While there's nothing that specifically calls out the Summoner's Eidolon ritual, I'm going to use the rules for casting time:
A spell that takes 1 minute to cast comes into effect just before your turn 1 minute later (and for each of those 10 rounds, you are casting a spell as a full-round action, just as noted above for 1-round casting times). These actions must be consecutive and uninterrupted, or the spell automatically fails. Emphasis mine
The rules for a full-round action state:
A full-round action requires an entire round to complete. Thus, it can't be coupled with a standard or a move action, though if it does not involve moving any distance, you can take a 5-foot step.
You must also maintain concentration for the entire duration (10 rounds for a 1 minute spell) of the casting:
When you begin a spell that takes 1 round or longer to cast, you must continue the invocations, gestures, and concentration from 1 round to just before your turn in the next round (at least). If you lose concentration after starting the spell and before it is complete, you lose the spell.
So you may make a 5-foot step every round, but injury, violent motion and other dangers force concentration checks and, if you miss your roll, you must restart the ritual.