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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.
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Contributor : Dario Prandi Connect in order to contact the contributor
Submitted on : Tuesday, November 26, 2013 - 5:41:48 PM
Last modification on : Friday, December 3, 2021 - 11:34:08 AM

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



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