| The problem of navigating a robot body through a terrain whose model is a priori known is well-solved problem in many cases. Comparatively, a lesser number of research results have been reported about the navigation problem in unknown terrains i.e., the terrains whose model are not a priori known. The focus of our work is to obtain an algorithmic framework that yields algorithms to solve certain navigational problems in unknown terrains. We consider a finite-sized two-dimensional terrain populated by a finite set of obstacles {dollar}O{dollar} = {dollar}{lcub}Osb1,Osb2,...,Osb{lcub}n{rcub}{rcub}{dollar} where {dollar}Osb{lcub}i{rcub}{dollar} is a simple polygon with a finite number of vertices. Consider a circular body R, of diameter {dollar}deltageq{dollar} O, capable of translational and rotational motions. R houses a computational device with storage capability. Additionally, R is equipped with a sensor system capable of detecting all visible vertices and edges. We consider two generic problems of navigation in unknown terrains: the Visit Problem, VP, and the Terrain model acquisition Problem, TP. In the visit problem, R is required to visit a sequence of destination points {dollar}dsb1,dsb2,...,dsb{lcub}M{rcub}{dollar} in the specified order. In the terrain model acquisition problem, R is required to acquire the model of the terrain so that it can navigate to any destination without using sensors and by using only the path planning algorithms of known terrains. We present a unified algorithmic framework that yields correct algorithms to solve both VP and TP. In this framework, R 'simulates' a graph exploration algorithm on an incrementally-constructible graph structure, called the navigation course, that satisfies the properties of finiteness, connectivity, terrain-visibility and local-constructibility. Additionally, we incorporate the incidental learning feature in our solution to VP so as to enhance the performance. We consider solutions to VP and TP using navigation courses based two geometric structures, namely the visibility graph and the Voronoi diagram. In all the cases, we analyze the performance of the algorithms for VP and TP in terms of the number of scan operations, the distance traversed and the computational complexity. |
