# Resilient Formation Reconfiguration for Leader-Follower Multi-UAVs
## 1 Introduction  
Compared with individual intelligence [1], the power contained in swarm intelligence has been increasingly utilized in recent years [2; 3; 4; 5; 6; 7]. Accordingly, the unmanned aerial vehicle (UAV) swarm, as one modern distributed system, has been extensively applied to numerous fields. For instance, multiple unmanned aerial vehicles (multi-UAVs) have broad uses in military actions, such as surveillance, reconnaissance, and strikes, as well as some civilian scenarios including performance and rescue [8]. It should be noted that the majority of the tasks mentioned above are executed on the basis of the formation control of the multi-UAVs, which has a tremendous influence on the performance of the whole distributed system. Formation control for multi-UAVs refers to the fact that a group of UAVs can form and maintain a specific geometry in order to collaboratively accomplish a series of goals and can adapt to changes in the external environment by adjusting the geometry [9; 10; 11]. In general, formation control can be divided into three phases: the initial formation phase, the formation maintenance phase, and the formation reconfiguration phase-the last phase has the most complexity and challenges. To the best of our knowledge, the majority of the existing research on formation reconfiguration for multi-UAVs is based on the assumptionof a fixed swarm size. Nonetheless, in actual flights, it is common for some members to disengage from the swarm due to accidents such as communication failure or physical damage. Meanwhile, it is also not uncommon for UAVs to leave or join the formation for mission changes. Under the aforementioned circumstances where the number of members is dynamic, multi-UAVs of good robustness are required to reconfigure the formation in a timely manner in accordance with the required tactics. Therefore, it is of practical significance to investigate the problems of formation reconfiguration for multi-UAVs under the condition of a dynamic swarm scale. For simplicity and good control, the leader-follower architecture is widely applied to the formation control of multi-UAVs [12; 13; 14]. However, the architecture is dependent on the leader so that the entire swarm is more inclined to collapse or become out of control if the leader has a communication failure or is unexpectedly shot down by the enemy [15]. When such accidents occur, adopting appropriate policies to select a new leader for the impaired multi-UAVs is required so that the expected geometry can be reformed. A hasty countermeasure of randomly appointing a member as the new leader can bring about disastrous consequences. The kinematic-information-based leader election mechanism proposed in [16] can be an effective method. Compared to single source information, electing the leader with the help of the information from multiple sources can be another feasible solution, which can synthesize the kinematic information and the non-kinematic information of each UAV to make decisions with more accuracy and reliability. As an uncertainty inference approach, the evidential reasoning (ER) rule can effectively fuse qualitative knowledge and quantitative data from multiple information sources in an explicable way. In comparison, the ER rule avoids the harsh a priori probability conditions of Bayesian inference and overcomes the defect of Dempster-Shafer evidence theory that cannot cope with conflicting evidence. With the superior ability to represent unknowns and uncertainties, the ER rule has been widely used to deal with the problems of multi-attribute decision analysis (MADA) [17; 18]. With the development of evidence theory, the belief rule base (BRB), an expert system capable of tolerating uncertainties, was created [19; 20]. The system contains a group of belief rules with some additional parameters determined by expert knowledge and uses the algorithm based on the ER rule as the core inference engine. This allows for good interpretability when using the BRB method for both the model structure and inference process.