## 1 Introduction
In [16], a combination of the virtual structure and path-tracking approaches is used to derive the formation architecture, and the controller is designed in such a way that the path derivative is left as a free input to synchronize the robots' motion. [PERSON] et al. [34] presented a constructive method to design output-feedback cooperative controllers that drive a group of robots with limited sensing ranges to perform desired formation tracking. Furthermore, in [17], this formation control method was applied to robots with limited sensing ranges to perform the desired formation. [PERSON] et al. [35] proposed a novel controller for the trajectory tracking of nonholonomic vehicles, which could guarantee a bounded velocity. Generally, a virtual structure can maintain the formation well for multiple robots and track the predefined trajectories precisely, which is applied in this paper to design the formation controller for multiple robots. However, the obstacles in the environment are not considered in the aforementioned references, which is an inevitable but significant issue for the practical formation control of robots to achieve the obstacle avoidance. A consensus-based cooperative formation control strategy with collision-avoidance capability for a group of multiple unmanned aerial vehicles (UAVs) was proposed in [36]. A control law based on the potential function and a formation control protocol based on graph theoretic considerations were proposed in [20; 21], respectively. In [37], a control law with onlineobstacle avoidance was discussed with online optimization to maintain the formation automatically. [PERSON] et al. [22] developed distributed controllers that could force a group of robots to perform a desired formation with no collision among any of the robots in the group. In [38], a formation strategy with the combination of the leader-following formation approach and potential function-based method was proposed. Although some research works have been undertaken to consider collision avoidance [39; 40; 41], few can be applied directly to robots, and keeping the tracking error as small as possible in the formation when encountering the obstacles is still challenging. Thus, considering the obstacles in the environment, a virtual-structure-based formation control design for groups of multiple mobile robots is proposed in this paper. The virtual-structure approach is applied to generate the basic trajectory for each robot in the group, and the trajectory is parameterized to keep this group in formation. A trajectory generator is established with the consideration of obstacles, where the potential function is designed to adjust the basic trajectories and generate new reference velocities, which can be used to replan the reference trajectories. Subsequently, a tracking controller is designed to achieve good tracking performance, and the guaranteed performance is achieved via the Lyapunov theorem. A comparative simulation is carried out to show the formation and tracking regarding obstacles. Besides this, a real robot experiment is implemented to further verify the effectiveness of the proposed control design. The main contributions are as follows:  
1. The potential function method is applied to the virtual-structure-based approach for the consideration of obstacles; thus, the algorithm can adapt to the practical environment. 2. A novel path parameter which parameterizes the basic trajectories is designed to adjust the weight of the formation and tracking in the moving process according to the situation that the formation encounters obstacles. The system can give priority to tracking rather than formation when encountering obstacles, meaning that the tracking errors of the team can be as small as possible. The remainder of this paper is organized as follows. In Section 2, the problem statement is given. In Section 3, the details of our formation controller are presented. Section 4, a simulation is implemented to prove the effectiveness of the proposed controller.