**3. Dynamic model of CA**

Quad-rotor CA systems typically have a cross "X" or plus "+" structure with four rotors attached to each side of the structure. When at the time all of four rotors revolve in the likewise direction, the quad rotor produces a vertical upward lift force, allowing it to move in landing positions, pitch, hover, yaw, roll, take-off.

Two frames, a reference Earth frame as well as a quad-rotor frame, can be used to define and characterise quad-rotor dynamics. Rotational and translational dynamics with 6 degrees of freedom (DoF) are common.

The following is a summary of the deciding set for 6DoF equation that describe the dynamic model of a conventional CA including a longitudinal axis of symmetry treated as a rigid body (**Figure 2**).

*Robust Control Algorithm for Drones DOI: http://dx.doi.org/10.5772/intechopen.105966*

**Figure 2.** *CAs' movements and angles description.*

*ψ*

$$\begin{cases} X = m[u + qw - rv] \\ Y = m[v + mu - pw] \\ Z = m[w + pv - qu] \\ \end{cases} \quad (1)$$

$$\begin{cases} L = I\_{X}\mathbf{p} + (I\_{ZZ} - I\_{YY})\eta + I\_{XZ}(r + pq) \\ M = I\_{Y}\eta q + (I\_{XX} - I\_{ZX})rp + I\_{XZ}(r^2 - p^2) \\ N = I\_{Z}\mathbf{z}r + (I\_{YY} - I\_{XX})qp + I\_{Z}\mathbf{z}(r^2 - p^2) \\ N = I\_{Z}\mathbf{z}r + (I\_{YY} - I\_{XX})qp + I\_{Z}\mathbf{z}(r - qr) \end{cases} \quad (2)$$

$$r = R\_{b}^{\mu}V\_{b}^{\xi} = \begin{bmatrix} \cos\theta\cos\psi & -\cos\theta\sin\psi + \sin\phi\sin\theta\cos\psi & -\sin\sin + \cos\sin\cos\theta \\ \cos\theta\sin\psi & \cos\phi\cos\psi + \sin\phi\sin\theta\sin\psi & -\sin\phi\cos\psi + \cos\phi\sin\theta \\ -\sin\theta & \sin\phi\cos\theta & \cos\phi\cos\theta \end{bmatrix} \quad (3)$$

$$\begin{bmatrix} q \\ \theta \\ \omega \\ \omega \end{bmatrix} = \begin{bmatrix} 1 & \sin\phi\frac{\sin\theta}{\cos\theta} & \cos\phi\frac{\sin\theta}{\cos\theta} \\ 0 & \cos\phi & -\sin\phi \\ 1 & 1 & 1 \end{bmatrix} \begin{bmatrix} p \\ q \\ r \end{bmatrix} \tag{4}$$

The aforementioned differential equations are nonlinear, linked, which means that each differential equation is dependent on variables that are represented by other nonlinear equations. In most cases, the analytical answers are unknown, and the only way to solve them is numerical. The free motion of a solid body subject to extrinsic forces *Fb* <sup>¼</sup> ½ � *XYZ <sup>T</sup>* and moments) *Mb* <sup>¼</sup> ½ � *LMN <sup>T</sup>* is described by 12 states. These variables are known as state variables in control system design because they entirely characterise the state of a physical system at any given moment. For completeness, the state variables are presented in **Table 3**.

1

cos *<sup>θ</sup>* cos *<sup>φ</sup>*

1 cos *θ*

5

*r*

0 sin *φ*

4


**Table 3.**

*6DoF equations of motion state variables.*

#### **3.1 Problem statement**

Nonlinear rotational dynamics can cause hindrance in actuated control torques when paired with modest imperfections in rotating alignments and propeller defects. With the help of internal feedback control scheme for the quadrotor attitude can eliminate the influence of these. External disturbances such as gusty winds, aerodynamic interacts with neighbouring structures, and ground impacts can all be compensated for using the same attitude controller.

In order to create and deploy robust control mechanisms for quadrotor CAs, the following technical difficulties must be explored in a research.

