Optimal Control Barrier Functions: Maximizing the Action Space Subject to Control Bounds
<|reference_start|>Optimal Control Barrier Functions: Maximizing the Action Space Subject to Control Bounds: This letter addresses the constraint compatibility problem of control barrier functions (CBFs), which occurs when a safety-critical CBF requires a system to apply more control effort than it is capable of generating. This inevitably leads to a safety violation, which transitions the system to an unsafe (and possibly dangerous) trajectory. We resolve the constraint compatibility problem by constructing a control barrier function that maximizes the feasible action space for first and second-order constraints, and we prove that the optimal CBF encodes a dynamical motion primitive. Furthermore, we show that this dynamical motion primitive contains an implicit model for the future trajectory for time-varying components of the system. We validate our optimal CBF in simulation, and compare its behavior with a linear CBF.<|reference_end|>
@article{beaver2024optimal,
    title={Optimal Control Barrier Functions: Maximizing the Action Space Subject
  to Control Bounds},
    author={Logan E. Beaver},
    journal={arXiv preprint arXiv:2402.17694},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.17694},
    primaryClass={math.OC cs.SY eess.SY}
}