I've been working for a while to connect the perception of affordances to motor abundance methods such as the uncontrolled manifold. I proposed the idea in this book chapter, and then I have a paper under review that is my first swing at making this work; the details of the hypothesis are in those, and I recommend you read them. The paper in particular has my most recent thinking spelled out as clearly as I can in the Introduction and Discussion sections.
As I've been chatting to people about progressing this programme, one thing that keeps coming up is 'why has no-one thought to do this before?'. This link simply seems so obvious to me, and to the people I'm talking to, but no-one has done it. I think I may have figured out why, though, and I thought I'd document the reason because I'm a sucker for these kinds of mysteries, especially when I think I've solved them.
I think the reason no-one has thought to connect affordances to UCM is that (almost) no ecological psychologist has been studying affordances as a solution to the control problem! Affordances are studied as solutions to the action selection problem only, and this seems to come from Warren. I'll link to some papers and lay out some thoughts for the record here.