Plow a 2D polygonal area

I have a problem that is similar to this that I am trying to solve:
"Given a randomly-shaped field, what is the best (fastest I guess) way to plow it? Every part of the field must be plowed, plowing outside the area is not a problem, and turning around is slower than going straight."

Basically, I'm in the situation of a farmer that wants to plow as fast as possible a weirdly-shaped field with no obstacle.

As far as I can tell, this is a covering problem for a simply-connected 2D space, but with some special restrictions.

It seems like it should be a common enough problem, but I can't seem to be able to find anything. I guess most fields have a shape similar enough to a rectangle and thus it is not an issue.

Is there any algorithm or numerical method that allows to solve this problem?

Thanks.

You'll find plenty of literature on this widely-studied problem, which is called complete coverage path planning. Many techniques have been applied with more or less success (genetic algorithms, etc.) but in the end the only viable technique is some variant/improvement on the boustrophedon decomposition algorithm, which is in the class of Morse decompositions.

Choset's paper is the founding document, but I found Xin Yu's PHD dissertation to be the best practical description. The problem is that Boustrophedon decompositions find only a single 'best' ploughing angle for all trapezoids, when some may certainly be better ploughed at some other angle.

Bochkarev and Smith recently described a way to minimize turns by exploiting the minimum altitudes of the polygons, but I found it difficult to grasp with my limited high-school maths.

I am currrently trying out an alternative approach, by taking a Boustrophedon decomposition at all the angles of the polygon and then layering all the resultant trapezoids sorted by a score based on area and minimum altitude. If it works out I'll try and remember to come back here to post the results.

Citations

Choset, Howie. "Coverage of Known Spaces: The Boustrophedon Cellular Dercomposition" Autonomous Robots 9, 247-253, 2000.

Xin, Yu. "Optimization Approaches for a Dubins Vehicle in Coverage Planning problem and Traveling Salesman Problems" PhD Dissertation, Auburn, Alabama, 2015.

Bochkarev, Stanislav and Smith, Stephen L. "On Minimizing Turns in Robot Coverage Path Planning" Automation Science and Engineering, 2016

StackExchange Computer Science Q#48796, answer score: 3