  In this paper, we study the singularities of locally flat systems, motivated
by the solution, if it exists, of the global motion planning problem for such
systems, in the spirit of \cite{CE_14}. More precisely, flat outputs may be
only locally defined because of the existence of points where they are singular
(a notion that will be made clear later), thus preventing from planning
trajectories crossing these points. Such points are of different types. Some of
them can be easily ruled out by considering another non singular flat output,
defined on an open set intersecting the domain of the former one and well
defined at the point in question. However, it might happen that no well-defined
flat outputs exist at all at some points. We call these points \emph{intrinsic}
singularities and the other ones \emph{apparent}. A rigorous defintion of these
points is introduced in terms of atlas and charts in the framework of the
differential geometry of jets of infinite order and Lie-B\"acklund isomorphisms
(see \cite{FLMR_99,Levine-09}). We then give a criterion allowing to
effectively compute intrinsic singularities. Finally, we show how our results
apply to global motion planning of the well-known example of non holonomic car.
