23 research outputs found
Lower bounds for the polygon exploration problem
We improve the best known lower bound for the polygon exploration problem from 1.2071 to 1.2825
Online Exploration of Polygons with Holes
We study online strategies for autonomous mobile robots with vision to
explore unknown polygons with at most h holes. Our main contribution is an
(h+c_0)!-competitive strategy for such polygons under the assumption that each
hole is marked with a special color, where c_0 is a universal constant. The
strategy is based on a new hybrid approach. Furthermore, we give a new lower
bound construction for small h.Comment: 16 pages, 9 figures, submitted to WAOA 201
Experimental data driven robot for pattern classification
In this paper the problem whether or not a human being can plan a tour for a mobile robot with a camera so that all changes in the room are detected within a time limit is investigated. A tour simulator and a game based on it are developed. The plan of the winner of the game is used for a driving real robot. It is shown that this plan is two times shorter (as Java bytecode for Lego RCX) than the average one
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
The Visibility Freeze-Tag Problem
In the Freeze-Tag Problem, we are given a set of robots at points inside some metric space. Initially, all the robots are frozen except one. That robot can awaken (or “unfreeze”) another robot by moving to its position, and once a robot is awakened, it can move and help to awaken other robots. The goal is to awaken all the robots in the shortest time. The Freeze-Tag Problem has been studied in different metric spaces: graphs and Euclidean spaces.
In this thesis, we look at the Freeze-Tag Problem in polygons, and we introduce the Visibility Freeze-Tag Problem, where one robot can awaken another robot by “seeing” it. Furthermore, we introduce a variant of the Visibility Freeze-Tag Problem, called the Line/Point Freeze Tag Problem, where each robot lies on an awakening line, and one robot can awaken another robot by touching its awakening line.
We survey the current results for the Freeze-Tag Problem in graphs, Euclidean spaces and polygons. Since the Visibility Freeze-Tag Problem bears some resemblance to the Watchman Route Problem, we also survey the background literature on the Watchman Route Problem. We show that the Freeze-Tag Problem in polygons and the Visibility Freeze-Tag Problem are NP-hard, and we present an O(n)-approximation algorithm for the Visibility Freeze-Tag Problem. For the Line/Point Freeze-Tag Problem, we give a polynomial time algorithm for the special case where all the awakening lines are parallel to each other. We prove that the general case is NP-hard, and we present an O(1)- approximation algorithm
Deterministic Symmetry Breaking in Ring Networks
We study a distributed coordination mechanism for uniform agents located on a
circle. The agents perform their actions in synchronised rounds. At the
beginning of each round an agent chooses the direction of its movement from
clockwise, anticlockwise, or idle, and moves at unit speed during this round.
Agents are not allowed to overpass, i.e., when an agent collides with another
it instantly starts moving with the same speed in the opposite direction
(without exchanging any information with the other agent). However, at the end
of each round each agent has access to limited information regarding its
trajectory of movement during this round.
We assume that mobile agents are initially located on a circle unit
circumference at arbitrary but distinct positions unknown to other agents. The
agents are equipped with unique identifiers from a fixed range. The {\em
location discovery} task to be performed by each agent is to determine the
initial position of every other agent.
Our main result states that, if the only available information about movement
in a round is limited to %information about distance between the initial and
the final position, then there is a superlinear lower bound on time needed to
solve the location discovery problem. Interestingly, this result corresponds to
a combinatorial symmetry breaking problem, which might be of independent
interest. If, on the other hand, an agent has access to the distance to its
first collision with another agent in a round, we design an asymptotically
efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201
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