From Reeds and Shepp's to continuous-curvature paths

IEEE Transactions on Robotics

Volumn 20, Issue 6, 2004, Pages 1025-1035

  Fraichard, Thierry ^a   Scheuer, Alexis ^b  

^a INRIA   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Nonholonomic vehicles; Smooth path planning

Indexed keywords

COLLISION AVOIDANCE; MATHEMATICAL MODELS; MOTION CONTROL; ROBOTICS; STEERING; UNMANNED VEHICLES;

CONTINUOUS CURVATURE; NONHOLONOMIC VEHICLES; SMOOTH PATH PLANNING;

MOTION PLANNING;

EID: 10944235431     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2004.833789     Document Type: Article

References (40)

1. J.-P. Laumond, "Feasible trajectories for mobile robots with kinematic and environment constraints," in Proc. Int. Conf. Intelligent Autonomous Systems, Amsterdam, The Netherlands, Dec. 1986, pp. 346-354.
2. J.-P. Laumond, Ed., Robot Motion Planning and Control, New York: Springer, 1998, vol. 229, Lecture Notes in Control and Information Science.
3. J. Barraquand and J.-C. Latombe, "On nonholonomic mobile robots and optimal maneuvering," Revue d'Intell. Artif., vol. 3, no. 2, pp. 77-103. 1989.
4. P. Jacobs and J. Canny, "Planning smooth paths for mobile robots," in Proc. IEEE Int. Conf. Robotics and Automation, Scottsdale, AZ, May 1989, pp. 2-7.
5. T. Fraichard, "Smooth trajectory planning for a car in a structured world," in Proc. IEEE Int. Conf. Robotics and Automation, vol. 1, Sacramento, CA, Apr. 1991, pp. 318-323.
6. P. Svestka and M. H. Overmars, "Probabilistic path planning," Dept. Comput. Sci., Utrecht Univ., Utrecht, The Netherlands, Tech. Rep. UU-CS-1995-22, May 1995.
7. L. E. Dubins, "On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents," Amer. J. Math., vol. 79, pp. 497-517, 1957.
8. J. A. Reeds and L. A. Shepp, "Optimal paths for a car that goes both forward and backward," Pacific J. Math., vol. 145, no. 2, pp. 367-393, 1990.
9. J.-D. Boissonnat, A. Cérézo, and J. Leblond, "A note on shortest paths in the plane subject to a constraint on the derivative of the curvature," INRIA, Rocquencourt, France, Res. Rep. 2160, Jan. 1994.
10. L. Kavraki, P. Svestka, I.-C. Latombe, and M. H. Overmars, "Probabilistic roadmaps for path planning in high dimensional configuration spaces," IEEE Trans. Robot. Automat., vol. 12, pp. 566-580, Aug. 1996.
11. E. Mazer, J.-M. Ahuactzin, and P. Bessière, "The Ariadne's Clew algorithm," J. Artif. Intell. Res., vol. 9, pp. 295-316, July-Dec. 1998.
12. J.-P. Laumond, P. E. Jacobs, M. Taïx, and R. M. Murray, "A motion planner for nonholonomic mobile robots," IEEE Trans. Robot. Automat. vol. 10, pp. 577-593, Oct. 1994.
13. S. Sekhavat and J.-P. Laumond, "Topological property for collision-free nonholonomic motion planning: The case of sinusoidal inputs for chained form systems," IEEE Trans. Robot. Automat., vol. 14. pp. 671-680, Oct. 1998.
14. H. J. Sussmann, "The Markov - Dubins problem with angular acceleration control," in Proc. IEEE Conf. Decision and Control, vol. 3, San Diego, CA, Dec. 1997, pp. 2639-2643.
15. K. Komoriya and K. Tanie, "Trajectory design and control of a wheel-type mobile robot using B-spline curve," in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Tsukuba, Japan, Sept. 1989, pp. 398-405.
16. A. Takahashi, T. Hongo, and Y. Ninomiya, "Local path planning and control for AGV in positioning," in Proc. IEEE/RSJInt. Conf. Intelligent Robots and Systems, Tsukuba, Japan, Sept. 1989, pp. 392-397.
17. W. L. Nelson, "Continuous curvature paths for autonomous vehicles," in Proc. IEEE Int. Conf. Robotics and Automation, vol. 3, Scottsdale, AZ, May 1989, pp. 1260-1264.
18. R. Liscano and D. Green, "Design and implementation of a trajectory generator for an indoor mobile robot," in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, Tsukuba, Japan, Sept. 1989, pp. 380-385.
19. Y. Kanayama and B. I. Hartman, "Smooth local path planning for autonomous vehicles," in Proc. IEEE Int. Conf. Robotics and Automation, vol. 3, Scottsdale, AZ, May 1989, pp. 1265-1270.
20. 2-splines for trajectory planning of autonomous vehicles," in Proc. IEEE Intelligent Vehicles Symp., Dearborn, MI, Oct. 2000, pp. 198-203.
21. H. Delingette, M. Hébert, and K. Ikeuchi, "Trajectory generation with curvature constraint based on energy minimization," in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, vol. 1, Osaka, Japan, Nov. 1991, pp. 206-211.
22. A. E. Bryson and Y. C. Ho, Applied Optimal Control. Bristol, PA: Hemisphere, 1975.
23. C. Fernandez, L. Gurvits, and Z. L. Li, "A variational approach to optimal nonholonomic motion planning," in Proc. IEEE Int. Conf. Robotics and Automation, vol. 1, Nagoya, Japan, May 1995, pp. 680-685.
24. S. Sekhavat, "Planification de mouvements sans collisions pour des systèmes non holonomes," Ph.D. dissertation, Inst. Nat. Polytech. Toulouse, Toulouse, France, 1995.
25. G. Lafferière and H. Sussmann, "A differential geometric approach to motion planning," in Nonholonomic Motion Planning, Z. Li and J. Canny, Eds. Norwell, MA: Kluwer, 1993, pp. 235-270.
26. R. M. Murray and S. S. Sastry, "Nonholonomic motion planning: Steering using sinusoids," IEEE Trans. Automat. Contr., vol. 38, pp. 700-716, Sept. 1993.
27. P. Rouchon, M. Fliess, M. Lévine, and P. Martin, "Flatness, motion planning and trailer system," in Proc. IEEE Conf. Decision and Control, San Antonio, TX, Dec. 1993, pp. 2700-2705.
28. J.-P. Laumond, S. Sekhavat, and F. Lamiraux, "Guidelines in nonholonomic motion planning for mobile robots," in Robot Motion Planning and Control, J.-P. Laumond, Ed. New York: Springer, 1998, vol. 229, Lecture Notes in Control and Information Science, pp. 1-53.
29. A. Bellaïche, J.-P. Laumond, and M. Chyba, "Canonical nilpotent approximation of control systems: Application to nonholonomic motion planning," in Proc. IEEE Int. Conf. Decision and Control, San Antonio, TX, 1993, pp. 2694-2699.
30. D. Tilbury, R. Murray, and S. Sastry, "Trajectory generation for the n-trailer problem using Goursat normal form," IEEE Trans. Automat. Contr., vol. 40, pp. 802-819, May 1995.
31. S. Monaco and D. Normand-Cyrot, "An introduction to motion planning under multi-rate digital control," in Proc. IEEE Int. Conf. Decision and Control, Tucson, AZ, 1992, pp. 1780-1785.
32. S. Sekhavat, F. Lamiraux, J.-P. Laumond, G. Bauzil, and A. Ferrand, "Motion planning and control for Hilare pulling a trailer: Experimental issues," in Proc. IEEE Int. Conf. Robotics and Automation, Albuquerque, NM, Apr. 1997, pp. 3306-3311.
33. F. Lamiraux and J.-P. Laumond, "Smooth motion planning for car-like vehicles," IEEE Trans. Robot. Automat., vol. 17, pp. 498-502, Aug. 2001.
34. E. Degtiariova-Kostova and V. Kostov, "Irregularity of optimal trajectories in a control problem for a car-like robot," INRIA, Sophia Antipolis, France, Res. Rep. 3411, Apr. 1998.
35. A. Scheuer and C. Laugier, "Planning sub-optimal and continuous-curvature paths for car-like robots," in Proc. IEEE /RSJ Int. Conf. Intelligent Robots and Systems, vol. 1, Victoria, BC, Canada, Oct. 1998, pp. 25-31.
36. A. Scheuer, "Planitication de chemins à courbure continue pour robot mobile non-holonome," Ph.D. dissertation, Inst. Nat. Polytech. Grenoble, Grenoble, France, Jan. 1998.
37. A. Scheuer and T. Fraichard, "Collision-free and continuous-curvature path planning for car-like robots," in Proc. IEEE Int. Conf. Robotics and Automation, vol. 1, Albuquerque, NM, Apr. 1997, pp. 867-873.
38. A. Scheuer, "Continuous-curvature path planning for car-like vehicles," in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems, vol. 2, Grenoble, France, Sept. 1997, pp. 997-1003.
39. T. Fraichard and J.-M. Ahuactzin, "Smooth path planning for cars," in Proc. IEEE Int. Conf. Robotics and Automation, Seoul, Korea, May 2091, pp. 3722-3727.
40. M. Abramovitz and I. A. Stegun, Eds., Handbook of Mathematical Functions. New York: Dover, 1965.