mlsanityData to 7 Oct 2026

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

arXiv 2007.11718 ↗First posted 22 Jul 2020eess.SY cs.RO cs.SYcited by 42

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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.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). First posted on arXiv 22 Jul 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 7; 2024: 10; 2025: 10; 2026: 5.

42 papers.

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  1. 2021Safe Reinforcement Learning Using Robust Control Barrier Functionscited by 44
  2. 2021Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violationscited by 36
  3. 2023Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Modelscited by 13
  4. 2023Model-based Dynamic Shielding for Safe and Efficient Multi-Agent Reinforcement Learningcited by 11
  5. 2023Online Control Barrier Functions for Decentralized Multi-Agent Navigationcited by 10
  6. 2022Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environmentscited by 8
  7. 2024CBF-LLM: Safe Control for LLM Alignmentcited by 8
  8. 2023Multi-Agent Reinforcement Learning Guided by Signal Temporal Logic Specificationscited by 6
  9. 2021Autonomous Navigation of Underactuated Bipedal Robots in Height-Constrained Environmentscited by 5
  10. 2024MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safetycited by 5
  11. 2023Neural Potential Field for Obstacle-Aware Local Motion Planningcited by 4
  12. 2021Model-Based Safe Reinforcement Learning with Time-Varying State and Control Constraints: An Application to Intelligent Vehiclescited by 3
30 more
  1. 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Modelscited by 3
  2. 2024Reinforcement Learning-based Receding Horizon Control using Adaptive Control Barrier Functions for Safety-Critical Systemscited by 3
  3. 2024DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safetycited by 3
  4. 2024Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environmentscited by 3
  5. 2025Residual Neural Terminal Constraint for MPC-based Collision Avoidance in Dynamic Environmentscited by 3
  6. 2024Agile Decision-Making and Safety-Critical Motion Planning for Emergency Autonomous Vehiclescited by 2
  7. 2025ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworkscited by 2
  8. 2022Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functionscited by 1
  9. 2022Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Mergingcited by 1
  10. 2023Risk-aware Safe Control for Decentralized Multi-agent Systems via Dynamic Responsibility Allocationcited by 1
  11. 2024Online Efficient Safety-Critical Control for Mobile Robots in Unknown Dynamic Multi-Obstacle Environmentscited by 1
  12. 2024Socially-Aware Shared Control Navigation for Assistive Mobile Robots in the Built Environmentcited by 1
  13. 2026CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environmentscited by 1
  14. 2026Learning Predictive Control with Deep Koopman Operators for Autonomous Vehicle Motion Planningcited by 1
  15. 2022Phy-Taylor: Physics-Model-Based Deep Neural Networkscited by 0
  16. 2022Safe Control and Learning Using Generalized Action Governorcited by 0
  17. 2023Adaptive Aggregation for Safety-Critical Controlcited by 0
  18. 2024SOMTP: Self-Supervised Learning-Based Optimizer for MPC-Based Safe Trajectory Planning Problems in Roboticscited by 0
  19. 2024Dynamic Neural Potential Field: Online Trajectory Optimization in the Presence of Moving Obstaclescited by 0
  20. 2025Certificated Actor-Critic: Hierarchical Reinforcement Learning with Control Barrier Functions for Safe Navigationcited by 0
  21. 2025Barrier Function Overrides For Non-Convex Fixed Wing Flight Control and Self-Driving Carscited by 0
  22. 2025Risk-Aware Safe Reinforcement Learning for Control of Stochastic Linear Systemscited by 0
  23. 2025Sample Efficient Certification of Discrete-Time Control Barrier Functionscited by 0
  24. 2025Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barrierscited by 0
  25. 2025Control Barrier Function for Aligning Large Language Modelscited by 0
  26. 2025PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehiclescited by 0
  27. 2025LA-RL: Language Action-guided Reinforcement Learning with Safety Guarantees for Autonomous Highway Drivingcited by 0
  28. 2026PC-Diffuser: Path-Consistent Capsule CBF Safety Filtering for Diffusion-Based Trajectory Plannercited by 0
  29. 2026Response-Aware Risk-Constrained Control Barrier Function With Application to Vehiclescited by 0
  30. 2026SRL-MPC: Shape-Aware Reinforcement Learned Model Predictive Controlcited by 0