# An Empirical Analysis of the Use of Real-Time Reachability for the Safety Assurance of Autonomous Vehicles

arXiv: https://arxiv.org/abs/2205.01419 · HTML: https://mlsanity.com/paper/2205.01419/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 105 references that are in the map.
- First posted on arXiv 3 May 2022.

## Builds on (most cited first, 26 of 26)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [A Survey of Autonomous Driving: Common Practices and Emerging Technologies](https://mlsanity.com/paper/1906.05113/) (2019)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [How Should a Robot Assess Risk? Towards an Axiomatic Theory of Risk in Robotics](https://mlsanity.com/paper/1710.11040/) (2017)
- [Robust Online Monitoring of Signal Temporal Logic](https://mlsanity.com/paper/1506.08234/) (2015)
- [Towards Verified Artificial Intelligence](https://mlsanity.com/paper/1606.08514/) (2016)
- [Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach](https://mlsanity.com/paper/2004.12273/) (2020)
- [Assessing Transferability from Simulation to Reality for Reinforcement Learning](https://mlsanity.com/paper/1907.04685/) (2019)
- [A Review of Formal Methods applied to Machine Learning](https://mlsanity.com/paper/2104.02466/) (2021)
- [Neural Simplex Architecture](https://mlsanity.com/paper/1908.00528/) (2019)
- [SOTER: A Runtime Assurance Framework for Programming Safe Robotics Systems](https://mlsanity.com/paper/1808.07921/) (2018)
- [Verification for Machine Learning, Autonomy, and Neural Networks Survey](https://mlsanity.com/paper/1810.01989/) (2018)
- [An Efficient Reachability-Based Framework for Provably Safe Autonomous Navigation in Unknown Environments](https://mlsanity.com/paper/1905.00532/) (2019)
- [Case Study: Verifying the Safety of an Autonomous Racing Car with a Neural Network Controller](https://mlsanity.com/paper/1910.11309/) (2019)
- [F1/10: An Open-Source Autonomous Cyber-Physical Platform](https://mlsanity.com/paper/1901.08567/) (2019)
- [CDDT: Fast Approximate 2D Ray Casting for Accelerated Localization](https://mlsanity.com/paper/1705.01167/) (2017)
- [Reachability-Based Safety Guarantees using Efficient Initializations](https://mlsanity.com/paper/1903.07715/) (2019)
- [A Hamilton-Jacobi Reachability-Based Framework for Predicting and Analyzing Human Motion for Safe Planning](https://mlsanity.com/paper/1910.13369/) (2019)
- [Reachable Sets for Safe, Real-Time Manipulator Trajectory Design](https://mlsanity.com/paper/2002.01591/) (2020)
- [Trusted Confidence Bounds for Learning Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2003.05107/) (2020)
- [Safe Platooning of Unmanned Aerial Vehicles via Reachability](https://mlsanity.com/paper/1503.07253/) (2015)
- [On Infusing Reachability-Based Safety Assurance within Probabilistic Planning Frameworks for Human-Robot Vehicle Interactions](https://mlsanity.com/paper/1812.11315/) (2018)
- [Algorithmic Verification of Continuous and Hybrid Systems](https://mlsanity.com/paper/1403.0952/) (2014)
- [A Hybrid Framework for Multi-Vehicle Collision Avoidance](https://mlsanity.com/paper/1703.07375/) (2017)

## Abstract (arXiv)

Recent advances in machine learning technologies and sensing have paved the way for the belief that safe, accessible, and convenient autonomous vehicles may be realized in the near future. Despite tremendous advances within this context, fundamental challenges around safety and reliability are limiting their arrival and comprehensive adoption. Autonomous vehicles are often tasked with operating in dynamic and uncertain environments. As a result, they often make use of highly complex components, such as machine learning approaches, to handle the nuances of sensing, actuation, and control. While these methods are highly effective, they are notoriously difficult to assure. Moreover, within uncertain and dynamic environments, design time assurance analyses may not be sufficient to guarantee safety. Thus, it is critical to monitor the correctness of these systems at runtime. One approach for providing runtime assurance of systems with components that may not be amenable to formal analysis is the simplex architecture, where an unverified component is wrapped with a safety controller and a switching logic designed to prevent dangerous behavior. In this paper, we propose using a real-time reachability algorithm for the implementation of the simplex architecture to assure the safety of a 1/10 scale open source autonomous vehicle platform known as F1/10. The reachability algorithm that we leverage (a) provides provable guarantees of safety, and (b) is used to detect potentially unsafe scenarios. In our approach, the need to analyze an underlying controller is abstracted away, instead focusing on the effects of the controller's decisions on the system's future states. We demonstrate the efficacy of our architecture through a vast set of experiments conducted both in simulation and on an embedded hardware platform.