RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Trudy MIAN, 2005, Volume 250, Pages 64–78 (Mi tm31)  

This article is cited in 6 scientific papers (total in 6 papers)

Robot Motion Planning: A Wild Case

J.-P. Gauthiera, V. M. Zakalyukinb

a Université de Bourgogne
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: A basic problem in robotics is a constructive motion planning problem: given an arbitrary (nonadmissible) trajectory $\Gamma$ of a robot, find an admissible $\varepsilon$-approximation (in the sub-Riemannian (SR) sense) $\gamma(\varepsilon)$ of $\Gamma$ that has the minimal sub-Riemannian length. Then, the (asymptotic behavior of the) sub-Riemannian length $L(\gamma (\varepsilon))$ is called the metric complexity of $\Gamma$ (in the sense of Jean). We have solved this problem in the case of an SR metric of corank 3 at most. For coranks greater than 3, the problem becomes much more complicated. The first really critical case is the 4–10 case (a four-dimensional distribution in $\mathbb {R}^{10}$. Here, we address this critical case. We give partial but constructive results that generalize, in a sense, the results of our previous papers.

Full text: PDF file (248 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2005, 250, 56–69

Bibliographic databases:
UDC: 517.977.1
Received in February 2005

Citation: J.-P. Gauthier, V. M. Zakalyukin, “Robot Motion Planning: A Wild Case”, Differential equations and dynamical systems, Collected papers, Trudy MIAN, 250, Nauka, MAIK Nauka/Inteperiodika, M., 2005, 64–78; Proc. Steklov Inst. Math., 250 (2005), 56–69

Citation in format AMSBIB
\Bibitem{GauZak05}
\by J.-P.~Gauthier, V.~M.~Zakalyukin
\paper Robot Motion Planning: A~Wild Case
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Trudy MIAN
\yr 2005
\vol 250
\pages 64--78
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm31}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200908}
\zmath{https://zbmath.org/?q=an:1138.70316}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2005
\vol 250
\pages 56--69


Linking options:
  • http://mi.mathnet.ru/eng/tm31
  • http://mi.mathnet.ru/eng/tm/v250/p64

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. J.-P. Gauthier, V. M. Zakalyukin, “Entropy Estimations for Motion Planning Problems in Robotics”, Proc. Steklov Inst. Math., 256 (2007), 62–79  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Gauthier J.-P., Zakalyukin V., “Nonholonomic Interpolation. for Kinematic Problems, Entropy and Complexity”, Mathematical Control Theory and Finance, 2008, 187–210  crossref  mathscinet  zmath  isi  scopus
    3. Gauthier J.-P., Jakubczyk B., Zakalyukin V., “Motion planning and fastly oscillating controls”, SIAM J. Control Optim., 48:5 (2010), 3433–3448  crossref  mathscinet  zmath  isi  scopus
    4. Boizot N., Gauthier J.-P., “On the Motion Planning of the Ball with a Trailer”, Math. Control Relat. Fields, 3:3, 1, SI (2013), 269–286  crossref  mathscinet  zmath  isi  elib  scopus
    5. Boizot N., Gauthier J.-P., “Motion Planning for Kinematic Systems”, IEEE Trans. Autom. Control, 58:6 (2013), 1430–1442  crossref  mathscinet  zmath  isi  elib  scopus
    6. Jean F., Prandi D., “Complexity of Control-Affine Motion Planning”, SIAM J. Control Optim., 53:2 (2015), 816–844  crossref  mathscinet  zmath  isi  elib  scopus
  •    . . .  Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:451
    Full text:127
    References:57

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021