Results and comparision between different control algorithms for a quadrotor using ArduPilot framework

SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 
Trang 170 
Results and comparision between 
different control algorithms for a 
quadrotor using ArduPilot framework 
 Nguyen Anh Quang1 
 Emmanuel Grolleau2 
 Ngo Khanh Hieu1 
1Ho Chi Minh City University of Technology,VNU-HCMUT 
2LIAS, ISAE – ENSMA, France 
(Manuscript Received on July 13th, 2015; Manuscript Revised October 16th, 2015) 
ABSTRACT: 
Determining the most suitable control 
algorithm for a system is not an easy task. In 
theory, each controller has its own 
advantages and disadvantages comparing 
to the others. However, in the real world, the 
behavior of the controller also depends on 
many other factors such as the calculating 
ability of the control board, the accuracy of 
the sensors, the way the hardware 
communicate with the others, etc. In order to 
find the pros and cons of each control 
algorithm in the real world, each of them has 
to be tested and then comparing their 
results. This article presents a simple way to 
test the behavior of various control 
algorithms, with the quadrotor as the control 
target and ArduPilot is the framework to 
create the firmware carrying multi 
controllers. At the end of this article, the 
results of 3 control algorithms: Original PID 
of ArduPilot, new developed PID and Integral 
Backstepping will be presented and 
compared. These data is created by using 
Software In The Loop simulation (SITL), a 
tool provided by ArduPilot to test the new 
developed firmware.
Key words: ArduPilot, control algorithm, quadrotor, PID, Integral Backstepping 
1. INTRODUCTION 
Quadrotor is a six degree of freedoms 
system which is only controlled by four fixed-
pitch equally-space rotors. In other words, even 
though the mechanically design is simple [1], this 
flying system is underactuated. The calculating 
for controlling this system will therefore be 
complicated. In theory, there are several control 
algorithms which is suitable for a quadrotor such 
as PID, Adaptive Control, Integral Backstepping 
[2], nonlinear H∞ [3] or LQR controllers [4]. 
.However, there is no optimized controller for 
this system. Since each method has its pros and 
cons, the control algorithm for a quadrotor should 
base on the environment of the real system as 
well as its objectives. A controller, which can has 
the ability to change the control method in 
specific situations and desires will therefore be 
the best solution in this case. In order to 
experience the pros and cons of control methods, 
we decide to use the ArduPilot, a very popular 
framework used to create the firmware for the 
autonomous unmanned system, as the framework 
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 
 Trang 171 
to develop a module to integrate new control 
algorithms for the quadrotor. Using SITL 
simulation, we can verify that this module is good 
enough for taking the experiment with the real 
system and give us some ideas about the good 
and bad side of the integrated controllers. 
2. QUADROTOR – FROM EQUATIONS TO 
INTEGRATED CODE 
By default, there are several ways to create 
the integrated code to control a system. This 
article will present a solution suitable for 
complex systems, in this case a quadrotor. The 
basic of this solution is based on new tools which 
can transfer Simulink models into C code, as can 
be seen in figure 1. 
Figure 1. From theoay to C code 
Using the Euler-Lagrange methods, the 
motion of the quadrotor plus frame is described 
by the following equations [6]: 
   
   
 
2 2
1 2 3 4 4 2
2 2
1 2 3 4 3 1
2 2 2 2
1 2 3 4
y z r
x x x
x z r
y y y
x y
z z
I I J lb
I I I
I I J lb
I I I
I I d
I I

 

 
 

  

  
  
 
         


 
        

 
      


 (1) 
The controlled targets of the equation (1) are 
the Euler angles roll, pitch, yaw, which is 
represented by , and f q y ; meanwhile, the 
control outputs are the angular speed of the four 
motors. In order to test the equations above, they 
has been described by MATLAB Simulink 
model and then put in blocks with the principle 
shown in figure 2. 
Figure 2. Blocks for the Simulink Model in 
MATLAB 
Figure 3. Simulink model for new PID 
controller 
Based on the flight path or the inputs values 
from the users, the desired Euler angles will be 
created and then converted into the angular speed 
of each motor of the quadrotor. The Controller 
block can contain any kind of controller, as long 
as developers can describe it with Simulink 
model. This Controller block is then handled by 
the Gene-auto to create the necessary code. For 
example, figure 3 and figure 4 shows the 
Simulink model for the PID controller 
controlling the outputs of the quadrotor and the C 
code generated by Gene-auto. 
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 
Trang 172 
Figure 4. Code generated with GeneAuto 
3. ARDUPILOT AND MODULE TO EMBED 
NEW CONTROLLERS 
ArduPilot is one of the popular framework 
to create the firmware for an autonomous 
unmanned vehicle. One of the most important 
benefits of this framework comparing to others is 
that it has a multilayer structure, as described in 
figure figure 5. With this structure, this 
framework can support multiple control boards. 
Figure 5. Multilayer structure of ArduPilot 
In Vietnam, this framework is also very 
famous for developers, who have been familiar 
with boards such as APM2.5 or APM2.6 and the 
ground control station called Mission Planner. 
However, this article will focus more about the 
code and the modified to make this framework 
become multi-controllers, which is useful for 
users in the future. 
The idea of this solution is simple, shown in 
figure 6. By default, ArduPilot has an original 
PID controller system, which control the rate of 
change of the Euler angles. In other words, this 
system handles the , and f q y by controlling 
, and f q y& & &, PID control algorithm is used to 
make the real values of the system become as 
close as possible with the desired values. A new 
module has been created and embedded into the 
framework. The principle of the new add-in 
module is that users can change the using 
controller with just a single switch. By 
minimizing the modification, this module can use 
all of the advantages of the original code, for 
example the multilayer structure and the 
readiness for specific control boards, and still 
made the ArduPilot become a multi-controller 
framework. 
As can be seen in this figure, if users choose 
to use the original controller, which is the default 
PID controller of ArduPilot mentioned above, 
nothing will change and the calculation process 
will be the same with the original code. However, 
when users decide to use a new controller, the 
calculating process will be changed and new 
control outputs will be generated based on the 
chosen control algorithm. 
Figure 6. General idea of the new add-in module 
4. ARDUPILOT AND CREATED MODULE 
TO EMBED NEW CONTROLLERS 
This article will focus on introducing two of 
the control algorithms which have been 
successfully embedded into ArduPilot 
framework using the solution above. 
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 
 Trang 173 
Figure 7. ArduPilot original PID controller 
These results not only confirm the 
availability of the add-in module but also gives 
the comparison required to get the pros and cons 
of each controller with the quadrotor. 
Unlike the original PID controls the rate of 
change of the Euler angles , and f q y& & &, the new 
PID controller in figure 3 calculates the angular 
speed of motors based on the Euler angles 
, and f q y . The differences between the two 
control algorithms are small, however, by 
changing from the rate of change into the Euler 
angles, new PID controller reduces the amount of 
calculation required. This conclusion can be 
concluded according to the comparison between 
figure 7 and figure 3 above. In fact, as mentioned, 
both control algorithm has its benefits and 
drawbacks, and from the results shown in part 4, 
the original controller has better responses than 
the new PID controller. 
“Backstepping control is a recursive 
algorithms that breaks down the controller into 
steps and progressively stabilizes each system” 
[2]. By adding an Integrator into the system to 
increase its robustness, the controller will 
become Integral Backstepping, which will not 
only work well with the dynamic of a quadrotor 
[5] but also make it is more stable with the 
disturbances [2]. Figure 8 introduces the IB 
controller used for a quadrotor. 
With the definitions in equations (2), the 
motion equations of the quadrotor in case using 
the Integral Backstepping control algorithm will 
become equation (3). In equations (2), the values 
of c and λ are the control constants of the control 
algorithm; meanwhile, e is the error between the 
desired values and the real Euler angles 
respectively [6]. 
Figure 8. IB controller for a quadrotor 
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 
Trang 174 
   
   
   
1 2 3 4
2
1 7 4 7 7 8 8 7 4 4
2
2 1 1 1 1 2 2 1 1 1
2
3 3 2 3 3 4 4
cos sin cos sin sin
cos sin sin sin cos
1
cos cos
1
1
x
y
r
d
y z r
dx r
x x
y
u
u
mU g c e c c e c z
I I JU I c e c c e c
I I
U I c e c c e c
    
    
  
 
     


   
 
 
     
          
 
          
 
     
   
3 2 2
2
4 5 3 5 5 6 6 5 3 31
z x r
d r
y y
x y
dz
z
I I J
I I
I I
U I c e c c e c
I
    
    
   
  











  
     
   

 
        
 

 (2) 
 
2
3
4
1
1
1 cos cos
y z r
r
x x x
z x r
r
y y y
x y
z z
x
y
I I J U
I I I
I I UJ
I I I
I I U
I I
UX u
m
U
Y u
m
U
Z g
m
  
  
  
 
   
   
  




   

 
   

   








 
 (3) 
By using MATLAB Simulink, the model of 
the Integral Backstepping can be described as in 
figure 9 and then embedded into the framework 
of ArduPilot. Users can choose to use this 
algorithm by using the new add-in module. 
5. RESULTS WITH NEW PID 
CONTROLLER IN SOFTWARE IN THE 
LOOP SIMULATION (SITL) 
Software In The Loop is a tool provided by 
ArduPilot to developers, which can be used to 
test new firmware and new modifications, in this 
case a new module to embed new controllers. 
Unlike Hardware In The Loop (HITL), which 
uses the virtual inputs with the real board to 
experience the the response of the real Hardware 
in some specific cases, SITL uses both virtual 
environment and hardware. Table 1 gives a 
simple comparison between two types of 
simulation. 
Table 1. HITL and SITL comparisons 
Using SITL with the same flight path, figure 
10 and figure 11 introduces the results with the 
original PID controller of ArduPilot and the new 
PID controller. 
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 
 Trang 175 
Figure 9. Integral Backstepping MATLAB Simulink model 
Figure 10. Pitch (left) and yaw (right) disired and response results with original and new PID 
Figure 11. Tracking result with old PID (left) and new PID (right) 
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 
Trang 176 
Figure 12. Tracking result with old PID (right) and IB controller (left) 
The tracking ability of the new PID 
controller is as good as the old one (figure 10). 
Although there are still some errors, the new PID 
control algorithm still can drive the quadrotor 
back to the desired flight path. Figure 11 gives a 
more detail result. When comparing between the 
desired Euler angles and the response ones, it can 
be seen that the new PID controller results follow 
really close with the desired values. It is not as 
good as the old one, however it can be concluded 
that the new PID is steady enough for a real test. 
6. RESULTS WITH INTEGRAL 
BACKSTEPPING IN SOFTWARE IN THE 
LOOP SIMULATION (SITL) 
Using the same flight path with the Integral 
Backstepping, figure 12 and figure 13 
demonstrate the results. Although the IB 
controller can trace the flight path well, there are 
some fluctuations as can be seen in figure 13. 
Nevertheless, as mentioned in the theory, IB 
controller has high robustness, which make the 
response of the system follow closely the desired 
values. Figure 14 give a more detail look for this 
conclusion. 
Figure 13. Pitch deired and response resutls with 
original PID and IB 
7. CONCLUSIONS 
With the results above, it is clearly that 
using the existence, open-source framework is 
one of the best solution to testing new control 
theory new modifications. With suitable changes, 
for example creating new add-in modules for 
necessary requirements, the modified firmware 
can use both the ready-to use structure of the 
original firmware and the benefits of the new 
code. 
TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K7- 2015 
 Trang 177 
Figure 14. IB controller and new PID controller 
PID control algorithm is one of the simplest 
one to control a system. It is well implemented to 
control various kind of system, one of them is the 
quadrotor. However, it is obviously that this is 
not the best solution and there are many other 
controller which is promising and need to be 
tested with the real things, not only by using the 
Simulink models. IB controller is one of them, 
which not only increases the robustness of the 
quadrotor but also has a very good tracking 
ability. 
The result with the SITL simulation proves 
that a modified firmware built by ArduPilot is 
ready to test in real flight, which will give more 
results, especially the real response of the control 
board in real environment. By understanding the 
pros and cons of each controller in specific 
situation, a changeable controller, which is the 
optimized controller, can be implemented for a 
real quadrotor in the future. 
So sánh và đánh giá khả năng điều 
khiển máy bay bốn chong chóng với các 
thuật toán khác nhau trên nền tảng 
ArduPilot 
 Nguyễn Quang Anh1 
 Emmanuel Grolleau2 
 Ngô Khánh Hiếu1 
1Ho Chi Minh City University of Technology, VNU-HCMUT 
2LIAS, ISAE – ENSMA, France 
TÓM TẮT: 
Trên lí thuyết, mỗi thuật toán điều khiển 
đều có những ưu và nhược điểm đặc trưng. 
Trên thực tế, khả năng điều khiển cơ hệ còn 
phụ thuộc vào nhiều yếu tố khác của cơ hệ 
và hệ thống điều khiển. Trong trường hợp 
này, cách duy nhất để xác định chính xác 
SCIENCE & TECHNOLOGY DEVELOPMENT, Vol 18, No.K7- 2015 
Trang 178 
phản ứng của một hệ điều khiển là thử 
nghiệm trên hệ thống thực và đánh giá kết 
quả. Dựa trên việc sử dụng một hệ thống 
phức tạp là máy bay bốn chong chóng, bài 
báo này trình bày phương pháp đưa các hệ 
điều khiển khác nhau vào ArduPilot. Mô 
phỏng Software In The Loop đã được sử 
dụng để thực nghiệm 3 thuật điều khiển khác 
nhau: PID gốc của ArduPilot, PID tự phát 
triển và Integral Backstepping. Qua đó, 
ngoài việc xác định khả năng của hệ điều 
khiển, bài báo cũng nêu lên một vài kết quả 
bước đầu với các hệ điều khiển này, xác 
nhận lại lí thuyết đã biết của các thuật toán 
này, đồng thời là bước quan trọng để xác lập 
các hệ số điều khiển trước khi tiến hành bay 
thực. 
Keyword: ArduPilot, thuật điều khiển quadrotor, PID, Integral Backstepping 
REFERENCES 
[1]. M. J. Cutler, Design and Control of an 
Autonomous Variable-Pitch Quadrotor 
Helicopter, M.Sc Thesis, Massachusetts 
Institute of Technology, 2012. 
[2]. S. J. Andrew Zulu, "A Review of Control 
Algorithms for Autonomous Quadrotors" 
Open Journal of Applied Sciences, pp. 547-
556, 2014. 
[3]. G. Raffo, M.G.Ortega and F.R.Rubio, "An 
integral predictive/nonlinear H∞ control 
structure for a quadrotor helicopter" 
Automatica, vol. 46, pp. 29-39, 2010. 
[4]. S. Bouabdallah, A. Noth et R. Siegwart, 
«PID vs LQ control techniques applied to an 
indoor micro quadrotor» IEEE/RSJ 
Internation Conference on Intelligent 
Robots and Systems, vol. 3, pp. 2451-2456, 
2004. 
[5]. Bouadallah.S et al, «Full control of a 
quadrotor» Intelligent Robots and Systems 
2007. IROS 2007, pp. 153-158, 2007. 
[6]. A. Benito, «Flight Control and Navigation 
of a Quadcopter» Poitiers, 2014.