# A predictive safety filter for learning-based racing control

arXiv: https://arxiv.org/abs/2102.11907 · HTML: https://mlsanity.com/paper/2102.11907/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2021.

## Built on by (most cited first, 20 of 20)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
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- [Discrete GCBF Proximal Policy Optimization for Multi-agent Safe Optimal Control](https://mlsanity.com/paper/2502.03640/) (2025)
- [MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safety](https://mlsanity.com/paper/2409.13867/) (2024)
- [Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon](https://mlsanity.com/paper/2309.11453/) (2023)
- [Safe multi-agent motion planning under uncertainty for drones using filtered reinforcement learning](https://mlsanity.com/paper/2311.00063/) (2023)
- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)
- [Learning-Aided Warmstart of Model Predictive Control in Uncertain Fast-Changing Traffic](https://mlsanity.com/paper/2310.02918/) (2023)
- [Drive Fast, Learn Faster: On-Board RL for High Performance Autonomous Racing](https://mlsanity.com/paper/2505.07321/) (2025)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [Driving from Vision through Differentiable Optimal Control](https://mlsanity.com/paper/2403.15102/) (2024)
- [A Survey of Reinforcement Learning-Based Motion Planning for Autonomous Driving: Lessons Learned from a Driving Task Perspective](https://mlsanity.com/paper/2503.23650/) (2025)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [Modular Control Architecture for Safe Marine Navigation: Reinforcement Learning and Predictive Safety Filters](https://mlsanity.com/paper/2312.01855/) (2023)
- [Safe Reinforcement Learning with a Predictive Safety Filter for Motion Planning and Control: A Drifting Vehicle Example](https://mlsanity.com/paper/2506.22894/) (2025)
- [Hamilton-Jacobi Reachability-Based Safe Reinforcement Learning for Emergency Collision Avoidance](https://mlsanity.com/paper/2606.15311/) (2026)
- [Safe and Generalizable Hierarchical Multi-Agent RL via Constraint Manifold Control](https://mlsanity.com/paper/2606.24010/) (2026)
- [End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers](https://mlsanity.com/paper/2607.20674/) (2026)
- [Guided Riemannian Optimization (GuRO): Bridging Model Predictive Control and Decision Transformers](https://mlsanity.com/paper/2608.23204/) (2026)

## Abstract (arXiv)

The growing need for high-performance controllers in safety-critical applications like autonomous driving has been motivating the development of formal safety verification techniques. In this paper, we design and implement a predictive safety filter that is able to maintain vehicle safety with respect to track boundaries when paired alongside any potentially unsafe control signal, such as those found in learning-based methods. A model predictive control (MPC) framework is used to create a minimally invasive algorithm that certifies whether a desired control input is safe and can be applied to the vehicle, or that provides an alternate input to keep the vehicle in bounds. To this end, we provide a principled procedure to compute a safe and invariant set for nonlinear dynamic bicycle models using efficient convex approximation techniques. To fully support an aggressive racing performance without conservative safety interventions, the safe set is extended in real-time through predictive control backup trajectories. Applications for assisted manual driving and deep imitation learning on a miniature remote-controlled vehicle demonstrate the safety filter's ability to ensure vehicle safety during aggressive maneuvers.