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


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
Issue number2
StatePublished - 3 Apr 1995


FundersFunder number
Digitial Equipment, Mitsubishi, and Toshiba Corporations
ESPRIT Basic Research Actions6546
Israeli Academy of Sciences
Netherlands’ Organization for Scientific Research
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


    Dive into the research topics of 'Reaching a goal with directional uncertainty'. Together they form a unique fingerprint.

    Cite this