EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy

TL;DR

This paper introduces EVORA, a framework for uncertainty-aware traversability learning and risk-aware planning for off-road autonomy. It jointly models aleatoric traction distributions and epistemic uncertainty via latent-space densities using evidential deep learning with Dirichlet posteriors and a novel ${L}^{ ext{UEMD}^2}$ loss, enabling calibrated traction predictions and robust OOD detection. Planning employs CVaR formulations, with a left-tail CVaR of traction (CVaR-Dyn) to forward simulate worst-case terrain effects and an auxiliary OOD-avoidance mechanism to mitigate epistemic risk, all integrated with a GPU-accelerated MPPI planner. Across synthetic and hardware experiments (RC car and legged robot), EVORA demonstrates improved navigation performance over nominal or purely expected-traction baselines, particularly in environments with multimodal traction and unseen terrain.

Abstract

Traversing terrain with good traction is crucial for achieving fast off-road navigation. Instead of manually designing costs based on terrain features, existing methods learn terrain properties directly from data via self-supervision to automatically penalize trajectories moving through undesirable terrain, but challenges remain to properly quantify and mitigate the risk due to uncertainty in learned models. To this end, this work proposes a unified framework to learn uncertainty-aware traction model and plan risk-aware trajectories. For uncertainty quantification, we efficiently model both aleatoric and epistemic uncertainty by learning discrete traction distributions and probability densities of the traction predictor's latent features. Leveraging evidential deep learning, we parameterize Dirichlet distributions with the network outputs and propose a novel uncertainty-aware squared Earth Mover's distance loss with a closed-form expression that improves learning accuracy and navigation performance. For risk-aware navigation, the proposed planner simulates state trajectories with the worst-case expected traction to handle aleatoric uncertainty, and penalizes trajectories moving through terrain with high epistemic uncertainty. Our approach is extensively validated in simulation and on wheeled and quadruped robots, showing improved navigation performance compared to methods that assume no slip, assume the expected traction, or optimize for the worst-case expected cost.

Figures (20)

• Figure 1: This work proposes to learn terrain traction, the ratio between achieved and commanded velocities, while quantifying the uncertainty in the learned model to plan risk-aware trajectories. (a) Aleatoric uncertainty is the inherent and irreducible uncertainty due to partial observability. For example, visually similar terrain may have different traction values due to complex interactions between the robot and vegetation. (b) Epistemic uncertainty is the model uncertainty due to distribution shift between training and test environments, limiting the reliability of the learned model at test time.
• Figure 2: Overview of the proposed uncertainty-aware traversability learning and risk-aware navigation methods. (a) For data collection, we drive the robot over interesting terrain to record traction values, robot positions, and build a semantic elevation map. We generate training dataset offline by extracting semantic and elevation features of the terrain and estimating empirical traction distributions along the traversed path. (b) Leveraging evidential deep learning natpn, we learn categorical distributions over discretized traction values to capture aleatoric uncertainty and estimate epistemic uncertainty by using a normalizing flow network Kobyzev2021flow to learn the densities of the traction predictor's latent features. The overall architecture is trained with the proposed uncertainty-aware loss defined for the Dirichlet distribution parameterized by the network outputs. (c) To handle aleatoric uncertainty, we propose a risk-aware planner that uses the left-tail conditional value at risk (CVaR) of the traction distribution to forward simulate the robot states when using the sampling-based model predictive control (MPC) method williams2017information. To handle epistemic uncertainty, we threshold the densities of the traction predictor's latent features in order to identify and avoid out-of-distribution (OOD) terrain with unreliable traction predictions via auxiliary planning costs.
• Figure 3: Example ground robots that can be modeled with unicycle or bicycle dynamics models. (a) RC car. (b) Differential-drive robot. (c) Legged robot.
• Figure 4: The proposed traversability pipeline maps elevation and semantic features to traction distributions that capture aleatoric uncertainty, and density for latent features that capture epistemic uncertainty. Terrain regions are deemed out-of-distribution (OOD) and later avoided during planning if the densities for the latent features are below a threshold. When the densities for latent features are above the threshold, the predicted traction distributions are reliable and inform downstream risk-aware planners (Sec. \ref{['sec:planning']}) to trade off the risk of immobilization with the time savings by traversing regions with uncertain traction.
• Figure 6: Difference between ${\text{EMD}^2}$ and CE. Given the ground truth $\mathbf{y}$ and the predictions $\mathbf{p}_1$ and $\mathbf{p}_2$, CE produces the same values while ${\text{EMD}^2}$ penalizes $\mathbf{p}_2$ more. In practice, ${\text{EMD}^2}$ is more desirable because it accounts for the cross-bin relationship among the discretized traction values.

Theorems & Definitions (2)

• Theorem 1
• proof