Dealing with the Ill-Conditioned Equations of Motion for Articulated
Figures
The paper discusses some of the challenges in designing an IK solver. The
authors describe Singular Value Decomposition which carefully chooses the
appropriate coordinate systems to reach the main system of equations we
need to solve. Our goals are minimizing our deviation, and the amount of
rotations needed by joints.
. The paper also explains the effect of error in measurement. If we can
accept some error on the end results, how does this translate to
conditions in the joint space. The worst cases happen, when it is very
easy to move in one direction, but very hard to move in the other (for
example, if all the joints are totally stretched out).
Finally the paper explains the "damped least square error" method to
actually solve the problem.