Mapping the path of an Arduino car?

Hello,

I have been working on a project for which I need to map the path of an Arduino car through a maze. I'm not sure how I can do this. Does anybody have ideas?

All electronic devices have to be either attached to the car or placed outside of the maze. I cannot place any devices on their own inside the maze unless the car puts them there.

[EDIT] I've also considered GPS, which is too inaccurate for this. I've also considered using some sort of a breadcrumb trail, but it might not exactly be the most practical given that my car is rather small and that it would be limited by the amount of "breadcrumb" that I put on the car before it goes in the maze.

[EDIT 2] Clarification on what exactly I'm trying to get at:

Let's say that I have an arbitrary maze of any construction, where the only certainty is that the walls cannot move. The passages could be of any size and shape and may vary throughout the maze. Passages may be above or below other passages. Etc. I want to make a car that can enter the maze and visit every part of it as efficiently as possible. The car will use image recognition to identify where potential paths are located, and as the car locates those potential paths, it will mark their location. Any opening that the car is able to traverse is considered a potential path. The car will track the locations where it has been. Using the location of potential paths and the data on where it has been, it will visit every part of this maze in an efficient manner. The car will not have any knowledge of the maze beforehand, and there is no goal other than visiting every part of the maze (so not like finding the exit or center. If an exit is found, it will treat it as a dead end and turn around). The car will know when it has explored the whole maze when it has taken every potential path, come to the end of each one, and has not found any new paths that haven't been explored.

What I was asking about is how I could go about making the robot capable of tracking where it has been and where it hasn't. I am trying to see how it might work using the method suggested here:

Dribble paint from the car?

Lol. I thought about that, but it seems a bit too clumsy. Looking for a more elegant solution. I've considered GPS, but it's too inaccurate.

How is the map going to be displayed once you have solved the maze ?

An aerosol can operate by a servo?

Breadcrumbs ?

Don't need to display the map in any way. I just need to track where the car has been and where it hasn't so that it doesn't go to the same dead end over and over again, for example.

You can start by tracing a wall to one side, left or right, doesn’t matter, as you enter the maze and follow it, eventually you end up at the exit. Just follow the wall

I'm not trying to find the exit, rather I want to map the whole maze. Assume that the entrance is the only way in or out...

it is very good chance you will have to go over the path you already have been on

I know that, but in any case, I would like to map out the whole maze. Going over a path that has already been traced in order to get to a new path is fine, but I don't want to go to the same dead end over and over and over... you get the idea

If you trace the wall and end up at the exit or entrance all you need is switch to the other wall and you should get the other half of the maze. i’d certainly explore this option if it was my task. or have 2 robots for faster mapping

Right now, actually navigating the maze is the easy part. Mapping it is what I can't figure out how to do. Basically, as the robot moves through the maze, I need to know where it is moving so that I can generate a map of the path it takes through the maze.

Is it a small maze or a large maze?

You could use lights emitting differing colors on stands above the maze. The car could have a color sensor on it. The car could be detecting, say, 3 colors and measuring the color intensity. A particular location on the maze would have 'unique' color intensity levels.

larger maze, how many Wifi access points can you detect? 3 or more WiFi signal strength readings could be used to form a coordinate system of points.

use the method optical mouse is using or mechanical wheel if you prefer

Surely if you can navigate the maze then you can map it. If it is a typical maze then it will be made up of a number of squares laid out in an X/Y pattern. When you are in any square test the 4 walls and save what you find in a 2 dimensional array.

Choose a coding scheme that allows you to draw the map of the maze, perhaps a 1 for open in the Y direction, 2 for open in the X direction, 4 for open in the -Y direction and 8 in the -X direction. Save the sum of the directions and you will have the data needed to map the maze

An overhead camera on a PC would work.

I don't want to make the assumption that it is a typical maze; rather, I would want it to work no matter what maze I put it in. Similarly, would like to avoid assuming that the top of the maze is open to the air.

If the maze is of some arbitrary design then how can you say

My suggested solution does not require that the top of the maze is open to the air

I mean to say that navigating it should (hopefully) be easier than actually mapping its path.

I was saying that in response to Jremington: