Controllability of the Dubins problem on surfaces

Abstract : Let M be a complete oriented 2-dim Riemannian manifold. We ask the following question. Given any (pi, vi) and (p(2), v(2)), v(i) velocity at p(i) is an element of M, i = 1, 2, is it possible to connect pi to p(2) by a curve gamma with arbitrary small geodesic curvature such that, for i = 1, 2, gamma is equal to v(i) at p(i)? In this paper, we prove that the answer to the question is positive if M verifies one of the following three conditions (a) M is compact, (b) M is asymptotically flat, (c) M has bounded non negative curvature outside a compact subset.
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Submitted on : Saturday, October 19, 2019 - 2:21:04 PM
Last modification on : Wednesday, October 30, 2019 - 9:35:20 AM

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Yacine Chitour, Mario Sigalotti. Controllability of the Dubins problem on surfaces. 44th IEEE Conference on Decision Control/European Control Conference (CCD-ECC), Dec 2005, Seville, Spain. ⟨hal-02320778⟩

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