Redundancy Resolution in Minimum-time Path Tracking of Robotic Manipulators

Alexander Reiter, Hubert Gattringer, Andreas Müller

Abstract

Minimum-time trajectories for applications where a geometric path is followed by a kinematically redundant robot’s end-effector may yield economical improvements in many cases compared to conventional manipulators. While for non-redundant robots the problem of finding such trajectories has been solved, the redundant case has not been treated exhaustively. In this contribution, the problem is split into two interlaced parts: inverse kinematics and trajectory optimization. In a direct optimization approach, the inverse kinematics problem is solved numerically at each time point. Therein, the manupulator’s kinematic redundancy is exploited by introducing scaled nullspace basis vectors of the Jacobian of differential velocities. The scaling factors for each time point are decision variables, thus the inverse kinematics is solved optimally w.r.t. the trajectory optimization goal, i.e. minimizing end time. The effectiveness of the presented method is shown by means of the example of a planar 4R manipulator with two redundant degrees of freedom.

References

  1. Andersson, J. (2013). A General-Purpose Software Framework for Dynamic Optimization. PhD thesis, Arenberg Doctoral School, KU Leuven.
  2. Bobrow, J., Dubowsky, S., and Gibson, J. (1985). Timeoptimal control of robotic manipulators along specified paths. International Journal of Robotics Research, 4(3):3-17.
  3. Bock, H. G. and Plitt, K. J. (1984). A multiple shooting algorithm for direct solution of optimal control problems. In Proceedings of the IFAC World Congress, pages 242-247. Pergamon Press.
  4. Bremer, H. (1988). Dynamik und Regelung mechanischer Systeme. Teubner Studienbücher.
  5. Chiacchio, P. (1990). Exploiting redundancy in minimumtime path following robot control. In Proc. American Control Conf., pages 2313-2318.
  6. Galicki, M. (2000). Time-optimal controls of kinematically redundant manipulators with geometric constraints. IEEE Transactions on Robotics and Automation, 16(1):89-93.
  7. Khatib, O. (1988). Augmented object and reduced effective inertia in robot systems. In American Control Conference 1988, pages 2140 - 2147. IEEE.
  8. Liégeois, A. (1977). Automatic supervisory control of the configuration and behavior of multibody mechanisms. IEEE Transactions on Systems Man and Cybernetics, 12:868-871.
  9. Ma, S. and Watanabe, M. (2004). Time optimal pathtracking control of kinematically redundant manipulators. JSME International Journal, 47(2):582-590.
  10. Nakamura, Y., Hanafusa, H., and Yoshikawa, T. (1987). Task-priority based redundancy control of robot manipulators. International Journal of Robotics Research, 6(2):3-15.
  11. Pfeiffer, F. and Johanni, R. (1986). A concept for manipulator trajectory planning. In International Conference on Robotics and Automation, pages 1399 - 1405. IEEE.
  12. Pham, Q.-C. (2014). A general, fast, and robust implementation of the time-optimal path parameterization algorithm. IEEE Transactions on Rob, 30(6):1533-1540.
  13. Shin, K. and McKay, N. (1985). Minimum-time control of robotic manipulators with geometric path constraints. IEEE Transactions on Automatic Control, 30(6):531- 541.
  14. Springer, K., Gattringer, H., and Staufer, P. (2013). On time-optimal trajectory planning for a flexible link robot. Journal of Systems and Control Engineering, 227(10):751-762.
  15. Wampler, C. (1987). Inverse kinematic functions for redundant manipulators. In IEEE International Conference on Robotics and Automation, pages 610 - 617.
  16. Whitney, D. E. (1969). Resolved motion rate control of manipulators and human prostheses. IEEE Transactions on Man-Machine Systems, 10(2):47 - 53.
  17. Yoshikawa, T. (1985a). Dynamic manipulability of robot manipulators. In IEEE International Conference on Robotics and Automation, volume 2, pages 1033- 1038.
  18. Yoshikawa, T. (1985b). Manipulability of robotic mechanisms. International Journal of Robotics Research, 4(2):3-9.
Download


Paper Citation


in Harvard Style

Reiter A., Gattringer H. and Müller A. (2016). Redundancy Resolution in Minimum-time Path Tracking of Robotic Manipulators . In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-758-198-4, pages 61-68. DOI: 10.5220/0005975800610068


in Bibtex Style

@conference{icinco16,
author={Alexander Reiter and Hubert Gattringer and Andreas Müller},
title={Redundancy Resolution in Minimum-time Path Tracking of Robotic Manipulators},
booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2016},
pages={61-68},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005975800610068},
isbn={978-989-758-198-4},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,
TI - Redundancy Resolution in Minimum-time Path Tracking of Robotic Manipulators
SN - 978-989-758-198-4
AU - Reiter A.
AU - Gattringer H.
AU - Müller A.
PY - 2016
SP - 61
EP - 68
DO - 10.5220/0005975800610068