  A Dubins path is a shortest path with bounded curvature. The seminal result
in non-holonomic motion planning is that (in the absence of obstacles) a Dubins
path consists either from a circular arc followed by a segment followed by
another arc, or from three circular arcs [Dubins, 1957]. Dubins original proof
uses advanced calculus; later, Dubins result was reproved using control theory
techniques [Reeds and Shepp, 1990], [Sussmann and Tang, 1991], [Boissonnat,
C\'er\'ezo, and Leblond, 1994].
  We introduce and study a discrete analogue of curvature-constrained motion.
We show that shortest "bounded-curvature" polygonal paths have the same
structure as Dubins paths. The properties of Dubins paths follow from our
results as a limiting case---this gives a new, "discrete" proof of Dubins
result.
