Geodesic
Entropy Estimations for Motion Planning Problems in Robotics
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 70-88

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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. 
@article{TM_2007_256_a3,
     author = {J.-P. Gauthier and V. M. Zakalyukin},
     title = {Entropy {Estimations} for {Motion} {Planning} {Problems} in {Robotics}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {70--88},
     publisher = {mathdoc},
     volume = {256},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_256_a3/}
}
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J.-P. Gauthier; V. M. Zakalyukin. Entropy Estimations for Motion Planning Problems in Robotics. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Dynamical systems and optimization, Tome 256 (2007), pp. 70-88. http://geodesic.mathdoc.fr/item/TM_2007_256_a3/