I have a small self-driving robot car with a camera, that I control from an application using image analysis.
I'm considering using Godot for a 3D simulation of the robot, i.e. I want to replace the physical robot with a model in a 3D world. So from Godot I will send the image from a camera on the model to my other application, which will do image analysis and send back commands to the robot in Godot (i.e. speed and orientation for wheels).
I have no experience with Godot, but from what I have read, this should be fairly simple.

The thing I'm a bit unsure about is how I best model the robot. I have looked at VehicleBody3D/VehicleWheel3D, and while they look like what I'm looking for, I'm not sure, it they are the best way of doing it. Mainly I'm concerned about the many parameters about spring/dampening etc., that may be hard to set correctly, and may be overkill as the robot in question doesn't have any suspension. It is just some hard wheels driving on a flat surface.

In this video you can see what the robot looks like, and the world I want to recreate in a simulation. I would greatly appreciate I'm someone has the time to give it a quick look, and can give some hints on what the best way to model the robot would be. Can I do it with 3x VehicleWheel3D where I control the steering and power? Or is there a better approach.

I don't need a perfect physics simulation, but it should preferably be able to handle a case like not allowing the robot to drive through walls etc. Like in the video at 3:15 where it drives into a wall to align the robot with the wall. If I could do that in the simulation, I would be very happy.

It depends on how much control you're willing to give over to the physics engine Godot has and whether or not you trust it to simulate and behave correctly. To me it looks like it's purely following the white line as a marker and isn't really doing anything that advanced. Considering you're having it simply follow a path, you could even use a FollowPath node which is built in for Godot, or use an agent to pre-set path along the white line and simply have the wheels animate to trick people.

This all has a degree of fakery to it of course, I think you need to give us more detail on what you're planning to do or make the decision yourself. I'm building an RTS game, so in my case I want to have very precise control over my vehicles and I'm willing to accept the fakery to do that. If you want a proper vehicle simulation for this robot you would need to tweak the vehicle controller a lot as you've recognised but that's also part of the process, you can't really skip or cheat it.

If you want vehicle controller steering behaviour, you should probably make heavy use of raycast checking to help the vehicle controller 'see' in front of it.

Thank you for taking your time to try to answer my vague question. My goal is not to have Godot steer the robot. That will be handled by a different program. So I don't think the FollowPath and agents are relevant for me.
Maybe I misunderstood the physics engine of Godot. I was expecting, that it could handle basic physics like collisions for me. From your answer I get the impression, that I should do this my self by use of raycast.
I think I need some more hands on experience with Godot, to find out what it can do, and what it can't. Then maybe later I can ask some more meaningful questions😃

No problem, being specific as possible is extremely helpful and I did generally get the idea from the video you posted, Godot can certainly handle physics collisions and you could do it that way, however the video gave me the impression you wanted it to follow along a path. This is also certainly possible to do with physics, except it would be a bit trickier, I was just thinking in terms of what results you wanted.