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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Volume 256, Pages 70–88 (Mi tm456)  
This article is cited in 7 scientific papers (total in 7 papers)

Entropy Estimations for Motion Planning Problems in Robotics

J.-P. Gauthiera, V. M. Zakalyukinb

a Université de Bourgogne
b M. V. Lomonosov Moscow State University
Full-text PDF (269 kB) Citations (7)
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Abstract: This is the concluding work of our series devoted to the evaluation of the complexity and entropy of a motion planning problem for a sub-Riemannian distribution. We consider some new cases of the dimension and codimension of the distribution, in particular, $(2,3)$, $(3,4)$, and some other that are one-step-bracket-generating. We summarize all known estimations for low-dimensional generic systems. They include all generic systems of corank less than 4 and other cases up to corank 10.
Received in June 2006
English version:
Proceedings of the Steklov Institute of Mathematics, 2007, Volume 256, Pages 62–79
DOI: https://doi.org/10.1134/S008154380701004X
Bibliographic databases:
UDC: 517.9+515.1
Language: Russian
Citation: J.-P. Gauthier, V. M. Zakalyukin, “Entropy Estimations for Motion Planning Problems in Robotics”, Dynamical systems and optimization, Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov, Trudy Mat. Inst. Steklova, 256, Nauka, MAIK «Nauka/Inteperiodika», M., 2007, 70–88; Proc. Steklov Inst. Math., 256 (2007), 62–79
Citation in format AMSBIB
\Bibitem{GauZak07}
\by J.-P.~Gauthier, V.~M.~Zakalyukin
\paper Entropy Estimations for Motion Planning Problems in Robotics
\inbook Dynamical systems and optimization
\bookinfo Collected papers. Dedicated to the 70th birthday of academician Dmitrii Viktorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2007
\vol 256
\pages 70--88
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm456}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336894}
\zmath{https://zbmath.org/?q=an:1152.93045}
\elib{https://elibrary.ru/item.asp?id=9482609}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2007
\vol 256
\pages 62--79
\crossref{https://doi.org/10.1134/S008154380701004X}
\elib{https://elibrary.ru/item.asp?id=13537759}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34248356351}
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    • This publication is cited in the following 7 articles:
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