Continuous-time Signal Temporal Logic Planning with Control Barrier Functions

Temporal Logic (TL) guided control problems have gained enormous interests in recent years. A wide range of properties, such as liveness and safety, can be specified through TL. On the other hand, Control Barrier Functions (CBF) have shown success in the context of safety critical applications that require constraints on the system states. In this paper, we consider linear cyber-physical systems with continuous dynamics, where controls are generated by digital computers in discrete time. We propose an offline trajectory planner for such systems subject to linear constraints given as Signal Temporal Logic (STL) formulas. The proposed planner is based on a Mixed Integer Quadratic Programming (MIQP) formulation that utilizes CBFs to produce system trajectories that are valid in continuous time; moreover we allow STL predicates with arbitrary time constraints, in which asynchronous control updates are allowed. We validate our theoretical results through numerical simulations.