It is clear that computing *G* is trivial when the map of the
environment is known. Using methods described by Dr. LaValle, and
mentioned above, it is easy to construct a similar information state
graph from *G*, and then search for a solution. Some details of this
are given below in section 5.

The interesting fact
is that it seams feasable to construct the information state graph
without knowing the map.
Recall that the limited robot described above needs to be capable of
following the bundary of *R* as well as the bitangents. It must also
be able to detect when a pursuit event occured, and when the boundary
or a bitangent has been reached. Using this information, the robot
could explore any given closed loop in *G* by traversing it in either
clockwise or counterclockwise fashion (the robot would need to know
when it has completed a full loop), and recording what events happened
on the way. This information could be used to construct the nodes and
edges in the information state graph, which could be searched and
executed without ever learning a map of *R*. The only remaining effort
is finding an algorighm that can be proven to correctly build the information
state graph, and implementing it.