# Risk-Based Safety Envelopes for Autonomous Vehicles Under Perception Uncertainty

arXiv: https://arxiv.org/abs/2107.09918 · HTML: https://mlsanity.com/paper/2107.09918/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2021.

## Built on by (most cited first, 4 of 4)

- [Perception Simplex: Verifiable Collision Avoidance in Autonomous Vehicles Amidst Obstacle Detection Faults](https://mlsanity.com/paper/2209.01710/) (2022)
- [Safe AI -- How is this Possible?](https://mlsanity.com/paper/2201.10436/) (2022)
- [Context-aware Risk Assessment and Its Application in Autonomous Driving](https://mlsanity.com/paper/2508.02919/) (2025)
- [Spatial Envelope MPC: High Performance Driving without a Reference](https://mlsanity.com/paper/2509.18506/) (2025)

## Abstract (arXiv)

Ensuring the safety of autonomous vehicles, given the uncertainty in sensing other road users, is an open problem. Moreover, separate safety specifications for perception and planning components raise how to assess the overall system safety. This work provides a probabilistic approach to calculate safety envelopes under perception uncertainty. The probabilistic envelope definition is based on a risk threshold. It limits the cumulative probability that the actual safety envelope in a fully observable environment is larger than an applied envelope and is solved using iterative worst-case analysis of envelopes. Our approach extends non-probabilistic envelopes - in this work, the Responsibility-Sensitive Safety (RSS) - to handle uncertainties. To evaluate our probabilistic envelope approach, we compare it in a simulated highway merging scenario against several baseline safety architectures. Our evaluation shows that our model allows adjusting safety and performance based on a chosen risk level and the amount of perception uncertainty. We conclude with an outline of how to formally argue safety under perception uncertainty using our formulation of envelope violation risk.