A popular choice is sensors that live on booms or wings and look down
at the walls from above. These can be simple reflective switches connected
to an eight-bit port on the micro. A perfectly adequate mouse can be constructed
using eight of these on each side. Say, seven for the walls and one each
shared to detect the forward wall.

The wing must be placed well forward of the wheels. You will need to see where the walls are before you get to them or the control problem is impossible.

As for other IR sensors these should really be AC coupled and synchronously
read. You might like to just use ready-made reflective switches designed
to work in adverse conditions.

The main problem with these arrangements are to do with the rotational
inertia they present to the mouse. However light you make them, they have
to live a relatively long way from the center of mass and so contribute
a relatively large component of the total inertia. As long as you are
prepared for that and don’t expect breathtaking turn performance, they can
have a lot going for them. Build them light and there will still be plenty of other things to worry about before rotational inertia becomes a limiting factor in performance.

These types of sensors can have a huge advantage in that they are able
to detect walls in adjacent cells. Since they must overhang the maze walls,
when you get to a post position, the outermost sensors will be able to
see any walls perpendicular to the direction of travel. This may save
you a lot of exploring – up to 50% if you are lucky.

Even though the sensors themselves are likely to be positioned quite
a long way apart – say 5-10mm – it is possible to get slightly better
resolution if you can get an analogue reading from them and interpolate
the distances.

If you have already decided that you want to run diagonally, ensure that the sensors extend far enough to cover the walls in this mode.

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