Using motion planning for knot untangling

International Journal of Robotics Research

Volumn 23, Issue 7-8, 2004, Pages 797-808

  Ladd, Andrew M ^a   Kavraki, Lydia E ^a  

^a Rice University   (United States)

Author keywords

Flexible objects; Knots; Motion planning; Probabilistic methods

Indexed keywords

ANNEALING; BENCHMARKING; COMPUTER SIMULATION; OPTIMIZATION; PROBABILISTIC LOGICS; PROBLEM SOLVING; ROBOTS; TOPOLOGY;

FLEXIBLE OBJECTS; KNOTS; PROBABILISTIC METHODS; PROTEIN FOLDING;

MOTION PLANNING;

EID: 3042629751     PISSN: 02783649     EISSN: None     Source Type: Journal    
DOI: 10.1177/0278364904045469     Document Type: Conference Paper

References (49)

1. Agol, I., Hass, J., and Thurston, W. 2002. 3-manifold knot genus is NP-complete. Annual ACM Symposium on Theory of Computing Proceedings of the 34th Annual ACM Symposium on Theory of Computing, Montreal, Canada, pp. 761-766.
2. Anerizis, C. N. 1999. The Mystery of Knots - Computer Programming for Knot Tabulation, Series on Knots and Everything, World Scientific, Singapore.
3. Apaydin, M. S., Singh, A. P., Brutlag, D. L., and Latombe, J.-C. 2001. Capturing molecular energy landscapes with probabilistic conformal roadmaps. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Seoul, Korea, May 21-26.
4. Apaydin, M. S., Brutlag, D. L., Guestrin, C., Hsu, D., and Latombe, J.-C. 2002. Stochastic roadmap simulation: An efficient representation and algorithm for analyzing molecular motion. International Conference on Computational Molecular Biology (RECOMB), Washington, DC, April.
5. Bayazit, O. B., Lien, J.-M., and Amato, N. M. 2002. Probabilistic roadmap motion planning for deformable objects. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11-15.
6. Benham, C., and Miller, D. 2000. Writhing and linking densities for closed, circular DNA. Journal of Knot Theory and its Ramifications 9(5):577-585.
7. Bern, M. et al. 1999. Emerging challenges in computational topology. Preprint (math/cs.CG/9909001).
8. Birman, J. S., Boldi, P., Rampichini, M., and Vigna, S. 2000. Towards an implementation of the b-h algorithm for recognizing the unknot. KNOTS-2000, Yongpyong Resort, Korea.
9. Butler, Z., Kotay, K., Rus, D., and Tomita, K. 2001. Cellular automata for decentralized control of self-reconfigurable robots. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Seoul, Korea, May 21-26.
10. Crisona, N., Kanaar, R., Gonzales, T., Zechiedrich, E., Klippel, A., and Cozzarelli, N. 1994. Processive recombination by wil-type gin and an enhancer-independent mutant. Journal of Molecular Biology 243:437-457.
11. Darcy, I. 2001. Biological distances on DNA knots and links. Journal of Knot Theory and its Ramifications 10(2):269-294.
12. Dai, X., and Diao, Y. 2000. The minimum of knot energy functions. Journal of Knot Theory and its Ramifications 9(6):713-724.
13. Deibler, R. W., Rahmati, S., and Zechiedrich, E. L. 2001. Topoisomerase IV, alone, unknots DNA in escherichia coli. Genes and Development 15:748-761.
14. Diao, Y., Ernst, C., and Van Rensburg, J. 1997. In search of a good polygonal knot energy. Journal of Knot Theory and its Ramifications 6(5):633-657.
15. Grzeszczuk, R. P., Huang, M., and Kauffman, L. H. 1996. Untangling knots by stochastic energy optimization. IEEE Visualization 1996, San Francisco, CA, pp. 279-286.
16. Grzeszczuk, R. P., Huang, M., and Kauffman, L. H. 1997. Physically-based stochastic simplification of mathematical knots. IEEE Transactions on Visualization and Computer Graphics 3(3):262-278.
17. Hass, J., and Lagarias, J. 2001. The number of Reidemeister moves needed for unknotting. Journal of the American Mathematical Society 14:399-428.
18. Hass, J., Lagarias, J. C., and Pippenger, N. 1997. The computational complexity of knot and link problems. 38th Annual Symposium on Foundations of Computer Science, Miami Beach, FL, October 20-22, pp. 172-181.
19. Hoste, J. and Thistlethwaite, M. 1998. The first 1,701,936 knots. Mathematical Intelligencer 20(4):33-48.
20. Hsu, D. 2000. Randomized Single-Query Motion Planning In Expansive Spaces, PhD thesis, Department of Computer Science, Stanford University.
21. Hsu, D., Latombe, J.-C., and Motwani, R. 1997. Path planning in expansive spaces. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Albuquerque, NM, pp. 2719-2726.
22. Hsu, D., Kindel, R., Latombe, J.-C., and Rock, S. 2001. Control-based randomized motion planning for dynamic environments. Algorithmic and Computational Robotics: New Directions: 4th International Workshop on the Algorithmic Foundations of Robotics (WAFR), pp. 247-264.
23. Jaeger, F., Vertigan, D. L., and Welsh, D.J.A. 1990. On the computational complexity of the Jones and Tutte polynomials. Mathematical Proceedings of the Cambridge Philosophical Society 108:35-53.
24. Jenkins, R. 1989, A Dynamic Approach to Calculating the Homfly Polynomial for Directed Knots and Links, Master's thesis, Carnegie Mellon University.
25. Kauffman, L. H. and Magarshak, Y. 1994. Graph invariants and the topology of RNA folding. Journal of Knot Theory and its Ramifications 3(3):233-245.
26. Kavraki, L. E., Švestka, P., Latombe, J.-C., and Overmars, M. H. 1996. Probabilistic roadmaps for path planning in high-dimensional configuration spaces. IEEE Transactions on Robotics and Automation 12(4):566-580.
27. Kuffner, J. J., and LaValle, S. M. 1999. Randomized kinodynamic planning. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Detroit, MI, pp. 473-479.
28. Kuffner, J. J., and LaValle, S. M. 2000a. RRT-connect: an efficient approach to single-query path planning. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), San Francisco, CA, April 24-28.
29. Kuffner, J. J., and LaValle, S. M. 2000b. Rapidly exploring random trees: progress and prospects. Algorithmic and Computational Robotics: New Directions: 4th International Workshop on the Algorithmic Foundations of Robotics (WAFR), Hanover, NH, pp. 293-308.
30. Kuffner, J. J., and LaValle, S. M. 2001. Randomized kinodynamic planning. International Journal of Robotics Research 20(5):378-400.
31. Ladd, A., and Kavraki, L. 2002. A measure theoretic analysis of PRM. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11-15.
32. Lamiraux, F., and Kavraki, L. E. 2001. Planning paths for elastic objects under manipulation constraints. International Journal of Robotics Research 20(3):188-208.
33. Lickorish, W.B.R. 1997. An Introduction to Knot Theory, Springer-Verlag, Berlin.
34. Ligocki, T., and Sethian, J. A. 1994. Recognizing knots using simulated annealing. Journal of Knot Theory and its Ramifications 3(4):477-495.
35. Phillips, J., Ladd, A., and Kavraki, L. 2002. Simulated knot tying. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11-15.
36. Pippenger, N. 1989. Knots in random walks. Discrete Applied Mathematics 25:273-278.
37. Postow, L., Peter, B. J., and Cozzarelli, N. R. 1999. Knot what we thought before: the twisted story of replication. BioEssays 21:805-808.
38. Sánchez, G., and Latombe, J.-C. 2001. A single-query bidirectional motion planner with lazy collision checking. Proceedings of International Symposium on Robotics, Seoul, Korea.
39. Scharein, R. 1988. Interactive Topological Drawing, PhD thesis, University of British Columbia.
40. Shaw, S. Y., and Wang, J. C. 1993. Knotting of a DNA chain during ring closure. Science 260(23):533-536.
41. Shaw, S. Y. and Wang, J. C. 1994. DNA knot formation in aqueous solutions. Journal of Knot Theory and its Ramifications 3(3):287-298.
42. Simon, J. 1994. Energy functions for polygonal knots. Journal of Knot Theory and its Ramifications 3:299-320.
43. Song, G., and Amato, N. 2001. Using motion planning to study protein folding pathways. International Conference on Computational Molecular Biology (RECOMB), Montreal, Canada, April, pp. 287-296.
44. Stasiak, A., Katritch, V., Bednar, J., Michoud, D., and Dubochet, J. 1996. Electrophoretic mobility of DNA knots. Nature 384(6605): 142-145.
45. Sumners, D. W. and Whittington, S. G. 1988. Knots in selfavoiding walks. Journal of Physics A: Mathematical and General 21:1689-1694.
46. Teodoro, M., Phillips, G. N., and Kavraki, L. E. 2002. A dimensionality reduction approach to modeling protein flexibility. International Conference on Computational Molecular Biology (RECOMB), Washington, DC, April.
47. Vassilvitskii, S., Suh, J., and Yim, M. 2002. A complete, local and parallel reconfiguration algorithm for cube style modular robots. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11-15.
48. Walter, J., Tsai, B., and Amato, N. 2002. Choosing good paths for fast distributed reconfiguration of hexagonal metamorphic robots. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), Washington, DC, May 11-15.
49. Wu, Y.-Q. 1996. Ming User Manual. See http://www.math.uiowa.edu/~wu/ming/ ming.pdf.