# Autonomous Vehicles Meet the Physical World: RSS, Variability, Uncertainty, and Proving Safety (Expanded Version)

arXiv: https://arxiv.org/abs/1911.01207 · HTML: https://mlsanity.com/paper/1911.01207/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2019.

## Built on by (most cited first, 10 of 10)

- [Data-centric Operational Design Domain Characterization for Machine Learning-based Aeronautical Products](https://mlsanity.com/paper/2307.07681/) (2023)
- [CooperRisk: A Driving Risk Quantification Pipeline with Multi-Agent Cooperative Perception and Prediction](https://mlsanity.com/paper/2506.15868/) (2025)
- [LLM-based Realistic Safety-Critical Driving Video Generation](https://mlsanity.com/paper/2507.01264/) (2025)
- [System Theoretic View on Uncertainties](https://mlsanity.com/paper/2303.04042/) (2023)
- [A Safe Self-evolution Algorithm for Autonomous Driving Based on Data-Driven Risk Quantification Model](https://mlsanity.com/paper/2408.12805/) (2024)
- [Incremental Validation of Automated Driving Functions using Generic Volumes in Micro- Operational Design Domains](https://mlsanity.com/paper/2512.11351/) (2025)
- [Defining Operational Conditions for Safety-Critical AI-Based Systems from Data](https://mlsanity.com/paper/2601.22118/) (2026)
- [Testing Autonomous Systems with Believed Equivalence Refinement](https://mlsanity.com/paper/2103.04578/) (2021)
- [Safe AI -- How is this Possible?](https://mlsanity.com/paper/2201.10436/) (2022)
- [VLM-CASE: Vision-Language Model Enabled Context-Adaptive Safety Envelopes for Anticipatory Safe Autonomous Driving](https://mlsanity.com/paper/2607.05180/) (2026)

## Abstract (arXiv)

The Responsibility-Sensitive Safety (RSS) model offers provable safety for vehicle behaviors such as minimum safe following distance. However, handling worst-case variability and uncertainty may significantly lower vehicle permissiveness, and in some situations safety cannot be guaranteed. Digging deeper into Newtonian mechanics, we identify complications that result from considering vehicle status, road geometry and environmental parameters. An especially challenging situation occurs if these parameters change during the course of a collision avoidance maneuver such as hard braking. As part of our analysis, we expand the original RSS following distance equation to account for edge cases involving potential collisions mid-way through a braking process. We additionally propose a Micro-Operational Design Domain (μODD) approach to subdividing the operational space as a way of improving permissiveness. Confining probabilistic aspects of safety to μODD transitions permits proving safety (when possible) under the assumption that the system has transitioned to the correct μODD for the situation. Each μODD can additionally be used to encode system fault responses, take credit for advisory information (e.g., from vehicle-to-vehicle communication), and anticipate likely emergent situations.