[Paper Review] Learning Risk-aware Costmaps for Traversability in Challenging Environments

David D. Fan, Dey, Sharmita+2 more|arXiv (Cornell University)|Jul 25, 2021

Anomaly Detection Techniques and ApplicationsComputer Science42 references41 citations

TL;DR

This paper proposes a deep learning approach to generate risk-aware costmaps for autonomous navigation in unstructured environments by directly learning Conditional Value-at-Risk (CVaR) from LiDAR point clouds. Using a novel distribution-free loss function, the method produces robust, computationally efficient costmaps that accurately capture tail risks without relying on Gaussian assumptions, outperforming baselines in generalization, outlier resilience, and inference speed on real-world legged robot data from challenging terrains such as caves and subway systems.

ABSTRACT

One of the main challenges in autonomous robotic exploration and navigation in unknown and unstructured environments is determining where the robot can or cannot safely move. A significant source of difficulty in this determination arises from stochasticity and uncertainty, coming from localization error, sensor sparsity and noise, difficult-to-model robot-ground interactions, and disturbances to the motion of the vehicle. Classical approaches to this problem rely on geometric analysis of the surrounding terrain, which can be prone to modeling errors and can be computationally expensive. Moreover, modeling the distribution of uncertain traversability costs is a difficult task, compounded by the various error sources mentioned above. In this work, we take a principled learning approach to this problem. We introduce a neural network architecture for robustly learning the distribution of traversability costs. Because we are motivated by preserving the life of the robot, we tackle this learning problem from the perspective of learning tail-risks, i.e. the Conditional Value-at-Risk (CVaR). We show that this approach reliably learns the expected tail risk given a desired probability risk threshold between 0 and 1, producing a traversability costmap which is more robust to outliers, more accurately captures tail risks, and is more computationally efficient, when compared against baselines. We validate our method on data collected a legged robot navigating challenging, unstructured environments including an abandoned subway, limestone caves, and lava tube caves.

Motivation & Objective

• To address the challenge of accurately modeling traversability risk in unstructured, uncertain environments where classical geometric methods fail due to sensor noise, localization errors, and complex terrain interactions.
• To develop a learning-based approach that directly estimates CVaR from raw LiDAR data, avoiding restrictive distributional assumptions like Gaussianity.
• To improve robustness to outliers and computational efficiency in traversability costmap generation for autonomous robotic navigation.
• To validate the method on diverse, real-world unstructured environments including lava tubes, limestone caves, and abandoned subways.
• To provide a scalable, end-to-end learning framework that generalizes well to out-of-distribution terrain while maintaining high accuracy in risk quantification.

Proposed method

• A convolutional neural network (CNN) is trained on raw or minimally processed LiDAR point clouds to predict a risk-aware costmap, with each cell representing the CVaR of traversability cost at a given confidence level α.
• A novel differentiable loss function is introduced that enforces monotonicity in quantile and CVaR predictions with respect to the risk threshold α, enabling direct training without distributional assumptions.
• The method uses a quantile regression-style loss to train the network to predict VaR (Value-at-Risk) and CVaR (Conditional Value-at-Risk), with a focus on tail risk estimation.
• Training labels are derived from simulated or real traversability cost distributions, with no need to assume a specific parametric form such as Gaussian.
• The network is trained end-to-end on six real-world datasets collected by a legged robot in diverse, unstructured environments, including caves and abandoned infrastructure.
• Evaluation uses pseudo-R² metrics for VaR and CVaR, along with implied α to assess calibration, and compares performance across in-distribution and out-of-distribution settings.

Experimental results

Research questions

• RQ1 Can a deep learning model learn CVaR-based traversability costmaps directly from LiDAR data without assuming a specific probability distribution?
• RQ2 How does the proposed distribution-free CVaR learning method compare to traditional handcrafted costmaps and models based on Gaussian assumptions in terms of robustness and accuracy?
• RQ3 To what extent does the learned costmap generalize to out-of-distribution environments such as limestone caves with high-risk features not seen during training?
• RQ4 Does the proposed method improve computational efficiency compared to classical costmap generation pipelines?
• RQ5 How well does the model capture tail risks (e.g., at α = 0.95) where traditional methods often fail due to sparse data or distributional mismatches?

Key findings

• The proposed CVaR-learning model outperforms handcrafted, L1-loss, and NLL-loss baselines in both VaR and CVaR prediction accuracy, especially at high risk thresholds (α ≥ 0.9).
• The model achieves pseudo-R² values close to 1.0 for VaR and CVaR across most α levels, with only a moderate drop at α = 0.95 due to data distribution constraints.
• On the out-of-distribution Limestone Cave dataset, the model maintains pseudo-R² > 0 across all α levels, demonstrating robust generalization despite high terrain complexity and novel features.
• The CVaR-learning method reduces inference time by nearly 5× compared to the handcrafted costmap approach, with a median computation time of 48.94 ms vs. 241.92 ms.
• The model shows strong calibration, with implied α values closely tracking the target α, indicating reliable risk quantification across diverse environments.
• The method successfully captures tail risks in real-world scenarios such as narrow passages, rubble, and wet surfaces, where traditional methods often fail or overestimate risk.