What's missing from this model is a variable rate of turn. You want to turn so that your front bump stays at roughly a fixed distance from the bollard line. As you go, you slowly turn the wheel sharper and sharper until reach your maximum turn radius or you are lined up with your space. You can slightly vary that fixed distance as you go to adjust for minor differences in your initial position. You can also aim for a bit to the right/far side of the space (, and then re-center on the space once you are lined up.
Yeah, the model is definitely contrived and I could try adding a lot more to it, but I still found it very useful just to understand how the path changes with the wheel turn.
Also, as a beginner, it's very hard to "feel" how much you're supposed to turn with variable rate — I guess this only comes with a ton of practice. In the driving school, the way we were taught all the parking maneuvers is to reverse straight until you catch some reference point, then immediately turn to the max for the sharpest turn.
Yea, this whole piece misses the fact that when a human is doing this maneuver, planning for all inputs is dynamic (not pre-cached) using feedback loop. We adjust as necessary (unless hitting a limit) to put the car in place. It is not like we plan the whole process and then close our eyes, execute all inputs and voila! car is now parked!
