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}
}
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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