Hybrid Control Barrier Functions for Continuous-Time Systems

Control barrier functions (CBFs) enable constraint satisfaction in controlled dynamical systems, by mapping state constraints into state-dependent input constraints. This article investigates the use of hybrid CBF formulations for constraint satisfaction in continuous-time systems. Augmenting CBFs with logic variables enables solving control problems that are not solvable by continuous, or even discontinuous, control. Examples include robust deadlock resolution for vehicles moving in the presence of bounded obstacles, and robust obstacle avoidance for nonholonomic vehicles required to maintain a nonzero forward speed. A recursive procedure for constructing hybrid high-order CBFs is proposed, thereby extending hybrid CBFs to systems with high-order safety constraints. The theoretical results are illustrated by several examples.