## 1 Introduction  
Due to the widespread practical applications of multi-agent systems (MASs) in various fields such as material transportation, environmental detection and civilian tasks, they have attracted the attention of many scholars in the past few decades, and many achievements have been made in the research of MASs, including but not limited to [1, 2, 3, 4, 5, 6]. The latest technological progress in the field of communication and computing has promoted the development of multi-agents, which can finish complex tasks that cannot usually be accomplished by a single agent. Various vehicles, such as aerial vehicles [7], unmanned surface vehicles [8], and mobile robots [9, 10], are used to enrich multi-agent systems. As one of the most attractive topics in the field of multi-agent systems, formation control has formed several typical control methods in many years of robot control research, including: leader-following method [11, 12], virtual structure method [13, 14], behavior-based method [15, 16]. Among these methods, the one that is mathematically easy-to-understand is the leader-follower method. Furthermore, the method has good scalability since it is easy to extend the problem of maintaining the expected distance and angle between leaders and followers to the multi-robots formation control problem in a similar manner. Therefore, this method is extensively utilized in multi-robots formation control, and it will be used in this paper. It is worth noting that the great majority of the available algorithms are constructed for simple integrator multi-agent systems. However, this would hinder their practical application, because there are many mechanical systems that are so complex that a simple integrator is insufficient to describe their dynamics. In practice, there are many mechanical systems that can be described as nonholonomic dynamics, such as mobile robots (e.g., [17, 18]). Therefore, cooperative control of nonholonomic systems as one of the important applications of consensus control has attracted many scholars' attention. In [19], the cooperative tracking rendezvous problem of nonholonomic mobile robots (NMRs)subject to uncertain and unmodeled dynamics has been investigated. In [20], the design of a distributed formation controller for multiple nonholonomic mobile robots without global position measurement information is considered. In [21], a protocol for shifting states is reached in order to achieve formation control. In addition, finite time cooperative control of nonholonomic mobile robots is studied in [22]. As it can easily find that vehicles with nonholonomic constraint characteristics can cause the system to underactuate, the characteristic of an under-actuated system is that the independent control input dimension is insufficient, resulting in mismatch with the system degree of freedom, which makes the control difficulty of the under-actuated system significantly higher than that of a fully-actuated system. Therefore, the system is expected to be fully-actuated. However, references [17; 18; 19; 20; 21; 22] mentioned above have not considered how to transform the under-actuated system into fully-actuated system. In addition, obstacle avoidance was not taken into account in the above studies on nonholonomic multi-mobile robot systems. In fact, in practical applications, robots will inevitably encounter obstacles, so it is necessary to consider the anti-collision problem of robots. So far, the existing research on obstacle avoidance methods has taken the form of the combination of various methods, and the research methods are diverse [23]. In [24], the collision avoidance of nonholonomic multi-robot formation systems is achieved without employing any potential functions. However, it can only avoid collisions between robots by keeping them in formation and satisfying distance constraints, and it cannot avoid other obstacles outside the system.