First, don't use 'literals' in your parser rules. Without a lot of experience in ANTLR, this will get you in to trouble. Create real lexer rules:
TURNTO: 'turnTo';
Now, you probably need to read through the tutorials on the ANTLR wiki and study the downloadable examples and make sure you understand them. Writing good grammars seems easy because the grammar language is trivial to learn, but in fact it requires quite a lot of knowledge. The first thing to realize though, is that the lexer has no knowledge of the parser - it merely tokenizes the input stream and passes those tokens to the parser - so the lexer patterns cannot be ambiguous - the parser rules can deal with potential differences.
ANTLR can probably handle your grammar without transforming it to LL(1) as ANTLR can handle LL(k) and usually works out what k is without your help. Is this your entire grammar? However, it is always best to left factor anyway:
statement: var ( TURNTO {etc} | TERMINATE DOT )