New Feedback Linearization-Based Control for Arm Trajectory Tracking of the Furuta Pendulum

The purpose of this paper is to introduce a new trajectory tracking controller applied to the Furuta pendulum; where the arm tracks a desired time-varying trajectory, while the pendulum remains regulated at the upward position. This controller is derived from the input-output feedback linearization technique. The rigorous analysis of the internal dynamics is presented, showing that the tracking error and the regulation error trajectories are uniformly ultimately bounded. Experimental results show the validity of the introduced theory. Additionally, a detailed experimental study is also presented, where a PID controller and an output tracking controller are compared with respect to the new algorithm, which presents the best performance.

[1]  José Ángel Acosta,et al.  A new swing-up law for the Furuta pendulum , 2003 .

[2]  Frédéric Mazenc,et al.  Tracking trajectories of the cart-pendulum system , 2003, Autom..

[3]  Ricardo Campa,et al.  Modelling and Control of a Spherical Inverted Pendulum on a Five-Bar Mechanism , 2015 .

[4]  Hebertt Sira-Ramírez,et al.  A linear differential flatness approach to controlling the Furuta pendulum , 2007, IMA J. Math. Control. Inf..

[5]  Yang Liu,et al.  Closed-loop tracking control of a pendulum-driven cart-pole underactuated system , 2008 .

[6]  Yang Liu,et al.  On tracking control of a pendulum-driven cart-pole underactuated system , 2008, Int. J. Model. Identif. Control..

[7]  Mark W. Spong,et al.  Underactuated mechanical systems , 1998 .

[8]  Qiguo Yan,et al.  Output tracking of underactuated rotary inverted pendulum by nonlinear controller , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[9]  Hubert Gattringer,et al.  Mechatronic design of a self-balancing three-dimensional inertia wheel pendulum , 2015 .

[10]  Hongnian Yu,et al.  Trajectory tracking control of an underactuated capsubot , 2015, Auton. Robots.

[11]  Bruno Siciliano,et al.  Modelling and Control of Robot Manipulators , 1997, Advanced Textbooks in Control and Signal Processing.

[12]  C. Aguilar-Ibáñez,et al.  Output feedback stabilization of the inverted pendulum system: a Lyapunov approach , 2012 .

[13]  Roy Featherstone,et al.  Angular momentum based balance controller for an under-actuated planar robot , 2016, Auton. Robots.

[14]  Ranjit Kumar Barai,et al.  Nonlinear state feedback controller design for underactuated mechanical system: a modified block backstepping approach. , 2014, ISA transactions.

[15]  Iraj Hassanzadeh,et al.  Input-Output Feedback Linearization Cascade Controller Using Genetic Algorithm for Rotary Inverted Pendulum System , 2008 .

[16]  Dong Eui Chang,et al.  Stabilizability of Controlled Lagrangian Systems of Two Degrees of Freedom and One Degree of Under-Actuation by the Energy-Shaping Method , 2010, IEEE Transactions on Automatic Control.

[17]  Masaki Izutsu,et al.  Swing-up of Furuta Pendulum by Nonlinear Sliding Mode Control , 2008 .

[18]  Rafael Kelly,et al.  Interconnection and damping assignment passivity‐based control of a class of underactuated mechanical systems with dynamic friction , 2011 .

[19]  T. C. Kuo,et al.  Adaptive PID with sliding mode control for the rotary inverted pendulum system , 2009, 2009 IEEE/ASME International Conference on Advanced Intelligent Mechatronics.

[20]  Juan Humberto Sossa Azuela,et al.  Stabilization of the Furuta Pendulum Based on a Lyapunov Function , 2007 .

[21]  Gisela Pujol,et al.  Stabilization of the Furuta Pendulum with backlash using H∞‐LMI technique: experimental validation , 2010 .

[22]  Juan Carlos Martínez-García,et al.  Experimental evaluation of regulated non-linear under-actuated mechanical systems via saturation-functions-based bounded control: the cart–pendulum system case , 2013 .

[23]  Warren N. White,et al.  Direct Lyapunov approach for tracking control of underactuated mechanical systems , 2009, 2009 American Control Conference.

[24]  José Ángel Acosta,et al.  Furuta's Pendulum: A Conservative Nonlinear Model for Theory and Practise , 2010 .

[25]  Ranjan Mukherjee,et al.  Impulsive Actuation in Robot Manipulators: Experimental Verification of Pendubot Swing-Up , 2014, IEEE/ASME Transactions on Mechatronics.

[26]  Dongkyoung Chwa,et al.  Orbital Stabilization of Inverted-Pendulum Systems via Coupled Sliding-Mode Control , 2009, IEEE Transactions on Industrial Electronics.

[27]  Rogelio Lozano,et al.  Non-linear Control for Underactuated Mechanical Systems , 2001 .

[28]  Ronald S. Fearing,et al.  Tracking fast inverted trajectories of the underactuated Acrobot , 1999, IEEE Trans. Robotics Autom..

[29]  M. Lopez-Martinez,et al.  Constructive feedback linearization of underactuated mechanical systems with 2-DOF , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[30]  José Ángel Acosta,et al.  A nonlinear hybrid controller for swinging-up and stabilizing the Furuta pendulum , 2013 .

[31]  Katsuhisa Furuta,et al.  Swing up control of inverted pendulum , 1991, Proceedings IECON '91: 1991 International Conference on Industrial Electronics, Control and Instrumentation.

[32]  Leonid B. Freidovich,et al.  New approach for swinging up the Furuta pendulum : theory and experiments , 2009 .

[33]  Faruk Kazi,et al.  PIαDβ controller design for underactuated mechanical systems , 2012, 2012 12th International Conference on Control Automation Robotics & Vision (ICARCV).

[34]  M Ramírez-Neria,et al.  Linear active disturbance rejection control of underactuated systems: the case of the Furuta pendulum. , 2014, ISA transactions.

[35]  K Furuta,et al.  Swing-up Control of Inverted Pendulum Using Pseudo-State Feedback , 1992 .

[36]  Mingjun Zhang,et al.  Hybrid control of the Pendubot , 2002 .

[37]  Galip Cansever,et al.  Stabilisation of a class of 2-DOF underactuated mechanical systems via direct Lyapunov approach , 2013, Int. J. Control.

[38]  Michal Salaj,et al.  Swinging up the Furuta Pendulum and its Stabilization Via Model Predictive Control , 2013 .

[39]  Rob Dekkers,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[40]  Z. Prime,et al.  On the dynamics of the furuta pendulum , 2011 .

[41]  Rahul Singh,et al.  Natural Frequency based Swing up of Rotary Inverted Pendulum and its Stabilization , 2014 .

[42]  Dong Eui Chang.  Pseudo‐energy shaping for the stabilization of a class of second‐order systems , 2012 .

[43]  Mohamed I. El-Hawwary,et al.  Adaptive Fuzzy Control of the Inverted Pendulum Problem , 2006, IEEE Transactions on Control Systems Technology.

[44]  Carlos Aguilar Ibáñez,et al.  The direct Lyapunov method for the stabilisation of the Furuta pendulum , 2010, Int. J. Control.

[45]  Romeo Ortega,et al.  Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment , 2002, IEEE Trans. Autom. Control..