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...onment can be modeled with a topological map, e.g., asa generalized Voronoi graph [2]; localization in thisparadigm is based on identifying nodes in the graph from geometric environmental information =-=[3]-=-, [14]. Our research uses the Bayesian approach. We sample the space, we measure the signal strength at regularly spaced locations, and calculate the probability distribution. Localization is a proble...

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...re robust to environmental variation and sensor noise. III. PLACES AT VORONOI JUNCTIONS Choset has been a main proponent for the use of Voronoi graphs in topological map-building and navigation [16], =-=[17]-=-. Choset and Nagatani [18] define a generalized Voronoi graph (GVG) as a one-dimensional set of points equidistant to the n closest obstacles in n dimensions, where a preset threshold determines wheth...

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... closest point in the interior of the edge, and co ∈ Ci. [14][16]. In the case that the closest point is on a vertex and the solid angle between the two edges (which share that common vertex) is smaller than 180°, those edges are considered as one as if there were only one edge. Also, the distance is just the closest distance from the point x to that closest point on an edge. The vector ∇di(x) is a unit vector in the direction from co to point x. [17]. 3.2 Generalized Voronoi Diagram (GVD): Our skeleton-based tool path generation algorithm is based on earlier work done by Choset et al [14][15]. For the sake of completeness, a brief review of the GVD and its incremental construction is briefly described here. In 2D plane embedded in 3d space, GVD is defined as a set of points equidistant to two closest edges Ci and Cj which called the two-equidistant edge (also called skeleton) [16]; In a plane, GVD is defined as. {x ∈ part : di(x) = dj(x)} or di(x) dj(x) = 0} (3) The algorithm starts at one of the seed points, which actually is the set of all vertices where only the solid angle between the two edges (which share one of those common vertex) is bigger than 180°. The common predic...

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...scent of m: { 1 if (cosθ, sin θ) ∝ ∇m(p − pt) ha(x) = (7) 0 otherwise. At nonsmooth points, the gradient ∇ is assumed to be extended in a standard way from nonsmooth analysis; see [4] in general, and =-=[3]-=- for the use of this in the context of sensor-based planning. In this general case, ha(x) = 1 if (cosθ, sin θ) is proportional to any vector in the generalized gradient [4]: { co lim i→∞ ∇m(pi − pt) :...

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... added at both the WPP (low-bandwidth) level and the DTS (high-bandwidth) level. At the low bandwidth level, our basic approach is to use the incremental Voronoi construction techniques introduced in =-=[51]-=- to add edges to the Voronoi diagrams as the computer vision algorithms detect obstacles and threats that were not included in an a priori known low resolution world map, which is assumed to be availa...

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...ng the GVD. First, the GVD can be constructed in continuous space. For example, Nageswara et al. [12] represent the obstacles as simple polygons and geometrically construct the GVD, and Choset et al. =-=[4]-=- simulate an agent “tracing out” the GVD as it moves through the environment. Second, the GVD can be constructed in discrete space, e.g. on grids. In this paper we focus on GVDs constructed on grids b...

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...ing in an unknown environment and coming repeatedly in contact with obstacles, where the aim is to learn enough about the environment so as to then be able to construct safe paths for the robot – see =-=[15, 16]-=- and the references therein. In this paper we consider the problem of discovering the shape of an unknown object O of R 3 through an adaptive process of probing its surface from the exterior. A probe ...

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...thods (Tunstel and Jamshidi 1994). The third and most sophisticated coverage scheme involved in map building is based on Voronoi diagrams that can be constructed iteratively (Choset and Burdick 2000 =-=Choset et al. 2000-=-). The main contribution of this paper is that it provides a valuable comparison between the performances of one newly proposed and six existing techniques for processing ultrasonic arc maps (UAMs) fo...