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Tracking Trajectories with a Robotic Manipulator with Singularities

  • Luis Gracia
  • Josep Tornero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4729)

Abstract

This research presents a trajectory control for non-redundant serial-link manipulators that is valid for trajectories with ordinary singularities of codimension one and non-ordinary singularities of any codimension. Firstly, it is presented a unified view of tracking algorithms for trajectories with ordinary singularities. Afterwards, several singularity classifications are indicated and illustrated. Then, it is developed a procedure to solve the indeterminate motion of non-ordinary singularities, which is applied to several cases. Finally, the proposed trajectory control is presented and simulated for the 2R manipulator case.

Keywords

Singularity classification adjoint Jacobian trajectory control 

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References

  1. 1.
    Sampei, M., Furuta, K.: Robot control in the neighborhood of singular points. IEEE Journal of Robotics and Automation 4(3), 303–309 (1988)CrossRefGoogle Scholar
  2. 2.
    Kieffer, J.: Manipulator inverse kinematics for untimed end-effector trajectories with ordinary singularities. International Journal of Robotics Research 11(3), 225–237 (1992)CrossRefGoogle Scholar
  3. 3.
    Nenchev, D.N.: Tracking Manipulator trajectories with ordinary singularities: a null space-based approach. The Int. Journal of Robotics Research 14(4), 399–404 (1995)CrossRefGoogle Scholar
  4. 4.
    Nenchev, D.N., Uchiyama, M.: Singularity-consistent path planning and motion control through instantaneous self-motion singularities of parallel-link manipulators. Journal of Robotic Systems 14(1), 27–36 (1997)zbMATHCrossRefGoogle Scholar
  5. 5.
    Nenchev, D.N., Tsumaki, Y., Uchiyama, M.: Singularity-consistent parameterization of robot motion and control. The Int. J. of Robotics Research 19(2), 159–182 (2000)CrossRefGoogle Scholar
  6. 6.
    Liegeois, A.: Automatic supervisory control of the configuration and behavior of multibody mechanisms. IEEE Trans. on Systems, Man and Cybernetics SMC-7, 868–871 (1977)Google Scholar
  7. 7.
    Stanisic, M.M., Pennock, G.R.: A non-degenerate kinematic solution of a seven-jointed robot manipulator. The Int. J. of Robotics Research 4(2), 10–20 (1985)CrossRefGoogle Scholar
  8. 8.
    Lloyd, J.E., Hayward, V.: Singularity-robust trajectory generation. The International Journal of Robotics Research 20(1), 38–56 (2001)CrossRefGoogle Scholar
  9. 9.
    Maciejewski, A.A., Klein, C.A.: Numerical filtering for the operation of robotic manipulators through kinematically singular configurations. J. of Rob. Syst. 5, 527–552 (1988)CrossRefGoogle Scholar
  10. 10.
    Chiacchio, P., Chiaverini, S., Sciavicco, L., Siciliano, B.: Closed-loop inverse kinematics schemes for constrained reundant manipulators with task space augmentation and task priority strategy. Int. Journal of Robotic Research 10(4), 410–425 (1991)CrossRefGoogle Scholar
  11. 11.
    Tsumaki, Y., Nenchev, D.N.: Jacobian adjoint matrix based approach to teleoperation. In: Int. Symp. On Microsystems, Intelligent Materials and Robots, Sendai, Japan, pp. 532–535 (1995)Google Scholar
  12. 12.
    Kieffer, J.: Differential analysis of bifurcations and isolated singularities for robots and mechanisms. IEEE Transactions on Robotics and Automation 10(1), 1–10 (1994)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Luis Gracia
    • 1
  • Josep Tornero
    • 1
  1. 1.Department of Systems Engineering and Control, Technical University of Valencia, Camino de Vera s/n, P.O. Box: 22012, ValenciaSpain

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