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.
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