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.

翻译：在本文中,我们讨论了如何为受激励因素制约的控制方块系统建造障碍证书,并通过审查固定翼无人驾驶航空器(无人驾驶航空器)避免碰撞的情况来推动这一讨论,特别是,本文件的理论发展被用于创建障碍证书,确保假定车辆以安全起始配置开始,今后所有时间,两架无人驾驶航空器不会相撞,在今后所有时间,确保机器人距离超过无人驾驶航空器所有对称组合的某些阈值,同时确保产出动因指令在规定的限度内;我们用20架无人驾驶航空器的模拟模型验证了模拟文件的理论发展,这些模拟模型保持了彼此之间的安全距离,即使其名义路径否则会造成碰撞,也保持了彼此之间的安全距离。