# Learning Risk-aware Costmaps for Traversability in Challenging Environments

arXiv: https://arxiv.org/abs/2107.11722 · HTML: https://mlsanity.com/paper/2107.11722/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 43 references that are in the map.
- First posted on arXiv 25 Jul 2021.

## Builds on (most cited first, 23 of 23)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [Image Inpainting for Irregular Holes Using Partial Convolutions](https://mlsanity.com/paper/1804.07723/) (2018)
- [Distributional Reinforcement Learning with Quantile Regression](https://mlsanity.com/paper/1710.10044/) (2017)
- [Risk-Constrained Reinforcement Learning with Percentile Risk Criteria](https://mlsanity.com/paper/1512.01629/) (2015)
- [LinkNet: Exploiting Encoder Representations for Efficient Semantic Segmentation](https://mlsanity.com/paper/1707.03718/) (2017)
- [Optimizing the CVaR via Sampling](https://mlsanity.com/paper/1404.3862/) (2014)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [NeBula: Quest for Robotic Autonomy in Challenging Environments; TEAM CoSTAR at the DARPA Subterranean Challenge](https://mlsanity.com/paper/2103.11470/) (2021)
- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [Deep Learning Tubes for Tube MPC](https://mlsanity.com/paper/2002.01587/) (2020)
- [PLGRIM: Hierarchical Value Learning for Large-scale Exploration in Unknown Environments](https://mlsanity.com/paper/2102.05633/) (2021)
- [Towards Resilient Autonomous Navigation of Drones](https://mlsanity.com/paper/2008.09679/) (2020)
- [Distributionally robust risk map for learning-based motion planning and control: A semidefinite programming approach](https://mlsanity.com/paper/2105.00657/) (2021)
- [Fast Approximate Clearance Evaluation for Rovers with Articulated Suspension Systems](https://mlsanity.com/paper/1808.00031/) (2018)
- [CVaR-based Flight Energy Risk Assessment for Multirotor UAVs using a Deep Energy Model](https://mlsanity.com/paper/2105.15189/) (2021)
- [Contact Inertial Odometry: Collisions are your Friends](https://mlsanity.com/paper/1909.00079/) (2019)
- [Path Planning and Navigation Inside Off-World Lava Tubes and Caves](https://mlsanity.com/paper/1803.02818/) (2018)
- [Autonomous Off-road Navigation over Extreme Terrains with Perceptually-challenging Conditions](https://mlsanity.com/paper/2101.11110/) (2021)
- [Points2Pix: 3D Point-Cloud to Image Translation using conditional Generative Adversarial Networks](https://mlsanity.com/paper/1901.09280/) (2019)
- [Optimizing tail risks using an importance sampling based extrapolation for heavy-tailed objectives](https://mlsanity.com/paper/2008.09818/) (2020)

## Built on by (most cited first, 12 of 12)

- [How Does It Feel? Self-Supervised Costmap Learning for Off-Road Vehicle Traversability](https://mlsanity.com/paper/2209.10788/) (2022)
- [RoadRunner -- Learning Traversability Estimation for Autonomous Off-road Driving](https://mlsanity.com/paper/2402.19341/) (2024)
- [EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy](https://mlsanity.com/paper/2311.06234/) (2023)
- [Learning Risk-Aware Costmaps via Inverse Reinforcement Learning for Off-Road Navigation](https://mlsanity.com/paper/2302.00134/) (2023)
- [Safe Navigation in Unstructured Environments by Minimizing Uncertainty in Control and Perception](https://mlsanity.com/paper/2306.14601/) (2023)
- [CooperRisk: A Driving Risk Quantification Pipeline with Multi-Agent Cooperative Perception and Prediction](https://mlsanity.com/paper/2506.15868/) (2025)
- [Bipedalism for Quadrupedal Robots: Versatile Loco-Manipulation through Risk-Adaptive Reinforcement Learning](https://mlsanity.com/paper/2507.20382/) (2025)
- [ZeST: A VLM-based Zero-Shot Traversability Navigation for Unknown Environments](https://mlsanity.com/paper/2508.19131/) (2025)
- [Risk-aware Meta-level Decision Making for Exploration Under Uncertainty](https://mlsanity.com/paper/2209.05580/) (2022)
- [METAVerse: Meta-Learning Traversability Cost Map for Off-Road Navigation](https://mlsanity.com/paper/2307.13991/) (2023)
- [Mars Traversability Prediction: A Multi-modal Self-supervised Approach for Costmap Generation](https://mlsanity.com/paper/2509.11082/) (2025)
- [ProTerrain: Probabilistic Physics-Informed Rough Terrain World Modeling](https://mlsanity.com/paper/2510.19364/) (2025)

## Abstract (arXiv)

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.