Energy-Based Swing-Up Control for a Remotely Driven Acrobot: Theoretical and Experimental Results

This brief concerns the energy-based swing-up control for a remotely driven acrobot (RDA) which is a 2-link planar robot with the first link being underactuated and the second link being remotely driven by an actuator mounted at a fixed base through a belt. An energy-based swing-up controller is designed via the Lyapunov stability theory. A global motion analysis of the RDA under the designed controller is provided focusing on the behavior of the closed-loop solution and the stability of the closed-loop equilibrium points. The conditions on control parameters for achieving a successful swing-up control are given. Furthermore, an experimental setup is described and experimental results are given to validate the presented theoretical results. The energy-based swing-up controller for the RDA is shown to be effective both theoretically and practically.

[1]  Simon X. Yang,et al.  Comprehensive Unified Control Strategy for Underactuated Two-Link Manipulators , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[2]  Chun-Yi Su,et al.  Adaptive variable structure set-point control of underactuated robots , 1999, IEEE Trans. Autom. Control..

[3]  Katsuhisa Furuta,et al.  Swinging up a pendulum by energy control , 1996, Autom..

[4]  Mark W. Spong,et al.  The swing up control problem for the Acrobot , 1995 .

[5]  Kevin M. Passino,et al.  c ○ 1997 Kluwer Academic Publishers. Printed in the Netherlands. Intelligent Control for an Acrobot , 1996 .

[6]  C.H. Moog,et al.  The structure of 2-bodies mechanical systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[7]  S. Sastry.  Nonlinear Systems: Analysis, Stability, and Control , 1999 .

[8]  Warren E. Dixon,et al.  Lyapunov-based set-point control of the Acrobot , 1998, Proceedings of the 1998 IEEE International Conference on Control Applications (Cat. No.98CH36104).

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

[10]  Xin Xin,et al.  Analysis of the energy‐based swing‐up control of the Acrobot , 2007 .

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

[12]  Scott A. Bortoff.  Advanced nonlinear robotic control using digital signal processing , 1994, IEEE Trans. Ind. Electron..

[13]  Reza Olfati-Saber,et al.  Normal forms for underactuated mechanical systems with symmetry , 2002, IEEE Trans. Autom. Control..

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

[15]  Anton S. Shiriaev,et al.  Partial stabilization of underactuated Euler-Lagrange systems via a class of feedback transformations , 2002, Syst. Control. Lett..

[16]  Mark W. Spong,et al.  The Pendubot: a mechatronic system for control research and education , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[17]  Chin-Wang Tao,et al.  Design of a Fuzzy Controller With Fuzzy Swing-Up and Parallel Distributed Pole Assignment Schemes for an Inverted Pendulum and Cart System , 2008, IEEE Transactions on Control Systems Technology.

[18]  R. Murray,et al.  Nonlinear controllers for non-integrable systems: the Acrobot example , 1990, 1990 American Control Conference.

[19]  R. Mattone,et al.  Control problems in underactuated manipulators , 2001, 2001 IEEE/ASME International Conference on Advanced Intelligent Mechatronics. Proceedings (Cat. No.01TH8556).

[20]  Sergej Celikovský,et al.  Advanced LMI based analysis and design for Acrobot walking , 2010, Int. J. Control.

[21]  S. Celikovsky,et al.  Partial exact linearization design for the Acrobot walking , 2008, 2008 American Control Conference.

[22]  Benjamin C. Kuo,et al.  AUTOMATIC CONTROL SYSTEMS , 1962, Universum:Technical sciences.

[23]  Rogelio Lozano,et al.  Energy based control of the Pendubot , 2000, IEEE Trans. Autom. Control..

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