3. Stewart-Gough platform with 3-DOF, architecture and mathematical foundation

Based on the fact that for the construction of real flight simulators with full movement contemplated as cyber-physical systems which include hardware and software, the classic platforms of Stewart Gough of 6-DOF have been used. In the current project, a platform of Stewart Gough has been designed modified to be conducted with a 3-DOF in a limited and low cost manner that restricts the superior ability to perform linear movements on the β (x, y, z) plane. Nonetheless, it will maintain its ability to lead any controlled orientation during an airplane flight in order to receive various effects of spatial disorientation to which the pilots are exposed in real life. Among them are the following that have been simulated in this project: (a) illusion of track; (b) approximation illusions; and (c) illusions due to land degradation or fusion. Through these robotic hardware and software platforms, both military and private pilots may be trained allowing them to develop spatial orientation skills in order to avoid potential catastrophic accidents.

In this research, the architecture proposed by Hunt [13] has been applied, which is known as the 3-RPS parallel robot. Such architecture consists of three identical RPS legs, whose lengths are changed with prismatic joints, while the platform moves with 3-DOF, as illustrated in Figure 1.

The basic equations used of the Stewart platform with 3-DOF according to [14–18], have been the following:

Figure 1. Schematic illustration of the design of the platform.

communication, increased bandwidth and continuous improvements in energy. The advantages and opportunities offered by the cyber-physical systems (CPS) have allowed innovation and improvement of the principles of engineering as Rajkumar mentioned in his research [9]. One of the main challenges that arises in the design and development of cyber-physical systems is the development of new methods of science and system design engineering to obtain a CPS that is compatible, reliable, integrated and synergistic in all the five-layers of functionality architecture with other cyber-physical systems. This research contributes to the design, development

Naturally CPS and mechatronics systems are different, each one follows different goals, but its subtle differences characteristics make those systems complementary; since CPS consider the mechatronic system as an integral part of them. Table 1

According to the works of [11, 12], the cyber-physical systems are composed of

This component has as areas of influence the Systems Engineering, Computation Engineering, Communication Engineering, and Control Engineering; all of these

This component refers to the mechatronic itself, which has as areas of influence Industrial Engineering, Mechanical Engineering, Electrical Engineering, and Electronic Engineering; all of these supported by the Product Lifecycle Management

Parameters Mechatronics CPS

Scalability ++ Stability + Robustness ++ Efficiency + + Autonomous ++ Energy efficiency + ++ Safety ++ ++

Reliability ++ + Accuracy ++ + Communication ++ ++

and implementation of a CPS following engineering principles.

shows the differences between mechatronic systems and CPS.

supported by the Application Lifecycle Management (ALM).

Maintainability/availability +

Compactness +

Differences between mechatronic systems and CPS.

2.3 Mechatronics and CPS

Military Engineering

two parts.

(PLM).

Table 1.

76

2.3.1 Software (Cyber)

2.3.2 Hardware (Physical)

Equations of vectors a1, a2 and a3:

$$\begin{aligned} \mathbf{a}\_1 &= \begin{bmatrix} \mathbf{g} & \mathbf{0} & \mathbf{0} \end{bmatrix}^\mathrm{T} \\ \mathbf{a}\_2 &= \begin{bmatrix} -\frac{1}{2}\mathbf{g} & \frac{\sqrt{3}}{2}\mathbf{g} & \mathbf{0} \end{bmatrix}^\mathrm{T} \\ \mathbf{a}\_3 &= \begin{bmatrix} -\frac{1}{2}\mathbf{g} & -\frac{\sqrt{3}}{2}\mathbf{g} & \mathbf{0} \end{bmatrix}^\mathrm{T} \end{aligned} \tag{1}$$

Equations of the vectors b1, b2 and b3:

$$\begin{aligned} \mathbf{b}\_1 &= \begin{bmatrix} \mathbf{h} & \mathbf{0} & \mathbf{0} \end{bmatrix}^\mathrm{T} \\ \mathbf{b}\_2 &= \begin{bmatrix} -\frac{1}{2}\mathbf{h} & \frac{\sqrt{3}}{2}\mathbf{h} & \mathbf{0} \end{bmatrix}^\mathrm{T} \\ \mathbf{b}\_3 &= \begin{bmatrix} -\frac{1}{2}\mathbf{h} & -\frac{\sqrt{3}}{2}\mathbf{h} & \mathbf{0} \end{bmatrix}^\mathrm{T} \end{aligned} \tag{2}$$

Equations of the prismatic joint represented by three points, namely q1, q2 and q3:

$$\mathbf{q}\_{\rm i} = \mathbf{p} + {}^{A}\mathbf{R}\_{\mathbf{B}} \bullet \mathbf{b}\_{\rm i} \,\,\mathrm{i} = \mathbf{1}, \,\mathrm{2}, \,\mathrm{3} \tag{3}$$

Equation of the position of vector p:

$$\mathbf{p} = \begin{bmatrix} \mathbf{p}\_{\mathbf{x}} & \mathbf{p}\_{\mathbf{y}} & \mathbf{p}\_{\mathbf{z}} \end{bmatrix}^{\mathrm{T}} \tag{4}$$

Equation of the rotation matrix <sup>A</sup>RB.

$${}^{A}\mathbf{R}\_{\rm B} = \begin{pmatrix} \mathbf{u}\_{\rm x} & \mathbf{v}\_{\rm x} & \mathbf{w}\_{\rm x} \\ \mathbf{u}\_{\rm y} & \mathbf{v}\_{\rm y} & \mathbf{w}\_{\rm y} \\ \mathbf{u}\_{\rm z} & \mathbf{v}\_{\rm z} & \mathbf{w}\_{\rm z} \end{pmatrix} \tag{5}$$

subsystem, which manages the components and assets of Unity 3D to create the virtual world that corresponds to the city of Manta, which is the destination of the

A New Real-Time Flight Simulator for Military Training Using Mechatronics and Cyber…

This layer consists of three subsystems that are: (1) communication subsystem manages the connection with the first layer using sockets and reads the flat file with the information of the roll, pitch and yaw of the plane; (2) kinematic control subsystem—obtains the information corresponding to the roll, pitch and yaw of the airplane to be able to reproduce its movements in the Stewart platform with three

subsystem—manages the LabView components to view in real time the roll, pitch,

In this research, we propose a model of the dynamic flight system, which is based on the models proposed by [6, 19, 20]. Figure 3 shows the interaction between the pilot, the airplane and the Stewart platform with three degrees of freedom. The pilot operates the flight simulator with a joystick, where it controls

degrees of freedom using servo motors; and (3) graphical user interface

and yaw values of the aircraft to operate the Stewart platform.

4.2 Flight simulator dynamic system

Architecture diagram of the flight simulator system.

DOI: http://dx.doi.org/10.5772/intechopen.86586

plane.

79

Figure 2.

4.1.2 Second layer

The equation of the joint q1 whose procedure is equivalent for q2 and q3:

$$\mathbf{q}\_1 = \begin{bmatrix} \mathbf{p}\_x \\ \mathbf{p}\_y \\ \mathbf{p}\_z \end{bmatrix} + \begin{bmatrix} \mathbf{u}\_x & \mathbf{v}\_x & \mathbf{w}\_x \\ \mathbf{u}\_y & \mathbf{v}\_y & \mathbf{w}\_y \\ \mathbf{u}\_z & \mathbf{v}\_z & \mathbf{w}\_z \end{bmatrix} \bullet \begin{bmatrix} \mathbf{h} \\ \mathbf{0} \\ \mathbf{0} \end{bmatrix} = \begin{bmatrix} \mathbf{p}\_x + \mathbf{h} \bullet \mathbf{u}\_x \\ \mathbf{p}\_y + \mathbf{h} \bullet \mathbf{u}\_y \\ \mathbf{p}\_z + \mathbf{h} \bullet \mathbf{u}\_z \end{bmatrix} \tag{6}$$

### 4. Flight simulator construction

#### 4.1 Architecture diagram of the flight simulator system

Figure 2 shows the architecture of the system consists of two layers.

#### 4.1.1 First layer

This layer consists of three subsystems that are: (1) subsystem of the flight simulator control, which handles the logic of the virtual flight of the plane applying mathematical, Physics, and aeronautical models; (2) communication subsystem, which manages the connection with the second layer using sockets, the TCP/IP protocol, and flat files containing the information of the roll, pitch and yaw, corresponding to the movement of the plane; and (3) graphical user interface

A New Real-Time Flight Simulator for Military Training Using Mechatronics and Cyber… DOI: http://dx.doi.org/10.5772/intechopen.86586

#### Figure 2.

Equations of vectors a1, a2 and a3:

Military Engineering

Equations of the vectors b1, b2 and b3:

Equation of the position of vector p:

Equation of the rotation matrix <sup>A</sup>RB.

q1 ¼

4. Flight simulator construction

4.1.1 First layer

78

px py pz

2 6 4

4.1 Architecture diagram of the flight simulator system

2 6 4

and q3:

a1 <sup>¼</sup> ½ � g00 <sup>T</sup>

<sup>2</sup> <sup>g</sup> ffiffi 3 p <sup>2</sup> g 0 h i<sup>T</sup>

> <sup>2</sup> <sup>g</sup> � ffiffi 3 p <sup>2</sup> g 0

<sup>2</sup> <sup>h</sup> ffiffi 3 p <sup>2</sup> h 0 h i<sup>T</sup>

> <sup>2</sup> <sup>h</sup> � ffiffi 3 p <sup>2</sup> h 0

Equations of the prismatic joint represented by three points, namely q1, q2

<sup>p</sup> <sup>¼</sup> px py pz

0

B@

The equation of the joint q1 whose procedure is equivalent for q2 and q3:

ux vx wx uy vy wy uz vz wz

Figure 2 shows the architecture of the system consists of two layers.

This layer consists of three subsystems that are: (1) subsystem of the flight simulator control, which handles the logic of the virtual flight of the plane applying mathematical, Physics, and aeronautical models; (2) communication subsystem, which manages the connection with the second layer using sockets, the TCP/IP protocol, and flat files containing the information of the roll, pitch and yaw, corresponding to the movement of the plane; and (3) graphical user interface

ux vx wx uy vy wy uz vz wz

> 3 7 5∙

h 0 0

2 6 4

2 6 4

h i<sup>T</sup>

qi <sup>¼</sup> <sup>p</sup> <sup>þ</sup> <sup>A</sup>RB∙bi, <sup>i</sup> <sup>¼</sup> <sup>1</sup>, <sup>2</sup>, <sup>3</sup> (3)

1

� �<sup>T</sup> (4)

CA (5)

3 7

<sup>5</sup> (6)

px þ h∙ux py þ h∙uy pz þ h∙uz

h i<sup>T</sup>

(1)

(2)

a2 <sup>¼</sup> � <sup>1</sup>

a3 <sup>¼</sup> � <sup>1</sup>

b2 <sup>¼</sup> � <sup>1</sup>

b3 <sup>¼</sup> � <sup>1</sup>

<sup>A</sup>RB <sup>¼</sup>

b1 <sup>¼</sup> ½ � h00 <sup>T</sup>

Architecture diagram of the flight simulator system.

subsystem, which manages the components and assets of Unity 3D to create the virtual world that corresponds to the city of Manta, which is the destination of the plane.
