We introduce a transformation of a Neural Radiance Field (NeRF) to an equivalent Poisson Point Process (PPP). This PPP transformation allows for rigorous quantification of uncertainty in NeRFs, in particular, for computing collision probabilities for a robot navigating through a NeRF environment. The PPP is a generalization of a probabilistic occupancy grid to the continuous volume and is fundamental to the volumetric ray-tracing model underlying radiance fields. Building upon this PPP representation, we present a chance-constrained trajectory optimization method for safe robot navigation in NeRFs. Our method relies on a voxel representation called the Probabilistic Unsafe Robot Region (PURR) that spatially fuses the chance constraint with the NeRF model to facilitate fast trajectory optimization. We then combine a graph-based search with a spline-based trajectory optimization to yield robot trajectories through the NeRF that are guaranteed to satisfy a user-specific collision probability. We validate our chance constrained planning method through simulations and hardware experiments, showing superior performance compared to prior works on trajectory planning in NeRF environments. Our codebase can be found at https://github.com/chengine/catnips, and videos can be found on our project page (https://chengine.github.io/catnips).

翻译：我们提出了一种将神经辐射场（NeRF）转换为等效泊松点过程（PPP）的方法。该PPP变换能够严格量化NeRF中的不确定性，特别是用于计算机器人在NeRF环境中导航时的碰撞概率。PPP是概率占据栅格在连续空间中的推广，并且是辐射场底层体素射线追踪模型的基础。基于此PPP表示，我们提出了一种用于NeRF中机器人安全导航的机会约束轨迹优化方法。我们的方法依赖于一种称为概率不安全机器人区域（PURR）的体素表示，该表示将机会约束与NeRF模型在空间上融合，以实现快速轨迹优化。随后，我们结合基于图的搜索与基于样条的轨迹优化，生成通过NeRF的机器人轨迹，并保证其满足用户指定的碰撞概率。我们通过仿真和硬件实验验证了我们的机会约束规划方法，结果表明其在NeRF环境轨迹规划方面优于现有工作。代码库可在 https://github.com/chengine/catnips 获取，视频可在项目页面（https://chengine.github.io/catnips）查看。