When I empty out intentions and relax in meditation, what is this force that moves my body in complex patterns?
That's chi, not wu wei.  Wu wei is more of an approach - one that can give rise to feelings of chi, aid in samatha meditation, etc.  Using chi is outside the scope of Buddhist practice, although Jwing-Ming Yang mentions its role in Buddhism in many of his qigong books.  Personally, I appreciate his effort, but his writings on the subject seem like a bit of a stretch to me.  You're better off just sitting on the cushion.  Meditation practice is complicated enough.  No need to add additional complexity.