9. Conclusion

Figure 4 shows both the quadrotor's altitude as function of time and the altitude of an identical quadrotor implementing an autopilot based on the classical PD framework [36] and flying in absence of wind. It is clear how the quadrotor implementing our control algorithm is able to fly at the desired altitude despite the fact that the payload is dropped at t = 40 s and a motor is turned off at t = 90 s. The quadrotor implementing the PD algorithm is unable to reach the desired altitude because of the large error in the vehicle's mass' estimate. Moreover, this quadrotor reaches a considerably higher altitude after the payload is dropped and crashes

Figure 4. Altitude of a quadrotor implementing the proposed control algorithm and altitude of an identical quadrotor

0 20 40 60 80 100 120 Ti me[s]

Mass Dropped Motor F ailure

The first plot in Figure 5 shows the control inputs (57) and (58). The second plot in Figure 5 shows the control inputs computed using a conventional MRAC framework [6] for a quadrotor tracking the same circular path despite a wind blowing at 6 m/s; numerical simulations show that quadrotors implementing the conventional MRAC framework are unable to fly in the presence of wind gusts faster than 6 m/s. It is clear that our autopilot requires a control effort that is smaller than the effort required by a conventional MRAC-based autopilot

after one of the propellers is turned off.

Prop osed Autopilo t PD-based Autopilo t

implementing an autopilot based on the classical PD control.

to fly in weaker wind.

0

0.5

1

r<sup>I</sup>

Z (t) [m]

1.5

2

2.5

96 Adaptive Robust Control Systems

In this chapter, we presented a robust MRAC architecture, which we employed to design autopilots for quadrotor helicopters. The proposed autopilot is the first to account for the fact that quadrotors are nonlinear time-varying dynamical systems, the exact location of the vehicle's center of mass is usually unknown, and the aircraft reference frame is centered at some point that does not necessarily coincide with the vehicle's barycenter. Moreover, our autopilot does not rely on the assumption that the Euler angles are small at all times and accounts both for the inertial counter-torque and the gyroscopic effect.

The applicability of our theoretical results has been illustrated by a numerical example and it is clearly shown how the proposed autopilot is able to track a given reference trajectory despite the fact that the payload is dropped during the mission, one of the motors is turned off, and the wind blows at the prohibitive velocity of 16 m/s. It is also shown that quadrotors implementing autopilots based on the classical PD framework crash if one of the propellers stops functioning. Lastly, it is shown that our autopilot requires a control effort that is smaller than the effort required by conventional MRAC-based autopilots to fly in less strong wind.
