Rigging of technical correct GARAGE DOOR with 4 parts

I modeled garage door using real referances. Every piece has exact dimensions and its place is right.
I created a simple model for you who want to try to rig this door.
I created a path which goes along the track and through axis of the hinges. I am not sure if it is correct and it matters (in collection “Extras” you can see another, hidden path which goes through wheels axis). I created Empties (cubes) with offset and used Follow Path. After that I linked door parts to the empties.
You can see that we have 3 hinges in the middle and plates with the roller wheels at the bottom of the door part1 and on the top of door part4. These are not positioned in the same vertical line like 3 middle hinges. Especially the top roller wheel has an extra distance.
I used Damped Track for each door part and targets are Empties (cubes) of the next door part.
3 door parts (in the middle) have origins in axis of hinges. The bottom one has the origin in the same vertical line as regular hinges. Damped Track of the top one is “looking to” top Empty (cube) and that`s why changed its position. I moved it back manually, but I got many issues anyway. 1. After going up axes of hinges are going apart, 2. roller wheels are not staying in the track, 3. door parts are colliding with each other in a certain point. I have tried Track To Constraint, but it does not work correctly. ( I thought it is similar to 3ds max “Look At”. I have tried to think another way and linked roller wheels to Empties in an opposite order, but I failed. I have used the other Path (hidden) goes through axes of roller wheels, but the problem is the same. What can I do??? What is wrong and what I missed in my thinking. I do not have a large knowledge on the rigging subject and do not know about Quaternions and other mathematical forms. Maybe I should change something in Rotation Order?
Here is the link to the filder with blend files: https://www.dropbox.com/sh/8vptlouuh2tnrqs/AABLofjMhmCX7umN4AVkC8UZa?dl=0

Hi, i think you are missing important part of this mecanisim, there should be another track on top that guides the first set off wheels only above the track. watch this video:https://www.youtube.com/watch?v=8cEcQJBSkKs

Hi, if you want to keep this setup then simply move the wheels on the first panel in:

The video in the link you gave me is showing little bit different system with extra track. My system is exactly how you see in the blend file. It is working in reality, so it should work in Blender. At the end of opening the top part of the door is rotating a little bit in the opposite direction than hinges normally.
That is a pity I still have no idea how to solve these all issues or create another rig… with bones for example?
Moving the top Empty back does not help as you suggest. The roller is going out of the track anyway.
I created also another path and scaled it up a little bit to give a distance to a new Empty (also using Damped Track) and it helped to keep wheel in the track, but only at the end. On the way up the new Empty is going out anyway. I still can`t find any solutions for other issues. There is only one tutorial I have found on YouTube, but the guy is showing a rig more for cartoony animation. My model has real construction and dimensions and more mechanics to think about.
Ok, now I see you mean the top roller move into the panel (not only the Empty)? But it is like this. I see I can move a little bit rollers on the hinges.

issue 3 is obvious, the angle of the side of the door is straight, otherwise it will do clipping if they are so close together…