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Re-configuring Knots to Simplify Manipulation

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Book cover Algorithmic Foundations of Robotics XII

Part of the book series: Springer Proceedings in Advanced Robotics ((SPAR,volume 13))

Abstract

Humans often change the geometry of flexible objects during manipulation so that the goal is easier to accomplish with either simple motions or simple controls. This paper explores how to change the geometry of a knot to allow simpler tying or untying. The paper presents algorithms that modify the knot configuration to allow the knot to be arranged into the correct topological structure or untangled by moving the tip of the string along a straight line, with only a few re-grasps. The paper also presents proof-of-concept physical experiments in which robot arms arrange and untangle several knots.

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References

  1. C.C. Adams. The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. American Mathematical Society, 2004.

    Google Scholar 

  2. J. W. Alexander. Topological invariants of knots and links. Trans. Amer. Math. Soc., 20:275–306, 1923.

    Google Scholar 

  3. Ted Ashton, Jason Cantarella, Michael Piatek, and Eric Rawdon. Knot tightening by constrained gradient descent. Experimental Mathematics, 20(1):57–90, 2011.

    Google Scholar 

  4. Stephen W. Attaway. The mechanics of friction in rope rescue. International Technical Rescue Symposium, 1999.

    Google Scholar 

  5. Devin J. Balkcom, Jeffrey C. Trinkle, and E. J. Gottlieb. Computing wrench cones for planar contact tasks. In ICRA, pages 869–875. IEEE, 2002.

    Google Scholar 

  6. J. Baranska, S. Przybyl, and P. Pieranski. Curvature and torsion of the tight closed trefoil knot. The European Physical Journal B - Condensed Matter and Complex Systems, 66(4):547–556, 2008.

    Google Scholar 

  7. Matthew P. Bell. Flexible Object Manipulation. Technical Report TR2010-663, Dartmouth College, Computer Science, Hanover, NH, February 2010.

    Google Scholar 

  8. Matthew P. Bell,WeifuWang (co-first author), Jordan Kunzika, and Devin Balkcom. Knottying with four-piece fixtures. International Journal of Robotics Research (IJRR), vol 33, no. 11:1481–1489, Sep, 2014.

    Google Scholar 

  9. Stephen Berard, Kevin Egan, and Jeffrey C. Trinkle. Contact modes and complementary cones. In ICRA, pages 5280–5286, 2004.

    Google Scholar 

  10. G. Burde. Knoten. Jahrbuch Ueberblicke Mathematik, pages 131–147, 1978.

    Google Scholar 

  11. Erik D. Demaine, Martin L. Demaine, Andrea Hawksley, Hiro Ito, Po-Ru Loh, Shelly Manber, and Omari Stephens. Making polygons by simple folds and one straight cut. In Revised Papers from the China-Japan Joint Conference on Computational Geometry, Graphs and Applications (CGGA 2010), Lecture Notes in Computer Science, pages 27–43, Dalian, China, November 3–6 2010.

    Google Scholar 

  12. John E. Hopcroft, Joseph K. Kearney, and Dean B. Krafft. A case study of flexible object manipulation. International Journal of Robotic Research, 10(1):41–50, 1991.

    Google Scholar 

  13. H. Inoue and M. Inaba. Hand-eye coordination in rope handling. Robotics Research: The first International Symposium, pages 163–174, 1985.

    Google Scholar 

  14. H Kang and J.T. Wen. Robotic knot tying in minimally invasive surgeries. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2002.

    Google Scholar 

  15. Hyosig Kang and John T.Wen. Endobot: a robotic assistant in minimally invasive surgeries. In Proc. IEEE International Conference on Robotics and Automation, volume 2, pages 2031–2036, 2001.

    Google Scholar 

  16. Hyosig Kang and J.T. Wen. Robotic assistants aid surgeons during minimally invasive procedures. Engineering in Medicine and Biology Magazine, IEEE, 20(1):94–104, Jan 2001.

    Google Scholar 

  17. L.H. Kauffman. Knots and Physics. K & E series on knots and everything.World Scientific, 1991.

    Google Scholar 

  18. Makoto Kudo, Yasuo Nasu, Kazuhisa Mitobe, and Branislav Borovac. Multi-arm robot control system for manipulation of flexible materials in sewing operation. Mechatronics, 10(3):371 – 402, 2000.

    Google Scholar 

  19. W.B.R. Lickorish. An Introduction to Knot Theory. Graduate Texts in Mathematics. Springer New York, 1997.

    Google Scholar 

  20. Charles Livingston. Knot theory. The carus mathematical monographs, Volume Twenty Four. The mathematical Association of America, Washington D.C., 1993.

    Google Scholar 

  21. Wen Hao Lui and Ashutosh Saxena. Tangled: Learning to untangle ropes with RGB-D perception. In 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan, November 3-7, 2013, pages 837–844, 2013.

    Google Scholar 

  22. J.H.Maddocks M. Carlen, B. Laurie and J. Smutny. Biarcs, global radius of curvature, and the computation of ideal knot shapes. Physical and numerical models in knot theory, 36 of Ser. Knots Everything:75–108, 2005.

    Google Scholar 

  23. Matthew T. Mason. Mechanics of Robotic Manipulation. MIT Press, Cambridge, MA, August 2001.

    Google Scholar 

  24. Eric J. Rawdon. Approximating the thickness of a knot. Ideal knots, 19 of Ser. Knots Everything:143–150, 1998.

    Google Scholar 

  25. Kurt Reidemeister. Elementare begrndung der knotentheorie. Abhandlungen aus dem Mathematischen Seminar der Universitt Hamburg, 5(1):24–32, 1927.

    Google Scholar 

  26. D. Rolfsen. Knots and Links. AMS/Chelsea Publication Series. AMS Chelsea Pub., 1976.

    Google Scholar 

  27. Mitul Saha and Pekka Isto. Motion planning for robotic manipulation of deformable linear objects. In Proc. IEEE International Conference on Robotics and Automation, pages 2478–2484, May 2006.

    Google Scholar 

  28. Mitul Saha and Pekka Isto. Manipulation planning for deformable linear objects. IEEE Transaction on Robotics, 23(6):1141–1150, December 2007.

    Google Scholar 

  29. Mitul Saha, Pekka Isto, and J.-C. Latombe. Motion planning for robotic knot tying. In Proc. International Symposium on Experimental Robotics, July 2006.

    Google Scholar 

  30. Zoe McCarthy TimothyWBretl. Quasi-static manipulation of a Kirchhoff elastic rod based on a geometric analysis of equilibrium configurations. International Journal of Robotics Research (IJRR), June 2013.

    Google Scholar 

  31. Hidefumi Wakamatsu, Eiji Arai, and Shinichi Hirai. Knotting/unknotting manipulation of deformable linear objects. International Journal of Robotics Research, 25:371–395, 2006.

    Google Scholar 

  32. Weifu Wang and Devin Balkcom. Grasping and folding knots. In IEEE International Conference on Intelligent Robots and Systems (ICRA), pages 3647–3654, 2016.

    Google Scholar 

  33. Weifu Wang and Devin Balkcom. Towards tying knots precisely. In IEEE International Conference on Intelligent Robots and Systems (ICRA), pages 3639–3646, 2016.

    Google Scholar 

  34. Weifu Wang, Matthew P. Bell, and Devin J. Balkcom. Towards arranging and tightening knots and unknots with fixtures. In International Workshop on the Algorithmic Foundations of Robotics, WAFR 2014, pages 677–694, 2014.

    Google Scholar 

  35. Weifu Wang, Matthew P. Bell, and Devin J. Balkcom. Towards arranging and tightening knots and unknots with fixtures. IEEE T. Automation Science and Engineering, 12(4):1318–1331, 2015.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dartmouth College Computer Science Department, Hanover, Germany

    Weifu Wang & Devin Balkcom

Authors
  1. Weifu Wang
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  2. Devin Balkcom
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Corresponding author

Correspondence to Weifu Wang .

Editor information

Editors and Affiliations

  1. Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA

    Ken Goldberg

  2. Electrical Engineering and Computer Sciences, University of California, Berkeley, CA, USA

    Pieter Abbeel

  3. Rutgers University, Piscataway, NJ, USA

    Kostas Bekris

  4. University of California, Berkeley, CA, USA

    Lauren Miller

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Wang, W., Balkcom, D. (2020). Re-configuring Knots to Simplify Manipulation. In: Goldberg, K., Abbeel, P., Bekris, K., Miller, L. (eds) Algorithmic Foundations of Robotics XII. Springer Proceedings in Advanced Robotics, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-030-43089-4_31

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