Aerospace and Electronic Systems Magazine July 2018 - 18

A Survey on Quadrotors
ized model of quadrotor to calculate the corresponding control
sequence for the given path. During the execution of control
layers, control angles and altitude are also active. These layers
provide control inputs, thereby allowing the UAV to perform the
two-dimensional path. During the execution of the trajectory, the
altitude controller holds the quadrotor to a previously set altitude
[79]. Moreover, this technique has been used in the attitude loop.
At low levels of thrust control it is satisfactory, but at higher levels of thrust, performance degrades due to vibration. One solution
to this problem is to apply a balance of reducing disparities in
attitudes by varying the matrix Q, but this leads to a degradation
of performance monitoring. A good compromise must be found
[43]. In [80], researchers have implemented iterative LQR simulation, which allows the quadrotor to hover properly. Still other
studies have used the same type of controller for position, yaw,
and tracking a reference trajectory. However, the LQR controller
has been designed with a linearized model to hover [81]. This
type of controller has also been used in the closed loop system to
stabilize the angular position of the UAV [72]. This method has
been adapted to the trajectory of the system.
Indeed, in order to optimize the system for a flight envelope
greater than the hover configuration, the researchers linearized
state space around each flight condition. Then, they applied the
conventional techniques for the LQR control gains associated with
any state. They considered the dynamic actuators but got only average performance in their flying experience [72]. Reference [82]
features a state-dependent Riccati equation control, which conserves nonlinearities of the system but uses active states in controller calculations. This work was tested by simulating attitude and
velocity loops and has given efficient results.

H-Infinity
In [83], a strategy for robust nonlinear control in order to resolve
the problem of quadrotor trajectory tracking is presented. The H-infinity controller effects the control structure, stabilizing the angular
movements. A backstepping control approach is used to track the
reference trajectory, stabilizing translational movements [83]. The
proposed backstepping H-infinity cascade strategy shows satisfactory results for trajectory tracking in the presence of disturbances
and uncertainties in parameters, as presented in [84]-[86], where a
predictive control strategy and robust H-infinity is used to resolve
the problem of quadrotor trajectory tracking. The proposed control
strategy has been designed to take into account external disturbances acting on all degrees of freedom. The control strategy has
been divided into two stages. First, it includes the use of a MBPC
for translational motion for the outer loop, which performed well
in tracking reference trajectory. Secondly, a robust control for the
stabilization of the quadrotor based on H-infinity theory has been
designed for the inner loop. This controller is also able to reject
disturbances by using Integral action in the state vector. Results
have shown a good track of multiple classes of trajectories and
have shown good performance provided by the internal nonlinear
H-infinity controller in the case of parametric uncertainties. The
usage of integral action in the inner and outer loop controllers has
the ability to work with prolonged disturbances that affect all de18

grees of freedom at different times. This method has shown an improvement over the backstepping.
Some researchers have studied H-infinity controller in the
closed loop system for position control. The simulation based on
a nonlinear model leads to satisfactory results [87]. In fact, they
managed to achieve the robustness of monitoring the proper reference trajectory and disturbance rejection with two degrees of
freedom. Also, they examine the effects of the combination of predictive control based on MBPC models with H-infinity controller
with two degrees of freedom [88]. The role of the controller is to
obtain solid stability and good control of the trajectory. The role
of the MBPC controller is to control the longitudinal and lateral
trajectory for a large envelope flight. The H-infinity controller has
been divided into two different loops. The internal loop stabilizes
the roll angle and pitch, yaw rate, and the vertical velocity. The
outer loop estimates the longitudinal and lateral speed, height, and
yaw. The outer loop is then closed with the MBPC controller. Disturbances and various input and output constraints were tested and
led to good performance. In [89], researchers have examined the
influence of robust linearization and GH infinity controller on the
quadrotor. The loop is applied to x, y, z, and psi. They deduced
that when the weighting functions are carefully chosen, the tracking error of the desired trajectory is satisfactory. Moreover, outputs
converge, even with the presence of disturbances and uncertainties
in the system parameters.

THE NONLINEAR CONTROL

Lyapunov Criteria
The Lyapunov stability is a mathematical translation of a physical
observation: If the total energy of a system dissipates, continuously
decreasing with time, then the system tends to return to a steady
state. The direct method therefore seeks to generate a scalar function of energy that admits a negative time derivative. The choice
of this function can lead us to perform stable control of a nonlinear
system, without linearizing or resolving differential equations of
the dynamic system.
Some authors used Lyapunov functions to ensure stability; they
got stable results, but not always good performance and precision.
Lyapunov's theorem is the basis for the design of sliding mode
control and backstepping.

Sliding Mode Control
Sliding mode control is a technique based on Lyapunov stability criteria. It's used in many works to stabilize the quadrotor.
Compared with other methods, SMC proves its utility for hard
missions of control. Because quadrotors have variable structure,
it is appropriate to apply the sliding mode control for this type of
system. This approach is particularly more relevant than controllers based on the linearization of the system around an operating
point, because they are not suited to large variations of dynamic
parameters. The advantage of sliding mode control is its insensitivity to modeling errors, parametric uncertainties, and other
disturbances, as shown in [90]. Once the system is sliding on
the sliding manifold, the behavior is governed by the structure

IEEE A&E SYSTEMS MAGAZINE

JULY 2018

Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine July 2018