Algorithmic approaches to optimal route planning

The field of computational geometry has addressed many problems that are of direct relevance in route planning problems for mobile robots. Examples include the computation of visibility graphs, shortest paths among obstacles, minimal time paths through varied terrain, and various other mission planning problems. In this paper, we survey some recent results and show some applications to computing optimal paths. Our goal is to provide precise geometric models and to analyze algorithms according to their worst-case asymptotic complexities. Our hope is that many of the techniques can be applied as 'black boxes' within the framework of a more complex, hueristic-based system to solve the real-world problem.