I'm trying to program an AI that operates in a world with various walls (essentially assume no thickness) as the only obstacles. The only data available is from an array of sensors spanning out from the front of the robot that detects the distance of an obstacle so long as it is < X distance units away (these are essentially arbitrary, other than that we know the robot can move anywhere between 1 and 4 of these units each turn). Data would essentially be a list like so: I am at (x,y), there is an obstacle at (m,n), (q,p) ... etc. Anyhow, I want to keep a representation of the world as its traversed, but I'm unsure of how to partition the world so I could apply any of the normal algorithms. I could see potentially dividing the world into a grid and counting squares with a wall passing through them as unpassable, but I can't see how to transform the data I acquire into such a grid. Any tips?

This type of problem is faced in real robotics regularly and comes under the title of SLAM: Simultaneous Localisation and Mapping. If you're solving this problem in a simulated world with known laws for movement and sensing and little to know uncertainty, then you wont need the complexity of solutions offered for solving SLAM problems with real robots operating in the real world. However, you will get some good ideas for how to tackle the problem from this literature, so I'd suggest taking a look. Before reading though, sit down and write out, in as much detail as you can, exactly what information your robot will have available to it and what information you want it to deduce from its environment.

Cheers,

Timkin