Smooth super twisting sliding mode based steering control for nonholonomic systems transformable into chained form

Waseem Abbasi; Fazal ur Rehman; Ibrahim Shah

Kybernetika (2018)

  • Volume: 54, Issue: 3, page 476-495
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Abbasi, Waseem, ur Rehman, Fazal, and Shah, Ibrahim. "Smooth super twisting sliding mode based steering control for nonholonomic systems transformable into chained form." Kybernetika 54.3 (2018): 476-495. <http://eudml.org/doc/294192>.

@article{Abbasi2018,
abstract = {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.},
author = {Abbasi, Waseem, ur Rehman, Fazal, Shah, Ibrahim},
journal = {Kybernetika},
keywords = {nonholonomic mechanical systems; chained form; steering control; smooth super twisting sliding mode control and lyapunov function},
language = {eng},
number = {3},
pages = {476-495},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Smooth super twisting sliding mode based steering control for nonholonomic systems transformable into chained form},
url = {http://eudml.org/doc/294192},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Abbasi, Waseem
AU - ur Rehman, Fazal
AU - Shah, Ibrahim
TI - Smooth super twisting sliding mode based steering control for nonholonomic systems transformable into chained form
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 3
SP - 476
EP - 495
AB - 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.
LA - eng
KW - nonholonomic mechanical systems; chained form; steering control; smooth super twisting sliding mode control and lyapunov function
UR - http://eudml.org/doc/294192
ER -

References

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  1. Abbassi, W., Rehman, F., 10.1155/2016/9617283, Math. Problems Engrg. 2016 (2016), 1-11. MR3576111DOI10.1155/2016/9617283
  2. Ge, S. sam, Wang, J., Lee, T. heng, Zhou, GY., 10.1002/rob.1010.abs, J. Field Robotics 18 (2001), 3, 119-133. DOI10.1002/rob.1010.abs
  3. Kolmanovsky, I., McClamroch, N. H., 10.1109/37.476384, IEEE Control Systems 15 (1995), 6, 20-36. DOI10.1109/37.476384
  4. Levant, A., 10.1080/0020717031000099029, Int, J. Control 76 (2003), 9-10, 924-941. Zbl1049.93014MR1999375DOI10.1080/0020717031000099029
  5. Zhen-Ying, L., Wang, C-Li., 10.3724/sp.j.1004.2011.00129, Acta Automat. Sinica 37 (2011), 2, 129-142. MR2848489DOI10.3724/sp.j.1004.2011.00129
  6. Li, P., Zheng, Z., 10.1002/asjc.377, Asian J. Control 14 (2012), 3, 851-858. MR2926015DOI10.1002/asjc.377
  7. Li, Z., Xiao, H., Yang, C., Zhao, Y., 10.1109/tsmc.2015.2398833, IEEE Trans. Systems Man Cybernetics: Systems 45 (2015), 10, 1313-1321. DOI10.1109/tsmc.2015.2398833
  8. Luque-Vega, L., Castillo-Toledo, B., Loukianov, A. G., 10.1016/j.jfranklin.2011.10.017, J. Franklin Inst. 349 (2012), 2, 719-739. MR2890423DOI10.1016/j.jfranklin.2011.10.017
  9. Mobayen, S., 10.1049/iet-cta.2014.1118, IET Control Theory Appl. 9 (2015), 8, 1294-1301. MR3364614DOI10.1049/iet-cta.2014.1118
  10. Mobayen, S., 10.1007/s11071-015-1897-4, Nonlinear Dynamics 80 (2015), 1-2, 669-683. MR3324289DOI10.1007/s11071-015-1897-4
  11. Mobayen, S., Baleanu, D., 10.1177/1077546315592516, J. Vibration Control 23, (2017), 8, 1285-1295. MR3635449DOI10.1177/1077546315592516
  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 
  13. Moreno, J. A., Osorio, M., 10.1109/tac.2012.2186179, IEEE Trans. Automat. Control 57 (2012), 4, 1035-1040. MR2952337DOI10.1109/tac.2012.2186179
  14. Murray, R. M., Sastry, S. S., 10.1109/cdc.1991.261508, In: Proc. 30th IEEE Conference on Decision and Control 2 (1991), pp. 1121-1126. MR1224308DOI10.1109/cdc.1991.261508
  15. Nagesh, I., Edwards, C., 10.1016/j.automatica.2013.12.032, Automatica 50 (2014), 3, 984-988. MR3174001DOI10.1016/j.automatica.2013.12.032
  16. Picó, J., Picó-Marco, E., Vignoni, A., Battista, H. De, 10.1016/j.automatica.2012.11.022, Automatica 49 (2013), 2, 534-539. MR3004721DOI10.1016/j.automatica.2012.11.022
  17. Rehman, F., 10.1111/j.1934-6093.2005.tb00235.x, Asian J. Control 7, (2005), 3, 256-265. DOI10.1111/j.1934-6093.2005.tb00235.x
  18. Shtessel, Y. B., Shkolnikov, I. A., Levant, A., 10.1016/j.automatica.2007.01.008, Automatica 43 (2007), 8, 1470-1476. MR2320533DOI10.1016/j.automatica.2007.01.008
  19. Sordalen, O. J., Egeland, O., 10.1109/9.362901, IEEE Trans. Automat. Control 40 (1995), 1, 35-49. MR1344316DOI10.1109/9.362901
  20. Wang, Y., Miao, Z., Zhong, H., Pan, Qi., 10.1109/tcst.2014.2375812, IEEE Trans. Control Systems Technol. 23 (2015), 4, 1440-1450. DOI10.1109/tcst.2014.2375812
  21. Utkin, V., Guldner, J., Shi, J., Ge, S., Lewis, F., 10.1201/9781420065619, Second Edition. Boca Raton: CRC Press, 2009. DOI10.1201/9781420065619

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