A Solution !...

(see J.P. Laumond, P. Jacobs, M. Taix and R. Murray, "A Motion Planner for Nonholonomic Mobile Robots" in IEEE T. on Robotics and Automation, 10 (5), Oct. 1994)

The number of maneuvers you have to do varies as the inverse of the square of the free-space !....

This result comes from the shape of the singular metric of the car.

... and if one pulls trailers ?...