What is the difference between joint space and task space in robot kinematics?

• A. Joint space is cartesian coordinates of the end-effector; task space is joint angles.
• B. Joint space refers to coordinates of each robot joint (angles or displacements); task space refers to end-effector pose (x, y, z and orientation).
• C. Joint space includes only rotational joints; task space includes prismatic joints.
• D. Both spaces are the same; end-effector pose is identical to joint angles.

Answer: (B)

In robot kinematics, you distinguish two ways of describing the robot’s state. Joint space describes the internal configuration of the robot by a set of joint variables: angles for revolute joints and linear displacements for prismatic joints. If there are R joints, the joint-space coordinates form a vector q = [q1, q2, ..., qR]. Task space, or the workspace, describes the end-effector’s pose in the world: its position in 3D (x, y, z) and its orientation (often represented as roll-pitch-yaw or a quaternion). This is the end-effector’s pose, sometimes called x.

These two descriptions are linked by forward kinematics, which give the end-effector pose as a function of the joint variables: x = f(q). Conversely, inverse kinematics tries to compute the joint variables from a desired end-effector pose. Velocities also bridge the spaces: the end-effector velocity ẋ is related to the joint rates q̇ through the Jacobian, ẋ = J(q) q̇. This shows how changes in joint variables produce motion in task space.

So the correct concept is that joint space is the coordinates of each joint, while task space is the end-effector’s position and orientation. The other options mix up what describes each space, or falsely claim they are the same, or restrict spaces by joint type.