Receding Horizon CBF-Based Multi-Layer Controllers for Safe Trajectory Generation

In this paper, we present a safe trajectory generation strategy for multi-layer control architectures. We develop a high-level, continuous-time trajectory generation strategy based on optimal control, which ensures the satisfaction of safety-critical constraints via Control Barrier Functions (CBFs). The proposed strategy leverages a receding horizon CBF-based optimal control problem formulation that, as the prediction horizon goes to infinity, generates system trajectories equivalent to the solution of the original (constrained) optimal control problem. Conversely, as the horizon approaches zero, the resulting trajectory is equivalent to the one obtained by applying a safety filter to the optimal (unconstrained) controller. Instrumental to our results is a novel characterization of CBFs in the context of control invariance of safe sets. The proposed approach is realized through a multi-layer implementation on a unicycle system in the context of autonomous navigation.