On sub-Riemannian geodesics in $SE(3)$ whose spatial projections do not have cusps

Remco Duits, Arpan Ghosh, Tom Dela Haije +1

We consider the problem ${\mathbf{P}}_{\mathbf{curve}}$ of minimizing $\underset{0}{\overset{L}{\int }}\sqrt{{\xi }^2+{\kappa }^2(s)}\mathrm{d}s$ for a curve $\mathbf{x}$ on $\mathbb{R}$ with fixed boundary points and…