Math & Kinematics

Redundancy Resolution

Redundancy resolution is the selection of a specific joint motion when a manipulator has more degrees of freedom than its task requires, leaving infinitely many inverse kinematics solutions. Standard techniques project secondary objectives, such as joint-limit avoidance, singularity avoidance, obstacle clearance, or posture preference, into the null space of the task Jacobian so they proceed without disturbing the primary end-effector motion.

Why it matters for physical AI

Seven-axis arms and humanoid torsos are now common precisely because redundancy buys dexterity and obstacle avoidance, but exploiting it requires principled resolution, whether by null-space control or learned whole-body policies.