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Entropy estimations for motion planning problems in robotics. (English. Russian original) Zbl 1152.93045
Proc. Steklov Inst. Math. 256, 62-79 (2007); translation from Tr. Mat. Inst. Steklova 256, 70-88 (2007).
Summary: 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.

93C85 Automated systems (robots, etc.) in control theory
37N35 Dynamical systems in control
53C17 Sub-Riemannian geometry
93C10 Nonlinear systems in control theory
Full Text: DOI
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