Math & Kinematics

Kinematic Redundancy

Kinematic redundancy is the property of a robot having more degrees of freedom than its task requires, as in a seven-DOF arm performing a six-DOF pose task. The surplus creates a null space of joint motions that leave the end-effector fixed, which controllers exploit for secondary objectives such as obstacle and singularity avoidance, joint-limit centering, or posture optimization.

Why it matters for physical AI

Redundant arms can keep elbows clear of humans and obstacles while holding a task pose, providing the workspace flexibility that cluttered, human-shared environments demand of deployed manipulators.