Locally optimal motion planning of nonholonomic systems

Journal of Robotic Systems

Volumn 14, Issue 11, 1997, Pages 767-788

  Dulȩba, Ignacy ^a  

^a WROCLAW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONTROLLABILITY; FUNCTIONS; PROBLEM SOLVING; ROBOTICS;

HERMES ALGORITHM; NONHOLOMIC SYSTEMS;

MOTION PLANNING;

EID: 0031273854     PISSN: 07412223     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-4563(199711)14:11<767::AID-ROB2>3.0.CO;2-S     Document Type: Article

References (14)

1. R. W. Brockett, "Control theory and singular riemannian geometry," in New Directions in Applied Mathematics, P. J. Hilton and G. S. Young Eds., Springer Verlag, 1981, pp. 11-27.
2. G. Lafferriere and H. J. Sussmann, "Motion planning for controllable systems without drift: A preliminary report," Report SYCON-90-04, Rutgers Center for Syst. & Contr., 1990.
3. H. Hermes, "Lie algebras of vector fields and local approximation of attainable sets," SIAM Journ. Contr. and Opt., 16(6), 715-728, 1978.
4. G. Jacob, "Lyndon discretization and exact motion planning," Proc. Europ. Contr. Conf., Grenoble, France, 1991, pp. 1507-1512.
5. J.-P. Laumond, et al., "A motion planner for nonholonomic mobile robots," IEEE Trans, on Rob. Autom., 10(5), 577-593, 1994.
6. J. A. Reeds and R. A. Shepp, "Optimal paths for a car that goes both forward and backwards," Pacific J. Math., 145(2), 367-393, 1990.
7. L. E. Dubins, "On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents," Am. J. Math., 79, 497-516, 1957.
8. R. M. Murray and S. S. Sastry, "Nonholonomic motion planning: Steering using sinusoids," IEEE Trans. Rob. Autom., 38(5), 700-716, 1993.
9. R. Mukherjee and D. P. Andersson, "Nonholonomic motion planning using Stokes's Theorem," Proc. IEEE Int. Conf. Rob. Autom., Atlanta, GA, 1993, pp. 802-809.
10. Y. Nakamura and R. Mukherjee, "Nonholonomic path planning of space robots via bidirectional approach," IEEE Trans. Rob. Autom., 7(4), 500-514, 1991.
11. S. Samuel and S. S. Keerthi, "Numerical determination of optimal non-holonomic paths in the presence of obstacles," Proc. IEEE Conf. Rob. Autom. Atlanta, GA, 1993, pp. 826-831.
12. H. Hermes, "On the synthesis of a stabilizing feedback control via Lie algebraic method," SIAM Journ. Contr. and Opt., 18(6), 352-361, 1980.
13. J.-P. Laumond, "Singularities and topological aspects in nonholonomic motion planning," in Nonholonomic Motion Planning, Z. Li and J. F. Canny, Eds., Kluwer Academic Publ., New York, 1992, pp. 149-199.
14. R. S. Strichartz, "The Campbell-Baker-Hausdorff-Dynkin Formula and solutions of differential equations," Journ. of Funct. Analysis, 72, 320-345, 1987.