## 1 Introduction
### Related Work  
Formation control, which is one of the most actively studied topics in the field of multi-agent systems, generally aims to drive multiple agents to achieve prescribed geometric constraints on their states [12]. [PERSON] et al. categorized the existing results on formation control into position-, displacement-, and distance-based according to types of sensed and controlled variables [12]. Under position-based control schemes, the agents sense and control their own positions concerning a global coordinate system to achieve the desired formation. Under displacement-based control schemes, the agents sense and control the relative positions of neighbors. As for the distance-based control scheme, the inter-agent distances are actively controlled, and the individual agent is assumed to be able to sense the relative positions of its neighbor. [PERSON] et al. proposed a position-based formation control scheme and applied it to coordinate the movements of multiple mobile robots [13]. [PERSON] et al. proposed the distance-based adaptive formation control laws for the leader-follower system. In [14], the developed controller enables all the agents to maintain the formation group and move with a constant reference velocity in a plane. Note that displacement-based formation control usually requires a balanced capability of sensing and communication for practical application. [PERSON] and [PERSON] studied connectivity preservation in displacement-based formation control. By adding appropriate weights to the edges in the graphs, they guarantee the connectivity of the network [15]. [PERSON] et al. studied the input-to-state stability of displacement-based formation control systems with directed and acyclic interaction topology [16]. Based on the Jacobi over-relaxation algorithm, [PERSON] has proposed a displacement-based formation control algorithm for single-integrator modeled agents in discrete-time domain [17]. Flocking control is a special category of formation control inspired by biological behavior and is also defined as behavior-based formation control [9]. Like some animal swarms, each individual in a multi-robot system will independently analyze the information and make actions based on local observations. Inspired by bird flocks, [PERSON] [9] first proposed three basic rules for flocking: collision avoidance, velocity matching, and flock centering. Based on these three basic rules, many valuable research works have been conducted. [PERSON] et al. investigated the orientation consistency of discrete-time model agents based on velocity matching rules. In [PERSON]'s model, the agents move at roughly the same velocity under noise interference, and the motion state of individual updates according to the average value of the agent and its neighbors' motion directions [18]. By introducing the vector field, [PERSON] et al. implemented a circular formation of fixed-wing unmanned aerial vehicles [19]. Based on noncooperative (defective or malicious) robots, [PERSON] et al. presented a resilient flocking algorithm for mobile robot swarms [20]. Some other works concentrate on the interactions and topologies in robot swarms. Based on the locust-inspired case study of coherently marching agents, [PERSON] et al. have investigated the balance between social feedback and noise as well as the relationship with collective coherence [21]. Moreover, they have demonstrated that the motif type constituting the networks has a paramount influence on group decision-making that cannot be explained solely in terms of degree distribution [22]. Besides, they have also suggested that the scale-free networks could accelerate building up a rapid collective response to cope with the environmental changes [23]. Although there has been a lot of work on flocking control, few researchers have focused on the swarm robustness in the procedure of flocking. Many researchers have devoted their efforts to implementing control strategies for large-scale swarms, where robots are often assumed to be cheap and fragile [24; 25].