In short, I'd like some AI (or anything) that can take any model, and make it walk, run, jump, climb, etc through an environment. I realize that this is the farthest thing from a trivial problem. I'm not up on the current state of research, or even if there is an official name for this problem domain. Can anyone point me in the right direction?

Specifically, I want to take as input:

A set of low-resolution sub-models, jointed together to form one larger model
Joint information, including degrees of freedom and range of movement
Weighted preferences for which surfaces on the model to use as "feet"
A virtual environment as a 3D model
A target position in the environment for the model to reach
A target velocity (including angular) for the model when it reaches said position
current position and velocity of each sub-model

and as output give:
The angles to place the joints at to achieve locomotion towards the target.

This specification may be a bit too general, because it would in theory perform acrobatics better than the most talented human. That'd be pretty neat, but implementing it is probably not practical, or necessary.

Google "reinforcement learning." An important algorithm here is "Q-learning." That said, if you're just running it in a simulation, then it's pretty nearly the same thing as "Value Iteration" or "Policy Iteration" -- just even slower. The issue with all of these techniques is that they take time that grows with the number of states in your state space, and with a uniform grid of states that number grows exponentially in the dimensionality of the state space. The upshot is you need to be clever to end up with a state that's small enough to actually do this stuff; you can only practically deal with state spaces that are 3-dimensional or so.

I hope that gives you some terms to google.

You might want to look into HyperNeat by Ken Stanley. He has a pretty active yahoo group and walking was something that has already been done with his project.

There are a ton of YouTube videos of people's bots (if you can call them that) that evolved how to locomote around via GA and/or NN. Look for their references in those.

Also take a look at Sumotori:

http://www.gravitysensation.com/sumotori/

It is (supposedly) 100% physics-based animation sumo wrestlers characters in a destroyable world. It is a small download, and for what it is, stupidly fun for a few mins. ;)