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arXiv · 1309.2571

Complexity of control-affine motion planning

Frédéric Jean·Dario Prandi
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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.

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Frédéric Jean, Dario Prandi. 2013-09-10. Complexity of control-affine motion planning. https://doi.org/10.1137/130950793

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