Constructive Barrier Certificates with Applications to Fixed-Wing Aircraft Collision Avoidance

In this paper we discuss how to construct a barrier certificate for a control affine system subject to actuator constraints. We motivate this discussion examining collision avoidance for fixed-wing aircraft. In particular, we show the theoretical development in this paper can be used to create a barrier certificate that can ensure that vehicles will not collide. We demonstrate in simulation how the constructed barrier certificate keeps vehicles at a safe distance from each other even though their nominal paths would otherwise cause collisions.