# A Multi-Robot Formation Platform based on an Indoor Global Positioning System
## 4 Experiments of Leader-Follower Formation Control
### The Experiment of Triangle Formation Maintaining with External Disturbance  
Considering the complex external environment in a practical application, introducing external disturbance is the best way to test the anti-interference capability of the platform, so as to verify the robustness of our platform. The external disturbances include lateral disturbance and longitudinal disturbance. The experiment was to use the platform and control the three robots maintaining a triangle formation with external disturbance while tracking a straight line. The initial pose of leader robots \(L\) was \((3.24~{}\text{m},2.29~{}\text{m},\pi/2)\), the linear velocity was \(\
u=0.05(\text{m}/\text{s})\) and angular velocity  
Figure 10: (**a**) Snapshots of the video about circle trajectory of the leader robot with one follower robot to realize a line formation. (**b**) Snapshots of the video about line trajectory of leader robot with three follower robots to realize a diamond formation.  
was \(\omega=0(\text{rad}/\text{s})\). The initial pose of follower robots \(F_{1}\) and \(F_{2}\) were \((2.61\text{ m},1.96\text{ m},\pi/2)\) and \((3.83\text{ m},2.10\text{ m},\pi/2)\). In addition, initial velocity of three robots were both 0. The velocity constraints of all the robots were set as \(v_{Max}=0.3(\text{m}/\text{s})\) and \(\omega_{Max}=\pi/6(\text{rad}/\text{s})\). The experiment video of line trajectory of a triangle formation maintaining with external disturbance can be found at Supplementary Materials [[https://youtu.be/HGQjjoYARJc](https://youtu.be/HGQjjoYARJc)]([https://youtu.be/HGQjjoYARJc](https://youtu.be/HGQjjoYARJc)).  
Figure 11 illustrates the robustness of the leader-follower formation process collected from the video at different times. The leader robot L led the two follower robots \(F_{1}\) and \(F_{2}\) and maintained a desired triangular formation \(l=0.30\text{ m}\); at T = 32 s and T = 50 s follower robot \(F_{1}\) received two external disturbances--the first external disturbance was longitudinal disturbance and the second external disturbance was lateral disturbance. As shown in Figure 12, when \(F_{1}\) moved with the external disturbance, compared with \(F_{2}\), its formation tracking errors changed fast, but finally, it also converged nearly to zero and achieved the triangle-like formation, as desired. These results demonstrate our multi-robot platform is fault-tolerant. During the process, though a robot of the system faces the external disturbances in the formation process, it can recover the desired formation quickly; moreover, the other robots are not affected. Therefore, our platform shows a good robustness under external disturbances.  
Figure 11: Snapshots of the video about line trajectory of a triangle formation maintaining with external disturbance.  
Figure 12: The formation tracking errors of the follower robots F1 and F2 in the experiment of triangle formation maintaining with external disturbance; (**a**) is the distance error of follower robots; (**b**) is the angular error of follower robots.  
For the above two types of leader-follower formation experiments, our platform can effectively implement the application of the existing theories and methods, and shows better scalability and robustness, since real-time and accurate pose information are supported by our indoor global-positioning system. Therefore, our platform is expected to be used as an available test platform to evaluate and verify the feasibility and correctness of the theoretical methods in the multi-robot formation.