Let's say that we have a smooth ($C^\infty$) vector filed (constant with resprect to time)
$f: \mathbb{R}^n \to \mathbb{R}^n$,
where $n \geq 2$.

We also have a "ship" that is always moving
(sailing over this vector field $f$ in $\mathbb{R}^n$)
at a constant relative speed $v > - \min_{\mathbf{x} \in \mathbb{R}^n} \|f(\mathbf{x})\|$.
This ship can only do "smooth" turns.

(In general) How hard of a problem it is to find an optimal "steering"
(a function $d: \mathbb{R} \to \mathbb{R}^n$, which maps time to a direction)
of the ship from coordiante $\mathbf{x}$ to coordiante $\mathbf{y}$
— optimal steering gives the quickest route.

Note. The solution is not necessarily unique.
The solution in the figure can be a little bit misleading.