Dubins and Reeds-Shepp Paths
A car cannot turn in place, so the shortest path between two poses, position plus heading, is not a straight line. Dubins showed that for a car that only drives forward, the shortest path is always made of at most three pieces: turns at the tightest radius and straight lines. Reeds and Shepp extended this to cars that can also reverse.
Drag the goal.
Six words
Write a left turn at minimum radius as L, a right turn as R, and a straight segment as S. Every shortest forward path is one of six words:
The planner computes all six lengths and keeps the shortest. Reeds-Shepp paths allow reversing and need 48 words, including cusps where the car changes direction. This page adds only the simplest extra option, driving an entire Dubins path in reverse, which already shows why reversing helps.
What to notice
Put the goal right beside the start, facing the same way. Forward only, the car must loop all the way around, since it cannot turn tightly enough to step sideways. Allow reverse and some of those cases get much shorter. A tighter turning radius shortens most paths. These paths are the building blocks for car-like planners such as Hybrid A* and for the steering step in RRT for cars.