PIETRA: Physics-Informed Evidential Learning for Traversing Out-of-Distribution Terrain

TL;DR

PIETRA addresses OOD generalization in off-road navigability by fusing physics priors with evidential learning in a Dirichlet posterior framework. It introduces an uncertainty-aware physics-informed loss and an explicit physics prior that activates when epistemic uncertainty is high, enabling a seamless balance between learned predictions and physics-based reasoning. The approach yields improved prediction accuracy and superior navigation performance under distribution shifts in both simulations and hardware, outperforming prior methods that either avoid OOD terrain or rely solely on physics priors. This work advances robust traversability estimation by leveraging physics to inform uncertainty and navigation decisions in challenging, unseen terrains. Its practical impact lies in safer, more reliable autonomous navigation in diverse environments where data scarcity and OOD conditions are common.

Abstract

Self-supervised learning is a powerful approach for developing traversability models for off-road navigation, but these models often struggle with inputs unseen during training. Existing methods utilize techniques like evidential deep learning to quantify model uncertainty, helping to identify and avoid out-of-distribution terrain. However, always avoiding out-of-distribution terrain can be overly conservative, e.g., when novel terrain can be effectively analyzed using a physics-based model. To overcome this challenge, we introduce Physics-Informed Evidential Traversability (PIETRA), a self-supervised learning framework that integrates physics priors directly into the mathematical formulation of evidential neural networks and introduces physics knowledge implicitly through an uncertainty-aware, physics-informed training loss. Our evidential network seamlessly transitions between learned and physics-based predictions for out-of-distribution inputs. Additionally, the physics-informed loss regularizes the learned model, ensuring better alignment with the physics model. Extensive simulations and hardware experiments demonstrate that PIETRA improves both learning accuracy and navigation performance in environments with significant distribution shifts.

Figures (10)

• Figure 1: Real-world navigation scenario where the robot, trained on flat ground and turf, encounters unseen tall vegetation and ramps while navigating to a goal. Unlike prior works that avoid OOD terrain, this work successfully navigates across OOD terrain to reach the goal by integrating physics knowledge into the traversability model.
• Figure 2: Conditional Value at Risk (CVaR) is the expected value of the worst-case $\alpha\in(0,1]$ portion of total probability and Value at Risk (VaR) is the worst-case $\alpha$-quantile for some random variable $Z$. We use both the left-tail and right-tail definitions proposed in cai2024evora.
• Figure 3: Overview of the proposed physics-informed evidential learning framework. In contrast to our prior work EVORA cai2024evora, this work explicitly embeds a physics prior in the Dirichlet posterior update and implicitly infuses physics knowledge via an uncertainty-aware, physics-informed loss during training.
• Figure 4: Terrain features used by the physics priors and how multiple potential traversability values are fused, as discussed in Sec. \ref{['sec:phys_prior_design']}. (a) Terrain slope. (b) Terrain height. (c) Inter-wheel distances of the front wheel pair and back wheel pair. (d) Inter-wheel distances of the left wheel pair and right wheel pair. (e) Multiple candidates are fused into a single estimated traversability PMF and combined with the uniform distribution to account for uncertainty.
• Figure 5: Overview of the simulation setup with synthetic rocky terrain, where the terrain unevenness is measured by the standard deviation of elevation in the robot footprint. The test maps are more uneven than the training and validation ones to induce distribution shift. During training and validation, only the data with terrain unevenness below the 50th percentile of the training dataset is used. Note that test maps are also used to evaluate navigation performance.