Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 16, Issue: 4, page 1018-1039
- ISSN: 1292-8119
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top- A.A. Agrachev, Exponential mappings for contact sub-Riemannian structures. J. Dyn. Control Syst.2 (1996) 321–358.
- A.A. Agrachev, Geometry of optimal control problems and Hamiltonian systems, in Nonlinear and Optimal Control Theory, Lect. Notes Math. CIME1932, Springer Verlag (2008) 1–59.
- A.A. Agrachev and Y.L. Sachkov, Control Theory from the Geometric Viewpoint. Springer-Verlag, Berlin (2004).
- A.A. Agrachev, U. Boscain, J.P. Gauthier and F. Rossi, The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. J. Funct. Anal.256 (2009) 2621–2655.
- G. Citti and A. Sarti, A cortical based model of perceptual completion in the roto-translation space. J. Math. Imaging Vis.24 (2006) 307–326.
- C. El-Alaoui, J.P. Gauthier and I. Kupka, Small sub-Riemannian balls on . J. Dyn. Control Syst.2 (1996) 359–421.
- V. Jurdjevic, Geometric Control Theory. Cambridge University Press (1997).
- J.P. Laumond, Nonholonomic motion planning for mobile robots, Lecture Notes in Control and Information Sciences229. Springer (1998).
- I. Moiseev and Y.L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV (2009), doi:. DOI10.1051/cocv/2009004
- J. Petitot, The neurogeometry of pinwheels as a sub-Riemannian contact structure. J. Physiology – Paris97 (2003) 265–309.
- J. Petitot, Neurogéometrie de la vision – Modèles mathématiques et physiques des architectures fonctionnelles. Éditions de l'École polytechnique, France (2008).
- L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mishchenko, The mathematical theory of optimal processes. Wiley Interscience (1962).
- Y.L. Sachkov, Exponential mapping in generalized Dido's problem. Mat. Sbornik194 (2003) 63–90 (in Russian). English translation in Sbornik: Mathematics194 (2003).
- Y.L. Sachkov, Discrete symmetries in the generalized Dido problem. Matem. Sbornik197 (2006) 95–116 (in Russian). English translation in Sbornik: Mathematics, 197 (2006) 235–257.
- Y.L. Sachkov, The Maxwell set in the generalized Dido problem. Matem. Sbornik197 (2006) 123–150 (in Russian). English translation in Sbornik: Mathematics197 (2006) 595–621.
- Y.L. Sachkov, Complete description of the Maxwell strata in the generalized Dido problem. Matem. Sbornik197 (2006) 111–160 (in Russian). English translation in: Sbornik: Mathematics197 (2006) 901–950.
- Y.L. Sachkov, Maxwell strata in Euler's elastic problem. J. Dyn. Control Syst.14 (2008) 169–234.
- Y.L. Sachkov, Conjugate points in Euler's elastic problem. J. Dyn. Control Syst.14 (2008) 409–439.
- Y.L. Sachkov, Cut locus and optimal synthesis in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV (submitted).
- A.V. Sarychev, The index of second variation of a control system. Matem. Sbornik113 (1980) 464–486 (in Russian). English translation in Math. USSR Sbornik41 (1982) 383–401.
- A.M. Vershik and V.Y. Gershkovich, Nonholonomic Dynamical Systems – Geometry of distributions and variational problems (in Russian), in Itogi Nauki i Tekhniki: Sovremennye Problemy Matematiki, Fundamental'nyje Napravleniya16, VINITI, Moscow (1987) 5–85. English translation in Encyclopedia of Math. Sci.16, Dynamical Systems7, Springer Verlag.
- E.T. Whittaker and G.N. Watson, A Course of Modern Analysis. An introduction to the general theory of infinite processes and of analytic functions; with an account of principal transcendental functions. Cambridge University Press, Cambridge (1996).
- S. Wolfram, Mathematica: a system for doing mathematics by computer. Addison-Wesley, Reading, USA (1991).
Citations in EuDML Documents
top- Igor Moiseev, Yuri L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane
- Ross M. Adams, Rory Biggs, Claudiu C. Remsing, Two-input control systems on the euclidean group SE (2)
- Ugo Boscain, Remco Duits, Francesco Rossi, Yuri Sachkov, Curve cuspless reconstruction via sub-riemannian geometry