Can you map without having a sense of direction just distance?

I’ve got a basic robot I’m building(from scrap parts) partly a challenge/waiting till budget improves but yeah.

Conceptually it’s a tail dragger design with two 360 servos(wheels) pulling a tail, the tail being a potentiometer attached to wheel/stick and it keeps the robot going straight(in my mind after calibtration) by the changing resitance and the servos will compensate by decreasing per appropriate side depending on potentiometer rotation direction.

Anyway… so I’ve got a bumper on one of the wheels, measured the diameter of the wheel/have circumference.

Then I have two bumpers in the front so this thing has a dumb logic of “go straight, run into something, if you can tell direction, do opposite, and keep going”.

So you can imagine a thing randomly driving around like this image. All it can do is measure distance, but has no sense of direction at all. But it can keep itself going straight.

So I’m wondering with that in mind, can you still create a map from that. See this LiDAR image generated by laser beam/known variables, probably known direction? I mean I would do distance(like travel of light for LiDAr with the wheels) but I can’t sit in one spot and do a 360 scan, that I can then compare against by moving the bot, and doing another 360 scan.

I’m also trying to think of a coordinate system that I would use to store. I don’t think I can fit all this data into 4kb(eeprom) and at the moment don’t have a way to store data from the arduino, would have to hook up an SD card or beam it by an ESP WiFi module… which I have to buy/get I just want to get something running this weekend which may not happen(because of coding lack of skill with regard to sketch, I’m a developer just not used to working with C/loop but work with Python).

Anyway any thoughts? It’s a neat little project I think, good exposure to ‘actual proramming’ with regard to being “closer to the metal”(I’m coming from the web side)

edit

I feel like the answer is obvious, of course. Just find where it hit “a wall” and then plot all of those points… but no direction! No 0,0 haha. But I think with a lot of math, it can be done, you treat the first point as your comparison point since the walls are static it should work… provided it actually goes straight.

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