# Dubins' problem is intrinsically three-dimensional

ESAIM: Control, Optimisation and Calculus of Variations (1998)

- Volume: 3, page 1-22
- ISSN: 1292-8119

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topMittenhuber, Dirk. "Dubins' problem is intrinsically three-dimensional." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 1-22. <http://eudml.org/doc/90519>.

@article{Mittenhuber1998,

author = {Mittenhuber, Dirk},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal arcs; Pontryagin's maximum principle; Dubins problem},

language = {eng},

pages = {1-22},

publisher = {EDP Sciences},

title = {Dubins' problem is intrinsically three-dimensional},

url = {http://eudml.org/doc/90519},

volume = {3},

year = {1998},

}

TY - JOUR

AU - Mittenhuber, Dirk

TI - Dubins' problem is intrinsically three-dimensional

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 1998

PB - EDP Sciences

VL - 3

SP - 1

EP - 22

LA - eng

KW - optimal arcs; Pontryagin's maximum principle; Dubins problem

UR - http://eudml.org/doc/90519

ER -

## References

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- [12] D. Mittenhuber: Dubins' problem in the hyperbolic plane using the open disc model, in Control Theory and its Applications, R. Sharpe ed., Can. Math. Soc. Conf. Proc. Ser., to appear. Zbl0980.53053MR1648713
- [13] D. Mittenhuber: Applications of the Maximum Principle to Problems in Lie Semigroups, in Semigroups in Algebra, Geometry, and Analysis, K. H. Hofmann, J. D. Lawson and E. B. Vinberg. eds., de Gruyter, Berlin, 1995, 311-336. Zbl0898.60092MR1350338
- [14] F. Monroy Pérez: Non-Euclidean Dubins' problem, in Control Theory and its Applications, R. Sharpe ed., Can. Math. Soc. Conf. Proc. Ser., to appear. MR1626545
- [15] F. Monroy Pérez: Non-Euclidean Dubins'problem: A control theoretic approach, PhD thesis, University of Toronto, 1995.
- [16] J.G. Ratcliffe: Foundations of Hyperbolic Manifolds, Springer, Berlin, New York, 1994. Zbl0809.51001MR1299730
- [17] J.A. Reeds, L.A. Shepp: Optimal paths for a car that goes both forwards and backwards, Pacific Journal of Mathematics, 145, 1990, 367-393. MR1069892
- [18] H.J. Sussmann: Shortest 3-dimensional paths with a prescribed curvature bound, in Proceedings of the 1995 IEEE Conference on Decision and Control, 1995, 3306-3312.

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