Neural Elevation Models for Terrain Mapping and Path Planning

TL;DR

This work presents Neural Elevation Models (NEMos), a terrain representation that jointly trains a NeRF density field and a differentiable height field from imagery to enable gradient-based path planning. The height field, learned via quantile regression, provides a continuous, differentiable surface used to guide smooth, feasible robot trajectories, while the NeRF component is discarded after training to yield a compact map. Experiments on simulated and real terrain imagery demonstrate high-quality reconstructions and smoother paths than traditional discrete DEM-based planning, validating the practical potential for terrain-aware navigation from cameras alone. Future work targets enriching the height field with semantic features and conducting rover-level validations.

Abstract

This work introduces Neural Elevations Models (NEMos), which adapt Neural Radiance Fields to a 2.5D continuous and differentiable terrain model. In contrast to traditional terrain representations such as digital elevation models, NEMos can be readily generated from imagery, a low-cost data source, and provide a lightweight representation of terrain through an implicit continuous and differentiable height field. We propose a novel method for jointly training a height field and radiance field within a NeRF framework, leveraging quantile regression. Additionally, we introduce a path planning algorithm that performs gradient-based optimization of a continuous cost function for minimizing distance, slope changes, and control effort, enabled by differentiability of the height field. We perform experiments on simulated and real-world terrain imagery, demonstrating NEMos ability to generate high-quality reconstructions and produce smoother paths compared to discrete path planning methods. Future work will explore the incorporation of features and semantics into the height field, creating a generalized terrain model.

Figures (4)

• Figure 1: Neural Elevation Model (NEMo) framework. Aerial imagery of terrain is captured and used to simultaneously train a radiance field and height field of the scene. The height field is then used as a continuous and differentiable map representation for gradient-based path planning.
• Figure 2: Height field training via quantile regression. Training images cast rays (depicted in light blue) into the scene, along which points are sampled (dark red). By minimizing the weighted quantile loss over the multitude of sampled points, we effectively regress the desired quantile of vertical NeRF density as height.
• Figure 3: RGB (left) and depth (right) renders from trained NEMos of the scenes used in our experiments. KT-22 is shown on the top row, and Red Rocks on the bottow row.
• Figure 4: Path planning on the NEMo height field. The initial A* path is shown in orange, while the refined path is shown in red. The refined paths from method designed for the implicit NEMo height field are smoother and more efficient.