Safe Navigation using Neural Radiance Fields via Reachable Sets

arXiv cs.RO / 4/30/2026

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Key Points

The paper addresses safe navigation for autonomous robots in cluttered environments with obstacles, goal regions, and ego objects of varying shapes.
It uses reachable set representations to capture the robot’s real-time capabilities in state space and to formulate what “safe navigation” must satisfy.
Neural Radiance Fields (NeRFs) are employed to compute, store, and manipulate volumetric obstacle/ego geometry for planning.
The path-planning problem is posed as constrained optimal control with linear matrix inequality (LMI) constraints.
Simulation experiments in two scenarios with many obstacles show that reachable-set-based constrained optimal control can achieve safe navigation.

Abstract

Safe navigation in cluttered environments is an important challenge for autonomous systems. Robots navigating through obstacle ridden scenarios need to be able to navigate safely in the presence of obstacles, goals, and ego objects of varying geometries. In this work, reachable set representations of the robot's real-time capabilities in the state space can be utilized to capture safe navigation requirements. While neural radiance fields (NeRFs) are utilized to compute, store, and manipulate the volumetric representations of the obstacles, or ego vehicle, as needed. Constrained optimal control is employed to represent the resulting path planning problem, involving linear matrix inequality constraints. We present simulation results for path planning in the presence of numerous obstacles in two different scenarios. Safe navigation is demonstrated through using reachable sets in the corresponding constrained optimal control problems.