3,564 research outputs found

    Polygon Exploration with Time-Discrete Vision

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    With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of useful accuracy does not allow the robot to scan continuously while in motion; instead, it has to stop each time it surveys its environment. This requirement was studied by Fekete, Klein and Nuechter for the subproblem of looking around a corner, but until now has not been considered in an online setting for whole polygonal regions. We give the first algorithmic results for this important algorithmic problem that combines stationary art gallery-type aspects with watchman-type issues in an online scenario: We demonstrate that even for orthoconvex polygons, a competitive strategy can be achieved only for limited aspect ratio A (the ratio of the maximum and minimum edge length of the polygon), i.e., for a given lower bound on the size of an edge; we give a matching upper bound by providing an O(log A)-competitive strategy for simple rectilinear polygons, using the assumption that each edge of the polygon has to be fully visible from some scan point.Comment: 28 pages, 17 figures, 2 photographs, 3 tables, Latex. Updated some details (title, figures and text) for final journal revision, including explicit assumption of full edge visibilit

    Optimally Computing the Shortest Weakly Visible Subedge for a Simple Polygon

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    Towards an Iterative Algorithm for the Optimal Boundary Coverage of a 3D Environment

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    This paper presents a new optimal algorithm for locating a set of sensors in 3D able to see the boundaries of a polyhedral environment. Our approach is iterative and is based on a lower bound on the sensors' number and on a restriction of the original problem requiring each face to be observed in its entirety by at least one sensor. The lower bound allows evaluating the quality of the solution obtained at each step, and halting the algorithm if the solution is satisfactory. The algorithm asymptotically converges to the optimal solution of the unrestricted problem if the faces are subdivided into smaller part

    Most vital segment barriers

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    We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

    Positional estimation techniques for an autonomous mobile robot

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    Techniques for positional estimation of a mobile robot navigation in an indoor environment are described. A comprehensive review of the various positional estimation techniques studied in the literature is first presented. The techniques are divided into four different types and each of them is discussed briefly. Two different kinds of environments are considered for positional estimation; mountainous natural terrain and an urban, man-made environment with polyhedral buildings. In both cases, the robot is assumed to be equipped with single visual camera that can be panned and tilted and also a 3-D description (world model) of the environment is given. Such a description could be obtained from a stereo pair of aerial images or from the architectural plans of the buildings. Techniques for positional estimation using the camera input and the world model are presented
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