Finite-time trajectory tracking control in a task space of robotic manipulators

This work addresses the problem of the accurate task space control subject to finite-time convergence. Dynamic equations of a rigid robotic manipulator are assumed to be uncertain. Moreover, globally unbounded disturbances are allowed to act on the manipulator when tracking the trajectory by the end-effector. Based on suitably defined task space non-singular terminal sliding vector variable and the Lyapunov stability theory, we derive a class of absolutely continuous Jacobian transpose robust controllers, which seem to be effective in counteracting uncertain dynamics, unbounded disturbances and (possible) kinematic and/or algorithmic singularities met on the end-effector trajectory. The numerical simulations carried out for a robotic manipulator of a SCARA type consisting of two revolute kinematic pairs and operating in a two-dimensional task space, illustrate performance of the proposed controllers.

[1]  Tesheng Hsiao,et al.  Robust Joint Position Feedback Control of Robot Manipulators , 2013 .

[2]  Arie Levant,et al.  Exact Differentiation of Signals with Unbounded Higher Derivatives , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[3]  Henk Nijmeijer,et al.  Global regulation of robots using only position measurements , 1993 .

[4]  Richard Colbaugh,et al.  Robust adaptive control of redundant manipulators , 1995, J. Intell. Robotic Syst..

[5]  Javier Moreno-Valenzuela,et al.  Operational space trajectory tracking control of robot manipulators endowed with a primary controller of synthetic joint velocity. , 2011, ISA transactions.

[6]  Carlos Canudas de Wit,et al.  A new model for control of systems with friction , 1995, IEEE Trans. Autom. Control..

[7]  A. N. Atassi,et al.  Separation results for the stabilization of nonlinear systems using different high-gain observer designs ☆ , 2000 .

[8]  Javier Moreno-Valenzuela,et al.  Manipulator motion control in operational space using joint velocity inner loops , 2005, Autom..

[9]  Jun Nakanishi,et al.  Operational Space Control: A Theoretical and Empirical Comparison , 2008, Int. J. Robotics Res..

[10]  Carlos Canudas de Wit,et al.  Trajectory tracking in robot manipulators via nonlinear estimated state feedback , 1992, IEEE Trans. Robotics Autom..

[11]  G. Oriolo,et al.  Robotics: Modelling, Planning and Control , 2008 .

[12]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[13]  Warren E. Dixon,et al.  Tracking Control for Robot Manipulators with Kinematic and Dynamic Uncertainty , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Leonid M. Fridman,et al.  Second-order sliding-mode observer for mechanical systems , 2005, IEEE Transactions on Automatic Control.

[15]  Alessandro De Luca,et al.  An Acceleration-based State Observer for Robot Manipulators with Elastic Joints , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[16]  Weiliang Xu,et al.  Angular acceleration estimation and feedback control: An experimental investigation , 2007 .

[17]  Jouni Mattila,et al.  Geometry-aided angular acceleration sensing of rigid multi-body manipulator using MEMS rate gyros and linear accelerometers , 2013, 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[18]  Chien Chern Cheah.  On duality of inverse Jacobian and transpose Jacobian in task-space regulation of robots , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..

[19]  D. M. Dawson,et al.  Adaptive control of redundant robot manipulators with sub-task objectives , 2008, ACC.

[20]  Alexander Dietrich,et al.  Prioritized multi-task compliance control of redundant manipulators , 2015, Autom..

[21]  Miroslaw Galicki,et al.  Finite-time control of robotic manipulators , 2015, Autom..

[22]  Bruno Siciliano,et al.  A closed-loop inverse kinematic scheme for on-line joint-based robot control , 1990, Robotica.

[23]  Erkan Zergeroglu,et al.  Robust tracking control of kinematically redundant robot manipulators subject to multiple self-motion criteria , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[24]  Waguih ElMaraghy,et al.  A Unified Approach for Independent Manipulator Joint Acceleration Control and Observation , 2003 .

[25]  S. Ali A. Moosavian,et al.  Modified transpose Jacobian control of robotic systems , 2007, Autom..

[26]  Hassan K. Khalil,et al.  A Nonlinear High-Gain Observer for Systems With Measurement Noise in a Feedback Control Framework , 2013, IEEE Transactions on Automatic Control.

[27]  Miroslaw Galicki.  Inverse-free control of a robotic manipulator in a task space , 2014, Robotics Auton. Syst..

[28]  Rafael Kelly,et al.  Robust asymptotically stable visual servoing of planar robots , 1996, IEEE Trans. Robotics Autom..

[29]  John Baillieul,et al.  Kinematic programming alternatives for redundant manipulators , 1985, Proceedings. 1985 IEEE International Conference on Robotics and Automation.

[30]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[31]  Hassan K. Khalil,et al.  High-gain observers in nonlinear feedback control , 2009, 2009 IEEE International Conference on Control and Automation.

[32]  Chien Chern Cheah,et al.  Asymptotic stability of robot control with approximate Jacobian matrix and its application to visual servoing , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[33]  W. Wolovich,et al.  A computational technique for inverse kinematics , 1984, The 23rd IEEE Conference on Decision and Control.

[34]  Xiang Li,et al.  Global task-space adaptive control of robot , 2013, Autom..

[35]  Chien Chern Cheah,et al.  Adaptive Tracking Control for Robots with Unknown Kinematic and Dynamic Properties , 2006, Int. J. Robotics Res..