  This paper is a sequel of arxiv:1709.09045 and deals with privileged
coordinates and nilpotent approximation of Carnot manifolds. By a Carnot
manifold it is meant a manifold equipped with a filtration by subbundles of the
tangent bundle which is compatible with the Lie bracket of vector fields. In
this paper, we single out a special class of privileged coordinates in which
the nilpotent approximation at a given point of a Carnot manifold is given by
its tangent group. We call these coordinates Carnot coordinates. Examples of
Carnot coordinates include Darboux coordinates on contact manifolds and the
canonical coordinates of the first kind of Goodman and Rothschild-Stein. By
converting the privileged coordinate of Bella\"iche into Carnot coordinates we
obtain an effective construction of Carnot coordinates, which we call
$\varepsilon$-Carnot coordinates. They form the building block of all systems
of Carnot coordinates. On a graded nilpotent Lie group they are given by the
group law of the group. For general Carnot manifolds, they depend smoothly on
the base point. Moreover, in Carnot coordinates at a given point, they are
osculated in a very precise manner by the group law of the tangent group at the
point.
