Off-Road Navigation via Implicit Neural Representation of Terrain Traversability

TL;DR

TRAIL tackles off-road navigation by learning an implicit, coordinate-based terrain representation from camera and LiDAR that encodes both geometric elevation and terrain bumpiness. A gradient-based planner combines an A* path search with differentiable trajectory optimization to jointly adjust path geometry and speed, guided by the terrain gradients. Simulation and field experiments show TRAIL outperforms geometry- and traction-based baselines, delivering smoother trajectories, adaptive speeds, and higher success rates, while reducing odometry-induced drift. The work demonstrates the value of perception-planning co-design via implicit representations for robust, terrain-aware autonomous navigation.

Abstract

Autonomous off-road navigation requires robots to estimate terrain traversability from onboard sensors and plan accordingly. Conventional approaches typically rely on sampling-based planners such as MPPI to generate short-term control actions that aim to minimize traversal time and risk measures derived from the traversability estimates. These planners can react quickly but optimize only over a short look-ahead window, limiting their ability to reason about the full path geometry, which is important for navigating in challenging off-road environments. Moreover, they lack the ability to adjust speed based on the terrain bumpiness, which is important for smooth navigation on challenging terrains. In this paper, we introduce TRAIL (Traversability with an Implicit Learned Representation), an off-road navigation framework that leverages an implicit neural representation to continuously parameterize terrain properties. This representation yields spatial gradients that enable integration with a novel gradient-based trajectory optimization method that adapts the path geometry and speed profile based on terrain traversability.

Figures (8)

• Figure 1: Top: Optimized trajectories overlaid on the blended cost map, generated by combining two cost maps with $50\%$ transparency (sampled at fixed grid resolution for visualization). The larger dark blocks represent higher geometric risk inflated using vehicle radius (e.g. the highlighted tree trunks) while finer greyscale variations correspond to predicted terrain bumpiness (e.g. grey regions around trees from tree roots). Redder trajectory segments indicate higher speed. Bottom: Corresponding onboard camera images. The optimized trajectories avoid hard obstacles, slow down when approaching bumpy regions, and speed up in smoother areas.
• Figure 2: Our perception module takes a camera image and a LiDAR point cloud and produces an implicit representation of various terrain properties (only the bump decoder is shown). The proposed planning and control framework then incorporates gradient information provided by the implicit representation into a novel gradient-based trajectory optimization framework, where speed profile and path geometry are co-optimized.
• Figure 3: Comparison of vertical acceleration from an IMU and low-traction events. Peaks in vertical acceleration generally coincide with periods of reduced traction. However, occasional false positives occur due to noisy velocity estimates, leading to misclassified high-traction regions (see right). Camera images are tone- and color-corrected for visibility.
• Figure 4: Inference time for the explicit decoder and implicit decoder vs. number of query points. Note that the explicit decoder outputs a fixed-size $100 \times 100$ grid map. Therefore, $10^4$ query points to the implicit decoder is equivalent to reconstructing a grid map with the same grid resolution as the explicit decoder. However, for planning and trajectory optimization, the required number of queries is usually far smaller than the full grid size.
• Figure 5: Grassland scenario. The robot’s forward direction ($x$) and leftward direction ($y$) are represented by the red and green axes, respectively. Examples of paths produced by Geo-20 (blue), WF-20 (orange), and TRAIL (green) are shown on the left. The bottom left corner shows the camera image from the robot. On the right side, the top shows the initial path generated by A$^\star$ overlayed on the geometric risk map. Bottom right shows the optimized trajectory overlayed on the predicted bumpiness value. The trajectory is color-coded by speed.