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All issues Volume 12 / No 1 (January 2006) ESAIM: COCV, 12 1 (2006) 139-168 References
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Issue
ESAIM: COCV
Volume 12, Number 1, January 2006
Page(s) 139 - 168
DOI https://doi.org/10.1051/cocv:2005035
Published online 15 December 2005
  1. R.A. Adams, Sobolev Spaces. Academic Press, New York (1975). [Google Scholar]
  2. E.L. Allgower and K. Georg, Continuation and Path Following. Acta Numerica (1992). [Google Scholar]
  3. J.M. Bismuth, Large Deviations and the Malliavin Calculus. Birkhäuser (1984). [Google Scholar]
  4. L. Cesari, Functional analysis and Galerkin's method. Mich. Math. J. 11 (1964) 385–418. [CrossRef] [Google Scholar]
  5. A. Chelouah and Y. Chitour, On the controllability and trajectories generation of rolling surfaces. Forum Math. 15 (2003) 727–758. [CrossRef] [MathSciNet] [Google Scholar]
  6. Y. Chitour, Applied and theoretical aspects of the controllability of nonholonomic systems. Ph.D. thesis, Rutgers University (1996). [Google Scholar]
  7. Y. Chitour, Path planning on compact Lie groups using a continuation method. Syst. Control Lett. 47 (2002) 383–391. [CrossRef] [Google Scholar]
  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. [Google Scholar]
  9. S.N. Chow and J.K. Hale, Methods of Bifurcation Theory. Springer, New York 251 (1982). [Google Scholar]
  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] [Google Scholar]
  11. Ge Zhong, Horizontal Path Spaces and Carnot-Carathéodory Metrics. Pacific J. Math. 161 (1993) 255–286. [MathSciNet] [Google Scholar]
  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. [Google Scholar]
  13. J.K. Hale, Applications of alternative problems. Lectures notes, Brown University (1971). [Google Scholar]
  14. M.W. Hirsch, Differential Topology. Springer, New York (1976). [Google Scholar]
  15. V. Jurdjevic, Geometric control theory. Cambridge Studies in Adv. Math., Cam. Univ. Press (1997). [Google Scholar]
  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. [Google Scholar]
  17. E.B. Lee and L. Markus, Foundations of Optimal Control Theory. Wiley, New York (1967). [Google Scholar]
  18. J. Leray and J. Schauder, Topologie et équations fonctionelles. Ann. Sci. Ecole Norm. Sup. 51 (1934) 45–78. [MathSciNet] [Google Scholar]
  19. T.Y. Li, Numerical solution of multivariate polynomial systems by homotopy continuation methods. Acta Numerica (1997) 399–436. [Google Scholar]
  20. W. Liu, An approximation algorithm for nonholonomic systems. SIAM J. Control Optim. 35 (1997) 1328–1365. [Google Scholar]
  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). [Google Scholar]
  22. P. Martin, Contribution à l'étude des systèmes différentiellement plats. Ph.D. thesis, École des Mines de Paris, Paris, France (1992). [Google Scholar]
  23. R. Montgomery, Abnormal Optimal Controls and Open Problems in Nonholonomic Steering. J. Dyn. Cont. Sys. 1 Plenum Pub. Corp. (1995) 49–90. [Google Scholar]
  24. R.M. Murray and S.S. Sastry, Steering nonholonomic systems using sinusoids, in Proc. IEEE Conference on Decision and Control (1990). [Google Scholar]
  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. [Google Scholar]
  26. P. Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symétriques de rang un. Ann. Math. 129 (1989) 1–60. [CrossRef] [Google Scholar]
  27. S.L. Richter and R.A. Decarlo, Continuation methods: Theory and Application. IEEE Trans. Circuits Syst. 30 (1983). [Google Scholar]
  28. E.D. Sontag, Mathematical Control Theory. Texts Appl. Math. 6, Springer-Verlag, New York, 2nd edition (1998). [Google Scholar]
  29. P. Souères and J.P. Laumond, Shortest paths synthesis for a car-like robot. IEEE Trans. Aut. Cont. 41 (1996) 672–688. [Google Scholar]
  30. R. Strichartz, Sub-Riemannian Geometry. J. Diff. Geom. 24 (1983) 221–263. [Google Scholar]
  31. H.J. Sussmann, A Continuation Method for Nonholonomic Path-finding Problems, in Proceedings of the 32nd IEEE CDC, San Antonio, TX (Dec. 1993). [Google Scholar]
  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). [Google Scholar]
  33. T. Wazewski, Sur l'évaluation du domaine d'existence des fonctions implicites réelles ou complexes. Ann. Soc. Polon. Math. 20 (1947). [Google Scholar]

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