Diagonal runs are a great way to save time – and crash.

If you want to run down the diagonals of a maze, you must be skinny.
The equivalent width of the passage running along a diagonal is only about
114mm. Clearly, you had better be thinner than this. The closer you are
to this width, the more accurately you must position yourself. Equally,
you don’t want to be too narrow or there may be stability problems on
high speed curves. There is more on this in the section on smooth turns.
Skinny also means that steering is more sensitive.

Sensors will have to work extra hard during diagonal runs. You no longer
have those nice perpendicular reflecting surfaces if you use side-looking
sensors. The sensing points are in different places that they were on
straight runs. The variation on wall distance is greater and the optimum
sensing points are asymmetric so you don’t get simultaneous left and right

All in all diagonal running is a lot more complex. So what can you gain?

Consider a series of steps in a maze. A left-right pair might require
two smooth turns at, say 140mm each at a maximum of 0.7m/s and will take
0.4 seconds. The same pair on the diagonal, without the entry and exit
quarter turns, takes a ground track of 250mm or so. Not much of a distance
saving but you may be able to cover this at a speed of, say 1m/s, in only
0.25 seconds. Now that is a saving worth having. In a maze designed to
reward diagonal runners you might shave as much as 30% of your running
time through these sections.

As with smooth turns, you will need to do some sums and plenty of experiments.
There are three kinds of turn associated with diagonal runs, each with
an entry and exit phase. You will need velocity/position profiles for
each of these.

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