## 1 Introduction  
With the development of automation [1; 2; 3; 4; 5], mobile robots have been widely applied due to their advantages in many fields, such as in environmental inspection, area reconnaissance, maritime search and rescue, etc. [6; 7]. However, reliance solely on a single robot cannot handle some complicated tasks; thus, the concept of groups of multiple robots has come into being [8; 9; 10]. Formation control is a significant technology for multiple robots [11; 12; 13; 14; 15] that can increase the system's robustness and efficiency, expand the range of exploration and reduce the system cost. Therefore, formation control for robots has received increasing attention over recent years. The main objective of formation control for groups of multiple robots is to track a predefined trajectory while maintaining a certain geometric pattern for the robots [16; 17; 18]. However, with regard to the practical environment, which is always complicated by the presence of obstacles [19], the aforementioned formation objective becomes a challenge. Therefore, collision avoidance is an inevitable but significant issue in the formation control of multiple mobile robots, which can improve the flexibility of robots when undertaking more complicated tasks in the real environment. Formation control can be roughly classed as three approaches [20; 21; 22; 23], which are leader-following, behavioral and virtual structures, respectively; a detailed review is presented below. The leader-following approach is the most widely used approach due to its good operability and ability to keep the formation even if the leader is perturbed by disturbances. This approach designates the leader and followers of the group. The leader tracks the predefined trajectory while the followers track the trajectory determined by the state of the leader. A leader-following formation control method for underactuated surface vehicles with model uncertainties and environmental disturbances was proposed in [24]. [PERSON] et al. [25] proposed the leader-following approach with the combination of Lyapunov-based sliding-mode control design in the formation of multiple robots. [PERSON] et al. [13] proposed sliding-mode control laws to control multiple robots in arbitrary formations, where the stability was guaranteed by the combination of local information and planned formation motion. [PERSON] et al. [26] designed the leader-following approach to steer robots along identical parallel paths with the least information exchange. [PERSON] et al. [27] design the cooperative controllers for robots. [PERSON] et al. [28] design the controller based on the assumption that only one agent knows the information of reference trajectory. [PERSON]. [29] proposed a leader-following approach considering the constraints of the control input. [PERSON] et al. [30] designed a directed formation control law based on the knowledge only of the neighbor's direction by using the integrator backstepping technique. [PERSON] et al. [31] proposed leader-following controller considering the time-varying delay and nonlinear dynamics. These studies exhibit good formation tracking performance for robots; however, since no feedback is provided by the follower, the leader-following approach cannot maintain the formation well when the follower is perturbed. This approach cannot achieve good formation tracking performance when encountering obstacles. Moreover, few applications of the behavioral approach are based on the formation control of robots due to the limited sensing range and difficulty of stability analysis [32], which makes it difficult for the robots to track the reference trajectories precisely. In contrast to the leader-following and behavioral approaches, the entire formation is predefined as a single entity in the virtual-structure approach since it has a rigid geometric relationship. When the virtual structure moves, it produces the reference trajectory for the tracking of each robot. In [33], a virtual-structure control strategy with mutual coupling between the robots is proposed.