You can buy kits that you build your own robots, such as ones that follow a line, or can navigate a room and turn if they bump into something - they normally are used to demonstrate theory behind robotics - you can also build the kits yourself entirely - i.e. soldering all the components and putting together the drive systems.
Also, reading up on things such as programmable micro-controllers (like the really small ones) that use simple logic such as IF and OR i.e. IF the white line goes to the left - the action would be power to stop one motor on the right spinning until the line comes back into view. Also, stepper motors and sensors are stuff you could read up on specifically.