  In this paper, we present a novel method for using Riemannian Motion Policies
on volumetric maps, shown in the example of obstacle avoidance for Micro Aerial
Vehicles (MAVs). While sampling or optimization-based planners are widely used
for obstacle avoidance with volumetric maps, they are computationally expensive
and often have inflexible monolithic architectures. Riemannian Motion Policies
are a modular, parallelizable, and efficient navigation paradigm but are
challenging to use with the widely used voxel-based environment
representations. We propose using GPU raycasting and a large number of
concurrent policies to provide direct obstacle avoidance using Riemannian
Motion Policies in voxelized maps without the need for smoothing or
pre-processing of the map. Additionally, we present how the same method can
directly plan on LiDAR scans without the need for an intermediate map. We show
how this reactive approach compares favorably to traditional planning methods
and is able to plan using thousands of rays at kilohertz rates. We demonstrate
the planner successfully on a real MAV for static and dynamic obstacles. The
presented planner is made available as an open-source software package.
