Free Access
Volume 12, Number 1, January 2006
Page(s) 139 - 168
Published online 15 December 2005
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975).
  2. E.L. Allgower and K. Georg, Continuation and Path Following. Acta Numerica (1992).
  3. J.M. Bismuth, Large Deviations and the Malliavin Calculus. Birkhäuser (1984).
  4. L. Cesari, Functional analysis and Galerkin's method. Mich. Math. J. 11 (1964) 385–418. [CrossRef]
  5. A. Chelouah and Y. Chitour, On the controllability and trajectories generation of rolling surfaces. Forum Math. 15 (2003) 727–758. [CrossRef] [MathSciNet]
  6. Y. Chitour, Applied and theoretical aspects of the controllability of nonholonomic systems. Ph.D. thesis, Rutgers University (1996).
  7. Y. Chitour, Path planning on compact Lie groups using a continuation method. Syst. Control Lett. 47 (2002) 383–391. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  8. Y. Chitour and H.J. Sussmann, Line-integral estimates and motion planning using a continuation method. Essays on Math. Robotics, J. Baillieul, S.S. Sastry and H.J. Sussmann Eds., IMA. Math. Appl. 104 (1998) 91–125.
  9. S.N. Chow and J.K. Hale, Methods of Bifurcation Theory. Springer, New York 251 (1982).
  10. A. Divelbiss and J.T. Wen, A Path Space Approach to Nonholonomic Motion Planning in the Presence of Obstacles. IEEE Trans. Robotics Automation 13 (1997) 443–451. [CrossRef]
  11. Ge Zhong, Horizontal Path Spaces and Carnot-Carathéodory Metrics. Pacific J. Math. 161 (1993) 255–286. [MathSciNet]
  12. K.A. Grasse and H.J. Sussmann, Global controllability by nice controls, Nonlinear controllability and optimal control. Dekker, NY. Mono. Text. Pure Appl. Math. 133 (1990) 33–79.
  13. J.K. Hale, Applications of alternative problems. Lectures notes, Brown University (1971).
  14. M.W. Hirsch, Differential Topology. Springer, New York (1976).
  15. V. Jurdjevic, Geometric control theory. Cambridge Studies in Adv. Math., Cam. Univ. Press (1997).
  16. G. Lafferriere, and H.J. Sussmann, Motion planning for controllable systems without drift, in Proc. Int. Conf. Robot. Auto. Sacramento, CA (1991) 1148–1153.
  17. E.B. Lee and L. Markus, Foundations of Optimal Control Theory. Wiley, New York (1967).
  18. J. Leray and J. Schauder, Topologie et équations fonctionelles. Ann. Sci. Ecole Norm. Sup. 51 (1934) 45–78. [MathSciNet]
  19. T.Y. Li, Numerical solution of multivariate polynomial systems by homotopy continuation methods. Acta Numerica (1997) 399–436.
  20. W. Liu, An approximation algorithm for nonholonomic systems. SIAM J. Control Optim. 35 (1997) 1328–1365. [CrossRef] [MathSciNet]
  21. W. Liu and H.J. Sussmann, Shortest paths for sub-Riemannian metrics on rank 2 distributions. Memoirs of the AMS, Formula 564 118 (1995).
  22. P. Martin, Contribution à l'étude des systèmes différentiellement plats. Ph.D. thesis, École des Mines de Paris, Paris, France (1992).
  23. R. Montgomery, Abnormal Optimal Controls and Open Problems in Nonholonomic Steering. J. Dyn. Cont. Sys. 1 Plenum Pub. Corp. (1995) 49–90.
  24. R.M. Murray and S.S. Sastry, Steering nonholonomic systems using sinusoids, in Proc. IEEE Conference on Decision and Control (1990).
  25. Cz. Olech, On the Wazewski equation, in Proc. of the conference, Topological methods in Differential Equations and Dynamical systems, Krakow (1996). Univ. Iagel. Acta Math. 36 (1998) 55–64.
  26. P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. Math. 129 (1989) 1–60. [CrossRef]
  27. S.L. Richter and R.A. Decarlo, Continuation methods: Theory and Application. IEEE Trans. Circuits Syst. 30 (1983).
  28. E.D. Sontag, Mathematical Control Theory. Texts Appl. Math. 6, Springer-Verlag, New York, 2nd edition (1998).
  29. P. Souères and J.P. Laumond, Shortest paths synthesis for a car-like robot. IEEE Trans. Aut. Cont. 41 (1996) 672–688. [CrossRef] [MathSciNet]
  30. R. Strichartz, Sub-Riemannian Geometry. J. Diff. Geom. 24 (1983) 221–263.
  31. H.J. Sussmann, A Continuation Method for Nonholonomic Path-finding Problems, in Proceedings of the 32nd IEEE CDC, San Antonio, TX (Dec. 1993).
  32. H.J. Sussmann, New Differential Geometric Methods in Nonholonomic Path Finding, in Systems, Models, and Feedback, A. Isidori and T.J. Tarn Eds. BirkhFormula user, Boston (1992).
  33. T. Wazewski, Sur l'évaluation du domaine d'existence des fonctions implicites réelles ou complexes. Ann. Soc. Polon. Math. 20 (1947).

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