Math & Kinematics

Task Space

Task space is the coordinate space in which a robot's goal is naturally expressed, most commonly the 6-DoF Cartesian pose of the end-effector, as opposed to joint space, which describes the robot's internal configuration. Controllers and planners map between the two using the forward kinematics and the Jacobian, and task-space control laws such as operational space control command end-effector wrenches or velocities directly. Redundant robots can exploit extra degrees of freedom in the null space of the task.

Why it matters for physical AI

Learned manipulation policies overwhelmingly output task-space end-effector actions because they transfer more easily across robots with different kinematics, a convention that underlies most cross-embodiment datasets and robot foundation models.