Robot Navigation in Unknown Generalized Polygonal Terrains using Vision Sensors

This paper considers the problem of navigating a point robot in an unknown two-dimensional terrain populated by disjoint generalized polygonal obstacles. A generalized polygon consists of a connected sequence of circular arcs and straight-line segments. The terrain model is not known a priori, but the robot is equipped with a vision sensor. A discrete vision sensor detects all visible (from a single position) portions of the obstacle boundaries in a single scan operation. The navigation problem deals with moving the robot through the terrain from a source position to a destination position, and the terrain model acquisition problem deals with autonomously building a model of the terrain. A complete solution to either problem is shown to require an infinite number of scan operations in cusp regions formed by a pair of convex and concave obstacle edges. Either problem is considered solved with a precision ∈ if the points that have not been scanned are those in a cusp region with a clearance less than ∈ from two obstacle edges. Three methods are proposed to solve both problems with a precision ∈ based on extensions of the generalized visibility graph, the generalized Voronoi diagram, and the trapezoidal decomposition. Then simplified versions of these structures are proposed to exactly solve the navigation and terrain model acquisition problems using a continuous vision sensor that detects all visible obstacle boundaries as the robot navigates along a path.