## 1 Introduction
In the formation, only the desired path or other behavior of the leader needs to be set, and then the follower can follow the leader with a predetermined position offset to realize the formation control. For this reason, the leader-follower method is widely used in practical engineering. Hence, the leader-follower method can be employed for the formation control. The concept of leader-follower was first proposed and successfully applied to the formation control of mobile robots [12; 13]. As the most commonly used formation control method at present, its basic idea is that all formation members are designated as the leader or follower. The leader controls the movement trend of the whole formation by navigating along the predetermined or temporarily set path. According to the distance and azimuth information relative to the leader, the follower follows the leader to realize formation control. The advantage of the leader-follower method is that the formation control structure is simple and easy to implement. In the formation, only the desired path or other behavior of the leader needs to be set, and then the follower can follow the leader with a predetermined position offset to realize the formation control. For the above reasons, the leader-follower method is widely used in practical engineering. The disadvantage of the method is that the formation system depends too much on the leader. A new multi-robot formation control method is known as the leader-follower method. The stability of the algorithm was proved by the simulation results [14]. The formation control problem was transformed into the problem of state consistency by the transformation of variables. A controller was designed to make a group of nonholonomic robots gradually converge to the desired formation along the specified trajectory [15]. When the external input was limited, the navigation and following formation problem of nonholonomic multi-mobile robots was discussed. Under the nonholonomic constraints, the external distributed sensor method was applied. The finite-time convergence problem of  
Figure 2: Common multi-robot formation [3]: (**a**) straight line; (**b**) wedge; (**c**) column; (**d**) triangle; (**e**) double row. multi-robot cooperative control was studied [16; 17]. The motion consistency problem of complex multi-robots was studied, and the dynamic formation of multi-mobile robots was realized by designing a distributed formation control law [18; 19]. The time-varying stability problem of planar multi-robots with nonholonomic constraints was studied [20; 21]. Assuming that there were many external disturbances in the system. The finite-time containment control problem of second-order multi-robot systems with mismatched disturbances was studied [21; 22]. The adaptive tracking control of omnidirectional mobile robots was analyzed under the conditions of state constraints and input saturation [23]. Assuming that there were multiple leaders, the cluster containment control problem of the robot system was researched [24]. The acquisition spacecraft operation of the space robot was analyzed. The collision avoidance compliance compound active disturbance rejection control problem of a robot was studied. Considering the post-capture unstable combined system, collision avoidance and compliant composite error active disturbance rejection control is proposed for the stabilization control. Numerical simulation verifies the effectiveness of the proposed collision avoidance and compliant control method [25; 26]. Most of the above studies focus on the leader-follower method implementation and external distributed sensor fusion. The multi-robot cooperative formation needs to closely combine the theories and algorithm simulation. This article combines the nonholonomic constrained mobile robot, graph theory, leader-follow formation control and trajectory tracking. The error analysis of the nonholonomic multi-robot system is implemented. Based on information consistency, the formation realization of single formation and multi-combination formation is completed.