# Learning Smooth State-Dependent Traversability from Dense Point Clouds

arXiv: https://arxiv.org/abs/2506.04362 · HTML: https://mlsanity.com/paper/2506.04362/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 30 references that are in the map.
- First posted on arXiv 4 Jun 2025.

## Builds on (most cited first, 22 of 22)

- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [NeuRBF: A Neural Fields Representation with Adaptive Radial Basis Functions](https://mlsanity.com/paper/2309.15426/) (2023)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Fast Traversability Estimation for Wild Visual Navigation](https://mlsanity.com/paper/2305.08510/) (2023)
- [TerrainNet: Visual Modeling of Complex Terrain for High-speed, Off-road Navigation](https://mlsanity.com/paper/2303.15771/) (2023)
- [Locomotion Policy Guided Traversability Learning using Volumetric Representations of Complex Environments](https://mlsanity.com/paper/2203.15854/) (2022)
- [STEP: Stochastic Traversability Evaluation and Planning for Risk-Aware Off-road Navigation](https://mlsanity.com/paper/2103.02828/) (2021)
- [Some Fundamental Aspects about Lipschitz Continuity of Neural Networks](https://mlsanity.com/paper/2302.10886/) (2023)
- [RoadRunner -- Learning Traversability Estimation for Autonomous Off-road Driving](https://mlsanity.com/paper/2402.19341/) (2024)
- [Direct LiDAR-Inertial Odometry: Lightweight LIO with Continuous-Time Motion Correction](https://mlsanity.com/paper/2203.03749/) (2022)
- [ScaTE: A Scalable Framework for Self-Supervised Traversability Estimation in Unstructured Environments](https://mlsanity.com/paper/2209.06522/) (2022)
- [EVORA: Deep Evidential Traversability Learning for Risk-Aware Off-Road Autonomy](https://mlsanity.com/paper/2311.06234/) (2023)
- [TERP: Reliable Planning in Uneven Outdoor Environments using Deep Reinforcement Learning](https://mlsanity.com/paper/2109.05120/) (2021)
- [Risk-Aware Off-Road Navigation via a Learned Speed Distribution Map](https://mlsanity.com/paper/2203.13429/) (2022)
- [OrbitGrasp: SE(3)-Equivariant Grasp Learning](https://mlsanity.com/paper/2407.03531/) (2024)
- [Learning to Model and Plan for Wheeled Mobility on Vertically Challenging Terrain](https://mlsanity.com/paper/2306.11611/) (2023)
- [TRG-planner: Traversal Risk Graph-Based Path Planning in Unstructured Environments for Safe and Efficient Navigation](https://mlsanity.com/paper/2501.01806/) (2025)

## Abstract (arXiv)

A key open challenge in off-road autonomy is that the traversability of terrain often depends on the vehicle's state. In particular, some obstacles are only traversable from some orientations. However, learning this interaction by encoding the angle of approach as a model input demands a large and diverse training dataset and is computationally inefficient during planning due to repeated model inference. To address these challenges, we present SPARTA, a method for estimating approach angle conditioned traversability from point clouds. Specifically, we impose geometric structure into our network by outputting a smooth analytical function over the 1-Sphere that predicts risk distribution for any angle of approach with minimal overhead and can be reused for subsequent queries. The function is composed of Fourier basis functions, which has important advantages for generalization due to their periodic nature and smoothness. We demonstrate SPARTA both in a high-fidelity simulation platform, where our model achieves a 91% success rate crossing a 40m boulder field (compared to 73% for the baseline), and on hardware, illustrating the generalization ability of the model to real-world settings. Our code will be available at https://github.com/neu-autonomy/SPARTA.