The C-space is the space of all possible configurations
of a robot.
Two somewhat different spaces of interest
are the task space and the workspace.
The task space is a space in which the robot's
task can be naturally expressed.
For example, if the task is to control the
position of the tip of a marker on a board,
then task space is the Euclidean plane.
If the task is to control the position and
orientation of a rigid body, then the task
space is the 6-dimensional space of rigid
body configurations.
You only have to know about the task, not
the robot, to define the task space.
The workspace is a specification of the configurations
that the end-effector of the robot can reach,
and has nothing to do with a particular task.
For example, a planar robot with 2 revolute
joints, limited to ranges of motion of 180
and 150 degrees, has the workspace shown here.
The workspace is often defined in terms of
the Cartesian points that can be reached by
the end-effector, but it is also possible
to include the orientation.
The set of positions that can be reached with
all possible orientations is sometimes called
the dexterous workspace.
So this concludes Chapter 2 on configuration
spaces.
In Chapter 3, we will focus on representing
configurations and velocities of rigid bodies.
