Finally, one property of systems that is important in some planning
algorithms is *symmetry*.^{14.1} A system
is symmetric if the following condition holds. If
there exists an action trajectory that brings the system from some
to some , then there exists another action trajectory
that brings the system from to by visiting the same
points in , but in reverse time. At each point along the path,
this means that the velocity can be negated by a different choice of
action. Thus, it is possible for a symmetric system to reverse any
motions. This is usually not possible for systems with drift. An
example of a symmetric system is the differential drive of Section
13.1.2. For the simple car, the
Reeds-Shepp version is symmetric, but the
Dubins version is not because the car cannot travel
in reverse.

Steven M LaValle 2012-04-20