Reaching a goal with directional uncertainty

Mark de Berg*, Leonidas Guibas, Dan Halperin, Mark Overmars, Otfried Schwarzkopf, Micha Sharir, Monique Teillaud

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We study two problems related to planar motion planning for robots with imperfect control, where, if the robot starts a linear movement in a certain commanded direction, we only know that its actual movement will be confined in a cone of angle α centered around the specified direction. First, we consider a single goal region, namely the "region at infinity", and a set of polygonal obstacles, modeled as a set S of n line segments. We are interested in the region Rα(S) from where we can reach infinity with a directional uncertainty of α. We prove that the maximum complexity of Rα(S) is O( n α5). Second, we consider a collection of k polygonal goal regions of total complexity m, but without any obstacles. Here we prove an O(k3m) bound on the complexity of the region from where we can reach a goal region with a directional uncertainty of α. For both situations we also prove lower bounds on the maximum complexity, and we give efficient algorithms for computing the regions.

Original languageEnglish
Pages (from-to)301-317
Number of pages17
JournalTheoretical Computer Science
Volume140
Issue number2
DOIs
StatePublished - 3 Apr 1995

Funding

FundersFunder number
Digitial Equipment, Mitsubishi, and Toshiba Corporations
ESPRIT Basic Research Actions6546
Israeli Academy of Sciences
NSF/ARPAIRI-9306544
Netherlands’ Organization for Scientific Research
SIMA
Stanford Integrated Manufacturing Association
Stanford SIMA Consortium
U.S.-Israeli Binational Science Foundation
National Science FoundationCCR-9215219, CCR-91-22103
Directorate for Computer and Information Science and Engineering9215219
German-Israeli Foundation for Scientific Research and Development
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

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