Perimeter Defense using a Turret with Finite Range and Service Times Article Swipe

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Shivam Bajaj , Shaunak D. Bopardikar , Alexander Von Moll , Eric Torng , David W. Casbeer ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2302.02186

We consider a perimeter defense problem in a planar conical environment comprising a single turret that has a finite range and non-zero service time. The turret seeks to defend a concentric perimeter against $N\geq 2$ intruders. Upon release, each intruder moves radially towards the perimeter with a fixed speed. To capture an intruder, the turret's angle must be aligned with that of the intruder's angle and must spend a specified service time at that orientation. We address offline and online versions of this optimization problem. Specifically, in the offline version, we establish that in general parameter regimes, this problem is equivalent to solving a Travelling Repairperson Problem with Time Windows (TRP-TW). We then identify specific parameter regimes in which there is a polynomial time algorithm that maximizes the number of intruders captured. In the online version, we present a competitive analysis technique in which we establish a fundamental guarantee on the existence of at best $(N-1)$-competitive algorithms. We also design two online algorithms that are provably $1$ and $2$-competitive in specific parameter regimes.

Related Topics

Turret (Architecture)

Range (Aeronautics)

Computer Science

Mathematics

Planar Transmission Line

Concentric Zone Model

Algorithm

Engineering

Geometry

Mathematical Analysis

Computer Graphics

Economics

Aerospace Engineering

Mechanical Engineering

Economy

Concepts

Turret Perimeter Online algorithm Range (aeronautics) Competitive analysis Conical surface Service (business) Computer science Time complexity Mathematics Planar Concentric Mathematical optimization Algorithm Engineering Upper and lower bounds Geometry Mathematical analysis Computer graphics (images) Economics Aerospace engineering Mechanical engineering Economy

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2302.02186
PDF: https://arxiv.org/pdf/2302.02186
OA Status: green
Cited By: 2
Related Works: 10
OpenAlex ID: https://openalex.org/W4319452364

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DOI: https://doi.org/10.48550/arxiv.2302.02186

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Title: Perimeter Defense using a Turret with Finite Range and Service Times

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Type: preprint

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Language: en

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Publication year: 2023

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Publication date: 2023-02-04

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Authors: Shivam Bajaj, Shaunak D. Bopardikar, Alexander Von Moll, Eric Torng, David W. Casbeer

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Landing page: https://arxiv.org/abs/2302.02186

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Concepts: Turret, Perimeter, Online algorithm, Range (aeronautics), Competitive analysis, Conical surface, Service (business), Computer science, Time complexity, Mathematics, Planar, Concentric, Mathematical optimization, Algorithm, Engineering, Upper and lower bounds, Geometry, Mathematical analysis, Computer graphics (images), Economics, Aerospace engineering, Mechanical engineering, Economy

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Cited by: 2

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Citations by year (recent): 2024: 1, 2023: 1

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abstract_inverted_index.consider	1
abstract_inverted_index.identify	113
abstract_inverted_index.intruder	39
abstract_inverted_index.non-zero	21
abstract_inverted_index.problem.	84
abstract_inverted_index.provably	165
abstract_inverted_index.radially	41
abstract_inverted_index.regimes,	96
abstract_inverted_index.regimes.	172
abstract_inverted_index.release,	37
abstract_inverted_index.specific	114, 170
abstract_inverted_index.turret's	54
abstract_inverted_index.version,	89, 135
abstract_inverted_index.versions	80
abstract_inverted_index.(TRP-TW).	110
abstract_inverted_index.algorithm	124
abstract_inverted_index.captured.	131
abstract_inverted_index.establish	91, 145
abstract_inverted_index.existence	151
abstract_inverted_index.guarantee	148
abstract_inverted_index.intruder,	52
abstract_inverted_index.intruders	130
abstract_inverted_index.maximizes	126
abstract_inverted_index.parameter	95, 115, 171
abstract_inverted_index.perimeter	3, 31, 44
abstract_inverted_index.specified	69
abstract_inverted_index.technique	141
abstract_inverted_index.Travelling	104
abstract_inverted_index.algorithms	162
abstract_inverted_index.comprising	11
abstract_inverted_index.concentric	30
abstract_inverted_index.equivalent	100
abstract_inverted_index.intruder's	63
abstract_inverted_index.intruders.	35
abstract_inverted_index.polynomial	122
abstract_inverted_index.algorithms.	156
abstract_inverted_index.competitive	139
abstract_inverted_index.environment	10
abstract_inverted_index.fundamental	147
abstract_inverted_index.Repairperson	105
abstract_inverted_index.optimization	83
abstract_inverted_index.orientation.	74
abstract_inverted_index.Specifically,	85
abstract_inverted_index.$2$-competitive	168
abstract_inverted_index.$(N-1)$-competitive	155
cited_by_percentile_year
countries_distinct_count	0
institutions_distinct_count	5
citation_normalized_percentile