GPU-Accelerated 3D Polygon Visibility Volumes for Synergistic Perception and Navigation

TL;DR

This paper addresses computing a 3D visibility volume for a convex planar ground region within a complex 3D scene, enabling UAVs to maintain visibility while navigating under mission constraints. It combines GPU-accelerated depth mapping using a cubemap around potential viewpoints with exact boolean geometry to construct a genus-0 visibility volume that respects a maximum line-of-sight distance. Key contributions include a theoretical construction for visibility volumes of convex polygons in 3D scenes, a practical end-to-end pipeline that derives the region from GIS data (e.g., OpenStreetMap) and refines it via per-vertex visibility spheres and their intersections using exact booleans. Finally, the approach provides a synergistic framework for simultaneous sensing and navigation in UAV guidance, navigation and control, with future work on field-of-view modeling, occlusion handling, and partial visibility.

Abstract

UAV missions often require specific geometric constraints to be satisfied between ground locations and the vehicle location. Such requirements are typical for contexts where line-of-sight must be maintained between the vehicle location and the ground control location and are also important in surveillance applications where the UAV wishes to be able to sense, e.g., with a camera sensor, a specific region within a complex geometric environment. This problem is further complicated when the ground location is generalized to a convex 2D polygonal region. This article describes the theory and implementation of a system which can quickly calculate the 3D volume that encloses all 3D coordinates from which a 2D convex planar region can be entirely viewed; referred to as a visibility volume. The proposed approach computes visibility volumes using a combination of depth map computation using GPU-acceleration and geometric boolean operations. Solutions to this problem require complex 3D geometric analysis techniques that must execute using arbitrary precision arithmetic on a collection of discontinuous and non-analytic surfaces. Post-processing steps incorporate navigational constraints to further restrict the enclosed coordinates to include both visibility and navigation constraints. Integration of sensing visibility constraints with navigational constraints yields a range of navigable space where a vehicle will satisfy both perceptual sensing and navigational needs of the mission. This algorithm then provides a synergistic perception and navigation sensitive solution yielding a volume of coordinates in 3D that satisfy both the mission path and sensing needs.

Figures (8)

• Figure 1: A visibility volume is shown (white) that encloses all 3D coordinates where a camera could view a user-specified triangular region located on the ground plane (gray) between two these buildings (beige, red) and maintain a distance of less than 50m from the region.
• Figure 2: The geometry for a portion of Destin, FL is shown extracted from the OpenStreetMap (OSM) OpenStreetMap database. OSM data queries take (latitude, longitude) queries and return rich geometric models.
• Figure 3: A cubemap construction is applied to compute the visibility sphere for a point as a combination of 6 mutually perpendicular 90 degree viewpoints in OpenGL.
• Figure 4: (a,j) visualize the stages of the region visibility computation and depict the interim steps where the geometry of the solution space changes.
• Figure 5: (a,b) show two views of the 3D volume encompassing all points that the sensor can be located and maintain view of the triangular region shown in Figure \ref{['fig:osm_model_with_triangle_region']}.