Modern farm tractors, guided by autopilots, maneuver across farm fields with position accuracy and repeatability better than an inch.  Automatic, precise vehicle control saves time and energy compared to sloppy operating.  It allows farmers to work more efficiently and spend less money on fertilizers and pesticides.  Consumers enjoy lower prices for high quality produce, and farm chemical waste and runoff are reduced. 
One of a tractor's primary tasks is pulling implements such as disks, mulch rippers, chisel plows, air seeders, box drills, planters, and the like, across fields in a uniform pattern of parallel lines.  These operations are often begun from an initial “A to B” (or simply “AB”) line.  A set of lines parallel to the AB line defines how the tractor covers a field.  Before real work can begin, the tractor and whatever implement it is pulling must both be established precisely on the AB line.  Guiding a large implement onto a line efficiently is not as easy as it sounds for either a human operator or an autopilot. 
Although an autopilot efficiently guides a tractor to a line, an implement towed behind takes a long time (and distance) to become established on the line within required tolerances.  One technique that has been tried to overcome this problem is to tune autopilot feedback parameters such that the tractor tends to overshoot when joining a desired path.  When the tractor overshoots, the implement arrives at the desired path sooner. ( An analogous maneuver is performed by a tractor-trailer driver who intentionally overshoots a turn at a street corner.  He drives the tractor to ensure that the trailer gets to its lane promptly rather than jumping the curb and only slowly approaching where it is supposed to go.) 
Overshoot provoked by tuning feedback gains in an autopilot is not easily controllable, however; there is no way to select an amount of overshoot for instance.  Furthermore, changing feedback gain to provoke overshoot can render the tractor unable to stay on its desired path reliably.  It also does not prevent undesirable actions such as jack-knifing; i.e. allowing the angle between tractor and implement to become too large. 
Other implement guidance challenges include guiding forward, pushed implements onto a line, and guiding rear implements along a line as long as possible as vehicle pulling them leaves a line. 
What are needed are autopilots for farm tractors (or any kind of vehicle) that guide the tractor so that towed implements, fixed rear implements or fixed forward implements join or leave desired paths efficiently, subject to constraints of good behavior such as not breaking draw bars, implements, etc.