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.

翻译：无人机任务通常需要满足地面位置与飞行器位置之间的特定几何约束。这类要求常见于飞行器与地面控制站需保持视距通信的场景，在无人机需利用摄像头等传感器对复杂几何环境中的特定区域进行感知的监视应用中同样至关重要。当地面位置扩展为凸二维多边形区域时，该问题变得更为复杂。本文阐述了一种可快速计算所有能够完整观测二维凸平面区域的三维坐标所构成体空间（称为"可见性体"）系统的理论与实现方法。该方案通过结合GPU加速深度图计算与几何布尔运算来生成可见性体。此类问题的求解需要运用复杂的三维几何分析技术，并需在不连续非解析曲面上执行任意精度算术运算。后处理阶段引入导航约束，进一步将封闭坐标空间限定为同时满足可见性与导航要求的区域。通过融合感知可见性约束与导航约束，可生成满足任务感知与航行需求的可航行空间范围。该算法最终提供了一种协同感知与导航的解决方案，能够输出同时满足任务路径与感知需求的三维坐标体空间。