A randomized greedy algorithm for piecewise linear motion planning
Yükleniyor...
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
MDPI
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
We 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.
Açıklama
Anahtar Kelimeler
Abstract simplicial complex, Barycentric subdivision, Contiguity of simplicial maps, Homotopic distance, Motion planning, Randomized algorithm
Kaynak
Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
N/A
Cilt
9
Sayı
19
