Abstract
Safe navigation in uncertain environments requires planning methods that integrate risk aversion with active perception. In this work, we present a unified framework that refines a coarse reference path by constructing tail-sensitive risk maps from Average Value-at-Risk statistics on an online-updated 3D Gaussian-splat Radiance Field. These maps enable the generation of locally safe and feasible trajectories. In parallel, we formulate Next-Best-View (NBV) selection as an optimization problem on the SE(3) pose manifold, where Riemannian gradient descent maximizes an expected information gain objective to reduce uncertainty most critical for imminent motion. Our approach advances the state-of-the-art by coupling risk-averse path refinement with NBV planning, while introducing scalable gradient decompositions that support efficient online updates in complex environments. We demonstrate the effectiveness of the proposed framework through extensive computational studies.
Abstract (translated)
在不确定环境中进行安全导航需要将风险规避与主动感知相结合的规划方法。本文提出了一种统一框架，通过在线更新的3D高斯光场（Gaussian-splat Radiance Field）上的平均值-at-风险统计量来构建尾部敏感的风险图，并用这些地图细化粗略参考路径，从而生成局部安全且可行的轨迹。同时，我们将下一个最佳视角（Next-Best-View, NBV）的选择表述为SE(3)姿态流形上的优化问题，在这个问题中使用黎曼梯度下降法来最大化预期信息增益的目标函数，以减少对即将发生的运动最为关键的不确定性。我们的方法通过将风险规避路径细化与NBV规划相结合，并引入可扩展的梯度分解来支持复杂环境中高效的在线更新，从而推进了当前的研究前沿。我们通过广泛的计算研究展示了所提框架的有效性。
URL
https://arxiv.org/abs/2510.06481
