This article is cited in 7 papers

Entropy Estimations for Motion Planning Problems in Robotics

J.-P. Gauthier^a, V. M. Zakalyukin<sup>b

a</sup> Université de Bourgogne
^b M. V. Lomonosov Moscow State University

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.

UDC: 517.9+515.1

Received in June 2006

 English version: Proceedings of the Steklov Institute of Mathematics, 2007, 256, 62–79

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