On-Line Trajectory Time-Scaling to Reduce Tracking Error

  • Emese Szádeczky-Kardoss
  • Bálint Kiss

The paper describes an on-line trajectory time-scaling control algorithm for wheeled mobile robots. To reduce tracking errors the controller modifies the velocity profile of the reference trajectory according to the closed loop behavior of the robot. The geometry of the reference trajectory is unchanged, only the time distribution varies during the motion. We give a control algorithm which uses time-scaled reference and a feedback calculated from the linearized error dynamics. The closed loop behavior is also studied together with the controllability of the linearized error dynamics.


Mobile Robot Tracking Error Reference Trajectory Biped Robot Rear Axle 
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  1. 1.
    Zefran M (1994) Review of the Literature on Time-Optimal Control of Robotic Manipulators, GRASP Laboratory, Department of Computer and Information Science, University of PennsylvaniaGoogle Scholar
  2. 2.
    Wu W, Chen H, Woo P-Y (2000) Time Optimal Path Planning for a Wheeled Mobile Robot, J. Robotic Syst. 17(11):585–591MATHCrossRefGoogle Scholar
  3. 3.
    Hollerbach J M (1984) Dynamic Scaling of Manipulator Trajectories, J. Dyn. Syst. Meas. Control, Trans. ASME 106(1):102–106MATHCrossRefGoogle Scholar
  4. 4.
    Sahar G, Hollerbach J M (1986) Planning of Minimum-Time Trajectories for Robot Arms, Int. J. Robot. Res. 5(3):90–100CrossRefGoogle Scholar
  5. 5.
    Moon S B, Ahmad S (1991) Time Scaling of Cooperative Multirobot Trajectories, IEEE Trans. Syst., Man, Cybern. 21(4):900–908CrossRefGoogle Scholar
  6. 6.
    Graettinger T J, Krogh B H (1989) Evaluation and Time-Scaling of Trajectories for Wheeled Mobile Robots, J. Dyn. Syst. Meas. Control, Trans. ASME 111:222–231Google Scholar
  7. 7.
    Dahl O, Nielsen L (1990) Torque-Limited Path Following by On-Line Trajectory Time Scaling, IEEE Trans. Robot. Automat. 6(5):554–561CrossRefGoogle Scholar
  8. 8.
    Kumagai A, Kohli D, Perez R (1996) Near-Minimum Time Feedback Controller for Manipulators Using On-Line Time Scaling of Trajectories, J. Dyn. Syst. Meas. Control, Trans. ASME 118:300–308MATHCrossRefGoogle Scholar
  9. 9.
    Bemporad A, Tarn T-J, Xi N (1999) Predictive Path Parameterization for Constrained Robot Control, IEEE Trans. Contr. Syst. Technol. 7(6):648–656CrossRefGoogle Scholar
  10. 10.
    Léine J (2004) On the Synchronization of a Pair of Independent Windshield Wipers, IEEE Trans. Contr. Syst. Technol. 12(5):787–795CrossRefGoogle Scholar
  11. 11.
    Szádeczky-Kardoss E, Kiss B (2006) Tracking Error Based On-Line Trajectory Time Scaling, In: Proceedings of 10th International Conference on Intelligent Engineering Systems (INES 2006), 80–85Google Scholar
  12. 12.
    Chevallereau C (2003) Time-Scaling Control for an Underactuated Biped Robot, IEEE Trans. Robot. Automat. 19(2):362–368CrossRefGoogle Scholar
  13. 13.
    Respondek W (1998) Orbital Feedback Linerization of Single-Input Nonlinear Control Systems, In: Proceedings of the IFAC NOLCOS'98, 499–504Google Scholar
  14. 14.
    Kiss B, Szádeczky-Kardoss E (2007) Tracking Control of Wheeled Mobile Robots with a Single Steering Input, In: Proceedings of the 4th International Conference on Informatics in Control, Automation and Robotics, unpublishedGoogle Scholar
  15. 15.
    Rouchon P, Fliess M, Lévine J, Martin Ph (1993) Flatness and Motion Planning: The Car with n-Trailers, In: Proceedings of the European Control Conference (ECC’93), 1518–1522Google Scholar
  16. 16.
    Cuesta F, Ollero A (2005) Intelligent Mobile Robot Navigation, In: Springer Tracts in Advanced Robotics, Springer, Berlin, 16Google Scholar
  17. 17.
    Dixon W E, Dawson D M, Zergeroglu E, Behal A (2001) Nonlinear Control of Wheeled Mobile Robots, In: Lecture Notes in Control and Information Sciences, Springer, Berlin/ Heidelberg/New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of Control Engineering and Information Technology Budapest University of Technology and EconomicsBudapestHungary

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