Safety from Fast, In-the-Loop Reachability with Application to UAVs

We present a runtime assurance (RTA) mechanism for ensuring safety of a controlled dynamical system and an application to collision avoidance of two unmanned aerial vehicles (UAVs). We consider a dynamical system controlled by an unverified and potentially unsafe primary controller that might, e.g., lead to collision. The proposed RTA mechanism computes at each time the reachable set of the system under a backup control law. We then develop a novel optimization problem based on control barrier functions that filters the primary controller when necessary in order to keep the system's reachable set within reach of a known, but conservative, safe region. The theory of mixed monotone systems is leveraged for efficient reachable set computation and to achieve a tractable optimization formulation. We demonstrate the proposed RTA mechanism on a dual multirotor UAV case study which requires a fast controller update rate as a result of the small time-scale rotational dynamics. In implementation, the algorithm computes the reachable set of an eight dimensional dynamical system in less than five milliseconds and solves the optimization problem in under one millisecond, yielding a controller update rate of 100Hz.