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Journal of Shanghai University >

2014 , Vol. 20 >Issue 4: 404 - 410

DOI: https://doi.org/10.3969/j.issn.1007-2861.2014.01.041

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Finite-Time Stabilization for a Class of Uncertain Nonholonomic Mobile Robots Based on Dynamic Feedback

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  • 1. Mathematics and Physics Department, Hohai University, Changzhou 213022, Jiangsu, China;
    2. College of IOT Engineering, Hohai University, Changzhou 213022, Jiangsu, China;
    3. School of Optical-Electrical and Computer Engineering, University of Shanghai for Science and
    Technology, Shanghai 200093, China

Received date: 2014-03-04

  Online published: 2014-08-25

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Abstract

This paper considers a finite-time stabilization problem for a class of uncertain nonholonomic mobile robots with dynamic inputs. Using input-state transformation, a three-input chained systems can be obtained. A discontinuous three-step switching controller is presented by applying the theory of finite-time stability and a new switching design algorithm, which can stabilize the closed-loop system to the original equilibrium point in a finite time interval. Simulation results show effectiveness of the proposed approach.

Key words： chained form system; dynamic feedback; finitetime stabilization; nonholonomic mobile robot; switching control

Cite this article

CHEN Hua1, CHEN Yi2, WANG Chao-li3, DU Qing-hui3, CHEN Jun-feng2 . Finite-Time Stabilization for a Class of Uncertain Nonholonomic Mobile Robots Based on Dynamic Feedback[J]. Journal of Shanghai University, 2014 , 20(4) : 404 -410 . DOI: 10.3969/j.issn.1007-2861.2014.01.041

References

[1] Brockett R W. Asymptotic stability and feedback stabilization [M]//Brockett R W, Millman R S, Sussmann H J, Eds. Differential geometric control theory. Virginia: Defense

Technical Information Center, 1983: 181-208.

[2] Murray R M, Sastry S S. Nonholonomic motion planning: steering using sinusoids [J]. IEEE Trans Automat Control, 1993, 38(5): 700-716.

[3] Tian Y P, Li S H. Exponential stabilization of nonholonomic dynamic systems by smooth timevarying control [J]. Automatica, 2002, 38(7): 1139-1146.

[4] Teel A, Murry R, Walsh G. Nonholonomic control systems: from steering to stabilization with sinusoids [C]//Proceedings of the 31st IEEE Conference on Decision Control. 1992: 1603-1609.
[5] Astolfi A. Discontinuous control of nonholonomic systems [J]. Syst Control Lett, 1996, 27(1): 37-45.

[6] Bloch A M, Drakunov S. Stabilization of a nonholonomic systems via sliding modes [C]//Proceedings of the 33rd IEEE Conference on Decision Control. 1994: 2961-2963.

[7] De Canudas W C, Szrdalen O J. Exponential stabilization of mobile robots with nonholonomic constraints [J]. IEEE Trans Automat Control, 1992, 37(11): 1791-1797.

[8] Sordalen O J, Egeland O. Exponential stabilization of nonholonomic chained systems [J]. IEEE Trans Automat Control, 1995, 40(1): 35-49.

[9] Soueres P, Balluchi A, Bicchi A. Optimal feedback control for line tracking with a boundedcurvature vehicle [J]. Int J Control, 2001, 74(10): 1009-1019.

[10] Hussein I I, Bloch A M. Optimal control of underactuated nonholonomic mechanical systems [J]. IEEE Trans Automat Control, 2008, 53(3): 668-682.

[11] Qu Z H, Wang J, Plaisted C E, et al. Global-stabilizing near-optimal control design for nonholonomic chained systems [J]. IEEE Trans Automat Control, 2006, 51(9): 1440-1456.

[12] Hong Y G, Wang J K, Xi Z R. Stabilization of uncertain chained form systems within finite settling time [J]. IEEE Trans Automat Control, 2005, 50(9): 1379-1384.

[13] 李世华, 田玉平. 移动小车的有限时间轨迹跟踪控制[J]. 东南大学学报: 自然科学版, 2004, 34(1): 113-116.

[14] Wu Y Q, Wang B, Zong G D. Finite-time tracking controller design for nonholonomic systems with extended chained form [J]. IEEE Transactions on Circuits and Systems-: Express Briefs, 2005, 52(11): 798-802.

[15] Campion G, Bastin G, D’andrca-Novel B. Structural properties and classification of kinematic and dynamic models of wheeled mobile robots [J]. IEEE Transactions on Robotics and Automation, 1996, 12(1): 47-62.

[16] 梁振英, 王朝立. 未校准视觉参数的非完整系统的鲁棒指数镇定[J]. 控制与决策, 2011, 26(7): 998-1003.

[17] Leroquais W, D’andrca-Novel B. Transformation of the kinematic models of restricted mobility wheeled mobile robots with a single platform into chain forms [C]//Proceedings of the 34th IEEE Conference on Decision Control. 1995: 3811-3816.

[18] 陈华, 王朝立, 杨芳, 等. 基于视觉伺服非完整移动机器人的有限时间饱和镇定[J]. 控制理论与应用, 2012, 29(6): 817-823.

[19] Qian C J, Li J. Global finite-time stabilization by output feedback for planar systems without observable linearization [J]. IEEE Trans Automat Control, 2005, 50(6): 885-890.

[20] 李世华, 丁世宏, 都海波, 等. 非光滑控制理论与应用[M]. 北京: 科学出版社, 2013: 123-125.

[21] Hong Y G. Finite-time stabilization and stabilizability of a class of controllable systems [J]. Systems and Control Letters, 2002, 46(4): 231-236.

[22] Huang X Q, Lin W, Yang B. Global finite-time stabilization of a class of uncertain nonlinear systems [J]. Automatica, 2005, 41(5): 881-888.
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