Safety Under Uncertainty: Tight Bounds with Risk-Aware Control Barrier Functions

Abstract

We propose a novel class of risk-aware control barrier functions (RA-CBFs) for the control of stochastic safety-critical systems. Leveraging a result from the stochastic level-crossing literature, we deviate from the martingale theory that is currently used in stochastic CBF techniques and prove that a RA-CBF based control synthesis confers a tighter upper bound on the probability of the system becoming unsafe within a finite time interval than existing approaches. We highlight the advantages of our proposed approach over the state-of-the-art via a comparative study on an mobile-robot example, and further demonstrate its viability on an autonomous vehicle highway merging problem in dense traffic.

arXiv comment7 pages, 4 figures, 5 tables, accepted at ICRA 2023

References in corpus (7)

• Congested Traffic States in Empirical Observations and Microscopic Simulations
• Control Barrier Function Based Quadratic Programs for Safety Critical Systems
• Adaptive Safety with Control Barrier Functions
• Multi-Robot Collision Avoidance under Uncertainty with Probabilistic Safety Barrier Certificates
• Probabilistic Safety Constraints for Learned High Relative Degree System Dynamics
• Wasserstein Control of Mirror Langevin Monte Carlo
• Fixed-Time Parameter Adaptation for Safe Control Synthesis