Hardware & control
Task space
Task space is a coordinate space used to express quantities directly relevant to a robot task, such as an end-effector pose, centre-of-mass position, gaze direction, contact force, or several objectives together. It describes what should be achieved, while joint space describes the robot configuration used to achieve it.
Also known as: operational space, Cartesian task space
Updated
A task selects controlled quantities
Khatib's operational-space formulation develops control directly in coordinates associated with a manipulation task. A hand position is a common example, but humanoid tasks can also include foot contacts, torso orientation, gaze and centre-of-mass motion.
Task space is therefore not always ordinary three-dimensional workspace. It can combine position, orientation, force or other outputs chosen for the objective. Every component needs a reference frame, units and convention.
Kinematics connects task and joint spaces
Forward kinematics maps a joint configuration to task quantities. The robot Jacobian relates their local velocities. Inverse kinematics searches for joint values that realise a desired task-space target.
The mapping is often many-to-one: a redundant humanoid can keep its hand fixed while changing elbow posture. Whole-body controllers use this freedom to balance priorities such as reaching, avoiding joint limits and maintaining foot contact. Near a singularity, some task-space motions require very large joint velocities or cannot be produced locally.
Commands must state their representation
An end-effector action may encode an absolute pose, a relative pose, a velocity or a wrench. Rotations may use matrices, quaternions, Euler angles or axis-angle vectors. Numerically similar arrays can therefore mean different actions.
Robot datasets should document the controlled link, parent and reference frames, rotation representation, units, update rate and mapping to low-level control. If several tasks are stacked, preserve priorities and weights. Task-space data without those conventions cannot be replayed reliably.
Sources
Related terms
Hardware & control
Joint space
Joint space is a coordinate space whose variables describe a robot's joint configuration, such as revolute-joint angles and prismatic-joint displacements. A point represents one configuration subject to the robot model and joint limits; a path or trajectory represents how that configuration changes.
Hardware & control
End effector
An end effector is a task-specific device attached to a robot manipulator’s mechanical interface so the robot can act on its environment, such as a gripper, hand or welding tool. It is distinct from the wrist or mounting flange, and from the tool centre point, which is only a coordinate frame used to plan the device’s motion.
Hardware & control
Robot Jacobian
A robot Jacobian is a configuration-dependent matrix that maps joint velocities to a specified task velocity, such as the linear and angular velocity of an end effector. It describes instantaneous motion, rather than the end effector's finite displacement or the forces needed to accelerate the robot.
Hardware & control
Inverse kinematics
Inverse kinematics (IK) finds robot configurations that satisfy a desired position, orientation or other geometric constraints. It reverses the question asked by forward kinematics: instead of computing where a hand or foot is from the joint values, it searches for joint values that place it at a target. A target can have multiple solutions or no feasible solution.
Hardware & control
Whole-body control
Whole-body control coordinates a humanoid’s full multibody state, actuated joints and environmental contacts to pursue several motion or force objectives while respecting constraints such as balance, joint limits and friction. It is a family of hierarchical or optimisation-based methods, not one algorithm; implementations may output joint positions, accelerations or torques.
Hardware & control
Coordinate frame
A coordinate frame is a defined origin and set of oriented axes used to express positions, orientations, motions, forces, or other spatial quantities. A value has no complete geometric meaning until its frame and convention are known. Transformations relate measurements expressed in frames such as world, robot base, camera, end effector, object, or sensor.