Successive Control Barrier Functions for Nonlinear Systems

We present the idea of successive control barrier functions for nonlinear (polynomial) control systems. Control Barrier Functions (CBFs) can be used to maintain safety properties for a system through the online modification of control inputs to ensure that the state remains inside a controlled invariant set that excludes a set of unsafe states. However, the synthesis of CBFs is quite difficult in practice, especially for nonlinear dynamical systems. Computationally inexpensive approaches employ relaxed control barrier conditions that result in relatively small control invariant sets. In turn, this can result in unnecessary modification of the nominal control input to keep the dynamics inside this set.