This path planning algorithm for a "moving and steering" vehicle appears to be working when testing it in our simulator. This means that the calculations are right and they seem to translate well from theory to practice. But...
The way I made my thing, at least for now, is that I set "waypoints" where I instruct the truck to change it's steering angle, either -1, 0 or 1. Waypoints have a "range" where when this "range" intersect with "the turning center" on the vehicle, the truck is considered to have "reached" the waypoint. So if my "range" is 10 cm, then I tell the truck to change direction 10 cm too early, making it miss the next waypoint because it's off course.
So the next step is to figure out of a way to make tiny adjustments to make the truck go back on the track.