Joint Space

The space described by a vector of all a robot's joint values — angles or displacements — used to describe its configuration.

Joint space arranges every one of a robot's joint variables into a single vector q = (q₁, …, qₙ), where n is the number of joints; a rotary joint contributes an angle and a linear joint contributes a displacement, and the set of every value q can take forms the joint space. The counterpart is task space (also called Cartesian space), which describes the robot by its end-effector pose instead; forward and inverse kinematics convert between the two. Planning and control are most direct in joint space, since motors are commanded in joint angles anyway and there's no issue of multiple inverse-kinematics solutions — but the path the end effector actually traces through physical space isn't obvious just by looking at joint-space values. Demonstration data recorded as joint angles reproduces the exact same motion on the same robot, but doesn't transfer directly to a robot with a different kinematic structure, which is why a lot of cross-embodiment work records actions as end-effector poses instead.

ExampleThe vector q that libfranka reads out — 7 joint angles, in radians — is a single point in the Franka arm's joint space; the O_T_EE reported at the same instant is its representation in task space.

Related

Task Space · Configuration Space (C-Space) · Forward Kinematics (FK) · Inverse Kinematics (IK) · Degrees of Freedom (DoF) · Action Space

Sources

Wikipedia: Configuration space (physics)（Robotic arm / joint space）
libfranka robot_state.h（q: measured joint position）
robosuite Documentation: Controllers（Joint Position / Velocity / Torque）