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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
https://doi.org/10.47460/athenea.v5i16.76
Simulation of remote control of a hexacopter with force
feedback in semi-structured environments
*Correspondencia: danilo.chavez@epn.edu.ec
*Correspondence: danilo.chavez@epn.edu.ec
Received (25/04/2023), Accepted (21/05/2024)
Abstract: This project simulates the flight of hexacopters in indoor environments. Through the design, modeling, and
implementation of environments, it imitates semi-structured environments with static obstacles, including a house, a
church, and a supermarket. Each environment displays different levels of difficulty. The application offers a choice
between two models of hexacopters, achieving more useful and interactive, and it includes the option of force feedback,
implemented with a force feedback joystick, warning the user about possible collisions, and giving the feeling of
presence to the operator. The haptic device limits the force applied. The application focuses on three-dimensional
scenes in semi-structured indoor environments, reproducing the environment variables (appearance, features, context)
of a real system; in this sense, the implementation of the simulator is a low-cost technique that offers several possible
scenarios without effects in the real world.
Keywords: hexacopters, haptic device, force feedback, simulation.
Simulación de control remoto de un hexacóptero con retroalimentación de fuerza en entornos
semiestructurados
Resumen: Este proyecto simula el vuelo de hexacópteros en ambientes interiores. A través del diseño, modelado e
implementación de entornos, imita entornos semiestructurados con obstáculos estáticos, incluyendo una casa, una
iglesia y un supermercado. Cada entorno muestra diferentes niveles de dificultad. La aplicación ofrece la posibilidad
de elegir entre dos modelos de hexacópteros, consiguiendo ser más útiles e interactivos, e incluye la opción de
retroalimentación de fuerza, implementada con un joystick de retroalimentación de fuerza, advirtiendo al usuario sobre
posibles colisiones, y dando la sensación de presencia al operador. El dispositivo háptico limita la fuerza aplicada. La
aplicación se centra en escenas tridimensionales en ambientes interiores semiestructurados, reproduciendo las
variables del entorno (aspecto, características, contexto) de un sistema real; En este sentido, la implementación del
simulador es una técnica de bajo coste que ofrece varios escenarios posibles sin efectos en el mundo real.
Palabras clave: hexacópteros, dispositivo háptico, retroalimentación de fuerza, simulación
Natasha Guadalupe
https://orcid.org/0009-0001-5913-4105
natasha.guadalupe.ng@gmail.com
Departamento de Automatización y
Control Industrial,
Escuela Politécnica Nacional
Quito, Ecuador
Danilo Chávez*
https://orcid.org/0000-0002-7529-9006
danilo.chavez@epn.edu.ec
Departamento de Automatización y
Control Industrial,
Escuela Politécnica Nacional
Quito, Ecuador
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
I. INTRODUCTION
The development of flight simulators is a solution to the education and training of students in various areas
of engineering. The advantages of using a flight simulator as a facilitating tool for the experience acquisition
are very high. The student can develop his capabilities since high-performance training stimulates the
mental, physical, and psychological aspects. In this way, the simulation allows them to obtain skills for a
proper flight, a realistic flight experience, and a high confidence level in the flight simulator. [1].
Computer simulation is often used to model systems for which analytical solutions cannot be found [2]. By
simulating the teleoperation of a hexacopter, focused on applications of three-dimensional scenarios in
internal semi-structured environments, reproducing the environment and its variables (appearance,
features, context), constitutes a technique of low cost that offers several possible scenarios without effects
in the real world.
We propose the Unity 3D video game engine utilization to simulate semi-structured environments with
static obstacles, and two models of hexacopters. In addition, the application has the option to use the
feedback force, which is carried out with the Microsoft SideWinder Force Feedback 2 Joystick haptic device;
this controller limits the force feedback applied, allowing warn the user about possible collisions, and giving
the feeling of presence to the operator. Finally, a series of tests are carried out to evaluate their performance.
Initially, menus, scenarios, and maps are validated to continue with the behavior of the hexacopters during
their flights, ending with user feedback on the handling of the Flight Simulator, which is done through a
survey that complements the previous evaluations.
II. UNMANNED AERIAL VEHICLE
An unmanned aerial vehicle (UAV) is defined as an aircraft without a crew, which may be reusable and can
maintain a level of controlled and sustained flight. This vehicle is powered by one or more engines [4].
Advances in UAVs have been significant so their applications increasing with time. One of the main reasons
is that they can be used for tasks that involve some difficulty or danger to conventional vehicles crewed by
people [5]. Also, UAVs acquire great importance in performing inspection, control, and sensing of high
chemical toxicity tasks, thus reducing human exposure. Each of them would imply a high cost and risk to
people, and loss of productivity without their use [6].
A. Hexacopter
A hexacopter is a type of UAV that consists of six rotors, arranged in four distinct configurations [7]. Among
the main characteristics of this type of vehicle is good stability, due to the opposite direction of rotation of
its propellers, which prevents it from rotating on its axis continuously due to the inertia of these. They also
have a good time in flight concerning UAVs of the smallest number of rotors, since they can carry larger
batteries and their motors work at fewer revolutions. Finally, it is important to emphasize their great power
and load capacity [8]. The possible configurations of a hexacopter are: Cross (+), X, Y6, and H (Fig. 1).
"A hexacopter exhibits flight performance comparable to that of a helicopter. It maneuvers by rotating its
propellers, which generate the necessary thrust for movement. Each engine can be controlled
independently, allowing for various translations and rotations by adjusting the speed of each axis as needed.
During a hexacopter's flight, several forces and torques are considered, including gravity, air friction, and
the torque produced by the propellers." (Fig. 2) [9].
The simpler movement is the ascent and descent vertical of the aircraft, which is possible with the increase
and decrease of the speed of the rotors of form equal and simultaneously [5].
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
The roll angle represents rotation around the 'x' axis, resulting in left or right movement, as shown in Figure
3a. To move left, the hexacopter decreases the thrust produced by the propellers on the left side while
increasing the thrust from the propellers on the right side. Conversely, to move right, the hexacopter
reduces the thrust from the propellers on the right side and simultaneously increases the thrust from the
propellers on the left side.
The pitch angle represents the "z" axis rotation, and generates the movements back and forth of the aircraft,
as shown in Fig. 3b. For forward movement, the hexacopter increases the thrust produced by the propellers
on the back and diminishes the thrust produced by the front propellers.
Yaw angle represents a rotation around the axis 'y' and is generated by increasing the thrust produced by
the propellers rotating in a clockwise direction, while decreasing the thrust produced by the propellers
rotating counter-clockwise, as shown in Fig. 3c. And turn, the opposite direction is achieved by decreasing
the thrust produced by the propellers rotating in a clockwise direction, while increases the thrust produced
by the propellers rotating counter-clockwise.
Fig 1. Configurations of a hexacopter: Cross (+), x (x), Y6, and H.
Fig. 2. Thrusts, torques, and angular velocities of a hexacopter [9].
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
(a) (b) (c)
Fig. 3. Movements of rotation of a hexacopter: a) Roll, b) Pitch, c) Yaw
B. Human machine interface
The human-machine interface (HMI) can be understood as the point of action in which a man comes in
contact with a machine [10]. The user can interact with reality, experiencing it and exploring it through
different HMI options, such as the force feedback joystick and the keyboard. The last mentioned device is
within the classification of haptic devices, since it involves the sense of touch, allowing one to enter a virtual
world closer to a real environment, where there is a set of characteristics of objects such as elasticity,
viscosity, adhesion, etc., which can be complemented by the force feedback [11].
C. Fictitious forces
Such forces explain the apparent acceleration of a body seen from a non-inertial reference system [12]. One
of the objectives pursued by the project is the evasion of static obstacles in semi-structured environments,
which proposes the creation of fictitious forces when the aircraft identifies an obstacle between the next
two elements: the hexacopter and the obstacle.
The use of fictitious forces is a simple and efficient method, these forces are arranged in such a way that
cover the aircraft environment and play the role of repelling any obstacle found in its field, increasing this
repulsion always decreases the distance between the two objects. The diameter of the environment of the
aircraft is defined considering the dimensions of the hexacopters and the environments, according to the
criteria of the author, a length of three times the diameter of the hexacopters, for the evasion of obstacles.
Fig. 4 observes the scheme of evasion of obstacles, where d is the distance in which begins repulsion of the
hexacopter towards the obstacle is found, and F is the fictitious force that will be sent as feedback towards
the haptic device, delivering the information of change of address to the user. The algorithm for the
calculation of this force depends on the magnitude of the distance.
Fig. 4. Scheme of evasion of obstacles
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
III. HEXACOPTER MODEL
To obtain the dynamic model based on equations that describe the position and orientation of the
hexacopters is assumed that each aircraft is a rigid body in space, subject to a main force, which corresponds
to the thrust, and three moments, that will generate the movements of the vehicle [13]. This behavior is
controlled by adjusting the angular speed of the rotors spinning through electric motors [14]; and the fixed
Center of mass and the origin of the coordinate system are considered coincidental, assuming that the
structure of the hexacopter is symmetric [13].
To describe the movement of the hexacopter we will need two systems of reference [14]: the earth system
and the body system. The Earth system is seen as inertial, which is defined as the absolute linear position
of the hexacopter (x, y, z). The body system uses the coordinates of North, East, and South. The origin of
this reference system is fixed at a point on the Earth's surface, and the axes are directed in the following
way: x - North - and eastward and z - downward. The angular position of the body concerning the inertial
system is defined using Euler angles: roll, pitch, and yaw. It is necessary to find the transformations of the
body to the inertial system, which is relied on to use the rotation matrix, starting with the rotations around
the axes [13].
By rotating each of the angles roll, pitch, and yaw, it gets the matrix of rotation R (1) for the transformation
of the system, inertial or fixed to the body, which is an orthogonal system.
=
coscos cossen +
cos + cos
cos cos
(7)
A. Kinematic Model [15]
Taking into account the motion of a rigid body decomposed into translation and rotation, and that the
equations governing these movements are the Newton – Euler, that is expressed as a function of the
linear speed of each axis of translation, V
x
, V
y
, and V
z
are the entries of the system and the speeds of the
aircraft
.
With the defined model, the rotation matrix (1) is used as a link between the Centre of mass reference
system and the fixed ground system.
(2)
Replacing (1) in (2) gets complete kinematic models depending on angles , θ and ψ.
It can be reduced through approximations of small angles, which is convenient in the simplification of the
trigonometrical laws, and presents an acceptable accuracy when the angle tends to zero, assuming θ→0
and →0, it has cos1, cosθ1 and sin0, sinθ0, obtaining:
(1)
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
=
cos
sen
0
cos
0
0 0 1
(3)
B. Dynamic Model
A dynamic model is applied to the scheme of the hexacopter of Fig. 5 and it is performed employing
Euler-Lagrange equations and Newton's laws [16]. The hexacopter has twelve States, which are [16]:
=,,,,,,,
,,
,,
(4)
Where and are the positions in the axes; y are the speed in the axes. are the
roll, pitch and yaw euler angles, respectively;
and
are the speed in the angles.
Euler Lagrange [15]
The Lagrangian is the sum of translational and rotational energy less the potential energy, defined by:
(5)
Where
is the kinetic energy of translation,
is the kinetic energy of rotation, and is the
energy potential of the hexacopter.
(6)
Where
is the translational force applied to the hexacopter, and
are the moments of roll, pitch and
yaw. For the translational dynamic of the vehicle, the Euler-Lagrange equation is:
(7)
Fig. 5. The hexacopter scheme
Developing:
Where
, from Fig. 6 with the reference in (O), the system is
.
signal is
the total thrust of the rotors. If
, and replacing
:
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
=+ + =
(8)
=
cos
cos
+
()
sen
cos
cos()
cos
cos()
(9)
From where is gets the translational dynamic model, that is observed in the equations (16), (17) y (18).
For the rotational dynamic, the equation is:
=
(10)
Through the vector of angular speed and the matrix of inertia, is developed the equation and is derived
each one of the terms, posing as the point of operation around the point of balance to , and
, i.e. , and and , and , where is the
stabilization of the system.
Therefore, the generalized moments can be expressed roll, pitch, and yaw with
,
and
respectively:
=
(
) (11)
=
(
) (12)
=
(
) (13)
Where
and
is the inertia of the hexacopter in and , respectively.
For roll, pitch, and yaw of the hexacopter movements, each rotor changes its direction of rotation and
speed, such movements should be carried out with the main force constant. The rotation of the
propellers produces a gyroscope effect [15]:
=
0
(14)
Where
is the rotational inertia of the propellers and is the speed total of the propellers [16]:
=
1
+
2
3
+
4
5
+
6
(15)
Where
,
are the angular velocities of each rotor.
Adding this effect, the rotational dynamic model is obtained [16] and shown in equations (19), (20) y
(21). Finally, the complete dynamic model of the hexacopter is [16]:
=
cossin cos+ sinsin
1
1
(16)
=
cossin sinsincos
1
1
(17)
= +
cos cos
1
1
(18)
=
+
2
(19)
=
+
3
(20)
=
+
4
(21)
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
Where is the drag factor and is the distance between the rotor and the center of the hexacopter.
The parameters of the dynamic model developed for the implementation of the model of the
hexacopters, according to [16], are presented in Table 1.
The engine for the development of the model is Tarot 4006; according to specifications and features,
they are specifically designed for aircraft with multiple rotors.
IV. RESULTS
For the development of environments and 3D models of the Simulator, we have used programs such as
Sweet Home 3D, SketchUp, and Blender 3D. Likewise, to integrate them and implement the Flight Simulator,
we have used the Unity 3D game engine, and through Visual Studio software implemented the dynamic
model of aircraft, and also the feedback of force, which is made possible through the use of the package of
Force Feedback Controller. The simulation is possible through a Force Feedback Joystick, or directly from
the computer keyboard.
For the calculation of the force that appears in the joystick as opposed to the movement exerted by the
user, when the aircraft is near an obstacle, taking into account the distance between the two objects, the
method chosen is the creation of fictitious forces around the hexacopter, creating a zone of repulsion to
the obstacles that are at the distance set in the programming, according to the dimensions of the aircraft.
Directions that take the fictitious forces that the user perceives through the controller are established
through the integration of eight spokes around the hexacopter, of which four are located in the positive
and negative X and Y axis and the other four correspond to the velocity, as shown in Fig. 6a. It is important
to understand how is related to the strength of feedback the distance between the hexacopter and the
obstacle; if the hexacopter is closer to a static object, i.e., whenever the distance is less, this force will
increase.
With this preamble, it can be concluded that the strength of feedback must be inversely proportional to the
distance. So it has been established a correspondence between both parameters.
=87
1
2+log (
3
)
(22)
Where F is the force feedback that appears on the joystick and d is the distance between the hexacopter
and the obstacle.
The algorithm implements the technique of fictitious forces raised previously, and is executed by the Flight
Simulator, which is responsible for measuring the distance between the hexacopter and the obstacle found,
and performs the calculation of the force on each iteration, fulfilling this way the purpose of increasing the
value of the force as it decreases the distance. The magnitude of the force calculated is limited to the range
[57.1, 35.1], a value dependent on the distance that lies in the interval [1, 9], considering that were designed
hexacopters with a measure of 3 units.
The proposed algorithm is developed taking into account the force allowed in the haptic device, values
ranging from 0 to 100, and that the user should perceive a force that advises the nearness of objects, but
that doesn't force to change the address. To have an idea of the dimensions of the hexacopters, and
distances in the environment generated by the simulator of flight, is important to understand the units of
these dimensions. This value is multiplied by 10, and thus, an equivalent value in centimeters, such that the
Simulator has hexacopters of 30 cm in diameter and a zone of evasion of the obstacle of 90 cm in diameter.
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
The address that is assigned to the force that is applied to the driver, when an obstacle is detected near the
hexacopter, is distinguished in Fig. 6b. The simulator applies one force at the same time, to optimize the
step of the aircraft by places narrow as doors or corridors.
To assess the proper functioning of the application, the elements of the Simulator and the behavior of the
hexacopters during its flight are validated, with obtaining feedback from users about the management of
the application, through a survey that complements the assessments conducted.
Table 1. Model parameters [16]
Name
Description
Value
Unit
Mass
1.83
kg
Drag factor
2.98e-6
Ns²
Length of center of
mass to the rotor
0.30
m
Gravity
9.8
m/s²
Rotational inertia
3.357e-5
kgm²
x, y inertia
0.0216
kgm²
Z inertia
0.0432
kgm²
To obtain feedback from the user regarding the operation of the Flight Simulator, we have conducted a
survey that complements the evaluations, and checks the fulfillment of objectives:
• Assess the degree of difficulty presenting the teleoperation learning of hexacopters.
• Determine which driver gives the user more comfort during flight maneuvers.
• Assess the simplicity and consistency of the interface, and check if its interactivity has an impact on the
user.
• Check if the assigned tasks are reached by users.
• Consider whether the force feedback system implemented helps to warn of possible collisions.
• Estimate the viewer that provides every type of camera, and establish what is more beneficial to the
user.
The sample size was 20 users, and 100% of the force feedback Joystick helped it to avoid possible collisions,
as well as provided an effect of reality, showing the importance of the presence of this feature in Flight
Simulator.
CONCLUSIONS
The Flight Simulator, which has three rooms with different levels of difficulty, semi-structured, was able to
simulate the (remote) teleoperation of two models of hexacopters, with the force feedback feature.
Additionally, the analysis of the dynamic model of the hexacopters allows the study and understanding of
their behavior.
The development and implementation were possible due to the control algorithm for the calculation of the
force that appears in the joystick, which is opposed to the movement exerted by the user when the aircraft
is near an obstacle. Establishing this force should be inversely proportional to the distance of the hexacopter
with the static obstacle.
The range of feedback that is perceived in the Force Feedback Joystick, was selected in such a way that
notes the proximity of a static obstacle, without forcing the change of direction, allowing this action to be
an exclusive decision of the user.
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
The simulator gives the user a sense of presence, through the use of a haptic device, offering an application
that warns about possible collisions of the hexacopters with static obstacles.
The development of a simple, intuitive, and friendly interface to the users, allowed offer a simulator of flight
that allows navigation by the application without difficulty, that offers the information, and helps timely.
ACKNOWLEDGMENT
Dr Aguilar has been partially supported by the Prometeo Project of the Ministry of Higher Education,
Science, Technology and Innovation of Ecuador.
REFERENCES
[1] E. Mercado, "Los simuladores de vuelo: su importancia," Mayo 2013. [En línea]. Available: http://aerowiki-
info.blogspot.com/2013/05/los-simuladores-de-vuelo-su-importancia.html.
[2] Clínica virtual, "Simulador del cuerpo humano en 3D en MSN," 7 julio 2015. [En línea]. Available:
http://clinicavirtual.weebly.com/noticias-medicas/simulador-del-cuerpo-humano-en-3d-en-msn.
[3] Aplicaciones y Operación con Drones/RPAS, "Origen y desarrollo de los drones," 9 Julio 2015. [En línea].
Available: http://drones.uv.es/origen-y-desarrollo-de-los-drones/.
[4] Grupo de aviación de caza, "Drones," Julio 2015.
[En línea]. Available:
http://www.simbolicodecaza.org/index.php?option=com_content&view=article&id=124:drones&catid=52
:articulos-profesionales-lunes&Itemid=194.
[5] A. Bachfischer, " Diseño, construcción y prueba de vehículo aéreo no tripulado," Julio 2014. [En línea].
Available: http://ricabib.cab.cnea.gov.ar/477/1/1Bachfischer.pdf.
[6] Asociación de Robótica, "Introducción a los UAVs," Febrero 2014.
[En línea]. Available: http://asrob.uc3m.es/index.php/Introducci%C3%B3n_a_los_UAVs.
[7] HelicamPeru, "Hexacopter," 2011. [En línea]. Available: http://helicamperu.com/hexacopter.
[8] A. López, "Elección del multicoptero," Septiembre 2011.
[En línea]. Available: http://diebotreise.blogspot.de/2011/09/eleccion-del-multicoptero.html.
[9] T. Magnusson, "Attitude Control of a Hexarotor," 2014.
[En línea]. Available: http://liu.diva-portal.org/smash/get/diva2:736152/FULLTEXT01.pdf.
[10] Copadata, "Interfaz hombre-máquina (HMI)," 2015.
[En línea]. Available: http://www.copadata.com/es/productos/product-features/interfaz-hombre-maquina-
hmi.html.
[11] L. Barrios y I. Galeano, "Interfaces hombre-máquina," 2014.
[En línea]. Available: http://jeuazarru.com/wp-content/uploads/2014/10/HMI.pdf.
[12] G-Blender, "Uso de texturas en Blender II UV," Agosto 2014. [En línea]. Available: http://www.g-
blender.org/uso-de-texturas-en-blender-ii-uv.
[13] P. Rodriguez, "Memoria," 2014.
[En línea]. Available: http://bibing.us.es/proyectos/abreproy/90168/fichero/Memoria.pdf.
[14] P. Dávila y J. Orna, "Diseño, construcción y control de un hexacóptero de monitoreo," Quito: Escuela
Politécnica Nacional, 2015.
[15] V. Espinosa y V. Moya, "Diseño y simulación de un algoritmo de control robusto para formación de
cuadricópteros," Quito, Ecuador, 2016.
[16] H. Nabil, "Dynamic Modeling and Control of a Quadrotor Using Linear and Nonlinear Approaches,"
Cairo: The American University in Cairo, 2014.
[17] A. Cerón y P. Bedoya, "Manual Básico De Unity 3d Como Apoyo Al Desarrollo Turístico Nacional,"
Pereira, Universidad Tecnológica de Pereira, 2014.
[18] Unity 3D, "Force feedback controller toolkit," Agosto 2012.
[En línea]. Available: http://forum.unity3d.com/threads/force-feedback-controller-toolkit.159297/.
[19] ConfigurarEquipos, "Configuración de equipos," Junio 2007.
[En línea]. Available: http://www.configurarequipos.com/doc532.html.
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Guadalupe N. and Chávez D. Simulation of remote control of a hexacopter with force feedback in semi-structured environments
THE AUTHORS
Natasha Guadalupe
Born on 29 January 1991 in the city of Quito, Ecuador. Finish their secondary studies in the "Espejo" women's
Experimental College. Currently pursuing their studies in the Escuela Politécnica Nacional, in electronics and
Control Engineering.
Danilo Chávez
Born on 1 April 1977 in Quito, Ecuador. Ended his secondary education at "Juan Pío Montúfar", and
graduated engineer in electronics and Control at the National Polytechnic School in 2001. He currently
works at the Faculty of Electrical and Electronic Engineering.
