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An Online Algorithm for Improving Performance in Navigation

Authors:

Avrim Blum,

Prasad ChalasaniAuthors Info & Claims

SIAM Journal on Computing, Volume 29, Issue 6

Pages 1907 - 1938

https://doi.org/10.1137/S0097539795290593

Published: 01 April 2000 Publication History

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Abstract

We consider the following scenario. A point robot is placed at some start location s in a 2-dimensional scene containing oriented rectangular obstacles. The robot must repeatedly travel back and forth between s and a second location t in the scene. The robot knows the coordinates of s and t but initially knows nothing about the positions or sizes of the obstacles. It can only determine the obstacles' locations by bumping into them. We would like an intelligent strategy for the robot so that its trips between s and t both are relatively fast initially and improve as more trips are taken and more information is gathered.

In this paper we describe an algorithm for this problem with the following guarantee: in the first $k \leq n$ trips, the average distance per trip is at most $O(\sqrt{n/k})$ times the length of the shortest s - t path in the scene, where n is the Euclidean distance between s and t . We also show a matching lower bound for deterministic strategies. These results generalize known bounds on the one-trip problem. Our algorithm is based on a novel method for making an optimal trade-off between search effort and the goodness of the path found. We improve this algorithm to a "smooth" variant having the property that for every $i \leq n,$ the robot's i th trip length is $O(\sqrt{n/i})$ times the shortest s - t path length.

A key idea of this paper is a method for analyzing obstacle scenes using a tree structure that can be defined based on the positions of the obstacles.

Cited By

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Albers SHellwig M(2017)Online Makespan Minimization with Parallel SchedulesAlgorithmica10.1007/s00453-016-0172-578:2(492-520)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s00453-016-0172-5
Ghosh SKlein R(2010)SurveyComputer Science Review10.1016/j.cosrev.2010.05.0014:4(189-201)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1016/j.cosrev.2010.05.001
Duncan CKobourov SKumar V(2006)Optimal constrained graph explorationACM Transactions on Algorithms10.1145/1159892.11598972:3(380-402)Online publication date: 1-Jul-2006
https://dl.acm.org/doi/10.1145/1159892.1159897

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An Online Algorithm for Improving Performance in Navigation

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Published In

SIAM Journal on Computing Volume 29, Issue 6

April 2000

337 pages

ISSN:0097-5397

Editor:
M. Yannakakis
Bell Labs., Murray Hill, NJ

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Society for Industrial and Applied Mathematics

United States

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Published: 01 April 2000

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Albers SHellwig M(2017)Online Makespan Minimization with Parallel SchedulesAlgorithmica10.1007/s00453-016-0172-578:2(492-520)Online publication date: 1-Jun-2017
https://dl.acm.org/doi/10.1007/s00453-016-0172-5
Ghosh SKlein R(2010)SurveyComputer Science Review10.1016/j.cosrev.2010.05.0014:4(189-201)Online publication date: 1-Nov-2010
https://dl.acm.org/doi/10.1016/j.cosrev.2010.05.001
Duncan CKobourov SKumar V(2006)Optimal constrained graph explorationACM Transactions on Algorithms10.1145/1159892.11598972:3(380-402)Online publication date: 1-Jul-2006
https://dl.acm.org/doi/10.1145/1159892.1159897

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Robot Navigation Based on Multi-sensor Data Fusion

Vision-Based Humanoid Robot Navigation in a Featureless Environment

Experience with rover navigation for lunar-like terrains

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