Trust your supervisor: quadrotor obstacle avoidance using controlled invariant sets

Supervision of a nominal controller, to enforce safety, is concerned with appropriately modifying the generated control inputs, if needed, in order to keep a control system within a set of safe states. An integral component in supervision is a controlled invariant set contained in the set of safe states. In this paper, we build on recent results on the computation of polytopic controlled invariant sets to present a supervision framework that computes the corrected inputs analytically and, hence, suitable for real-time control. The framework is validated on the task of quadrotor obstacle avoidance by forcing the vehicle to navigate within controlled invariant sets of the obstacle-free space. The results are experimentally demonstrated on a Crazyflie 2.0 quadrotor.