Fast terminal sliding mode tracking of non-holonomic systems with exponential decay rate

In this study, a recursive singularity-free, fast terminal sliding mode control method, which is able to avoid the possible singularity during the control phase, is applied for a finite-time tracking control of a class of non-holonomic systems. The reaching control law is proposed to guarantee the existence of the sliding mode around the fast terminal sliding surface and zero-tracking errors are achieved in finite time with an exponential decay rate. Simulation results are illustrated on three benchmark examples of chained-form non-holonomic systems: a wheeled mobile robot, an under-actuated rigid body and a front-wheel-drive car. The results demonstrate that the proposed control law achieves favourable tracking performance for non-holonomic systems.

[1]  E. Ryan.  On Brockett's Condition for Smooth Stabilizability and its Necessity in a Context of Nonsmooth Feedback , 1994 .

[2]  Shihua Li,et al.  Finite-time tracking control of multiple nonholonomic mobile robots , 2012, J. Frankl. Inst..

[3]  Francesc Guinjoan,et al.  Maximum power point tracking based on slidingmode control for output-series connected converters in photovoltaic systems , 2014 .

[4]  Yuqiang Wu,et al.  State-feedback stabilisation for stochastic non-holonomic systems with time-varying delays , 2012 .

[5]  Jun Fu,et al.  Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping , 2013, Autom..

[6]  Xinghuo Yu,et al.  Terminal sliding mode control design for uncertain dynamic systems , 1998 .

[7]  Wei Xing Zheng,et al.  New approach to second-order sliding mode control design , 2013 .

[8]  Krzysztof Tchon,et al.  Constrained motion planning of nonholonomic systems , 2011, Syst. Control. Lett..

[9]  Chian-Song Chiu,et al.  Derivative and integral terminal sliding mode control for a class of MIMO nonlinear systems , 2012, Autom..

[10]  Liang Yang,et al.  Nonsingular fast terminal sliding‐mode control for nonlinear dynamical systems , 2011 .

[11]  Zhen-Ying Liang,et al.  Robust Stabilization of Nonholonomic Chained Form Systems with Uncertainties: Robust Stabilization of Nonholonomic Chained Form Systems with Uncertainties , 2011 .

[12]  Alireza Mohammad Shahri,et al.  Adaptive robust time-varying control of uncertain non-holonomic robotic systems , 2012 .

[13]  Shuzhi Sam Ge,et al.  Robust adaptive neuro-fuzzy control of uncertain nonholonomic systems , 2004, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004..

[14]  Xinghuo Yu,et al.  Fast terminal sliding-mode control design for nonlinear dynamical systems , 2002 .

[15]  Vahid Johari Majd,et al.  An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems , 2012, Math. Comput. Simul..

[16]  Xinghuo Yu,et al.  Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances , 2013, Autom..

[17]  E. Moulay,et al.  Finite time stability and stabilization of a class of continuous systems , 2006 .

[18]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[19]  Michael Defoort,et al.  Higher-order sliding mode observer for estimation of tyre friction in ground vehicles , 2014 .

[20]  Ian R. Petersen,et al.  Sliding mode control of two-level quantum systems , 2010, Autom..

[21]  Zhong-Ping Jiang,et al.  Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance , 2013, Syst. Control. Lett..

[22]  Bin Wang,et al.  Finite-time tracking controller design for nonholonomic systems with extended chained form , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Saleh Mobayen,et al.  Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method , 2015 .

[24]  Ilya Kolmanovsky,et al.  Developments in nonholonomic control problems , 1995 .

[25]  V. J. Majd,et al.  A finite-time tracker for nonholonomic systems using recursive singularity-free FTSM , 2011, Proceedings of the 2011 American Control Conference.

[26]  Yuanyuan Wu,et al.  Robust stabilization of delayed nonholonomic systems with strong nonlinear drifts , 2010 .

[27]  Yu-Ping Tian,et al.  Time‐varying linear controllers for exponential tracking of non‐holonomic systems in chained form , 2007 .