# Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functions

arXiv: https://arxiv.org/abs/2502.15006 · HTML: https://mlsanity.com/paper/2502.15006/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 92 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 30 of 51)

- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review](https://mlsanity.com/paper/1805.00909/) (2018)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Deep Dynamics Models for Learning Dexterous Manipulation](https://mlsanity.com/paper/1909.11652/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [DeepReach: A Deep Learning Approach to High-Dimensional Reachability](https://mlsanity.com/paper/2011.02082/) (2020)
- [Information Theoretic Model Predictive Control: Theory and Applications to Autonomous Driving](https://mlsanity.com/paper/1707.02342/) (2017)
- [Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificates](https://mlsanity.com/paper/2101.05436/) (2021)
- [Agile But Safe: Learning Collision-Free High-Speed Legged Locomotion](https://mlsanity.com/paper/2401.17583/) (2024)
- [Adversarial camera stickers: A physical camera-based attack on deep learning systems](https://mlsanity.com/paper/1904.00759/) (2019)
- [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021)
- [Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learning](https://mlsanity.com/paper/2112.12288/) (2021)
- [STORM: An Integrated Framework for Fast Joint-Space Model-Predictive Control for Reactive Manipulation](https://mlsanity.com/paper/2104.13542/) (2021)
- [How to Train Your Neural Control Barrier Function: Learning Safety Filters for Complex Input-Constrained Systems](https://mlsanity.com/paper/2310.15478/) (2023)
- [Variational Inference MPC for Bayesian Model-based Reinforcement Learning](https://mlsanity.com/paper/1907.04202/) (2019)
- [Model-Predictive Control via Cross-Entropy and Gradient-Based Optimization](https://mlsanity.com/paper/2004.08763/) (2020)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence](https://mlsanity.com/paper/2106.15980/) (2021)
- [Solving Stabilize-Avoid Optimal Control via Epigraph Form and Deep Reinforcement Learning](https://mlsanity.com/paper/2305.14154/) (2023)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [GCBF+: A Neural Graph Control Barrier Function Framework for Distributed Safe Multi-Agent Control](https://mlsanity.com/paper/2401.14554/) (2024)
- [High-Accuracy Low-Precision Training](https://mlsanity.com/paper/1803.03383/) (2018)
- [Physical Adversarial Attacks For Camera-based Smart Systems: Current Trends, Categorization, Applications, Research Challenges, and Future Outlook](https://mlsanity.com/paper/2308.06173/) (2023)
- [Robust Model Predictive Path Integral Control: Analysis and Performance Guarantees](https://mlsanity.com/paper/2102.09027/) (2021)
- [L1-Adaptive MPPI Architecture for Robust and Agile Control of Multirotors](https://mlsanity.com/paper/2004.00152/) (2020)
- [Nonlinear MPC for Collision Avoidance and Controlof UAVs With Dynamic Obstacles](https://mlsanity.com/paper/2008.00792/) (2020)
- [Verification and Synthesis of Control Barrier Functions](https://mlsanity.com/paper/2104.14001/) (2021)
- [Variational Inference MPC using Normalizing Flows and Out-of-Distribution Projection](https://mlsanity.com/paper/2205.04667/) (2022)

## Built on by (most cited first, 1 of 1)

- [A Control Barrier Function-Constrained Model Predictive Control Framework for Safe Reinforcement Learning](https://mlsanity.com/paper/2604.06463/) (2026)

## Abstract (arXiv)

A common problem when using model predictive control (MPC) in practice is the satisfaction of safety specifications beyond the prediction horizon. While theoretical works have shown that safety can be guaranteed by enforcing a suitable terminal set constraint or a sufficiently long prediction horizon, these techniques are difficult to apply and thus are rarely used by practitioners, especially in the case of general nonlinear dynamics. To solve this problem, we impose a tradeoff between exact recursive feasibility, computational tractability, and applicability to ``black-box'' dynamics by learning an approximate discrete-time control barrier function and incorporating it into a variational inference MPC (VIMPC), a sampling-based MPC paradigm. To handle the resulting state constraints, we further propose a new sampling strategy that greatly reduces the variance of the estimated optimal control, improving the sample efficiency, and enabling real-time planning on a CPU. The resulting Neural Shield-VIMPC (NS-VIMPC) controller yields substantial safety improvements compared to existing sampling-based MPC controllers, even under badly designed cost functions. We validate our approach in both simulation and real-world hardware experiments. Project website: https://mit-realm.github.io/ns-vimpc/.