A randomized greedy algorithm for piecewise linear motion planning

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dc.authorid0000-0002-5628-7798en_US
dc.authorscopusid56907018600en_US
dc.contributor.authorOrtiz C.
dc.contributor.authorLara A.
dc.contributor.authorGonzález J.
dc.contributor.authorBorat, Ayşe
dc.date.accessioned2022-02-17T10:52:19Z
dc.date.available2022-02-17T10:52:19Z
dc.date.issued2021en_US
dc.departmentBTÜ, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümüen_US
dc.description.abstractWe describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle R, and outputs an explicit system of piecewise linear motion planners for R. The algorithm is designed in such a way that the cardinality of the output is probabilistically close (with parameters chosen by the user) to the minimal possible cardinality.This yields the first automated solution for robust-to-noise robot motion planning in terms of simplicial complexity (SC) techniques, a discretization of Farber’s topological complexity TC. Besides its relevance toward technological applications, our work reveals that, unlike other discrete approaches to TC, the SC model can recast Farber’s invariant without having to introduce costly subdivisions. We develop and implement our algorithm by actually discretizing Macías-Virgós and Mosquera-Lois’ notion of homotopic distance, thus encompassing computer estimations of other sectional category invariants as well, such as the Lusternik-Schnirelmann category of polyhedra.en_US
dc.identifier.doi10.3390/math9192358en_US
dc.identifier.issn22277390
dc.identifier.issue19en_US
dc.identifier.scopusqualityN/Aen_US
dc.identifier.urihttps://hdl.handle.net/20.500.12885/1823
dc.identifier.volume9en_US
dc.identifier.wosqualityN/Aen_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.institutionauthorBorat, Ayşe
dc.language.isoenen_US
dc.publisherMDPIen_US
dc.relation.ispartofMathematicsen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectAbstract simplicial complexen_US
dc.subjectBarycentric subdivisionen_US
dc.subjectContiguity of simplicial mapsen_US
dc.subjectHomotopic distanceen_US
dc.subjectMotion planningen_US
dc.subjectRandomized algorithmen_US
dc.titleA randomized greedy algorithm for piecewise linear motion planningen_US
dc.typeArticleen_US

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