# Stochastic Model Predictive Control with a Safety Guarantee for Automated Driving: Extended Version

arXiv: https://arxiv.org/abs/2009.09381 · HTML: https://mlsanity.com/paper/2009.09381/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2020.

## Built on by (most cited first, 13 of 13)

- [End-to-end Autonomous Driving: Challenges and Frontiers](https://mlsanity.com/paper/2306.16927/) (2023)
- [Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomy](https://mlsanity.com/paper/2309.01267/) (2023)
- [Uncertainty-Aware DRL for Autonomous Vehicle Crowd Navigation in Shared Space](https://mlsanity.com/paper/2405.13969/) (2024)
- [Predictive Control for Autonomous Driving with Uncertain, Multi-modal Predictions](https://mlsanity.com/paper/2310.20561/) (2023)
- [Proactive Emergency Collision Avoidance for Automated Driving in Highway Scenarios](https://mlsanity.com/paper/2310.17381/) (2023)
- [VLM-UDMC: VLM-Enhanced Unified Decision-Making and Motion Control for Urban Autonomous Driving](https://mlsanity.com/paper/2507.15266/) (2025)
- [Myopically Verifiable Probabilistic Certificates for Safe Control and Learning](https://mlsanity.com/paper/2404.16883/) (2024)
- [Safe and Non-Conservative Trajectory Planning for Autonomous Driving Handling Unanticipated Behaviors of Traffic Participants](https://mlsanity.com/paper/2406.13396/) (2024)
- [Enhanced Safety in Autonomous Driving: Integrating Latent State Diffusion Model for End-to-End Navigation](https://mlsanity.com/paper/2407.06317/) (2024)
- [Identifying Reaction-Aware Driving Styles of Stochastic Model Predictive Controlled Vehicles by Inverse Reinforcement Learning](https://mlsanity.com/paper/2308.12069/) (2023)
- [Scalable Multi-modal Model Predictive Control via Duality-based Interaction Predictions](https://mlsanity.com/paper/2402.01116/) (2024)
- [Human-aligned Safe Reinforcement Learning for Highway On-Ramp Merging in Dense Traffic](https://mlsanity.com/paper/2503.02624/) (2025)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)

## Abstract (arXiv)

Automated vehicles require efficient and safe planning to maneuver in uncertain environments. Largely this uncertainty is caused by other traffic participants, e.g., surrounding vehicles. Future motion of surrounding vehicles is often difficult to predict. Whereas robust control approaches achieve safe, yet conservative motion planning for automated vehicles, Stochastic Model Predictive Control (SMPC) provides efficient planning in the presence of uncertainty. Probabilistic constraints are applied to ensure that the maximal risk remains below a predefined level. However, safety cannot be ensured as probabilistic constraints may be violated, which is not acceptable for automated vehicles. Here, we propose an efficient trajectory planning framework with safety guarantees for automated vehicles. SMPC is applied to obtain efficient vehicle trajectories for a finite horizon. Based on the first optimized SMPC input, a guaranteed safe backup trajectory is planned using reachable sets. This backup is used to overwrite the SMPC input if necessary for safety. Recursive feasibility of the safe SMPC algorithm is proved. Highway simulations show the effectiveness of the proposed method regarding performance and safety.