Projective Reeds-Shepp car on $S^2$ with quadratic cost
| dc.creator | Boscain, Ugo | |
| dc.creator | Rossi, Francesco | |
| dc.date | 2008-05-30 | |
| dc.date.accessioned | 2026-07-07T09:41:55Z | |
| dc.date.available | 2026-07-07T09:41:55Z | |
| dc.description | Fix two points $x,\bar{x}\in S^2$ and two directions (without orientation) $η,\barη$ of the velocities in these points. In this paper we are interested to the problem of minimizing the cost $$ J[γ]=\int_0^T g_{γ(t)}(\dotγ(t),\dotγ(t))+ K^2_{γ(t)}g_{γ(t)}(\dotγ(t),\dotγ(t)) ~dt$$ along all smooth curves starting from $x$ with direction $η$ and ending in $\bar{x}$ with direction $\barη$. Here $g$ is the standard Riemannian metric on $S^2$ and $K_γ$ is the corresponding geodesic curvature. The interest of this problem comes from mechanics and geometry of vision. It can be formulated as a sub-Riemannian problem on the lens space L(4,1). We compute the global solution for this problem: an interesting feature is that some optimal geodesics present cusps. The cut locus is a stratification with non trivial topology. | |
| dc.identifier | https://arxiv.org/abs/0805.4800 | |
| dc.identifier | http://arxiv.org/abs/0805.4800 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161996 | |
| dc.subject | Optimization and Control | |
| dc.subject | Differential Geometry | |
| dc.subject | 49J15; 53C17 | |
| dc.title | Projective Reeds-Shepp car on $S^2$ with quadratic cost | |
| dc.type | text |