To make any useful contribution to something as heavy as a suitcase, you're going to need quite a bit of power. Packaging and installing all the components on an existing suitcase would take a substantial amount of work.
An approach I've seen used successfully on electrically assisted bikes is to fit a powered trolley behind the bike to act as a pusher. It seems to me that you might be able to come up with a two-wheel trolley that one corner of the suitcase can sit in, containing a battery and motors operated by a pressure sensor on the suitcase handle. If you're feeling ambitious you could integrate this with the suitcase's own integral wheels, but I think that will be much harder to package and you might want to defer that. Perhaps you'll have time for that as well during your twelve weeks, but I suggest you get the standalone version working first - very little of the work on that will have been wasted if you decide to continue with 'phase 2' in the same project.
In other words, take an iterative approach and do the parts that will show the greatest value first. That's the electrics and electronics and control logic.