118 5.2.1 Definition of the control problem, 118 5.2.2 Previous 1D results, difficulties of the 2D and 3D generalizations . . . . 120 5.2.3 Statement of the main results, p.123 ,
125 5.3.1 Haraux and Jaffard 's result, p.129 ,
133 5.5.1 Reduction of the problem 133 5.5.2 Proof strategy for the genericity of (B k ), p.140 ,
A representation theorem for solutions of the helmholtz equation and resolvent estimates for the laplacian Analysis, et cetera : research papers published in honor of Jürgen Moser's 60th birthday, pp.39-76, 1990. ,
Control Theory from the Geometric Viewpoint, pp.31-86, 2004. ,
DOI : 10.1007/978-3-662-06404-7
Genericity of simple eigenvalues for elliptic PDE's. Proceedings of the, pp.413-418, 1975. ,
Continuation and path following, Acta Numerica, vol.26, issue.87, pp.1-64, 2008. ,
DOI : 10.1007/BF01390054
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.7009
Reconstruction of Small Inhomogeneities from Boundary Measurements, Lecture Notes in Mathematics, vol.1846, issue.154, p.156, 2004. ,
DOI : 10.1007/b98245
Families of exponentials : the method of moments in controllability problems for distributed parameter systems, p.121, 1995. ,
Ingham-Beurling type theorem with weakened gap conditions, Acta Mathematica Hungarica, vol.97, issue.1/2, pp.55-95, 2002. ,
DOI : 10.1023/A:1020806811956
Controllability for Distributed Bilinear Systems, SIAM Journal on Control and Optimization, vol.20, issue.4, p.114, 1982. ,
DOI : 10.1137/0320042
URL : http://authors.library.caltech.edu/4635/1/BALsiamjco82.pdf
Local controllability of a 1-D Schr??dinger equation, Journal de Math??matiques Pures et Appliqu??es, vol.84, issue.7, pp.851-956, 2005. ,
DOI : 10.1016/j.matpur.2005.02.005
Controllability of a quantum particle in a moving potential well, Journal of Functional Analysis, vol.232, issue.2, pp.328-389, 2006. ,
DOI : 10.1016/j.jfa.2005.03.021
URL : https://hal.archives-ouvertes.fr/hal-00825517
The tangent space in sub-riemannian geometry, Sub-Riemannian Geometry, pp.1-78, 1996. ,
Geometry of nonholonomic systems, Robot Motion Planning and Control, chapter, p.28, 1998. ,
DOI : 10.1007/BFb0036071
Differential Geometry : Manifolds, Curves, and Surfaces, volume 115 of Graduate Texts in Mathematics, p.97, 1988. ,
DOI : 10.1007/978-1-4612-1033-7
Harmonic analysis, volume 2 of The collected works of Arne Beurling, Birkhäuser, p.121, 1989. ,
Dexterous Grippers: Putting Nonholonomy to Work for Fine Manipulation, The International Journal of Robotics Research, vol.59, issue.7, pp.427-442, 2002. ,
DOI : 10.1177/027836402321261968
Nonholonomic Mechanics and Control, Interdisciplinary Applied Mathematics, vol.24, issue.8, 2003. ,
DOI : 10.1007/b97376
Numerical Optimization-Theoretical and Practical Aspects, p.58, 2006. ,
Singular Trajectories and their Role in Control Theory, Mathématiques et Applications SMAI, vol.40, p.93, 2002. ,
Groupe et Algèbre de Lie, 1972. ,
Control Theory and Singular Riemannian Geometry, New Directions in Applied Mathematics, 1981. ,
DOI : 10.1007/978-1-4612-5651-9_2
Geometric Control of Mechanical Systems, Texts in Applied Mathematics, vol.49, p.22, 2004. ,
DOI : 10.1007/978-1-4899-7276-7
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups, IEEE Transactions on Automatic Control, vol.45, issue.8, p.26, 2000. ,
DOI : 10.1109/9.871753
On the motion planning of rolling surfaces, Forum Math, vol.15, issue.108, pp.727-758, 2003. ,
Path planning on compact Lie groups using a homotopy method, Systems & Control Letters, vol.47, issue.5, pp.383-392, 2002. ,
DOI : 10.1016/S0167-6911(02)00235-9
A continuation method for motion planning problems ESAIM : Control, Optimisation and Calculus of Variations, pp.139-168, 2006. ,
On conditions that prevent steady-state controllability of certain linear partial differential equations. Discrete and Continuous Dynamical Systems, pp.643-672, 2006. ,
Genericity results for singular curves, Journal of Differential Geometry, vol.73, issue.1, pp.45-73, 2006. ,
DOI : 10.4310/jdg/1146680512
URL : https://hal.archives-ouvertes.fr/hal-00086357
Singular Trajectories of Control-Affine Systems, SIAM Journal on Control and Optimization, vol.47, issue.2, p.93, 2008. ,
DOI : 10.1137/060663003
URL : https://hal.archives-ouvertes.fr/hal-00086397
Line-Integral Estimates and Motion Planning Using the Continuation Method, Essays on methematical robotics, pp.91-125, 1998. ,
DOI : 10.1007/978-1-4612-1710-7_4
Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung, Math. Ann, vol.117, issue.26, pp.98-115, 1940. ,
DOI : 10.1142/9789812776921_0005
Inverse acoustic and electromagnetic scattering theory, Applied Mathematical Sciences, vol.93, issue.154, p.156, 1998. ,
DOI : 10.1007/978-1-4614-4942-3
Global asymptotic stabilization for controllable systems without drift, Mathematics of Control, Signals, and Systems, vol.2, issue.3, pp.295-312, 1992. ,
DOI : 10.1007/BF01211563
On the controllability of 2-D incompressible perfect fluids, Journal de Mathématique Pures et Appliquées, vol.75, issue.3, pp.155-188, 1996. ,
Analyse mathématique et calcul scientifique pour les sciences et les techniques, p.161, 1986. ,
A path space approach to nonholonomic motion planning in the presence of obstacles, IEEE Transactions on Robotics and Automation, vol.13, issue.3, pp.443-451, 1997. ,
DOI : 10.1109/70.585905
Partial Differential Equations, Graduate Studies in Mathematics, vol.19, p.157, 1999. ,
Flatness and defect of non-linear systems: introductory theory and examples, International Journal of Control, vol.4, issue.6, pp.1327-1361, 1995. ,
DOI : 10.1109/9.73561
Motion Planning and Fastly Oscillating Controls, SIAM Journal on Control and Optimization, vol.48, issue.5, p.22, 2010. ,
DOI : 10.1137/090761884
Nilpotent Lie groups, Springer Lecture Notes in Mathematics, vol.562, p.28, 1976. ,
DOI : 10.1007/BFb0087594
4. Vector Fields and Nilpotent Lie Algebras, Symbolic Computation : Applications to Scientific Computing, pp.77-96, 1989. ,
DOI : 10.1137/1.9781611971033.ch4
Models for free nilpotent Lie algebras, Journal of Algebra, vol.135, issue.1, pp.177-191, 1991. ,
DOI : 10.1016/0021-8693(90)90156-I
Séries lacunaires et contôle semi-interne des vibrations d'une plaque rectangulaire, Journal de Mathématique Pures et Appliquées, vol.69, pp.457-465, 1986. ,
Pointwise and Spectral Control of Plate Vibrations, Revista Matem??tica Iberoamericana, vol.7, issue.125, pp.1-24, 1991. ,
DOI : 10.4171/RMI/103
Variation et optimisation de forme, Mathématiques et Applications SMAI, vol.48, p.136, 2005. ,
DOI : 10.1007/3-540-37689-5
URL : https://hal.archives-ouvertes.fr/hal-00013871
Perturbation of the boundary in Boundary-Value Problems of Partial Differential Equations, p.134, 2005. ,
DOI : 10.1017/CBO9780511546730
Nilpotent and High-Order Approximations of Vector Field Systems, SIAM Review, vol.33, issue.2, pp.238-264, 1991. ,
DOI : 10.1137/1033050
Convex Analysis and Minimization Algorithm I, volume 305 of A series of Comprehensive Studies in Mathematics, p.108, 1993. ,
Some trigonometrical inequalities with applications to the theory of series, Mathematische Zeitschrift, vol.3, issue.2, pp.367-369, 1936. ,
DOI : 10.1112/plms/s2-38.1.458
Estimates of the constants in generalized Ingham's inequality and applications to the control of the wave equation, Asymptotic Analysis, vol.28, pp.3-4181, 2001. ,
On a theorem of Ingham, The Journal of Fourier Analysis and Applications, vol.41, issue.5, pp.577-582, 1997. ,
DOI : 10.1007/BF02648885
Singular Internal Stabilization of the Wave Equation, Journal of Differential Equations, vol.145, issue.1, pp.184-215, 1998. ,
DOI : 10.1006/jdeq.1997.3385
Uniform estimation of sub-riemannian balls, Journal of Dynamical and Control Systems, vol.7, issue.4, pp.473-500, 2001. ,
DOI : 10.1023/A:1013154500463
URL : https://hal.archives-ouvertes.fr/hal-01010757
An approximate algorithm for nonholonomic motion planning, p.38, 2008. ,
A global convergent steering algorithm for regular nonholonomic systems, Proceedings of 44th IEEE Conference on Decision and Control, pp.29-30, 2005. ,
Geometric Control Theory, volume 51 of Cambridge Studies in Advanced Mathematics, p.31, 1997. ,
Pseudo-périodicité et séries de Fourier lacunaires Annales Scientifiques de l'Ecole Normale Supérieure, pp.93-150, 1962. ,
DOI : 10.24033/asens.1108
URL : http://archive.numdam.org/article/ASENS_1962_3_79_2_93_0.pdf
Perturbation theory for linear operators, p.160, 1976. ,
Riemannian geometry, Studies in Mathematics. de Gruyter, vol.1, p.108, 1982. ,
DOI : 10.1515/9783110905120
A further note on a theorem of Ingham and simultaneous observability in critical time, Inverse Problems, vol.20, issue.5, pp.1649-1661, 2004. ,
DOI : 10.1088/0266-5611/20/5/020
URL : https://hal.archives-ouvertes.fr/hal-00084027
Fourier series in control theory, Monographs in Mathematics, p.121, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00086863
On moment theory and controllability of one-dimensional vibrating systems and heating processes, p.121, 1992. ,
DOI : 10.1007/BFb0039513
A general strategy for computing steering controls of systems without drift, [1991] Proceedings of the 30th IEEE Conference on Decision and Control, pp.29-63, 1991. ,
DOI : 10.1109/CDC.1991.261506
A differential geometry approach to motion planning, Nonholonomic Motion Planning, pp.235-270 ,
Motion control of drift-free, left-invariant systems on Lie groups, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1539-1554, 1995. ,
DOI : 10.1109/9.412625
Lecture notes on entire functions, volume 150 of Translations of mathematical monographs, p.129, 1996. ,
Motion of two rigid bodies with rolling constraint, IEEE Transactions on Robotics and Automation, vol.6, issue.1, pp.62-72, 1990. ,
DOI : 10.1109/70.88118
Problèmes aux limites non homogènes et application, volume 1 of Travaux et recherches mathématiques, p.146, 1968. ,
An Approximation Algorithm for Nonholonomic Systems, SIAM Journal on Control and Optimization, vol.35, issue.4, pp.1328-1365, 1997. ,
DOI : 10.1137/S0363012993260501
Rolling bodies with regular surface: controllability theory and applications, IEEE Transactions on Automatic Control, vol.45, issue.9, pp.1586-1599, 2000. ,
DOI : 10.1109/9.880610
Flat systems: open problems, infinite dimensional extension, symmetries and catalog, Advances in the Control of Nonlinear Systems, Lecture Notes in Control and Information Sciences, pp.33-57, 2001. ,
DOI : 10.1007/BFb0110378
Flat systems, equivalence and trajectory generation, 2003. ,
URL : https://hal.archives-ouvertes.fr/cel-00392180
Abnormal Minimizers, SIAM Journal on Control and Optimization, vol.32, issue.6, p.93, 1994. ,
DOI : 10.1137/S0363012993244945
A tour of subriemannian geometries, their geodesics, and applications, volume 91 of Mathematical Surveys and Monographs, pp.31-96, 2002. ,
Nilpotent bases for a class of nonintegrable distributions with applications to trajectory generation for nonholonomic systems, Mathematics of Control, Signals, and Systems, vol.38, issue.5, pp.58-75, 1994. ,
DOI : 10.1007/BF01211485
A Mathematical Introduction to Robotic Manipulation, CRC, vol.8, issue.86, pp.12-85, 1994. ,
Nonholonomic motion planning: steering using sinusoids, IEEE Transactions on Automatic Control, vol.38, issue.5, pp.700-716, 1993. ,
DOI : 10.1109/9.277235
URL : http://authors.library.caltech.edu/7315/1/MURieeetac93.pdf
Reconstructions From Boundary Measurements, The Annals of Mathematics, vol.128, issue.3, pp.531-576, 1988. ,
DOI : 10.2307/1971435
Acoustic and Electromagnetic Equations -Integral Representations for Harmonic Problems, Applied Mathematical Sciences, vol.144, issue.156, p.157, 2001. ,
A framework for the stabilization of general nonholonomic systems with an application to the plate-ball mechanism, IEEE Transactions on Robotics, vol.21, issue.2, pp.162-175, 2005. ,
DOI : 10.1109/TRO.2004.839231
Generic simplicity of the eigenvalues of the Stokes system in two space dimensions Advances in Differential Equations, pp.987-1023, 2001. ,
On a Constrained Approximate Controllability Problem for the Heat Equation: Addendum, Journal of Optimization Theory and Applications, vol.2, issue.5, pp.183-190, 2003. ,
DOI : 10.1023/A:1024747710420
Any two points of a totally nonholonomic space may be connected by an admissible line, Uch. Zap. Ped. Inst. im. Liebknechta, issue.2, p.26, 1938. ,
Remarks on incompleteness of {e i?nt }, non averaging sets, and entire functions, Proceedings of the American Mathematical Society, pp.365-369, 1951. ,
Hypoelliptic differential operators and nilpotent groups, Acta Mathematica, vol.137, issue.0, pp.247-320, 1976. ,
DOI : 10.1007/BF02392419
Control of a quantum particle in a moving potential well, 2nd IFAC Workshop on Lagrangian and Hamiltonian Methods for nonlinear Control, p.114, 2003. ,
Etude des sommes d'exponentielles, Actualités Sci. Ind. Hermann, p.121, 1959. ,
Méthodes mathématiques pour les sciences physiques, Collection Enseignement des Sciences. Hermann, vol.162, p.163, 1998. ,
Différentiation de problèmes aux limites par rapport au domaine, pp.152-154, 1991. ,
Control of systems without drift via generic loops, IEEE Transactions on Automatic Control, vol.40, issue.7, pp.1210-1219, 1995. ,
DOI : 10.1109/9.400490
A comprehensive introduction to differential geometry III. Publish or Perish, p.88, 1975. ,
Accessible Sets, Orbits, and Foliations with Singularities, Proceedings of the London Mathematical Society, vol.3, issue.4, pp.699-713, 1974. ,
DOI : 10.1112/plms/s3-29.4.699
Orbits of families of vector fields and integrability of distributions. Transactions of the, pp.171-188, 1973. ,
A General Theorem on Local Controllability, SIAM Journal on Control and Optimization, vol.25, issue.1, pp.158-194, 1987. ,
DOI : 10.1137/0325011
Two new methods for motion planning for controllable systems without drift, European Control Conference, pp.1501-1506, 1991. ,
New Differential Geometric Methods in Nonholonomic Path Finding, Systems, Models, and Feedback : Theory and Applications, pp.365-384, 1992. ,
DOI : 10.1007/978-1-4757-2204-8_24
A continuation method for nonholonomic path-finding problems, Proceedings of 32nd IEEE Conference on Decision and Control, pp.2718-2723, 1993. ,
DOI : 10.1109/CDC.1993.325689
Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories, [1991] Proceedings of the 30th IEEE Conference on Decision and Control, p.15, 1991. ,
DOI : 10.1109/CDC.1991.261338
Lie Bracket Extensions and Averaging: The Single-Bracket Case, Nonholonomic Motion Planning, pp.109-147, 1993. ,
DOI : 10.1007/978-1-4615-3176-0_4
Partial Differential Equations I, Applied Mathematical Sciences, vol.115, p.149, 1996. ,
Partial Differential Equations II, Applied Mathematical Sciences, vol.116, issue.154, p.156, 1996. ,
Endogenous configuration space approach to mobile manipulators: A derivation and performance assessment of Jacobian inverse kinematics algorithms, International Journal of Control, vol.11, issue.14, pp.1387-1419, 2003. ,
DOI : 10.1109/9.293207
Singularity robust jacobian inverse kinematics for mobile manipulators Advances in Robot Kinematics : Analysis and Design, pp.155-164, 2008. ,
Contôle optimal : théorie et applications, Mathématiques Concrètes. Vuibert, p.22, 2005. ,
On the controllability of bilinear quantum systems, Mathematical Models and Methods for Ab Initio Quantum Chemistry, p.114, 2000. ,
DOI : 10.1007/978-3-642-57237-1_4
URL : https://hal.archives-ouvertes.fr/hal-00536518
Nonhomogeneous Nilpotent Approximations for Nonholonomic Systems With Singularities, IEEE Transactions on Automatic Control, vol.49, issue.2, pp.261-266, 2004. ,
DOI : 10.1109/TAC.2003.822872
Nonholonomic dynamical systems, geometry of distributions and variational problems, Dynamical Systems VII, volume 16 of Encyclopedia of Mathematical Sciences, p.28, 1994. ,
Sur l'évaluation du domaine d'existence des fonctions implicites réelles ou complexes, Ann. Soc. Polon. Math, vol.20, issue.87, pp.81-120, 1947. ,
objectif de cette thèse est, d'une part, de fournir des méthodes de planification de mouvements pour les systèmes non-holonomes, et d'autre part ,
Planification de mouvements, systèmes non-holonomes, géométrie sousriemannienne , approximation nilpotente, méthode de continuation, problème de roulement, équation de Schrödinger, contrôlabilité spectrale, minimalité des familles exponentielles, contrôlabilité générique ,