We were successfully able to define multiple constraints and have the figure adjust to them interactively. For example, when we constrain the feet and pull on an arm, then the figure moves its hips, shoulders, and arm to reach towards the new arm constraint.
While this mostly seemed to work, we ran into some problems with local minima. In particular, it seemed to get confused when putting the arms over the head, since this required multiple shoulder rotations as well as elbow rotations. It would sometimes choose to violate constraints and minimize joint movement rather than fully solving the constraints. This may be partly due to the non-continuous constraint function which give a large fixed penalty to violating the legal angle constraints. The optimization therefore gets stuck before it reaches its goal and fails to find another way around.
We also found Powell's method to be very slow, since it needed so many function evaluations per iteration, and each of those required numerous matrix multiplications of floating point numbers. On a 3.0GHz machine, the system was usable but not fully smooth; on older machines, the slowness was noticeable and annoying. Conjugate gradient, while much faster, also got completely stuck very easily.
Using these techniques, we constructed a few key frames and linearly interpolated between them to produce the following demonstration animation. Of all of the poses, M was the most difficult since the joint angles for raising arms above one's head are non-trivial. Once the arms were above the head, getting the hands to point down was an additional challenge. It turned out that the skeleton we were using didn't even have enough degrees of freedom for the wrists, so we added one more for each. A more accurate model of what motions and positions are easy or hard might make posing easier.