# Is configuration space same as joint space?

For robotic manipulator like the one on the picture:

are the configuration space and joint space equivalent? I am trying to understand difference between the two...

In order to answer my own question Configuration space and Joint space must be defined.

Configuration space of a rigid body is a minimum set of parameters that can determine position of each point in that body or Configuration space is set of all possible configurations of that body.

Configuration space of the end-effector is set of all possible positions and orientations of the end-effector, while Configuration space of the robot is the set of all possible positions and orientations for each rigid link of the robot. Shape of the Configuration space depends on which rigid body it refers to.

Joint space is set of all joint parameters. In case of the robot in the picture those are its joint angles.

For the robotic manipulator in the picture it can be assumed that its configuration is completely determined by its joint parameters. It can be said that Configuration space and Joint space are equivalent for this robot (give or take few mathematical definitions of equivalent).

In robotics the configuration space is exactly the joint space of the manipulator.

Differently, to indicate the space where the forward kinematic law maps the joints configuration into, we use the terms task space and operational space, equivalently.

• This is true for a non-redundant manipulator. Back than, I was searching for a difference between two terms. A redundant manipulator can achieve the same configuration with different joint parameters. In that case, configuration space is not equal to joint space. Aug 25, 2014 at 8:04
• In robotics the term "configuration" refers to current configuration of the joints. The redundancy has to do with the mapping between the configuration of the joints and the task-space (i.e. the pose of the end-effector). Said that, we can still use the term "configuration space" as a synonym of joint space. The configuration is of the joints, not of the end-effector. This is the common usage. Aug 25, 2014 at 10:36
• I was going with the original definition of the configuration space lis.csail.mit.edu/pubs/tlp/spatial-planning.pdf According to this definition, joint space (space of joint angles or translation) is not nearly the same as configuration space, although it may be used as its parametrization... Aug 25, 2014 at 15:43
• Ok, sorry, I was rather pointing to the common meaning in the robotics community instead. Aug 26, 2014 at 12:42

Configuration space refers to the set of all possible configurations of the end-effector, the tool frame in this case. Joint space is the set of joint parameters which describe the overall configuration of the robotic manipulator. Forward kinematics are used to map the Joint space to the Configuration space and Inverse kinematics do the opposite.

• Thank you for your answer! I agree that this holds for the Configuration space of the end-effector, not the Configuration space of the robot. When I was asking this question, I was refering to the Configuration space of the robot. Feb 4, 2014 at 12:22
• This is an incorrect answer. Forward kinematics is used to map from joint space/configuration space to task space/Cartesian space! Apr 22, 2021 at 12:34