Contract-Based Control Synthesis with Barrier Functions for Vehicular Mission Planning

We present a compositional control synthesis method based on assume-guarantee contracts with application to correct-by-construction design of vehicular mission plans. In our approach, a mission-level specification expressed in a fragment of signal temporal logic (STL) is decomposed into formulas whose predicates are defined on non-overlapping time intervals. The STL formulas are then mapped to aggregations of contracts associated with continuously differentiable time-varying control barrier functions. The barrier functions are used to constrain the lower-level control synthesis problem, which is solved via quadratic programming. Our approach can mitigate the conservatism of previous methods for task-driven control based on under-approximations. We illustrate its effectiveness on a case study motivated by vehicular mission planning under safety constraints as well as constraints imposed by traffic regulations under vehicle-to-vehicle and vehicle-to-infrastructure communication.