Robust Control Barrier-Value Functions for Safety-Critical Control.

This paper works towards merging two popular approaches in the control community for safety control: Hamilton-Jacobi (HJ) reachability analysis and Control Barrier Functions (CBFs). HJ Reachability has methods for direct construction of value functions that provide safety guarantees and safe controllers, however the online implementation can be overly conservative and/or rely on jumpy bang-bang control. The CBF community has methods for safe-guarding controllers in the form of point-wise optimization programs such as CBF-QP, where the CBF-based safety certificate is used as a constraint. However, finding a valid CBF for a general dynamical system is challenging. This paper merges these two methods by introducing a new reachability formulation inspired by the structure of CBFs that constructs a Control Barrier-Value Function (CBVF). We verify that CBVF is a viscosity solution to a novel Hamilton-Jacobi-Isaacs Variational Inequality and preserves the same safety guarantee as the original reachability formulation. Finally, we propose an online Quadratic Program formulation whose solution is always an optimal control signal, which is inspired by the CBF-QP. We demonstrate the benefit of using the CBVFs for double-integrator and Dubins car systems by comparing it to previous methods.