When they are not fighting and only following you through the dungeon make the pets use some sort of invisible railing system. Let me explain.
I noticed that my pet is always getting stucked when trying to follow me in the dungeon. If i'm too fast and left him 2 or more rooms behind me, he start trying to get back to me in straight line, that often result in the bot getting stucked in the wall.
Why don't for each dungeon draw an invisible rail throught the whole dungeon. That way the bot can follow that "route" and not getting stucked at all. Only time he can get out of the rail is when fighting. As soon as the combat end, the bot go back on the rail ready to follow you again.