Polygon guarding with orientation

Pratap Tokekar, Volkan Isler

Research output: Contribution to journalConference articlepeer-review

6 Scopus citations


The art gallery problem is a classical sensor placement problem that asks for the minimum number of guards required to see every point in an environment. The standard formulation does not take into account self-occlusions caused by a person or an object within the environment. Obtaining good views of an object from all orientations is important for surveillance and visual tracking applications. We study the art gallery problem under a constraint, termed Δ-guarding, that ensures that all sides of any convex object are always visible in spite of self-occlusion. Our contributions in this paper are two-fold: we first prove that Ω(√n) guards are always necessary for Δ-guarding the interior of a simple polygon having n vertices. Next, we study the problem of Δ-guarding a set of line segments connecting points on the boundary of the polygon. This is motivated by applications where an object or person of interest can only move along certain paths in the polygon. We present a constant factor approximation algorithm for this problem - one of the few such results for art gallery problems.

Original languageEnglish (US)
Article number6906978
Pages (from-to)1014-1019
Number of pages6
JournalProceedings - IEEE International Conference on Robotics and Automation
StatePublished - Sep 22 2014
Event2014 IEEE International Conference on Robotics and Automation, ICRA 2014 - Hong Kong, China
Duration: May 31 2014Jun 7 2014

Bibliographical note

Publisher Copyright:
© 2014 IEEE.


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