A `retraction´ method for terrain model acquisition

The following problem, called the terrain model acquisition problem, is considered: a point robot R is placed in a finite-sized two-dimensional obstacle terrain populated by a set O = O₁O₂, . . ., O _n} of unknown polygonal obstacles. Each obstacle O _i is a finite-sized polygon with a finite number of vertices. Initially the number of obstacles in the terrain and 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 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. A solution based on the retraction method is proposed that has the advantage of keeping the robot as far as possible from the obstacles during the navigation. A method for terrain model acquisition by a circular robot R of radius r, (r>O) is presented