Multivalued distance maps for motion planning on surfaces with moving obstacles

IEEE Transactions on Robotics and Automation

Volumn 14, Issue 3, 1998, Pages 427-436

  Kimmel, Ron ^a   Kiryati, Nahum ^a   Bruckstein, Alfred M ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Front propagation; Level sets; Moving obstacles; Multivalued distance map; Path planning

Indexed keywords

ALGORITHMS; CONSTRAINT THEORY; MOTION PLANNING; OBJECT RECOGNITION;

MULTIVALUED DISTANCE MAPS;

ROBOTICS;

EID: 0032095561     PISSN: 1042296X     EISSN: None     Source Type: Journal    
DOI: 10.1109/70.678452     Document Type: Article

References (30)

1. D. Adalsteinsson and J. A. Sethian, "A fast level set method for propagating interfaces," J. Comput. Phys., vol. 118, pp. 269-277, 1995.
2. E. Adin and A. M. Bruckstein, "Navigation in a dynamic environment," Tech. Rep. CIS #9101, Ctr. Intell. Syst., Technion, Haifa, Israel, Jan. 1991.
3. H. Blum, "Biological shape and visual science," J. Theoret. Bio., vol. 38, pp. 205-287, 1973.
4. D. L. Chopp, " Computing minimal surfaces via level set curvature flow," J. Comput. Phys., vol. 106, no. 1, pp. 77-91, May 1993.
5. E. W. Dijkstra, "A note on two problems in connection with graphs," Numer. Math., vol. 1, pp. 269-271, 1959.
6. C. L. Epstein and M. Gage, "The curve shortening flow," A. Chorin and A. Majda, Eds. Wave Motion: Theory, Modeling, and Computation. New York: Springer-Verlag, 1987.
7. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics. Reading, MA: Addison-Wesley, 1964.
8. K. Kant and S. Zucker, "Toward efficient trajectory planning: The pathvelocity decomposition," Int. J. Robot. Res., vol. 5, no. 3, pp. 72-89, 1986.
9. _, "Planning collision-free trajectories in time-varying environments: A two-level hierarchy," in Proc. Int. Conf. Robot. Automat., 1988, pp. 1644-1649.
10. R. Kimmel, A. Amir, and A. M. Bruckstein, "Finding shortest paths on surfaces," Curves and Surfaces in Geometric Design, P. Laurent, A. Le Méhautié, and L. L. Schumaker, Eds. Wellesley, MA: A. K. Peters, 1994, pp. 259-268.
11. _,"Finding shortest paths on surfaces using level sets propagation," IEEE Trans. Pattern Anal. Machine Intell., vol. 17, pp. 635-640, June 1995.
12. R. Kimmel and G. Sapiro, "Shortening three dimensional curves via two dimensional flows," Int. J. Comput. Math. Appl., vol. 29, no. 3, pp. 49-62, 1995.
13. R. Kimmel and J. A. Sethian, "Applications of fast marching methods to robotic navigation and construction of optimal paths," submitted for publication.
14. N. Kiryati and G. Székely, "Estimating shortest paths and minimal distances on digitized three dimensional surfaces," Pattern Recognit., vol. 26, no. 11, pp. 1623-1637, 1993.
15. K. J. Kyriakopoulos and G. N. Saridis, "An integrated collision prediction and avoidance scheme for mobile robots in nonstationary environments," Automatica, vol. 29, no. 2, pp. 309-322, 1993.
16. _, "Optimal and suboptimal motion planning for collision avoidance of mobile robots in nonstationary environments," J. Intell. Robot. Syst.: Theory Appl., vol. 11, no. 3, pp. 223-267, 1995.
17. J. C. Latombe, Robot Motion Planning. Boston, MA: Kluwer, 1991.
18. J. S. B. Mitchell, D. M. Mount, and C. H. Papadimitriou, "The discrete geodesic problem," SIAM J. Comput., vol. 16, no. 4, pp. 647-668, 1987.
19. J. S. B. Mitchell, D. Payton, and D. Keirsey, "Planning and reasoning for autonomous vehicle control," Int. J. Intell. Syst., vol. 2, pp. 129-198, 1987.
20. S. Osher and C. W. Shu, " High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations," SIAM J. Numer. Anal., vol. 28, no. 4, pp. 907-922, Aug. 1991.
21. S. J. Osher and J. A. Sethian, "Fronts propagating with curvature dependent speed: Algorithms based on Hamilton-Jacobi formulations," J. Comput. Phys., vol. 79, pp. 12-49, 1988.
22. G. Sapiro and A. Tannenbaum, "Affine invariant scale-space," Int. J. Comput. Vis., vol. 11, no. 1, pp. 25-44, 1993.
23. J. T. Schwartz, M. Sharir, and J. Hopcroft, Eds., Planning, Geometry, and Complexity of Robot Motion. Norwood, NJ: Ablex, 1987.
24. J. A. Sethian, "A review of recent numerical algorithme for hypersurfaces moving with curvature dependent speed," J. Differ. Geom., vol. 33, pp. 131-161, 1990.
25. _, "A marching level set method for monotonically advancing fronts," Proc. Nat. Acad. Sci., vol. 93, no. 4, 1996.
26. M. Sharir and A. Schorr, "On shortest paths in polyhedral spaces," SIAM J. Comput., vol. 1, no. 15, pp. 193-215, 1986.
27. J. N. Tsitsiklis, "Efficient algorithms for globally optimal trajectories," IEEE Trans. Automat. Contr., vol. 40, pp. 1528-1538, 1995.
28. T. Tsubouchi and S. Arimoto, " Behavior of a mobile robot navigated by an "iterated forecast and planning" scheme in the presence of multiple moving obstacles, in Proc. IEEE Int. Conf. Robot. Automat., 1994, vol. 3, pp. 2470-2475.
29. E. Wolfson and E. L. Schwartz, "Computing minimal distances on polyhedral surfaces," IEEE Trans. Pattern Anal. Machine Intell., vol. 11, pp. 1001-1005, 1989.
30. A. Zelinsky, "Using path transforms to guide the search for findpath in 2-D," Int. J. Robot. Res., vol. 13, no. 4, pp. 315-315, 1994.