Task Space

The space that directly describes what a task cares about, usually the end effector's position and orientation.

Task space is the counterpart to joint space. Joint space describes a robot by its joint angles; task space directly describes whatever the task actually cares about, which by default means the end effector's — the gripper or tool's — position and orientation. Per Lynch and Park's textbook Modern Robotics, how task space is defined depends on the task, not the robot: drawing on paper only needs a flat 2D coordinate, while manipulating a rigid body needs a full 6D pose. Because it's commonly expressed in Cartesian xyz coordinates, it's also called Cartesian space; Oussama Khatib introduced operational-space control in 1980, with the landmark paper following in 1987, and called it operational space. Converting joint angles to task space uses forward kinematics; the reverse uses inverse kinematics. Some VLA models define their actions in task space, others work directly in joint space.

ExampleOpenVLA outputs a 3D end-effector translation, 3D rotation, and 1D gripper open/close value — a task-space action. ACT on the ALOHA platform instead outputs a 14-dimensional joint target across both arms directly — a joint-space action.

Also called

Cartesian Space, Operational Space

Related

Joint Space · Workspace · End-Effector Pose · Inverse Kinematics (IK) · Operational Space Control · Jacobian Matrix

Sources

Modern Robotics (Lynch & Park, 2017), 2.5 Task Space and Workspace
Wikipedia: Robot kinematics
Wikipedia: Oussama Khatib（operational space formulation, 1980）