Introduction

As an aerial platform, UAV has been widely used to execute forest fire monitoring (Yuan et al. (J Intell Robot Syst 88:635–654, 2017), Yuan et al. (J Intell Robot Syst 93:337–349, 2019), Yuan et al. (Can J For Res 45:783–792, 2015)), search and rescue (Erdos et al. (IEEE Trans Aerosp Electron Syst 28(5):32–37, 2013)), powerline/pipeline inspection (Li et al. (Knowledge-based power line detection for UAV surveillance and inspection systems. In International Conference Image and Vision Computing, Christchurch, New Zealand, 2008)), and reconnaissance and surveillance (Deng et al. (J Commun 9:687–692, 2014)) tasks by equipping task-oriented payloads. Due to the limited coverage and payload capabilities, single UAV usually fails to provide wide-area observation and fine-grained information. To solve this difficult problem, multi-UAVs have been deployed to cooperatively execute the difficult tasks, thus significantly improving the task efficiency. As one of the crucial units to ensure the formation flight safety of multi-UAVs, the cooperative control module embedded in each UAV receives the states from neighboring UAVs and generates the control actions for regulating the cooperative behaviors. Recently, leader-following, behavior-based, virtual structure, collision avoidance, and algebraic graph methods have been used to design effective formation control methods (Zhang and Mehrjerdi (A survey on multiple unmanned vehicles formation control and coordination: Normal and fault situations. In International conference on unmanned aircraft systems (ICUAS), Atlanta, USA, 2013)). Moreover, by considering the wake vortices among UAVs in the formation team, close formation control methods are also investigated to keep the relative positions for avoiding the collisions (Pachter et al. (J Guidance Control Dyn 24(2):246–254, 2001), Riceand et al. (Int J Aerosp Eng, 2016:15, 2016), Shan and Liu (J Guidance Control Dyn 28(6):1316–1320, 2005), Zhang and Liu (Robust design of close formation flight control via uncertainty and disturbance estimator. In AIAA Guidance, Navigation, and Control Conference, California, USA, 2016)). It should be pointed out that these aforementioned results mainly focus on the development of cooperative control methods for multi-UAVs without the consideration of unexpected situations, such as in-flight faults and disturbances.