Null-Space Posture Control

Key Insight

An arm with more than six joints is redundant — many different joint configurations place the hand in exactly the same pose — and the set of joint motions that move the joints without moving the hand is the null space of the Jacobian. This project uses that spare freedom to do two jobs at once: track an end-effector trajectory with the primary task while quietly nudging the elbow toward a comfortable "home" posture with the leftover motion. The same trick is the foundation of collision avoidance, joint-limit avoidance, and natural-looking motion on 7-DoF and humanoid arms.