Controllability of the Dubins problem on surfaces

Yacine Chitour (1) , Mario Sigalotti (2, 3)

1 L2S - Laboratoire des signaux et systèmes
2 APICS - Analysis and Problems of Inverse type in Control and Signal processing
3 INRIA Lorraine

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.

Domaines: Mathématiques [math]

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. ⟨10.1109/cdc.2005.1582361⟩. ⟨hal-02320778⟩