A Task Space Approach for Planar Optimal Robot Tube Following

Matthias Oberherber, Hubert Gattringer, Andreas Müller, Michael Schachinger

Abstract

The classical optimal path following problem considers the problem of moving optimally along a predefined geometric path under technological restrictions. In contrast to optimal path following, optimal tube following allows deviations from the initial path within a predefined tube to reduce cost even more. The present paper proposes a modern approach that treats this non-convex problem in task space. This novel method also provides a simple way to derive optimal trajectories within a tube described in terms of polygonal lines. Numerical examples are presented that allow to compare the proposed method to existing joint space approaches.

References

  1. Antonelli, G., Chiaverini, S., Palladino, M., Gerio, G. P., and Renga, G. (2005). Joint space point-to-point motion planning for robots: An industrial implementation. In Ztek, P., editor, Proceedings of the 16th IFAC World Congress.
  2. Bobrow, J. E., Dubowsky, S., and Gibson, J. S. (1985). Time-optimal control of robotic manipulators along specified paths. International Journal Robotics Resarch, 4:3-17.
  3. Bremer, H. (2008). Elastic Multibody Dynamics: A Direct Ritz Approach. Springer Verlag, Heidelberg.
  4. DeBoor, C. (1978). A practical guide to splines. Springer.
  5. Debrouwere, F., Van Loock, W., Pipeleers, G., and Swevers, J. (2014). Time-optimal tube following for robotic manipulators. In Advanced Motion Control (AMC),2014 IEEE 13th International Workshop on, pages 392-397.
  6. Gattringer, H., Oberherber, M., and Springer, K. (2014). Extending continuous path trajectories to point-topoint trajectories by varying intermediate points. International Journal of Mechanics and Control, 15(01):35-43.
  7. Geu Flores, F. and Kecskemthy, A. (2012). Time-optimal path palanning along specified trajectories. In Gattringer, H. and Gerstmayr, J., editors, Multibody System Dynamics, Robotics and Control, pages 1-15.
  8. Johanni, R. (1988). Optimale Bahnplanung bei Industrierobotern. Technische Universität München.
  9. Johnson, S. G. (2011). The NLopt nonlinear-optimization package.
  10. Mørken, K., Reimers, M., and Schulz, C. (2009). Computing intersections of planar spline curves using knot insertion. Comput. Aided Geom. Des., 26(3):351-366.
  11. Pfeiffer, F. and Johanni, R. (1987). A concept for manipulator trajectory planning. IEEE Journal of Robotics and Automation, 3(2):115 -123.
  12. Pham, Q. (2013). A general, fast, and robust implementation of the time-optimal path parameterization algorithm. CoRR, abs/1312.6533.
  13. Piegl, L. A. and Tiller, W. (1997). The NURBS book (2. ed.). Monographs in visual communication. Springer.
  14. Rajan, V. (1985). Minimum time trajectory planning. In Robotics and Automation. Proceedings. 1985 IEEE International Conference on, volume 2, pages 759- 764.
  15. Reynoso-Mora, P., Chen, W., and Tomizuka, M. (2013). On the time-optimal trajectory planning and control of robotic manipulators along predefined paths. In American Control Conference (ACC), 2013, pages 371- 377.
  16. Shiller, Z. and Dubowsky, S. (1988). Global time optimal motions of robotic manipulators in the presence of obstacles. In Robotics and Automation, 1988. Proceedings., 1988 IEEE International Conference on, pages 370-375 vol.1.
  17. Shin, K. G. and McKay, N. D. (1986). A dynamic programming approach to trajectory planning of robotic manipulators. Automatic Control, IEEE Transactions on, 31(6):491-500.
  18. Siciliano, B., Sciavicco, L., Villani, L., and Oriolo, G. (2009). Robotics - Modelling, Planning and Control. Advanced Textbooks in Control and Signal Processing series. Springer.
  19. Verscheure, D., Demeulenaere, B., Swevers, J., De Schutter, J., and Diehl, M. (2009a). Time-optimal path tracking for robots: A convex optimization approach. Automatic Control, IEEE Transactions on, 54(10):2318- 2327.
  20. Verscheure, D., Diehl, M., De Schutter, J., and Swevers, J. (2009b). Recursive log-barrier method for on-line time-optimal robot path tracking. In American Control Conference, 2009. ACC 7809., pages 4134 -4140.
  21. Zaverucha, G. (2005). Approximating polylines by curved paths. In Mechatronics and Automation, 2005 IEEE International Conference, volume 2, pages 758-763 Vol. 2.
  22. Zou, A.-M., Hou, Z.-G., Tan, M., and Liu, D. (2006). Path planning for mobile robots using straight lines. In Networking, Sensing and Control, 2006. ICNSC 7806. Proceedings of the 2006 IEEE International Conference on, pages 204-208.
Download


Paper Citation


in Harvard Style

Oberherber M., Gattringer H., Müller A. and Schachinger M. (2016). A Task Space Approach for Planar Optimal Robot Tube Following . In Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO, ISBN 978-989-758-198-4, pages 327-334. DOI: 10.5220/0005980303270334


in Bibtex Style

@conference{icinco16,
author={Matthias Oberherber and Hubert Gattringer and Andreas Müller and Michael Schachinger},
title={A Task Space Approach for Planar Optimal Robot Tube Following},
booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},
year={2016},
pages={327-334},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005980303270334},
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 - A Task Space Approach for Planar Optimal Robot Tube Following
SN - 978-989-758-198-4
AU - Oberherber M.
AU - Gattringer H.
AU - Müller A.
AU - Schachinger M.
PY - 2016
SP - 327
EP - 334
DO - 10.5220/0005980303270334