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.
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.