolmanovsky, I., McClamroch, N. H.: Developments in nonholonomic control problems..IEEE Control Systems 15 (1995), 6, 20-36. 10.1109/37.476384
Reference: [4] Levant, A.: Higher-order sliding modes, differentiation and output-feedback control..Int, J. Control 76 (2003), 9-10, 924-941. Zbl 1049.93014, MR 1999375, 10.1080/0020717031000099029
Reference: [5] Zhen-Ying, L., Wang, C-Li.: Robust stabilization of nonholonomic chained form systems with uncertainties..Acta Automat. Sinica 37 (2011), 2, 129-142. MR 2848489, 10.3724/sp.j.1004.2011.00129
Reference: [6] Li, P., Zheng, Z.: Global finite-time stabilization of planar nonlinear systems with disturbance..Asian J. Control 14 (2012), 3, 851-858. MR 2926015, 10.1002/asjc.377
Reference: [7] Li, Z., Xiao, H., Yang, C., Zhao, Y.: Model predictive control of nonholonomic chained systems using general projection neural networks optimization..IEEE Trans. Systems Man Cybernetics: Systems 45 (2015), 10, 1313-1321. 10.1109/tsmc.2015.2398833
Reference: [8] Luque-Vega, L., Castillo-Toledo, B., Loukianov, A. G.: Robust block second order sliding mode control for a quadrotor..J. Franklin Inst. 349 (2012), 2, 719-739. MR 2890423, 10.1016/j.jfranklin.2011.10.017
Reference: [9] Mobayen, S.: Fast terminal sliding mode tracking of non-holonomic systems with exponential decay rate..IET Control Theory Appl. 9 (2015), 8, 1294-1301. MR 3364614, 10.1049/iet-cta.2014.1118
Reference: [10] Mobayen, S.: Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method..Nonlinear Dynamics 80 (2015), 1-2, 669-683. MR 3324289, 10.1007/s11071-015-1897-4
Reference: [11] Mobayen, S., Baleanu, D.: Linear matrix inequalities design approach for robust stabilization of uncertain nonlinear systems with perturbation based on optimally-tuned global sliding mode control..J. Vibration Control 23, (2017), 8, 1285-1295. MR 3635449, 10.1177/1077546315592516
Reference: [12] Moreno, J. A., Osorio, M.: A Lyapunov approach to second-order sliding mode controllers and observers..In: Proc. 47th IEEE Conference on Decision and Control 2008, pp. 2856-2861
Reference: [13] Moreno, J. A., Osorio, M.: Strict Lyapunov functions for the super-twisting algorithm..IEEE Trans. Automat. Control 57 (2012), 4, 1035-1040. MR 2952337, 10.1109/tac.2012.2186179
Reference: [14] Murray, R. M., Sastry, S. S.: Steering nonholonomic systems in chained form..In: Proc. 30th IEEE Conference on Decision and Control 2 (1991), pp. 1121-1126. MR 1224308, 10.1109/cdc.1991.261508
Reference: [15] Nagesh, I., Edwards, C.: A multivariable super-twisting sliding mode approachtor: A field-oriented control approach..Automatica 50 (2014), 3, 984-988. MR 3174001, 10.1016/j.automatica.2013.12.032
Reference: [16] Picó, J., Picó-Marco, E., Vignoni, A., Battista, H. De: Stability preserving maps for finite-time convergence: super-twisting sliding-mode algorithm..Automatica 49 (2013), 2, 534-539. MR 3004721, 10.1016/j.automatica.2012.11.022
Reference: [17] Rehman, F.: Feedback stabilization of nonholonomic control systems using model decomposition..Asian J. Control 7, (2005), 3, 256-265. 10.1111/j.1934-6093.2005.tb00235.x
Reference: [18] Shtessel, Y. B., Shkolnikov, I. A., Levant, A.: Smooth second-order sliding modes: Missile guidance application..Automatica 43 (2007), 8, 1470-1476. MR 2320533, 10.1016/j.automatica.2007.01.008
Reference: [19] Sordalen, O. J., Egeland, O.: Exponential stabilization of nonholonomic chained systems..IEEE Trans. Automat. Control 40 (1995), 1, 35-49. MR 1344316, 10.1109/9.362901
Reference: [20] Wang, Y., Miao, Z., Zhong, H., Pan, Qi.: Simultaneous stabilization and tracking of nonholonomic mobile robots: A Lyapunov-based approach..IEEE Trans. Control Systems Technol. 23 (2015), 4, 1440-1450. 10.1109/tcst.2014.2375812
Reference: [21] Utkin, V., Guldner, J., Shi, J., Ge, S., Lewis, F.: Sliding Mode Control in Electro-mechanical Systems..Second Edition. Boca Raton: CRC Press, 2009. 10.1201/9781420065619


Files Size Format View
Kybernetika_54-2018-3_4.pdf 1.533Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo