# Case Study: Verifying the Safety of an Autonomous Racing Car with a Neural Network Controller

arXiv: https://arxiv.org/abs/1910.11309 · HTML: https://mlsanity.com/paper/1910.11309/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Oct 2019.

## Built on by (most cited first, 17 of 17)

- [Towards Guaranteed Safe AI: A Framework for Ensuring Robust and Reliable AI Systems](https://mlsanity.com/paper/2405.06624/) (2024)
- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [Reachability Analysis of a General Class of Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.06531/) (2022)
- [Risk Verification of Stochastic Systems with Neural Network Controllers](https://mlsanity.com/paper/2209.09881/) (2022)
- [Autonomous Driving Small-Scale Cars: A Survey of Recent Development](https://mlsanity.com/paper/2404.06229/) (2024)
- [Vehicle: Interfacing Neural Network Verifiers with Interactive Theorem Provers](https://mlsanity.com/paper/2202.05207/) (2022)
- [Safe Reach Set Computation via Neural Barrier Certificates](https://mlsanity.com/paper/2404.18813/) (2024)
- [Certifying Robustness of Learning-Based Keypoint Detection and Pose Estimation Methods](https://mlsanity.com/paper/2408.00117/) (2024)
- [Safety Monitoring for Learning-Enabled Cyber-Physical Systems in Out-of-Distribution Scenarios](https://mlsanity.com/paper/2504.13478/) (2025)
- [Formal Verification of Stochastic Systems with ReLU Neural Network Controllers](https://mlsanity.com/paper/2103.05142/) (2021)
- [Analyzing Neural Network Robustness Using Graph Curvature](https://mlsanity.com/paper/2410.19607/) (2024)
- [ModelGuard: Runtime Validation of Lipschitz-continuous Models](https://mlsanity.com/paper/2104.15006/) (2021)
- [Partial End-to-end Reinforcement Learning for Robustness Against Modelling Error in Autonomous Racing](https://mlsanity.com/paper/2312.06406/) (2023)
- [Neural Network Based Model Predictive Control for an Autonomous Vehicle](https://mlsanity.com/paper/2107.14573/) (2021)
- [An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehicles](https://mlsanity.com/paper/2205.01419/) (2022)
- [Creating a Formally Verified Neural Network for Autonomous Navigation: An Experience Report](https://mlsanity.com/paper/2411.14163/) (2024)
- [From Decoupled to Coupled: Robustness Verification for Learning-based Keypoint Detection with Joint Specifications](https://mlsanity.com/paper/2603.05604/) (2026)

## Abstract (arXiv)

This paper describes a verification case study on an autonomous racing car with a neural network (NN) controller. Although several verification approaches have been proposed over the last year, they have only been evaluated on low-dimensional systems or systems with constrained environments. To explore the limits of existing approaches, we present a challenging benchmark in which the NN takes raw LiDAR measurements as input and outputs steering for the car. We train a dozen NNs using two reinforcement learning algorithms and show that the state of the art in verification can handle systems with around 40 LiDAR rays, well short of a typical LiDAR scan with 1081 rays. Furthermore, we perform real experiments to investigate the benefits and limitations of verification with respect to the sim2real gap, i.e., the difference between a system's modeled and real performance. We identify cases, similar to the modeled environment, in which verification is strongly correlated with safe behavior. Finally, we illustrate LiDAR fault patterns that can be used to develop robust and safe reinforcement learning algorithms.