Free access
Issue
ESAIM: COCV
Volume 9, March 2003
Page(s) 485 - 508
DOI http://dx.doi.org/10.1051/cocv:2003024
Published online 15 September 2003
  1. A. Bellaïche, The tangent space in sub-Riemannian geometry, edited by A. Bellaïche and J.-J. Risler, Sub-Riemannian Geometry. Birkhäuser, Progr. Math. (1996).
  2. A. Bellaïche, F. Jean and J.-J. Risler, Geometry of nonholonomic systems, edited by J.-P. Laumond, Robot Motion Planning and Control. Springer, Lecture Notes Inform. Control Sci. 229 (1998).
  3. A. Bellaïche, J.-P. Laumond and J. Jacobs, Controllability of car-like robots and complexity of the motion planning problem, in International Symposium on Intelligent Robotics. Bangalore, India (1991) 322-337.
  4. J.F. Canny, The Complexity of Robot Motion Planning. MIT Press (1988).
  5. W.L. Chow, Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung. Math. Ann. 117 (1940) 98-115. [CrossRef]
  6. G. Comte and Y. Yomdin, Tame geometry with applications in smooth analysis. Preprint of the IHP-RAAG Network (2002).
  7. M. Gromov, Carnot-Carathéodory spaces seen from within, edited by A. Bellaïche and J.-J. Risler, Sub-Riemannian Geometry. Birkhäuser, Progr. Math. (1996).
  8. W. Hurewicz and H. Wallman, Dimension Theory. Princeton University Press, Princeton (1948).
  9. F. Jean, Paths in sub-Riemannian geometry, edited by A. Isidori, F. Lamnabhi-Lagarrigue and W. Respondek, Nonlinear Control in the Year 2000. Springer-Verlag (2000).
  10. F. Jean, Complexity of nonholonomic motion planning. Int. J. Control 74 (2001) 776-782. [CrossRef] [MathSciNet]
  11. F. Jean, Uniform estimation of sub-Riemannian balls. J. Dynam. Control Systems 7 (2001) 473-500. [CrossRef] [MathSciNet]
  12. A.N. Kolmogorov, On certain asymptotics characteristics of some completely bounded metric spaces. Soviet Math. Dokl. 108 (1956) 385-388.
  13. I. Kupka, Géométrie sous-riemannienne, in Séminaire N. Bourbaki, Vol. 817 (1996).
  14. J.-P. Laumond, Controllability of a multibody mobile robot. IEEE Trans. Robotics Automation 9 (1993) 755-763. [CrossRef]
  15. J.-P. Laumond, S. Sekhavat and F. Lamiraux, Guidelines in nonholonomic motion planning for mobile robots, edited by J.-P. Laumond, Robot Motion Planning and Control. Springer, Lecture Notes Inform. Control Sci. 229 (1998).
  16. J. Mitchell, On Carnot-Carathéodory metrics. J. Differential Geom. 21 (1985) 35-45. [MathSciNet]
  17. T. Nagano, Linear differential systems with singularities and an application to transitive Lie algebras. J. Math. Soc. Japan 18 (1966) 398-404. [CrossRef] [MathSciNet]
  18. J.T. Schwartz and M. Sharir, On the ``piano movers" problem II: General techniques for computing topological properties of real algebraic manifolds. Adv. Appl. Math. 4 (1983) 298-351. [CrossRef]
  19. H.J. Sussmann, An extension of theorem of Nagano on transitive Lie algebras. Proc. Amer. Math. Soc. 45 (1974) 349-356. [CrossRef] [MathSciNet]
  20. A.M. Vershik and V.Ya. Gershkovich, Nonholonomic dynamical systems, geometry of distributions and variational problems, edited by V.I. Arnold and S.P. Novikov, Dynamical Systems VII. Springer, Encyclopaedia Math. Sci. 16 (1994).