Once I had the mechanics done, I started to work on the programming. Setting the speed of the servos was easy enough:

import microbit

microbit.pin0.set_analog_period(20)
microbit.pin0.write_analog(int(25 + 100 * degrees / 180))

But then making it turn exactly 90° or travel exactly 10cm required some careful experimentation with timing.

Once I had that, hooking up the distance sensor was easy. It's an analog SHARP range finder, so all I needed was to read the analog pin. Then I added some simple logic for finding out in which direction the obstacle is further away, and voila, object avoidance:

And that's it. All the code sits in the repository: https://bitbucket.org/thesheep/micro-bot/src