I want to build path planning with voronoi diagram. So first of all, I have to build 2D map of robot's environment and then partition their boundaries with voronoi diagram. And then i will convert this map to topological map in order to compute it's shortest path. But this resultant path also must obey traffic law. So now i am confusing with applying GPS system. If i will use GPS , i will get four dimensions (attitude , longitude , height and time). So my question is: 1) How to convert the resultant output of GPS to 2D map? 2) Have I to need apply other sensors ( sonarsensor and camera) to get 2D map? 3) Can I use only GPS system in my mobile robot?(without sonarsensor and camera) P.S my mobile robot is inteneded to travel in township situation but static environment. Thanks in advance.

This problem (and in particular the use of Voronoi diagrams of mapped regions for path planning)has been well studied. You should try using a simple search method such as [google] before posting here, which would make life a lot easier for you. For example, a simple search of 'robot voronoi mapping' returns the following as the top link

http://www.cs.columbia.edu/~pblaer/projects/path_planner/