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Identifying Hazardous Shapes in the Plane

This paper explores the problem of identifying the shapes of
invisible hazardous entities in R2 by a set S = {s1, s2, . . . , sk} of mobile
sensors (autonomous robots). A hazardous entity, H, is a region that
affects the operation of robots that either penetrate the area or come
in contact with it. In this paper, we propose algorithms for searching
a rectangular region for a stationary hazardous entity, where some a
priori geometrical knowledge is given (e.g., edge size range), and if such
an entity exists, then determine the area that it occupies. We explore
entities that are convex in nature such as line segment, circles (discs),
and simple convex shapes. The objectives are to minimize the distance
travelled by the robots during the search phase, and to minimize the
number of robots that are required to identify the region covered by the
hazardous entity. The number of robots required to locate H is three or
four robots when H is a line segment, two or three robots when H is a
circle, and seven robots are sufficient when H is a triangle. Our results
extend to n-vertex convex shapes and we show that 2n + 1 robots are
sufficient to determine the coverage of H.