In this paper, a robust geometric navigation algorithm, designed on the special Euclidean group SE(3), of a quadrotor is proposed. The equations of motion for the quadrotor are obtained using the Newton–Euler formulation. The geometric navigation considers a guidance frame which is designed to perform autonomous flights with a convergence to the contour of the task with small normal velocity. For this purpose, a super twisting algorithm controls the nonlinear rotational and translational dynamics as a cascade structure in order to establish the fast and yet smooth tracking with the typical robustness of sliding modes. In this sense, the controller provides robustness against parameter uncertainty, disturbances, convergence to the sliding manifold in finite time, and asymptotic convergence of the trajectory tracking. The algorithm validation is presented through experimental results showing the feasibility of the proposed approach and illustrating that the tracking errors converge asymptotically to the origin.