A 'retraction' method for terrain model acquisition

We consider the following problem (called the terrain model acquisition problem): A point robot R is placed in a finite-sized two-dimensional obstacle terrain populated by a set 0 = {01,02, ,On} of unknown polygonal obstacles. Each obstacle Oi is a finite-sized polygon with a finite number of vertices. Initially the number of obstacles in the terrain is unknown to R . And also, the number and the locations of vertices of each obstacle are unknown to R . The robot is equipped with sensors that detect all vertices and edges that are visible from the present location of the robot. The robot is required to navigate and acquire the complete terrain model in a finite amount of time. In this paper we propose a solution based on the retraction method, and this method has the advantage of keeping the robot as far as possible from the obstacles during the navigation. We also present a method for terrain model acquisition by a circular robot R of radius r , (r >O).