Fixed-time output tracking control for extended nonholonomic chained-form systems with state observers

This paper deals with the fixed-time tracking control problem of extended nonholonomic chained-form systems with state observers. According to the structure characteristic of such chained-form systems, two subsystems are considered to design controllers, respectively. First of all, using the fixed-time control theory, a controller is proposed to make the first tracking error subsystem converge to zero in bounded time independent initial state. Second, a state observer is proposed to estimate the unmeasurable states of the second subsystem. And the precise state estimation can be presented from the observer within finite time; moreover, the upper bound of time is a constant independent on the initial estimation error. Third, a fixed-time controller is designed to drive all states of the second chained-form subsystem to zero within pre-calculated time. Finally, the effectiveness of the proposed control scheme is validated by simulation results.

[1]  Alessandro Astolfi,et al.  Discontinuous control of high-order generalized chained systems , 1999 .

[2]  Xuzhi Lai,et al.  A Novel Robust Control Method for Motion Control of Uncertain Single-Link Flexible-Joint Manipulator , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[3]  I. Kolmanovsky,et al.  Hybrid feedback laws for a class of cascade nonlinear control systems , 1996, IEEE Trans. Autom. Control..

[4]  Chaoli Wang,et al.  Saturated tracking control for nonholonomic mobile robots with dynamic feedback , 2013 .

[5]  Claude Samson,et al.  Velocity and torque feedback control of a nonholonomic cart , 1991 .

[6]  H. Sira-Ramírez,et al.  Dynamical discontinuous feedback control of nonlinear systems , 1990 .

[7]  Fangzheng Gao,et al.  Finite-time stabilization for a class of nonholonomic feedforward systems subject to inputs saturation. , 2016, ISA transactions.

[8]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[9]  Shuzhi Sam Ge,et al.  Stabilization of uncertain nonholonomic systems via time-varying sliding mode control , 2004, IEEE Transactions on Automatic Control.

[10]  Wilfrid Perruquetti,et al.  Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems , 2003, Autom..

[11]  Yu Qiu,et al.  Visual Servo Tracking of Wheeled Mobile Robots With Unknown Extrinsic Parameters , 2019, IEEE Transactions on Industrial Electronics.

[12]  Yiguang Hong,et al.  Stabilization of uncertain chained form systems within finite settling time , 2005, IEEE Transactions on Automatic Control.

[13]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[14]  Claude Samson,et al.  Feedback control of a nonholonomic wheeled cart in Cartesian space , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

[15]  He Chen,et al.  An energy-optimal solution for transportation control of cranes with double pendulum dynamics: Design and experiments , 2018 .

[16]  Qing-Long Han,et al.  An Overview of Recent Advances in Fixed-Time Cooperative Control of Multiagent Systems , 2018, IEEE Transactions on Industrial Informatics.

[17]  Zhong-Ping Jiang,et al.  Robust exponential regulation of nonholonomic systems with uncertainties , 2000, Autom..

[18]  Xiaoxia Yang,et al.  Capabilities of extended state observer for estimating uncertainties , 2009, 2009 American Control Conference.

[19]  Jean-Baptiste Pomet.  Explicit design of time-varying stabilizing control laws for a class of controllable systems without drift , 1992 .

[20]  Linda Bushnell,et al.  Stabilization of multiple input chained form control systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[21]  Kui Li,et al.  Finite-time tracking control for extended nonholonomic chained-form systems with parametric uncertainty and external disturbance , 2018 .

[22]  Denis Dochain,et al.  Discontinuous feedback stabilization of minimum-phase semilinear infinite-dimensional systems with application to chemical tubular reactor , 2002, IEEE Trans. Autom. Control..

[23]  Xi Chen,et al.  Global Finite-Time Stabilization for Nonholonomic Mobile Robots Based on Visual Servoing , 2014 .

[24]  Muhammad Sarfraz,et al.  Robust stabilizing control of nonholonomic systems with uncertainties via adaptive integral sliding mode , 2017 .

[25]  Ning Sun,et al.  Antiswing Cargo Transportation of Underactuated Tower Crane Systems by a Nonlinear Controller Embedded With an Integral Term , 2019, IEEE Transactions on Automation Science and Engineering.

[26]  Dennis S. Bernstein,et al.  Geometric homogeneity with applications to finite-time stability , 2005, Math. Control. Signals Syst..

[27]  A. Ailon,et al.  Control Strategies for Driving a Group of Nonholonomic Kinematic Mobile Robots in Formation Along a Time-Parameterized Path , 2012, IEEE/ASME Transactions on Mechatronics.

[28]  Zhong-Ping Jiang,et al.  A recursive technique for tracking control of nonholonomic systems in chained form , 1999, IEEE Trans. Autom. Control..

[29]  Jun Ye,et al.  Tracking control for nonholonomic mobile robots: Integrating the analog neural network into the backstepping technique , 2008, Neurocomputing.

[30]  S. Shankar Sastry,et al.  Stabilization of trajectories for systems with nonholonomic constraints , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[31]  Michael V. Basin,et al.  Continuous Fixed-Time Controller Design for Mechatronic Systems With Incomplete Measurements , 2018, IEEE/ASME Transactions on Mechatronics.

[32]  Xiaoyu Hu,et al.  Fast Fixed-Time Nonsingular Terminal Sliding Mode Control and Its Application to Chaos Suppression in Power System , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[33]  Andrey Polyakov,et al.  Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems , 2012, IEEE Transactions on Automatic Control.

[34]  Gerd Hirzinger,et al.  An adaptive control for a free-floating space robot by using inverted chain approach , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[35]  S. Bhat,et al.  Continuous finite-time stabilization of the translational and rotational double integrators , 1998, IEEE Trans. Autom. Control..

[36]  Ning Sun,et al.  Nonlinear Motion Control of Underactuated Three-Dimensional Boom Cranes With Hardware Experiments , 2018, IEEE Transactions on Industrial Informatics.

[37]  Fumio Miyazaki,et al.  A stable tracking control method for an autonomous mobile robot , 1990, Proceedings., IEEE International Conference on Robotics and Automation.

[38]  Jinjun Shan,et al.  Fixed-Time Consensus Control of Multiagent Systems Using Input Shaping , 2019, IEEE Transactions on Industrial Electronics.

[39]  Daniel Liberzon,et al.  Hybrid feedback stabilization of systems with quantized signals , 2003, Autom..

[40]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[41]  Yongchun Fang,et al.  An Energy-based Nonlinear Coupling Control for Offshore Ship-mounted Cranes , 2018, Int. J. Autom. Comput..

[42]  Hua Chen,et al.  Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation , 2014 .

[43]  Qing-Long Han,et al.  An Explicit Estimate for the Upper Bound of the Settling Time in Fixed-Time Leader-Following Consensus of High-Order Multivariable Multiagent Systems , 2019, IEEE Transactions on Industrial Electronics.

[44]  Menghua Zhang,et al.  Finite-time model-free trajectory tracking control for overhead cranes subject to model uncertainties, parameter variations and external disturbances , 2019, Trans. Inst. Meas. Control.

[45]  Sergey V. Drakunov,et al.  Stabilization of a nonholonomic system via sliding modes , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.