How do robots sense the world and decide how to move?

A robot rolls into a room it has never seen before. There's a chair, a wall, a cat, a patch of sunlight. The robot has no eyes the way you do, no skin, no ears — and yet, somehow, it stops just before the chair leg, turns, and glides around it. How? Let's open the robot up and follow what happens between "the world" and "the move."
First, the robot has to take in the world — and it does this with sensors. A sensor is just a part that turns something out in the world into a number the robot can use. A camera turns light into numbers. A microphone turns sound into numbers. A bumper turns a gentle bonk into the number "1." Wherever you have a sense, a robot has a gadget that measures it instead.
