The robot will be constrained by nonholonomic constraints.  This means that the robot will be unable to move sideways and there will be a minimum turning radius.

The planner has two parts: the holonomic and nonholonomic planners.  The first will create a collision-free path that assumes no constraints on the robot's movements.  The latter takes the path from the first and recursively decomposes the path into sub-paths until the entire path is feasible.  The set of the types of possible curves for the sub-paths (there are 48 of them) is called Reeds and Shepp curves.

The holonoic path planner provides a free path to the goal, but not an optimal one.  After running the nonholonomic path planner, the general efficiency of the path is improved (still not optimal but good).  The accuracy around areas of clutter is still far from being optimal.  To try to improve this, a system that randomly takes two points and tries to connect them using an RS curve.  It does this as many times as possible in the time allowed for the path planning.

There are still cases where the planner cannot get a path that has few reversals in it.  In these casese, after some optimimization time has passed, a request is made for the holonomic planner to create a new free path.  It tries creating the new path backward, which changes the potential field.

Using these techniques the author was able to make a significantly faster path planner, and in addition creates a shorter path.

The author does though make several references to the speed difference that could be achieved using newer and faster hardware.  There is no discussion in the paper about how the previous work, of Michel Taix, would have been affected by a similar improvement in technology.  The author states that his planner is 1 to 2 orders of magnitude faster.  It is quite possible that in actuality that speed difference is entirely hardware related.