# Confusion over configuration space, workspace and task space

I have been watching Kevin Lynch's videos on Coursera in this series on the basics of robotics. From that I gathered these are the definitions.

configuration space is the space of all configurations of the robot.

workspace is a specification of the configurations that the end-effector of the robot can reach

task space is a space in which the robot's task can be naturally expressed

• Is the workspace contained in the configuration space since the end-effector is part of the robot? I understand that the configuration space is for each rigid link of the robot from this answer and the end-effector is a link.

• Is it possible to have a task space that is beyond the configuration space?

Two of these terms describe mathematical spaces (Configuration and Task spaces), and one (Workspace) the physical space in which the robot operates. Acknowledging they are related, but they are not the same "type of thing".

I recommend having a look at the QUT Robot academy videos by Peter Corke:

Which define configuration space as the mathematical set of all possible joint configurations. Task space the mathematical set of all possible end effector poses. And, workspace as the physical volume of all reachable end point positions".

No I don't believe it's possible to have a task space "beyond" the configuration space.

• Are end point positions different from end effector poses? Sep 17, 2021 at 23:42
• Yes I believe so. Some positions/locations can be achieved by a variety of effector poses. Sep 18, 2021 at 0:15
• I am confused now. What's meant by end point positions? The final configuration of the robot? Sep 18, 2021 at 11:36
• The understanding I have taken away (and I am not an expert, so please check) is that end point positions are a position in physical space. The workspace that the robot arm can reach. For some end points at the extremities of the workspace there may be only one configuration of the arm and effector (I.e, end effector pose) that can reach that point. For other points there may be multiple poses that reach the one spot. Sep 18, 2021 at 17:03
• As an analogy, think of a point in front of your chest and quite close, and one of your arms as the robot arm. You can reach the point with your shoulder joint and elbow arcing up high and your hand and wrist coming downwards to the point, alternatively you can reach the point with your shoulder and elbow arcing downwards and your hand and wrist coming upwards to the same point. For an end point that is well inside your workspace there are multiple poses that can reach there. For a point at the maximum stretch of your arm there might be only one pose you can physically achieve to get there. Sep 18, 2021 at 17:11