One sequence is:
[Up] [Up] [Turn](Pink) [*] [*] [P0], where
* must be a turn in same direction. For example,
[Up] [Up] [Left](Pink) [Left] [Left] [P0] should work.
First, it seems clear that we need at least:
A P0 at the end to ensure some repetition (since we have only six actions to choose from) and some means to turn around when we are at the end of a 'spire' in the cross, which would require two turns in the same direction.
This would give something along the lines of:
[-] [-] [-] [Left/Right]* [Left/Right]* [P0], where
* are in the same direction.
We obviously need something else, though, because:
We need a way to move towards and away from the center pink square while we are in a 'spire'. Given we start at the end of a 'spire' and are facing the center, the easiest way out is to move forward by two (i.e.,
[Up] [Up] [-] [-] [-] [-]).
However, we just need a bit of additional logic:
We have a way to move in and out of 'spires', but we currently have no way to 'select' a 'spire'. To do so, we have to rotate to each 'spire' of the cross, but we should only do that if we are at the center square; one simple way to do this is to have
[Left/Right](Pink) after we move forward.
Notice, however, there is no one answer:
As long as we have some pattern similar to
[Up] [Up] [Turn] [Turn] [Turn] [P0], where one turn is conditioned on Pink and the other two turns are in the same direction (i.e., the Pink-conditioned turn need not be in the same direction as the two other turns, and the order of turns does not matter, so long as the turns occur after the forward motion), we have a solution.