They aren't exactly random. Even if you can't see them they spawn at the same position the moment you enter the dungeon or reset it and begin walking in the exactly same pattern. To avoid the first pat for example I would reset the dungeons, count ten seconds, then start the 5 second CM countdown and go - that moment the pat will be moving to the center of the room from the right, your path will be clear. The rest of the dungeon works accordingly after that. Every mob or pat will be in the same spot at the exact same second if you always start the dungeon with the same timing.
Needless to say that this applies to all other dungeons as well.