singular value decomposition

In my first Ph.D. project, I robotically replicated the motion of the humerus as recorded via motion capture while subjects performed activities typical of an active amputee. The first task of this project was to program the position and orientation of the humerus onto the robot. In this post, I describe my method for accomplishing this task. To me, this is an interesting topic because it uses the same concepts as my previous post on establishing the position and orientation of a rigid body; but, the pen and paper are replaced by a robot and motion-tracking system.

The Singular Value Decomposition (SVD) is an incredibly useful tool with a staggering number of applications in seemingly unrelated fields. In this post I want to write about how the SVD is utilized to determine the orientation of a body segment from the skin markers attached to it. It's an interesting application of the SVD because it has straightforward geometrical interpretation.