Abstract
Nomenclature jAj = cardinality of a set A A , A, @A = interior, closure, and boundary of a set A, respectively C = cost of an aircraft reconnaissance tour , m d x;x0 = length of shortest aircraft path from state x to state x0, m nsamples = actual number of samples to build a roadmap nsamples = estimated number of samples to build a roadmap rmin = Dubins aircraft minimum turn radius R = s-dimensional Euclidean space S = circle parameterized by angle radians ranging from 0 to 2 SE(2) = special Euclidean group R S T = set fT 1; T 2; . . . ; T ng of n targets to be photographed by aircraft V T i = visibility region of ith target Va = Dubins aircraft airspeed X = aircraft state space x = aircraft state vector x; y = Dubins aircraft Earth-fixed Cartesian coordinates, m = parameter controls ratio of translational vs rotational density of roadmap = Dubins aircraft azimuth angle, rad 2 = set of all subsets of a set A
Published Version
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