640 research outputs found
Polygon Exploration with Time-Discrete Vision
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
Online Searching with an Autonomous Robot
We discuss online strategies for visibility-based searching for an object
hidden behind a corner, using Kurt3D, a real autonomous mobile robot. This task
is closely related to a number of well-studied problems. Our robot uses a
three-dimensional laser scanner in a stop, scan, plan, go fashion for building
a virtual three-dimensional environment. Besides planning trajectories and
avoiding obstacles, Kurt3D is capable of identifying objects like a chair. We
derive a practically useful and asymptotically optimal strategy that guarantees
a competitive ratio of 2, which differs remarkably from the well-studied
scenario without the need of stopping for surveying the environment. Our
strategy is used by Kurt3D, documented in a separate video.Comment: 16 pages, 8 figures, 12 photographs, 1 table, Latex, submitted for
publicatio
Algorithms for Monotone Paths with Visibility Properties
Constructing collision-free paths in Euclidean space is a well-known problem in computational geometry having applications in many fields that include robotics, VLSI, and covert surveillance. In this thesis, we investigate the development of efficient algorithms for constructing a collision-free path that satisfies directional and visibility constraints. We present algorithms for constructing monotone collision-free paths that tend to maximize the visibility of the boundary of obstacles. We also present implementation of some monotone path planning algorithms in Java Programming Language
Detours admitting short paths
Finding shortest paths between two vertices in a weighted graph is a well explored problem and several efficient algorithms for solving it have been reported. We propose a new variation of this problem which we call the Detour Admitting Shortest Path Problem (DASPP).We present an efficient algorithm for solving DASPP. This is the first algorithm that constructs a shortest path such that each edge of the shortest path admits a detour with no more than k−hops. This algorithm has important applications in transportation networks. We also present implementation issues for the detour admitting shortest path algorithm
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