## 5 Conclusions and Future Work  
Based on the theory of automatic control and the nonholonomic system, this article studies the formation problem of nonholonomic constrained multi-robot tracking the leader's movement while maintaining the ideal formation. The formation communication protocol of multi-robot cooperative movement is established. Through the mathematical analysis of nonholonomic constraints, the motion models and motion system error models of the leader robot and follower robot are constructed respectively. Then the convergence of formation control strategy in this article is proved theoretically by the Lyapunov function. The feasibility of formation control of the multi-robot system with the nonholonomic constraints is verified by MATLAB simulation. By comparing with the simulation results of other navigator formation control algorithms, the effectiveness of the GCF algorithm is verified.  
In order to illustrate the effectiveness of the group consistency control designed in this article, the comparison of the two with and without group strategy are implemented. Then, two simulation results are obtained. The comparison of the two simulation results shows that the convergence time of formation control using the group strategy is less than that of the algorithm without the group strategy under the same formation. In order to better show the feasibility of the algorithm proposed, the comparison is performed with PFC  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Project** & **PFC** & **GCF** \\ \hline \(v_{max}\) (m/s) & 30 & 30 \\ \(l_{F,L}\) (m) & 40 & 40 \\ Convergence time (s) & 4 & 3 \\ Number of robots & 9 & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Data comparison table between PFC and GCF.  
Figure 14: (a) Trajectories of ten robots on the plane by GCF in spiral formation; (b) Formation position error of each following robot.  
algorithms. Through the comparison of the two algorithms, the convergence time of the algorithm in this article can be 25% less than that of PFC. Compared with PFC, the number of robots is poor. However, the overall comparison of the formation control algorithm can be acceptable in theoretical analysis and simulation. Hence, the formation control algorithm has effectiveness and feasibility. Because there are many uncertain conditions in the real robot systems, such as external noise and nonlinear interference, the formation control problem of nonholonomic constrained multi-mobile robot systems with external interference would be studied in the future.  
Conceptualization, H.Z.; methodology, H.Z. and K.D.; formal analysis, N.W. and L.D.; data curation, H.Z. and K.D.; writing--original draft preparation, H.Z. and K.D.; writing--review and editing, H.Z.; visualization, K.D. and N.W.; supervision, H.Z.; funding acquisition, H.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 51505335; the Industry University Cooperation Collaborative Education Project of the Department of Higher Education of the Ministry of Education of China, grant number 202102517001; the Doctor Startup Project of TUTE, grant number KYQD 1806.  
Not applicable.  
The authors declare no conflict of interest.