# Dubins' Problem on Surfaces II: Nonpositive Curvature

@article{Sigalotti2006DubinsPO,
title={Dubins' Problem on Surfaces II: Nonpositive Curvature},
author={M. Sigalotti and Y. Chitour},
journal={SIAM J. Control. Optim.},
year={2006},
volume={45},
pages={457-482}
}
• Published 2006
• Mathematics, Computer Science
• SIAM J. Control. Optim.
Let M be a complete, connected, two-dimensional Riemannian manifold with nonpositive Gaussian curvature K. We say that M satisfies the unrestricted complete controllability (UCC) property for the Dubins problem if the following holds: given any $(p_1,v_1)$ and $(p_2,v_2)$ in TM, there exists, for every $\eps > 0$, a curve $\gamma$ in M, with geodesic curvature smaller than $\eps$, such that $\gamma$ connects $p_1$ to $p_2$ and, for $i=1,2$, $\dot\gamma$ is equal to $v_i$ at $p_i$. Property UCC… Expand
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