Barrier Functions: Bridging the Gap between Planning from Specifications and Safety-Critical Control

Real-life control systems are hierarchies of interacting layers; often consisting of a planning layer, a trajectory generation layer, and a trajectory-following layer. Independently designing the layers without taking the interactions between layers into account makes it difficult to obtain safety guarantees when executing a high-level plan. In this paper we combine ideas from safety-critical control and high-level policy synthesis to develop a principled connection between a high-level planner in a low-dimensional space, and a low-level safety-critical controller acting in the full state space. We introduce a new type of simulation relation and show that barrier functions can be used to abstract a high-dimensional system via the relation. As a result, we obtain provably correct execution of high-level policies by low-level optimization-based controllers. The results are demonstrated with a quadrotor surveillance example.