# Parameter-Conditioned Reachable Sets for Updating Safety Assurances Online

arXiv: https://arxiv.org/abs/2209.14976 · HTML: https://mlsanity.com/paper/2209.14976/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2022.

## Built on by (most cited first, 12 of 12)

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [SAFE-GIL: SAFEty Guided Imitation Learning for Robotic Systems](https://mlsanity.com/paper/2404.05249/) (2024)
- [Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomy](https://mlsanity.com/paper/2309.01267/) (2023)
- [One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environments](https://mlsanity.com/paper/2412.09989/) (2024)
- [AnySafe: Adapting Latent Safety Filters at Runtime via Safety Constraint Parameterization in the Latent Space](https://mlsanity.com/paper/2509.19555/) (2025)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functions](https://mlsanity.com/paper/2505.11755/) (2025)
- [Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments](https://mlsanity.com/paper/2508.03428/) (2025)
- [Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walker](https://mlsanity.com/paper/2409.16301/) (2024)
- [Permissive Safety Through Trusted Inference: Verifiable Belief-Space Neural Safety Filters for Assured Interactive Robotics](https://mlsanity.com/paper/2606.02562/) (2026)
- [Robots that Suggest Safe Alternatives](https://mlsanity.com/paper/2409.09883/) (2024)

## Abstract (arXiv)

Hamilton-Jacobi (HJ) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. However, the provided safety assurances are often predicated on the assumption that once deployed, the system or its environment does not evolve. Online, however, an autonomous system might experience changes in system dynamics, control authority, external disturbances, and/or the surrounding environment, requiring updated safety assurances. Rather than restarting the safety analysis from scratch, which can be time-consuming and often intractable to perform online, we propose to compute textitparameter-conditioned reachable sets. Assuming expected system and environment changes can be parameterized, we treat these parameters as virtual states in the system and leverage recent advances in high-dimensional reachability analysis to solve the corresponding reachability problem offline. This results in a family of reachable sets that is parameterized by the environment and system factors. Online, as these factors change, the system can simply query the corresponding safety function from this family to ensure system safety, enabling a real-time update of the safety assurances. Through various simulation studies, we demonstrate the capability of our approach in maintaining system safety despite the system and environment evolution.