  This paper presents a novel on-line path planning method that enables aerial
robots to interact with surfaces. We present a solution to the problem of
finding trajectories that drive a robot towards a surface and move along it.
Triangular meshes are used as a surface map representation that is free of
fixed discretization and allows for very large workspaces. We propose to
leverage planar parametrization methods to obtain a lower-dimensional
topologically equivalent representation of the original surface. Furthermore,
we interpret the original surface and its lower-dimensional representation as
manifold approximations that allow the use of Riemannian Motion Policies
(RMPs), resulting in an efficient, versatile, and elegant motion generation
framework. We compare against several Rapidly-exploring Random Tree (RRT)
planners, a customized CHOMP variant, and the discrete geodesic algorithm.
Using extensive simulations on real-world data we show that the proposed
planner can reliably plan high-quality near-optimal trajectories at minimal
computational cost. The accompanying multimedia attachment demonstrates
feasibility on a real OMAV. The obtained paths show less than 10% deviation
from the theoretical optimum while facilitating reactive re-planning at kHz
refresh rates, enabling flying robots to perform motion planning for
interaction with complex surfaces.
