Let's say we are given a closed race track with a given and constant width. I am to implement an algorithm which finds both shortest path trajectory and minimum curvature trajectory for the car.
I have found a paper (F. Braghin et al. / Computers and Structures 86 (2008) 1503-1516) which explains both the shortest path trajectory and the minimum curvature trajectory.
I understood the shortest path equations except (8) but couldn't understand any equations in the minimum curvature path trajectory. Could someone please explain those equations?