A. A. Agrachev, D. Barilari, and U. Boscain, Introduction to Riemannian and Sub- Riemannian geometry, 2016.
DOI : 10.4171/163-1/1

F. [. Agrachev, A. Boarotto, and . Lerario, Homotopically invisible singular curves, Calculus of Variations and Partial Differential Equations, vol.87, issue.3, p.56105, 2017.
DOI : 10.1090/S0002-9947-1958-0094807-0

R. [. Agrachev and . Gamkrelidze, Exponential representation of flows and a chronological enumeration, Mat. Sb. (N.S.), vol.107, issue.639, pp.467-532, 1978.

A. [. Agrachëv and . Sarychev, Filtrations of a Lie algebra of vector fields and the nilpotent approximation of controllable systems, Dokl. Akad. Nauk SSSR, vol.295, issue.4, pp.777-781, 1987.

A. [. Agrachev and . Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.13, issue.6, pp.635-690, 1996.
DOI : 10.1016/S0294-1449(16)30118-4

URL : https://doi.org/10.1016/s0294-1449(16)30118-4

Y. [. Agrachev and . Sachkov, Control theory from the geometric viewpoint, of Encyclopaedia of Mathematical Sciences Control Theory and Optimization, II, 2004.
DOI : 10.1007/978-3-662-06404-7

U. [. Barilari, M. Boscain, and . Sigalotti, Geometry, analysis and dynamics on sub-Riemannian manifolds Lecture notes from the IHP Trimester held at the Institut Henri Poincaré, Paris and from the CIRM Summer School " Sub-Riemannian Manifolds: From Geodesics to Hypoelliptic Diffusion, EMS Series of Lectures in Mathematics. European Mathematical Society (EMS), vol.1, issue.2, 2014.

U. Boscain, G. Charlot, R. Ghezzi, and M. Sigalotti, Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces, Sub-Riemannian geometry, pp.438-455, 1996.
DOI : 10.5802/afst.794

URL : https://hal.archives-ouvertes.fr/hal-00464414

L. [. Bryant and . Hsu, Rigidity of integral curves of rank 2 distributions, Inventiones Mathematicae, vol.30, issue.no. 1127, pp.435-461, 1993.
DOI : 10.1007/BF01232676

E. [. Bonfiglioli, F. Lanconelli, . M. Uguzzoni-[-bs90-]-r, G. Bianchini, and . Stefani, Stratified Lie groups and potential theory for their sub-Laplacians Graded approximations and controllability along a trajectory, SIAM J. Control Optim, vol.28, issue.4, pp.903-924, 1990.

B. Franchi, R. Serapioni, F. Serra, and . Cassano, Rectifiability and perimeter in the Heisenberg group, Math. Ann, vol.321, issue.3, pp.479-531, 2001.

]. V. Gru70 and . Gru?in, A certain class of hypoelliptic operators, Mat. Sb. (N.S.), vol.83, issue.125, pp.456-473, 1970.

]. F. Jea14 and . Jean, Control of nonholonomic systems: from sub-Riemannian geometry to motion planning, SpringerBriefs in Mathematics

M. [. Juillet and . Sigalotti, Pliability, or the Whitney extension theorem for curves in Carnot groups, Analysis & PDE, vol.406, issue.7, pp.1637-1661, 2017.
DOI : 10.1007/s12220-017-9807-2

URL : https://hal.archives-ouvertes.fr/hal-01285215

G. [. Le-donne and . Speight, Lusin approximation for horizontal curves in step 2 Carnot groups, Calculus of Variations and Partial Differential Equations, vol.47, issue.4, 2016.
DOI : 10.4171/RMI/201

]. L. Rif14 and . Rifford, Sub-Riemannian geometry and optimal transport, SpringerBriefs in Mathematics

F. and S. Cassano, Some topics of geometric measure theory in carnot groups Geometry, analysis and dynamics on sub-Riemannian manifolds, EMS Series of Lectures in Mathematics, vol.1, p.324, 2016.

]. G. Spe16 and . Speight, Lusin approximation and horizontal curves in Carnot groups, Rev. Mat. Iberoam, vol.32, issue.4, pp.1423-1444, 2016.

]. H. Sus76 and . Sussmann, Some properties of vector field systems that are not altered by small perturbations, J. Differential Equations, vol.20, issue.2, pp.292-315, 1976.

]. E. Tré00 and . Trélat, Some properties of the value function and its level sets for affine control systems with quadratic cost, J. Dynam. Control Systems, vol.6, issue.4, pp.511-541, 2000.

]. S. Vod06 and . Vodopyanov, Differentiability of curves in the category of Carnot manifolds, Doklady Mathematics, vol.74, issue.2, pp.686-691, 2006.

I. [. Vodopyanov and . Pupyshev, Whitney-type theorems on extension of functions on Carnot groups, Doklady Mathematics, vol.73, issue.1, pp.731-752, 2006.
DOI : 10.1134/S1064562406010236

]. S. Zimar and . Zimmerman, The Whitney extension theorem for C 1 , horizontal curves in the Heisenberg group, J. Geom. Anal