  The problem of motion planning for affine control systems consists of
designing control inputs that drive a system from a well-defined initial to
final states in a desired amount of time. For control systems with drift,
however, understanding which final states are reachable in a given time, or
reciprocally the amount of time needed to reach a final state, is often the
most difficult part of the problem. We address this issue in this paper and
introduce a new method to solve motion planning problems for affine control
systems, where the motion desired can have indefinite boundary conditions and
the time required to perform the motion is free. The method extends on our
earlier work on motion planning for systems without drift. A canonical example
of parallel parking of a unicycle with constant linear velocity is provided in
this paper to demonstrate our algorithm.
