Open-loop control laws for a vehicle towing three trailors

A vehicle pulling a train of three trailers has to go from a point P0 to a point Pf, both of them in the (X, Y)-plane, during a given time interval [0, tf]. During its motion the pulling vehicle has to move in such a manner that none of the vehicles will collide with a circular shaped obstacle that is located between the points. By using the concept of path controllability, and a method of trial and error, control laws are derived for the pulling vehicle control mechanism, such that the above-mentioned maneuver can be performed.