Original post:

In my current playthough I don't have many robots yet, but it seems that there might be a problem with priorities and or Haul Urgently. Most likely Haul Urgently.

I had set some items to be hauled urgently and no matter what the hauler bot would still prioritze the non-urgent hauls. And I checked, no other pawn was currently set to haul any of those items. And in the end those items were hauled by pawns and animals.

There's nothing related logged during the replication of the issue.
To produce this log i loaded my save and immediately drafted all my pawns.
Found my hauler bot mk2, then emptied out a few storage spaces and let the hauler complete its current task. It was to gather a stack of wood to a storage crate, so I set a couple of different things to be urgently hauled and then clicked on the bot's arrow to force it to move and abort its current task, but after it went for that same wood stack again. And after letting it complete that task it went on to another non-urgent stack and then went on to just treat every item as non-urgent. Dealing with the urgent items in the order they would have been normally handled as non-urgent.
The bot's Haul is at priority 3 and haul+ at 2. (it was at 3 the first time I noticed this, but increasing priority didn't change things)

So whatever the issue is, might be hidden deeper in the logs. (They've become a lot longer than I remember..)
https://gist.github.com/6065f761c83c7971cb414da8765d98c7