The arm is the same 2D RR arm manipulator described in Section 2 (Figure 2). Assume that the arm is capable of gathering information about the objects in its environment via its sensors. To simplify the discussion, assume that those are tactile sensors - i.e. the arm can detect an obstacle when it comes in contact with one. The human operator can of course view the entire workspace, Figure 3. The task is as before - to move the arm from position S to position T in the arm's work space.
The arm can be defined in terms of the shoulder angle 
and the
elbow angle 
. The set of all configurations ( , )
define the arm's configuration space (C-space), which can be represented
as the surface of a common two-torus. An arm configuration in W-space
corresponds to a point in C-space. This mapping preserves
continuity; small change in W-space position corresponds to a small
change in the C-space position. A geodesic line between two points
on the torus (a straight line in the plane ( , )) is the
``shortest path'' between the points: four such paths can actually
appear [6].