Composition of Safety Constraints With Applications to Decentralized Fixed-Wing Collision Avoidance

In this paper we discuss how to construct a barrier certificate for a control affine system subject to actuator constraints and motivate this discussion by examining collision avoidance for fixed-wing unmanned aerial vehicles (UAVs). In particular, the theoretical development in this paper is used to create a barrier certificate that ensures that two UAVs will not collide for all future times assuming the vehicles start in a safe starting configuration. We then extend this development by discussing how to ensure that multiple safety constraints are simultaneously satisfied in a decentralized manner (e.g., ensure robot distances are above some threshold for all pairwise combinations of UAVs for all future times) while ensuring output actuator commands are within specified limits. We validate the theoretical developments of this paper in the simulator SCRIMMAGE with a simulation of 20 UAVs that maintain safe distances from each other even though their nominal paths would otherwise cause a collision.