Math & Kinematics

Joint Space

Joint space is the coordinate space whose axes are a robot's joint variables, so a configuration of an n-joint arm is a point in an n-dimensional space, in contrast to task or Cartesian space, which describes the end-effector pose. Motion planning, collision checking, and most learned policies operate in joint space, with forward kinematics mapping it to task space.

Why it matters for physical AI

Whether policies act in joint space or task space is a recurring design decision, trading direct hardware correspondence and singularity-free execution against intuitive, embodiment-transferable commands.