## 1 Introduction
Therefore, the artificial potential field method proposed in [25] is suitable for the unknown environment with relatively high real-time requirements for obstacle avoidance and will be used in this paper. In [26], formation control of the multi-agent under the constraints of visibility and communication has been studied and a feedback control strategy that can realize obstacle avoidance and internal collision avoidance of robots has been proposed. In [27], an obstacle avoidance control strategy including a leader-following formation model and obstacle avoidance separation distance model has been proposed to ensure that the mobile robots formed a formation while avoiding collision. Among various obstacle avoidance methods, the artificial potential field method realizes robot obstacle avoidance by a repulsion potential field around obstacles. With the advantages of a clear physical principle and low algorithm complexity, it is widely used in the research of robot obstacle avoidance control [28; 29; 30]. In [31], the repulsion field and the gravitational field function through the artificial potential field method have been introduced to ensure that the robot can form a formation and avoid obstacles while tracking the target. In [32], obstacles between robots were expressed as a new form of potential function by invoking the concept of an electric field. In [33], \(H_{\infty}\) analysis was conducted on the undesired effect of an artificial potential field to give the formation good robustness in obstacle avoidance, and the control effect based on Lyapunov stability theory was proved. Note that some of the aforementioned literature has research on leader-following formation tracking control of nonholonomic mobile robots considering collision avoidance. However, few studies consider converting under-actuated systems into fully-actuated and obstacle avoidance systems at the same time. Motivated by the above discussion, the following issues are discussed by us. The transverse function will be applied to transform the under-actuated system into a fully-actuated system. Meanwhile, the repulsive potential field function will be introduced for robot obstacle avoidance, and the adaptive laws for each robot are designed for estimating the unknown parameter of the tracked trajectory. The contributions of this paper are formally summarized as follows:  
* For the nonholonomic mobile robot model studied in this paper, since the number of output state variables is larger than the number of input controls, it is considered to be an under-actuated system. The transverse function will be applied to transform the under-actuated system into a fully-actuated system. * In order to describe the effect of obstacles on the robot, the repulsive potential field function is introduced. The effect of potential field on mobile robots is taken into account in the system tracking error to obtain the corrected position error. In addition, to deal with the unknown parameters of the desired trajectory, the adaptive laws are designed. The paper is organized as follows. Section 2 gives some preliminaries and problem formulation. The design procedure of leader-following formation control for nonholonomic mobile robots considering obstacle avoidance is demonstrated in Section 3. Section 4 shows the simulation result. The conclusion of this paper can be seen in Section 5.