Global continuous finite‐time tracking of robot manipulators

This paper addresses the global finite-time tracking of robot manipulators. The commonly used linear proportional-derivative (PD) plus (PD+) scheme is extended to achieve the global finite-time tracking by replacing the linear errors with nonsmooth but continuous exponential errors. The global finite-time stability of the closed loop with the proposed nonlinear PD plus control is shown using Lyapunov's direct method and finite-time stability. Simulations performed on a two-degree-of-freedom manipulator are provided to illustrate the effectiveness and the improved performance of the formulated algorithm. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  Danko Brezak,et al.  Global positioning of robot manipulators with mixed revolute and prismatic joints , 2006, IEEE Transactions on Automatic Control.

[2]  Suguru Arimoto,et al.  Is a local linear PD feedback control law effective for trajectory tracking of robot motion? , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[3]  Ming Liu,et al.  Decentralized control of robot manipulators: nonlinear and adaptive approaches , 1999, IEEE Trans. Autom. Control..

[4]  Wei Lin,et al.  Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems , 2006, IEEE Transactions on Automatic Control.

[5]  Jie Huang,et al.  On an output feedback finite-time stabilization problem , 2001, IEEE Trans. Autom. Control..

[6]  R. Ortega,et al.  A semiglobally stable output feedback PI2D regulator for robot manipulators , 1995, IEEE Trans. Autom. Control..

[7]  Rafael Kelly,et al.  PD control with feedforward compensation for robot manipulators: analysis and experimentation , 2001, Robotica.

[8]  H. Nijmeijer,et al.  Robust control of robots via linear estimated state feedback , 1994, IEEE Trans. Autom. Control..

[9]  Jose Alvarez-Ramirez,et al.  On the PID tracking control of robot manipulators , 2001 .

[10]  Brad Paden,et al.  Globally asymptotically stable ‘PD+’ controller for robot manipulators , 1988 .

[11]  Patrizio Tomei,et al.  Adaptive PD controller for robot manipulators , 1991, IEEE Trans. Robotics Autom..

[12]  Lu Ren,et al.  Integration of saturated PI synchronous control and PD feedback for control of parallel manipulators , 2006, IEEE Transactions on Robotics.

[13]  Yorgo Istefanopulos,et al.  A new variable structure PID-controller design for robot manipulators , 2005, IEEE Transactions on Control Systems Technology.

[14]  Yu Tang,et al.  Terminal sliding mode control for rigid robots , 1998, Autom..

[15]  Yunhui Liu,et al.  Dynamic sliding PID control for tracking of robot manipulators: theory and experiments , 2003, IEEE Trans. Robotics Autom..

[16]  Z. Qu,et al.  Robust tracking control of robots by a linear feedback law , 1991 .

[17]  Masayoshi Tomizuka,et al.  Decentralized robust control of mechanical systems , 2000, IEEE Trans. Autom. Control..

[18]  Gerd Hirzinger,et al.  Perfect position/force tracking of robots with dynamical terminal sliding mode control , 2001, J. Field Robotics.

[19]  R. Kelly.  Global positioning of robot manipulators via PD control plus a class of nonlinear integral actions , 1998, IEEE Trans. Autom. Control..

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

[21]  Zhihong Man,et al.  Continuous finite-time control for robotic manipulators with terminal sliding mode , 2003, Autom..

[22]  Chun-Yi Su,et al.  Variable structure control of robotic manipulator with PID sliding surfaces , 1998 .

[23]  Peter C. Müller,et al.  A Global Asymptotic Stable Output Feedback PID Regulator for Robot Manipulators , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[24]  R. Kelly,et al.  PD control with computed feedforward of robot manipulators: a design procedure , 1994, IEEE Trans. Robotics Autom..

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

[26]  Hong Ren Wu,et al.  A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators , 1994, IEEE Trans. Autom. Control..

[27]  Paolo Rocco,et al.  Stability of PID control for industrial robot arms , 1996, IEEE Trans. Robotics Autom..

[28]  Romeo Ortega,et al.  Adaptive motion control of rigid robots: a tutorial , 1988, Proceedings of the 27th IEEE Conference on Decision and Control.

[29]  H. Nijmeijer,et al.  Bounded output feedback tracking control of fully actuated Euler-Lagrange systems , 1998 .

[30]  M. de Mathelin,et al.  Robust control of robot manipulators: A survey , 1999 .

[31]  Raymond Gorez,et al.  Globally stable PID-like control of mechanical systems , 1999 .

[32]  Zhong-Ping Jiang,et al.  Finite-Time Stabilization of Nonlinear Systems With Parametric and Dynamic Uncertainties , 2006, IEEE Transactions on Automatic Control.

[33]  Tae-Yong Kuc,et al.  An adaptive PID learning control of robot manipulators , 2000, Autom..

[34]  Suguru Arimoto,et al.  PID control of robotic manipulator with uncertain Jacobian matrix , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[35]  Warren E. Dixon,et al.  Global adaptive output feedback tracking control of robot manipulators , 2000, IEEE Trans. Autom. Control..

[36]  Li-Chen Fu,et al.  A fully adaptive decentralized control of robot manipulators , 2006, Autom..

[37]  Jie Huang,et al.  Finite-time control for robot manipulators , 2002, Syst. Control. Lett..

[38]  Mahmoud Tarokh.  Decoupled nonlinear three-term controllers for robot trajectory tracking , 1999, IEEE Trans. Robotics Autom..