# Backstepping Based Formation Control of Quadrotors with the State Transformation Technique
## 4 Simulation Results and Analysis
### Simulation Results and Analysis
Figure 4:2 The results of the comparison simulation for the formation control of quadrotors about the \(4\pi\) circular trajectory: the red dashed line is the result of the backstepping-based formation control with small angle assumption (SAA), and the green dashed line is the result of the proposed formation control with the state transformation technique (STT). Figure 4:3 The formation errors for each of the three axis about the \(4\pi\) circular trajectory: (**a**) backstepping-based formation control with SAA; (**b**) proposed formation control with the state transformation technique (STT). Next, we set the trajectory so that the quadrotor rotates three times in 10 s as shown in Figures 17-20. In this case, as shown in Figure 18, larger reference attitude angles are required for faster rotation. As shown in Figures 17 and 18, we can confirm that the proposed formation control using the state transformation technique allows the follower quadrotor to properly trail the leader. However, as shown in Figures 19 and 20, the general formation control using SAA does not. A fact, if we set the values of gain small, the quadrotor system does not diverge. However, if we set up more rotating trajectories within the same time, we can confirm that the follower quadrotor diverges like in Figures 19 and 20 when we use the formation control with SAA. Figure 4:4 The reference angles of the follower quadrotors for the formation control about the \(4\pi\) circular trajectory: the dashed line indicates the reference attitude angles that enable the quadrotor to converge to the desired formation, and the solid line is the result of the simulation about attitude responses of the follower quadrotors. (**a**) Backstepping-based formation control with SAA; (**b**) proposed formation control with the state transformation technique (STT). Figure 4:5 The results of the comparison simulation for the formation control of the second follower quadrotors about the \(6\pi\) circular trajectory: the solid line indicates the results of leader quadrotor; the green dashed line is the result of the proposed formation control with the state transformation technique (STT). We have carried out further simulations considering disturbance in order to demonstrate the superiority and effectiveness of the controller proposed in this paper. Quadrotors can experience disturbances such as wind during a flight. So, through the simulation considering disturbance, we can deal with the more practical environment. We can verify the effectiveness of the controller by looking at whether the proposed controller maintains good performance even with disturbance. We compared the performance between the proposed formation control using the state transformation technique to derive the reference attitude angles and the method using SAA to derive the reference attitude angles in the same simulation conditions as Figures 17 and 18. We set the  
Figure 4:6 The results of the comparison simulation for the formation control of the first follower quadrotors about the \(6\pi\) circular trajectory: the solid line indicates the results of the leader quadrotor; the red dashed line is the result of the backstepping-based formation control with SAA. Figure 4:7 The reference angles of the second follower quadrotors for the formation control about the \(6\pi\) circular trajectory: the dashed line indicates the reference attitude angles that enable the second follower quadrotor to converge to the desired formation, and the solid line is the result of the simulation about attitude responses of the second follower quadrotors. disturbance environment that each follower quadrotor receives a force in each direction of \(x\) and \(y\) axis at 3 s as shown in Figure 4:8  
For disturbances below a certain size, both the case of using the small angle assumption and the case of using the state transformation technique show good tracking performance.