Nonholonomic distance to polygonal obstacles for a car-like robot of polygonal shape

IEEE Transactions on Robotics

Volumn 22, Issue 5, 2006, Pages 1040-1047

  Robuffo Giordano, Paolo ^a   Vendittelli, M ^a   Laumond, Jean Paul ^b   Souères, Philippe ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b LAAS CNRS   (France)

Author keywords

Car like robots; Nonholonomic distance; Optimal control theory; Shortest paths

Indexed keywords

COLLISION AVOIDANCE; COMPUTATIONAL GEOMETRY; MOBILE ROBOTS; MOTION PLANNING; OPTIMAL CONTROL SYSTEMS;

CAR-LIKE ROBOTS; NONHOLONOMIC DISTANCE; SHORTEST PATHS;

ROBOTICS;

EID: 33750217511     PISSN: 15523098     EISSN: None     Source Type: Journal    
DOI: 10.1109/TRO.2006.878956     Document Type: Article

References (17)

1. J. Latombe, Robot Motion Planning. Boston, MA: Kluwer, 1991.
2. J.-P. Laumond and P. Souères, "Metric induced by the shortest paths for a car-like mobile robot," in Proc. Int. Conf. Intell. Robots Syst., 1993, pp. 1299-1303.
3. L. 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. 497-516, 1957.
4. J. Reeds and R. Shepp, "Optimal paths for a car that goes both forward and backwards," Pacific J. Math., vol. 2, p. 145, 1990.
5. J. Boissonnat, A. Cerezo, and J. Leblond, "Shortest paths of bounded curvature in the plane," in Proc. IEEE Int. Conf. Robot. Autom., Nice, France, May 1992, pp. 2315-2320.
6. H. J. Sussmann and W. Tang, Shortest paths for the Reeds-Shepp car: A worked-out example of the use of geometric techniques in nonlinear optimal control, Rutgers Univ., New Brunswick, NJ, Rep. SYCON-91-10, 1991.
7. P. Souères and J.-P. Laumond, "Shortest path synthesis for a car-like robot," IEEE Trans. Autom. Control, vol. 41, no. 5, pp. 672-688, May 1996.
8. G. Desaulniers, "On shortest paths for a car-like robot maneuvering around obstacles," Robot. Anton. Syst., vol. 17, pp. 139-148, 1996.
9. J. Reif and H. Wang, "The complexity of the two dimensional curvature-constrained shortest-path problem," in Robotics: The Algorithmic Perspective, P. K. Agarwal, L. E. Kavraki, and M. T. Mason, Eds. Natick, MA: A.K. Peters, 1998.
10. S. Fortune and G. Wilfong, "Planning constrained motions," in Proc. ACM STOCS, 1988, pp. 445-459.
11. B. Mirtich and J. Canny, "Using skeletons for nonholonomic path planning among obstacles," in Proc. IEEE Int. Conf. Robot. Autom., May 1992, vol. 3, pp. 2533-2540.
12. P. Moutarlier, B. Mirtich, and J. Canny, "Shortest paths for a car-like robot to manifolds in configuration space," Int. J. Robot. Res., vol. 15, no. 1, pp. 36-60, Feb. 1996.
13. M. Vendittelli, J.-P. Laumond, and C. Nissoux, "Obstacle distance for car-like robots," IEEE Trans. Robot. Autom., vol. 15, no. 4, pp. 678-691, Aug. 1999.
14. M. Vendittelli, J.-P. Laumond, and P. Souères, "Shortest paths to obstacles for a polygon car-like robot," in Proc. Conf. Decision Control, 1999, pp. 17-22.
15. L. Pontryagin, V. Boltyansky, R. Gamkrelidze, and E. Mischenko, The Mathematical Theory of Optimal Processes. New York: Wiley, 1962.
16. A. Bellaïche, "The tangent space in sub-Riemannian geometry," in Sub-Riemannian Geometry, A. Bellaïche and J.-J. Risler, Eds. Cambridge, MA: Birkhäuser, 1996, pp. 1-78.
17. P. Souères, J.-Y. Fourquet, and J.-P. Laumond, "Set of reachable positions for a car," IEEE Trans. Autom. Control, vol. 39, no. 8, pp. 1626-1630, Aug. 1994.