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On the Codimension One Motion Planning Problem

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Abstract.

In this paper, we improve the results of [5] related to motion planning problems for corank one sub-Riemannian (SR) metrics. First, we give the exact estimate of the metric complexity, in the generic 3-dimensional case. (Only bounds from above and from below were given in [5].) Second, we show that the general expression for the metric complexity (that was proven to hold generically in the C∞ case, or under certain nonvanishing condition (C) in the analytic case) is, in fact, always true under condition (C), on the complement of a subset of codimension infinity, in the set of C∞ “motion planning problems.” Both results are constructive, i.e., an “asymptotic optimal synthesis” is exhibited in both cases.

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Authors and Affiliations

  1. Laboratoire LE2I, UMR CNRS 5158, Université de Bourgogne, BP 47870, 21078, Dijon CEDEX, France

    J.-P. Gauthier

  2. Moscow State University, Leninskie Gory, 1, 119993, Moscow, Russia

    V. Zakalyukin

Authors
  1. J.-P. Gauthier
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  2. V. Zakalyukin
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Correspondence to J.-P. Gauthier or V. Zakalyukin.

Additional information

2000 Mathematics Subject Classification. 53C17, 49J15, 34H05.

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Gauthier, JP., Zakalyukin, V. On the Codimension One Motion Planning Problem. J Dyn Control Syst 11, 73–89 (2005). https://doi.org/10.1007/s10883-005-0002-6

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  • DOI: https://doi.org/10.1007/s10883-005-0002-6

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