Those with a background in linear algebra may be familiar with the concept of a nullspace. The idea of a vector in the input space that produces a zero vector in the output space is especially interesting as we consider the Jacobian of a robot manipulator. Nullspace movement can be used to perform collision avoidance and multi-objective optimization for redundant manipulators. This notebook gives some background on what a nullspace actually is, as well as some practical examples of how nullspace movement can be applied.
Check out the static notebook here.
Download the notebook and run it yourself here.
Awesome explanations! Very accessible to a geek like me with a very little background on the topic.