We formalize a novel interpretation of Neural Radiance Fields (NeRFs) as giving rise to a Poisson Point Process (PPP). This PPP interpretation allows for rigorous quantification of uncertainty in NeRFs, in particular, for computing collision probabilities for a robot navigating through a NeRF environment model. 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 model, 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, showing superior performance compared with two other methods for trajectory planning in NeRF environment models.
翻译:我们对神经辐射场(NeRFs)的新解释正式化为产生Poisson点进程(PPP ) 。 这种PPP解释允许对NeRFs的不确定性进行严格的量化,特别是用于计算在NeRF环境模型中导航的机器人的碰撞概率。 PPP是将概率占用网格的概括化为连续体积,对于光谱场背后的量子射线模型至关重要。 我们以这个PPPP模型为基础,为NeRFs的安全机器人导航提供了一种受机会限制的轨迹优化方法。 我们的方法依赖于一种叫作“概率不安全机器人区域”的 voxel 代表, 即空间将机会限制与 NERF 模型连接, 以便利快速轨迹优化。 我们然后将基于图形的搜索与基于浮标的轨迹的轨迹优化结合起来, 通过NRFSF系统产生机器人轨道轨迹,保证满足用户特有的碰撞概率。 我们通过模拟验证我们的机会受限的规划方法,显示优于NRF环境模型的两种轨迹规划方法。</s>