Newer robotic vacuums (not sure specifically for roombas) have a lidar sensor on the top that maps all the rooms that it travels through. It also knows the exact position of the dock in those rooms and its own position, so after that’s done it’s just a simple pathfinding algorithm like in a video game.
For a diy robot this is obviously too complicated, unless you’re using something a bit more powerful like a Raspberry Pi and have some advanced programming knowledge. In that case, you could probably make a similar room map with a sonar or just with the good old “bump into every single wall” method.
The two easier methods would be an algorithm that determines your location by the distance traveled and turns taken (you’ll need precise motors, ideally steppers) or an IR led and directional receivers, but this will only work with line of sight, so maybe use this for the last couple of meters.
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