# Quadrotor Formation Strategies Based on Distributed Consensus and Model Predictive Controls
## 8 Discussion  
In the simulation of the comprehensive maneuver, the leader performs a series of maneuvers while carrying out the assigned quests. The quadrotor trajectories in Figure 13 show that the followers carry out the formation flight well based on the proposed formation strategies. Furthermore, from the top view of the quadrotor trajectories in Figure 14, the designated formation pattern is maintained throughout the flight. Although the formation pattern slightly deforms during the turn, it recovers soon after the turn.  
In the vertical motion, the leader climbs to the desired altitude at the designated climb rate in three stages, **R1**, **R2**, and **R3**, as shown in Figure 15. Moreover, the followers can keep up with the leader's vertical motion with the proposed formation strategy in Section 5.2.2. In Figure 15, oscillation in the altitude and climb rate can be observed throughout the flight. The oscillation can be seen more clearly in Figure 19, which is a zoom-in view of the vertical motion responses in Figure 15 during the time interval of 190 to 210 seconds. The oscillation is caused by the coupling effects between the horizontal and vertical motions in the 6 DOF nonlinear EOMs. The quadrotor tilts while tracking the waypoints as shown in Figures 16 and 17, which disturbs the equilibrium condition and causes the altitude to change. Since the equilibrium condition is disturbed, the altitude control algorithm will engage to regain the equilibrium condition in the vertical motion and therefore result in the oscillating phenomenon.  
In the horizontal motion, the responses of the pitch and roll angles in Figures 16 and 17 show that the angles remain in an acceptable range (\(\pm 25^{\circ}\)) throughout the flight. Furthermore, the yaw angle is well-controlled, close to zero, by the dual-loop PI control as shown in Figure 18. Additionally, the responses of the pitch and roll angles before and after the upward circling motion are shown in Figures 20 and 21, respectively. Before the quadrotors initiate and after the quadrotors finish the upward circling motion, they are simply performing a straight flight with a \(90^{\circ}\) turn. According to the results illustrated in Figures 20 and 21, the formation strategies in the horizontal motion are fully adequate to perform the formation in straight flight. Even during the turn, the pitch and roll angles stay in an acceptable range (\(\pm 25^{\circ}\)).  
Figure 18: Quadrotor yaw angle throughout the comprehensive maneuver.  
Figure 19: Zoom-in of the responses of altitude and climb rate during 190 to 210 seconds.  
Figure 20: Responses of pitch and roll angles from start to 55 seconds.  
A zoom-in figure of the responses of the attitude during the upward circling motion is shown in Figure 22. The figure zooms in the responses in the time interval of 80 to 100 seconds during the upward circling motion. In this 20-second interval, the quadrotors travel about \(1/4\) of a circle in an \(xy\) plane. During the upward circling motion, the leader has to change its direction frequently to stay on the circle track as well as the followers to stay in formation. The results in Figure 22 show that the pitch and roll angles are still within an acceptable range for leader and followers. The followers can keep up with leader's horizontal motion, or, in other words, to stay in formation during the upward circling motion with the proposed formation strategy in Section 5.2.1. The yaw angles of the leader and followers are controlled closed to zero with the dual-loop PI control in the upward circling motion as shown in Figures 18 and 22.  
Figure 21: Responses of pitch and roll angles from 255 to 280 seconds.