# Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function

arXiv: https://arxiv.org/abs/2007.11718 · HTML: https://mlsanity.com/paper/2007.11718/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2020.

## Built on by (most cited first, 30 of 49)

- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violations](https://mlsanity.com/paper/2108.01846/) (2021)
- [Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.15512/) (2023)
- [Online Control Barrier Functions for Decentralized Multi-Agent Navigation](https://mlsanity.com/paper/2303.04313/) (2023)
- [Model-based Dynamic Shielding for Safe and Efficient Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2304.06281/) (2023)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [CBF-LLM: Safe Control for LLM Alignment](https://mlsanity.com/paper/2408.15625/) (2024)
- [Multi-Agent Reinforcement Learning Guided by Signal Temporal Logic Specifications](https://mlsanity.com/paper/2306.06808/) (2023)
- [Reinforcement Learning-based Receding Horizon Control using Adaptive Control Barrier Functions for Safety-Critical Systems](https://mlsanity.com/paper/2403.17338/) (2024)
- [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)
- [Autonomous Navigation of Underactuated Bipedal Robots in Height-Constrained Environments](https://mlsanity.com/paper/2109.05714/) (2021)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Model-Based Safe Reinforcement Learning with Time-Varying State and Control Constraints: An Application to Intelligent Vehicles](https://mlsanity.com/paper/2112.11217/) (2021)
- [Neural Potential Field for Obstacle-Aware Local Motion Planning](https://mlsanity.com/paper/2310.16362/) (2023)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety](https://mlsanity.com/paper/2407.00616/) (2024)
- [Agile Decision-Making and Safety-Critical Motion Planning for Emergency Autonomous Vehicles](https://mlsanity.com/paper/2409.08665/) (2024)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Probabilistically safe and efficient model-based reinforcement learning](https://mlsanity.com/paper/2504.00626/) (2025)
- [Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environments](https://mlsanity.com/paper/2508.03428/) (2025)
- [Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocation](https://mlsanity.com/paper/2305.13467/) (2023)
- [Certificated Actor-Critic: Hierarchical Reinforcement Learning with Control Barrier Functions for Safe Navigation](https://mlsanity.com/paper/2501.17424/) (2025)
- [ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworks](https://mlsanity.com/paper/2509.16614/) (2025)
- [Meta-Reinforcement Learning for Robust and Non-greedy Control Barrier Functions in Spacecraft Proximity Operations](https://mlsanity.com/paper/2602.07335/) (2026)
- [Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Merging](https://mlsanity.com/paper/2212.00618/) (2022)
- [Online Efficient Safety-Critical Control for Mobile Robots in Unknown Dynamic Multi-Obstacle Environments](https://mlsanity.com/paper/2402.16449/) (2024)
- [Socially-Aware Shared Control Navigation for Assistive Mobile Robots in the Built Environment](https://mlsanity.com/paper/2405.17279/) (2024)
- [Safe model-based Reinforcement Learning via Model Predictive Control and Control Barrier Functions](https://mlsanity.com/paper/2512.04856/) (2025)
- [Learning Safety-Guaranteed, Non-Greedy Control Barrier Functions Using Reinforcement Learning](https://mlsanity.com/paper/2602.00366/) (2026)
- [CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environments](https://mlsanity.com/paper/2603.06921/) (2026)

## Abstract (arXiv)

The optimal performance of robotic systems is usually achieved near the limit of state and input bounds. Model predictive control (MPC) is a prevalent strategy to handle these operational constraints, however, safety still remains an open challenge for MPC as it needs to guarantee that the system stays within an invariant set. In order to obtain safe optimal performance in the context of set invariance, we present a safety-critical model predictive control strategy utilizing discrete-time control barrier functions (CBFs), which guarantees system safety and accomplishes optimal performance via model predictive control. We analyze the stability and the feasibility properties of our control design. We verify the properties of our method on a 2D double integrator model for obstacle avoidance. We also validate the algorithm numerically using a competitive car racing example, where the ego car is able to overtake other racing cars.