I think science would develop to a point where we could travel around our universe! If technology doubles every 18 months then we should be able to develop sophisticated space craft to transport us around the galaxy! However the universe is infinitely bigger! Even travelling at the speed of light which is impossible… The universe is 46 billion light years wide… meaning we’d need to travel at light speed for 46 billion years to cross it! Something that isn’t possible as we won’t live that long or travel that fast!
That is just too hard to predict! We haven’t even started exploring our own galaxy!
For serious exploration, we probably need to go faster than light. Nobody would want to go on a spaceship for their entire life, just so that their children or grandchildren will land on an unknown planet… This is why you see things like “warp drives” or “cryogenic freezing” in science fiction – to make the travel bearable. We will need something like that! And we don’t know if that’s possible at all 🙂
The question of whether the universe has an edge (or whether it is infinite) will, I think, be answered by theoretical physics, not by exploration. As Aled says, the edge of the universe is *at least* 46 billion light years away (the size of the *observable universe*)! To get there, the technology we need would have to be *extremely awesome* – probably too awesome for us! 🙂