Differential flatness has become an important concept in the
development of steering methods. It was introduced by Fliess,
Lévine, Martin, and Rouchon in [344]; see also
[726]. Intuitively, a system is said to be *differentially flat* if a set of variables called *flat outputs*
can be found for which all states and actions can be determined from
them without integration. This specifically means that for a system
with
and
, there exist
*flat outputs* of the form

such that there exist functions and for which

and

One example is the simple car pulling trailers, expressed in (13.19); the flat outputs are the position in of the last trailer. This property was used for motion planning in [578]. Recent works on the steering of differentially flat systems include [578,813,833].

Steven M LaValle 2020-08-14