I didn't get why they are travelling with Ursa in After Earth. And what is their desired travel plan (obviously not earth)?
If I recall correctly, the Ursa was on the ship for training purposes. It was there for the ship's crew to try and learn more about the creatures and train other rangers to "ghost". Ultimately, when the ship crashed, it escaped.
As for their intended travel plan, I don't think it was ever alluded to, aside from being Cypher's "last voyage". Ultimately they get caught up in the asteroid shower, take a jaunt through a wormhole and voila - Earth. It clearly wasn't there intended destination, not least given Cypher's reluctance to even set down there.