Active Next-Best-View Optimization for Risk-Averse Path Planning

TL;DR

The paper tackles risk-averse navigation in unknown 3D environments by integrating online $3D$ Gaussian Splatting mapping with risk-based path refinement and Next-Best-View optimization on the $SE(3)$ manifold. It introduces $AV@R$-based safety fields over a Gaussian Splatting radiance representation and a forward-looking environment masking strategy to constrain NBV searches to risk-relevant regions. A localized, safety-guaranteed replanning loop combines A*-style local planning with a trajectory-aware NBV objective that uses proximity-weighted Fisher information and decomposable gradients for real-time updates. Experiments in Habitat Gibson demonstrate safer trajectories with higher $AV@R$ and focused environment reconstruction, validating the approach's practicality for perception-driven, risk-aware navigation in complex scenes.

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.

Figures (5)

• Figure 1: Block diagram of the proposed risk-averse trajectory planning as in Algorithm \ref{['alg:trajectory-planning']}. Each cycle the system updates the 3D Gaussian point cloud via SLAM, computes a risk field, synthesizes a safe local path, masks the environment around that path, selects high-risk splats, and evaluates candidate NBV poses over this focused subset. Executing the control and sensing actions steers the robot toward its goal while simultaneously gathering informative observations.
• Figure 2: This shows a safe proxy subgoal selection as explained in Subsection \ref{['subsec:V-A']}. A safe subgoal $\bar{z}_{j+1}$ () is chosen within a ball centered at the current unsafe subgoal $z_{j+1}$ (). Robot is depicted by $\blacktriangle$ and the connected blue dots show the planned local trajectory $\mathcal{Z}_j^s$.
• Figure 3: Illustration of risk-aware environment masking to guide NBV selection, focusing on locally relevant Gaussians to maximize expected information gain and improve map accuracy. (a) Schematic of the masking process, showing Gaussian points near the trajectory in the masked region. (b) Subset of 3D Gaussian points selected within each safe zone to maximize information gain.
• Figure 4: Shortest path ($$) and risk-averse path ($$) shown in two representative environments; the risk-averse trajectory avoids high-risk regions at the expense of additional length.
• Figure 5: Results from the Swormville scene (Gibson dataset). (a) Top-down map showing the ground-truth shortest path ($$) and the executed risk-averse trajectory ($$). (b) 3-D Gaussian-splat reconstruction of the scene; only the forward-looking masked region relevant to the task was used for learning, illustrating the sparse, task-focused sensing.

Theorems & Definitions (1)

• Theorem 1