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Journal Articles SIAM Journal on Control and Optimization Year : 2015

Complexity of control-affine motion planning

Abstract

In this paper we study the complexity of the motion planning problem for control- affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is to generalize these notions and results to systems with a drift. Accordingly, we present various definitions of complexity, as functions of the curve that is approximated, and of the precision of the approximation. Due to the lack of time- rescaling invariance of these systems, we consider geometric and parametrized curves separately. Then, we give some asymptotic estimates for these quantities. As a byproduct, we are able to treat the long time local controllability problem, giving quanti- tative estimates on the cost of stabilizing the system near a non-equilibrium point of the drift.

Dates and versions

hal-00909748 , version 1 (26-11-2013)

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Frédéric Jean, Dario Prandi. Complexity of control-affine motion planning. SIAM Journal on Control and Optimization, 2015, 53 (2), pp.816-844. ⟨10.1137/130950793⟩. ⟨hal-00909748⟩
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