## 1 Introduction  
In recent years, the advantages of multi-agent systems (MASs) over individual agents [1] have become increasingly prominent. MASs are characterized by significantly higher working efficiency and enhanced compatibility, which have attracted extensive attention from researchers in various fields. In the realm of practical engineering, with the exponential growth of network information and the increasing complexity of missions, the coordination control of multiple mobile robots [2] multiple unmanned aerial vehicles [3] and multiple marine surface vehicles [4] has emerged as a crucial research area. These multi-agent systems play a vital role in modern engineering applications, such as industrial automation, intelligent transportation, and marine exploration. For multi-agent formation tracking control, the core goal is to enable multiple agents to collaboratively track a target while moving in a coordinated manner to maintain a predefined formation geometry. This not only requires precise motion control of each agent but also effective communication and cooperation among them. In this process, maintaining connectivity and avoiding collisionsare not only challenging aspects but also fundamental requirements for the stable operation of the multi-agent system. Ensuring seamless communication between robots to maintain connectivity is essential for coordinated movement, while collision-avoidance mechanisms are crucial to prevent potential accidents and ensure the safety and efficiency of the entire system. In the field of multi-agent formation control, a diverse array of strategies has been developed, each with its own unique characteristics and applications. Prominent among these are the leader-follower strategy [5], behavior-based strategy [6], and virtual structure strategy [7]. The leader-follower strategy stands out as one of the most widely adopted and fundamental approaches. Its popularity can be attributed to its simplicity and efficiency. In a leader-follower system, each follower robot only needs to focus on perceiving the information transmitted by its adjacent leader. This significantly reduces the computational burden on individual robots, as they are not required to process a vast amount of data related to the entire external environment. NMRs' formation control has become a hot research topic due to its important applications in all aspects, such as target searching, environmental monitoring, resource exploring, and area data acquiring. Therefore, a large number of consensus control issues have been reported [8; 9; 10; 11; 12; 13; 14; 15; 16]. In [9], the trajectory tracking problem in the formation control of robots was studied. The authors in [10] proposed the angle-constrained-based adaptive formation shape and maneuvering control for NMRs, respectively. The result in [11] suggested a solution for the formation problem using full consensus in torque-controlled NMRs, accounting for the absence of velocity measurements and time-varying communication delays. In earlier studies, most scholars did not consider the internal dynamics of robots. To solve this problem, the use of fuzzy logic systems (FLSs) is a very effective method [17; 18; 19; 20]. Hence, for unicycle-type mobile robots, a leader-follower (L-F) formation control protocol was proposed in [16]. In [17], the formation control problem of NMRs with unknown dead zones was studied. The results in [18] show the feasibility of the finite-time neural network adaptive control scheme based on dynamic surface technique. For high-order nonlinear systems, [19] proposed a robust fuzzy adaptive finite-time control scheme. In practice, the limitations of the speed and position of the NMRs are often overlooked. The running speed and distance between NMRs should be kept within a certain range. The constraints of the robot velocity variables are just as important as the constraints of the output variables, and it makes sense to consider the full-state constraints when designing the controller.