51 research outputs found
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
Approximation Algorithms for the Two-Watchman Route in a Simple Polygon
The two-watchman route problem is that of computing a pair of closed tours in
an environment so that the two tours together see the whole environment and
some length measure on the two tours is minimized. Two standard measures are:
the minmax measure, where we want the tours where the longest of them has
smallest length, and the minsum measure, where we want the tours for which the
sum of their lengths is the smallest. It is known that computing a minmax
two-watchman route is NP-hard for simple rectilinear polygons and thus also for
simple polygons. Also, any c-approximation algorithm for the minmax
two-watchman route is automatically a 2c-approximation algorithm for the minsum
two-watchman route. We exhibit two constant factor approximation algorithms for
computing minmax two-watchman routes in simple polygons with approximation
factors 5.969 and 11.939, having running times O(n^8) and O(n^4) respectively,
where n is the number of vertices of the polygon. We also use the same
techniques to obtain a 6.922-approximation for the fixed two-watchman route
problem running in O(n^2) time, i.e., when two starting points of the two tours
are given as input.Comment: 36 pages, 14 figure
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
Multi-Agent Deployment for Visibility Coverage in Polygonal Environments with Holes
This article presents a distributed algorithm for a group of robotic agents
with omnidirectional vision to deploy into nonconvex polygonal environments
with holes. Agents begin deployment from a common point, possess no prior
knowledge of the environment, and operate only under line-of-sight sensing and
communication. The objective of the deployment is for the agents to achieve
full visibility coverage of the environment while maintaining line-of-sight
connectivity with each other. This is achieved by incrementally partitioning
the environment into distinct regions, each completely visible from some agent.
Proofs are given of (i) convergence, (ii) upper bounds on the time and number
of agents required, and (iii) bounds on the memory and communication
complexity. Simulation results and description of robust extensions are also
included
- …