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.