I remember seeing a video discussion recently from NASA guys who calculated the shift of Andromeda over 8 years and determined that Andromeda would indeed hit the Milky Way in a few billion years.

A reporter was confused when the presenter said the solar system would be fine, and asked a followup question about it. The scientist's reply was essentially "we're talking about gravity on such a huge scale by bodies that are so far apart that the chance that our solar system would be significantly disrupted is astronomically unlikely."

I'm at work or I'd go hunt for the source, but I know it was a conference earlier this year and it was in the middle of the video.