Concerning the pedites extraordinarii, I think this is speculation on that part of some authors. I know of no support in the ancient sources for that claim. Some of the equites extraordinarii (Polybios 6.31) were quartered near the Consul's volones in camp and may have therefore been under his immediate control on the battlefield.
Polybios states (6.40) that when an army is on the march, the extraordinarii form the vanguard if the enemy is ahead of them and the rearguard if the enemy is behind. This indicates that when formed for battle, the extraordinarii would be positioned on the extreme right of the formation.
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