# Multi-Step Model Predictive Safety Filters: Reducing Chattering by Increasing the Prediction Horizon

arXiv: https://arxiv.org/abs/2309.11453 · HTML: https://mlsanity.com/paper/2309.11453/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 29 references that are in the map.
- First posted on arXiv 20 Sep 2023.

## Builds on (most cited first, 16 of 16)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Solving Rubik's Cube with a Robot Hand](https://mlsanity.com/paper/1910.07113/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Learning-based Model Predictive Control for Safe Exploration](https://mlsanity.com/paper/1803.08287/) (2018)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Automatic Instrument Segmentation in Robot-Assisted Surgery Using Deep Learning](https://mlsanity.com/paper/1803.01207/) (2018)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Linear model predictive safety certification for learning-based control](https://mlsanity.com/paper/1803.08552/) (2018)
- [A predictive safety filter for learning-based racing control](https://mlsanity.com/paper/2102.11907/) (2021)
- [SABLAS: Learning Safe Control for Black-box Dynamical Systems](https://mlsanity.com/paper/2201.01918/) (2022)
- [A computationally efficient robust model predictive control framework for uncertain nonlinear systems -- extended version](https://mlsanity.com/paper/1910.12081/) (2019)
- [Zeus: A System Description of the Two-Time Winner of the Collegiate SAE AutoDrive Competition](https://mlsanity.com/paper/2004.08752/) (2020)
- [Barrier Bayesian Linear Regression: Online Learning of Control Barrier Conditions for Safety-Critical Control of Uncertain Systems](https://mlsanity.com/paper/2204.03801/) (2022)
- [Robust Predictive Output-Feedback Safety Filter for Uncertain Nonlinear Control Systems](https://mlsanity.com/paper/2212.08900/) (2022)

## Built on by (most cited first, 5 of 5)

- [Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents](https://mlsanity.com/paper/2410.11671/) (2024)
- [Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learning](https://mlsanity.com/paper/2604.13192/) (2026)
- [Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvements](https://mlsanity.com/paper/2508.01833/) (2025)
- [Who Plays First? Optimizing the Order of Play in Stackelberg Games with Many Robots](https://mlsanity.com/paper/2402.09246/) (2024)
- [When the Governor Becomes the Disturbance: Control-Generated Disturbance and Cost-Aware Backoff in Governed Tool-Using Agents](https://mlsanity.com/paper/2610.09037/) (2026)

## Abstract (arXiv)

Learning-based controllers have demonstrated superior performance compared to classical controllers in various tasks. However, providing safety guarantees is not trivial. Safety, the satisfaction of state and input constraints, can be guaranteed by augmenting the learned control policy with a safety filter. Model predictive safety filters (MPSFs) are a common safety filtering approach based on model predictive control (MPC). MPSFs seek to guarantee safety while minimizing the difference between the proposed and applied inputs in the immediate next time step. This limited foresight can lead to jerky motions and undesired oscillations close to constraint boundaries, known as chattering. In this paper, we reduce chattering by considering input corrections over a longer horizon. Under the assumption of bounded model uncertainties, we prove recursive feasibility using techniques from robust MPC. We verified the proposed approach in both extensive simulation and quadrotor experiments. In experiments with a Crazyflie 2.0 drone, we show that, in addition to preserving the desired safety guarantees, the proposed MPSF reduces chattering by more than a factor of 4 compared to previous MPSF formulations.