  In this paper we study the sub-Finsler geometry as a time-optimal control
problem. In particular, we consider non-smooth and non-strictly convex
sub-Finsler structures associated with the Heisenberg, Grushin, and Martinet
distributions. Motivated by problems in geometric group theory, we characterize
extremal curves, discuss their optimality, and calculate the metric spheres,
proving their Euclidean rectifiability.
