# T-CBF: Traversability-based Control Barrier Function to Navigate Vertically Challenging Terrain

arXiv: https://arxiv.org/abs/2503.06083 · HTML: https://mlsanity.com/paper/2503.06083/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 41 references that are in the map.
- First posted on arXiv 8 Mar 2025.

## Builds on (most cited first, 28 of 28)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances](https://mlsanity.com/paper/1709.07523/) (2017)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [Motion Planning and Control for Mobile Robot Navigation Using Machine Learning: a Survey](https://mlsanity.com/paper/2011.13112/) (2020)
- [Elevation Mapping for Locomotion and Navigation using GPU](https://mlsanity.com/paper/2204.12876/) (2022)
- [How Does It Feel? Self-Supervised Costmap Learning for Off-Road Vehicle Traversability](https://mlsanity.com/paper/2209.10788/) (2022)
- [Multi-Layered Safety for Legged Robots via Control Barrier Functions and Model Predictive Control](https://mlsanity.com/paper/2011.00032/) (2020)
- [Learning Inverse Kinodynamics for Accurate High-Speed Off-Road Navigation on Unstructured Terrain](https://mlsanity.com/paper/2102.12667/) (2021)
- [GrASPE: Graph based Multimodal Fusion for Robot Navigation in Unstructured Outdoor Environments](https://mlsanity.com/paper/2209.05722/) (2022)
- [Learning Safe, Generalizable Perception-based Hybrid Control with Certificates](https://mlsanity.com/paper/2201.00932/) (2022)
- [Direct LiDAR-Inertial Odometry: Lightweight LIO with Continuous-Time Motion Correction](https://mlsanity.com/paper/2203.03749/) (2022)
- [Learning Barrier Functions with Memory for Robust Safe Navigation](https://mlsanity.com/paper/2011.01899/) (2020)
- [VI-IKD: High-Speed Accurate Off-Road Navigation using Learned Visual-Inertial Inverse Kinodynamics](https://mlsanity.com/paper/2203.15983/) (2022)
- [Toward Wheeled Mobility on Vertically Challenging Terrain: Platforms, Datasets, and Algorithms](https://mlsanity.com/paper/2303.00998/) (2023)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [High-Speed Accurate Robot Control using Learned Forward Kinodynamics and Non-linear Least Squares Optimization](https://mlsanity.com/paper/2206.08487/) (2022)
- [Learning to Model and Plan for Wheeled Mobility on Vertically Challenging Terrain](https://mlsanity.com/paper/2306.11611/) (2023)
- [Neural Control Barrier Functions for Safe Navigation](https://mlsanity.com/paper/2407.19907/) (2024)
- [Learning Terrain-Aware Kinodynamic Model for Autonomous Off-Road Rally Driving With Model Predictive Path Integral Control](https://mlsanity.com/paper/2305.00676/) (2023)
- [PIETRA: Physics-Informed Evidential Learning for Traversing Out-of-Distribution Terrain](https://mlsanity.com/paper/2409.03005/) (2024)
- [Terrain-Attentive Learning for Efficient 6-DoF Kinodynamic Modeling on Vertically Challenging Terrain](https://mlsanity.com/paper/2403.16419/) (2024)
- [Safe Navigation and Obstacle Avoidance Using Differentiable Optimization Based Control Barrier Functions](https://mlsanity.com/paper/2304.08586/) (2023)
- [Safe Navigation in Unstructured Environments by Minimizing Uncertainty in Control and Perception](https://mlsanity.com/paper/2306.14601/) (2023)
- [Data-Driven Robust Barrier Functions for Safe, Long-Term Operation](https://mlsanity.com/paper/2104.07592/) (2021)
- [Verti-Bench: A General and Scalable Off-Road Mobility Benchmark for Vertically Challenging Terrain](https://mlsanity.com/paper/2502.11426/) (2025)
- [Guaranteed-Safe MPPI Through Composite Control Barrier Functions for Efficient Sampling in Multi-Constrained Robotic Systems](https://mlsanity.com/paper/2410.02154/) (2024)
- [Safe Control for Soft-Rigid Robots with Self-Contact using Control Barrier Functions](https://mlsanity.com/paper/2311.03189/) (2023)

## Built on by (most cited first, 2 of 2)

- [Failing Gracefully: Mitigating Impact of Inevitable Robot Failures](https://mlsanity.com/paper/2608.05313/) (2026)
- [Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields](https://mlsanity.com/paper/2610.20255/) (2026)

## Abstract (arXiv)

Safety has been of paramount importance in motion planning and control techniques and is an active area of research in the past few years. Most safety research for mobile robots target at maintaining safety with the notion of collision avoidance. However, safety goes beyond just avoiding collisions, especially when robots have to navigate unstructured, vertically challenging, off-road terrain, where vehicle rollover and immobilization is as critical as collisions. In this work, we introduce a novel Traversability-based Control Barrier Function (T-CBF), in which we use neural Control Barrier Functions (CBFs) to achieve safety beyond collision avoidance on unstructured vertically challenging terrain by reasoning about new safety aspects in terms of traversability. The neural T-CBF trained on safe and unsafe observations specific to traversability safety is then used to generate safe trajectories. Furthermore, we present experimental results in simulation and on a physical Verti-4 Wheeler (V4W) platform, demonstrating that T-CBF can provide traversability safety while reaching the goal position. T-CBF planner outperforms previously developed planners by 30% in terms of keeping the robot safe and mobile when navigating on real world vertically challenging terrain.