not to mention you need the expansion cards themselves. I suppose you could just wing it and only use the homeworlds from the base game and just do a custom robot variant.
Robot mat is not enough to play single with different starting worlds.
You need also 14 counters - for solitare game to play Gathering Storm, and another 4 counters to play solitare Rebel vs Imperium. You need also (as you know) 2 custom dices (you can use 2 d6, but you must remeber what every number on them means).
Better option IMO are solitare rules: http://www.boardgamegeek.com/filepage/31272
I recommend Jeff Kunkel's Solitaire version after 2 edit.
I want to recommend buying this exellent expansion -The Gathering Storm is really worth this couple of dollars.Slight exaggeration coming from Mr. obvious I know; $25 isn't exactly a bank-breaker, but it still ain't chump change either.