Design and control of a central-rotor type pentacopter design and implementation capable of contacting to and moving on wall surface

Abstract

This paper explores the design and control of a center-rotor type pentacopter that can move in contact with a wall to accurately measure cracks in a concrete outer wall. A center rotor pentacopter is a type of pentacopter that uses an electric ducted fan (EDF) motor and two axis servomotors at the center of gravity of the quadcopter. Center-rotor pentacopters are characterized by the ability to generate thrust in the desired direction using two servomotors and an EDF motor to maintain a stable attitude without tilting or leaning during flight. In this paper, the mathematical modeling of a center-rotor pentacopter was verified through simulation and compared with a regular quadcopter. We also simulated the thrust of the center rotor to see how much it could withstand when a sudden gust of wind occurred. Then, we built a pentacopter and measured the cracks and calculated the width of the cracks through the actual pentacopter in addition to flight experiments. The results showed the advantages and applicability of the pentacopter.

Introduction

Recently, the number of facilities subject to maintenance has been increasing due to the aging of facilities. The number of class 1–2 facilities under the Special Act on Safety Management of Domestic Facilities is estimated to be 87,124 as of 2017. In addition, the aging rate is expected to increase to more than 40% in the next 20 years. ¹ In the United States, Japan, and other countries, the aging of bridge facilities has been in full swing since the 2010s, and measures are being taken to address it. The allowable crack width in each country is mostly 0.4 mm or less, which requires early detection of cracks. ² The classical way to measure this is by performing a visual inspection by a human operator using a specialized vehicle. However, this can lead to human casualties such as worker falls, and it can also require road closures for inspections. Therefore, in recent years, researchers have been actively working on replacing this by using drones. The images taken by drones are used to measure cracks of concrete outer wall in various ways, including image processing and artificial intelligence.^3–8 In the work of Kim et al., used drones to inspect the outside of a dam was able to measure cracks larger than 0.9 mm while staying about 8 m away from the wall. ³ and Kim et al. to measure cracks smaller than 0.5 mm, a drone was flown as close as possible to an outer wall to take pictures, and the images were then processed to estimate the width of cracks smaller than 0.25 mm. ⁴ Another study used deep learning techniques to detect cracks in concrete and measure their width.^5,6 To measure cracks and ensure the reliability of the measurements, the resolution of the camera and the shooting distance are fundamentally important. Therefore, to measure cracks in concrete outer walls of bridges, dams, apartments, etc. with a drone, the drone must be able to maintain a stable distance from the wall and move smoothly. Furthermore, during noncontact flight, sudden exposure to gusts of wind can lead to unexpected displacement or attitude oscillations, significantly compromising flight stability and posing challenges in flight control. Gusts in GPS-shadowed areas such as the underside of a bridge can cause the drone to lose not only the location of the crack, but also its flight position. One of the simplest ways to maintain a stable distance from the wall and withstand sudden gusts of wind is to contact the wall. Most drones used for wall crack detection and measurement use common drone-shaped airframes, such as DJI's Phantom. However, these airframes have the disadvantage that the impact on the drone during a collision is not negligible, as shown by Kim et al., which analyzed the collision of a drone and a wall, and it is difficult to move the airframe after contact. ⁹ Therefore, wall-climbing robots have been widely studied to solve these problems.^10–13 One example is a wall-climbing drone. In the work of Myeong et al., wall-climbing drones are designed to contact to a wall by tilting the aircraft 90° instantaneously. According to the paper, the success rate of contacting to the wall is high, but there is a possibility of failure, and further research on stability is needed.^10,11 In addition, the recently developed wall-climbing quadruped robot (MARVEL) uses electromagnets to climb walls, which has the disadvantage that it can only climb structures made of steel and is not applicable to walls made of concrete. ¹² Also, drones that have studied contact to mitigate collisions with walls have the problem of not being able to move after contact. ¹³ To solve these problems, this study proposes a central rotor pentacopter drone with a horizontal flight capability that can be vertically contacted to an outer wall while minimizing the attitude change of the drone and can move smoothly over the wall surface even after contacting the wall.

Configuration of the central-rotor type pentacopter system

Hardware design of the central-rotor type pentacopter

The central-rotor type pentacopter consists of three main parts: Quad Rotor Part (QRP), Central Rotor Part (CRP), and Wall Contact Part (WCP), as shown in Figure 1. The QRP is the main driving part for controlling the posture and altitude of the aircraft and has the same quadcopter structure traditionally used. CRP is composed of electric ducted-fan (EDF) motor for generating thrust, as shown in Figure 2, and two servo motors for controlling roll and pitch angles. Figure 3(left) shows the direction of thrust when the pitch angle of the central rotor is 90°, and the aircraft moves horizontally forward at this time. Figure 3(right) shows the situation when the roll angle is 90°, and the aircraft moves horizontally in the y-axis direction. WCP is located on the front of the aircraft and helps to absorb the impact of the aircraft when contacted to the wall, as well as ensuring smooth movement in both horizontal and vertical directions after contact. The omni wheel used for this purpose is a specialized wheel design where auxiliary wheels (small rollers), as seen in the omni wheel part of Figure 4, are arranged around the main wheel at right angles, allowing the main wheel to move forward and backward while the auxiliary wheels can rotate independently from side to side. This configuration, consisting of Inner and Outer roller pairs, enables the wheel to move in all directions, hence referred to as an omnidirectional wheel, and it has already been applied to omnidirectional wheeled mobile robots. ¹⁴ Therefore, considering these advantages, the omni-wheels were placed at four locations of the WCP as shown in Figure 4, and springs were applied to both ends of the wheel's axis to mitigate airframe shock and reduce vibration due to the step between the inner roller and outer roller. Figure 5 shows the case where the front of the WCP is contacted to the wall. In the left figure, the central rotor thrust $F_{c1}$ is used to contact the WCP perpendicular to the wall without changing its attitude. In addition, as in the right figure, diagonal thrust $F_{c2}$ is used to apply forces $F_x$ and $F_y$ , allowing the WCP to contact to the wall while also enabling horizontal movement in the y-direction.

Figure 1.

Central-rotor type pentacopter configuration diagram.

Figure 2.

Central-rotor drive configuration diagram.

Figure 3.

Direction of thrust according to the angle of the central rotor.

Figure 4.

Configuration for wall contact part.

Figure 5.

Wall contact and movement of the aircraft according to the direction of the central rotor thrust.

Modeling of central-rotor type pentacopter

Figure 6 defines the coordinates for modeling a pentacopter. The angular velocity of rotor $({\omega }_1,\dots ,{\omega }_4,{\omega }_c)$ torque $({\tau }_{M_1},\dots ,{\tau }_{M_4},{\tau }_{M_c})$ and force $(F_1,\dots ,F_4,F_c)$ generated by the five rotors are represented. The inertial frame uses NED (North, East, Down) and Euler angles of roll $(\varphi )$ , pitch $(\theta )$ , and yaw $(\psi )$ are defined. Additionally, an H-frame is defined for the interpretation of the central rotor model. To interpret the force ( $F_H$ ) generated by the central rotor as the force ( $F_c$ ) acting on the aircraft, the transformation matrix from the frame of the central rotor, known as the H frame, to the aircraft frame is derived as shown in equation (2). The process to obtain this transformation matrix is as follows. First, Figure 7 shows the relationship between the body frame and the H frame in Figure 6. To obtain the homogeneous transformation matrix from the body frame to frame 1, the matrix ^bT₁ is calculated as shown in equation (1). In this case, the rotation matrix is the rotation matrix about the x-axis ( ${\theta }_x$ is the rotation angle about the x-axis in the body frame and frame 1.)

$${}^b{T}_1=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\mathrm{C}}_{{\theta }_x}& -{\mathrm{S}}_{{\theta }_x}& -d_0\\ 0& S_{{\theta }_x}& C_{{\theta }_x}& l_0\\ 0& 0& 0& 1\end{array}\right]$$

(1)

Figure 6.

Coordinate systems of the pentacopter.

Figure 7.

Diagram between body frame and H frame.

To obtain the forward kinematics for converting the force $F_H$ in the H frame to the frame 1, D-H parameters need to be determined. ¹⁵ The D-H parameters for this purpose are shown in Table 1. If the position of the central rotor is not at the center of mass of the drone body, the force generated at the central rotor creates a moment on the aircraft. In this study, we resolve the issue by adjusting the position of the central rotor to align with the aircraft's center of mass (d₀= 0.1, l_o= 0). Subsequently, we compute the ⁽*⁾T_i matrix following equation (3) to facilitate forward kinematics calculations. (i = 1’, 2, 2’, H, where #=1, 2, 3, 4) Utilizing equations (1)–(3), we derive the transformation matrix ^bT_H from the H frame to the body frame. Finally, in accordance with equation (4), we express the force ( $F_c$ ) in the body frame. Equation (5) represents $F_H\in {\mathbb{R}}^{4\times 1}$ , indicating the force of the central rotor in the H frame.

$$\begin{array}{rl}{}^b{T}_H& ={}^b{T}_1^1{T}_{1^{\mathrm{\prime }}}^{1\mathrm{\prime }}{T}_2^2{T}_{2^{\mathrm{\prime }}}^{2\mathrm{\prime }}{T}_H\\ & =\left[\begin{array}{cccc}{\mathrm{S}}_{\theta 1}{\mathrm{S}}_{\theta 2}& -{\mathrm{C}}_{\theta 1}& {\mathrm{S}}_{\theta 1}{\mathrm{C}}_{\theta 2}& 0\\ {\mathrm{C}}_{\theta 2}& 0& -{\mathrm{S}}_{\theta 2}& 0\\ {\mathrm{C}}_{\theta 1}{\mathrm{S}}_{\theta 2}& {\mathrm{S}}_{\theta 1}& {\mathrm{C}}_{\theta 1}{\mathrm{C}}_{\theta 2}& 0\\ 0& 0& 0& 1\end{array}\right]\end{array}$$

(2)

where

$${}^{(}{*}^{)}{T}_i=\left[\begin{array}{cccc}{\mathrm{C}}_{{\theta }_{\mathrm{\#}}}& -{\mathrm{C}}_{{\alpha }_{\mathrm{\#}}}{\mathrm{S}}_{{\theta }_{\mathrm{\#}}}& {\mathrm{S}}_{{\alpha }_{\mathrm{\#}}}{\mathrm{S}}_{{\theta }_{\mathrm{\#}}}& a_{\mathrm{\#}}{\mathrm{C}}_{{\theta }_{\mathrm{\#}}}\\ {\mathrm{S}}_{{\theta }_{\mathrm{\#}}}& {\mathrm{C}}_{{\alpha }_{\mathrm{\#}}}{\mathrm{C}}_{{\theta }_{\mathrm{\#}}}& -{\mathrm{S}}_{{\alpha }_{\mathrm{\#}}}{\mathrm{C}}_{{\theta }_{\mathrm{\#}}}& a_{\mathrm{\#}}{\mathrm{S}}_{{\theta }_{\mathrm{\#}}}\\ 0& {\mathrm{S}}_{{\alpha }_{\mathrm{\#}}}& {\mathrm{C}}_{{\alpha }_{\mathrm{\#}}}& d_{\mathrm{\#}}\\ 0& 0& 0& 1\end{array}\right]$$

(3)

$$F_c={}^b{T}_H^{}{F}_H$$

(4)

where

$$F_H=[00-|F_{\mathrm{H}}|1{]}^T$$

(5)

Table 1.

D-H parameters for the pentacopter.

	$\theta$	$d$	$a$	$\alpha$
$1\to 1^{\mathrm{\prime }}$	${\theta }_1*$	$d_1$	$-l_1$	$0\circ$
$1^{\mathrm{\prime }}\to 2$	$90\circ$	$0$	$0$	$90\circ$
$2\to 2^{\mathrm{\prime }}$	${\theta }_2*+90\circ$	$d_2$	$l_2$	$0$
$2^{\mathrm{\prime }}\to H$	$0$	$0$	$l_3$	$-90\circ$

Next, to generate force in the desired direction from the central rotor, we need to determine the roll ( ${\theta }_2$ ) and pitch ( ${\theta }_1$ ) angles of the central rotor. Figure 8 illustrates the relationship between the desired force $(F_{desired})$ and the force $(F_c^{\mathrm{\prime }})$ generated by the central rotor, in the direction the pentacopter intends to move. Here, $F_c^{\mathrm{\prime }}$ is represented as a column vector with dimensions $F_c^{\mathrm{\prime }}\in {\mathbb{R}}^{3\times 1}$ , as shown in equation (6), redefined as a column vector with three elements excluding the last element of $F_{\mathrm{c}}$ from equation (4). The magnitude of $F_{desired}$ in Figure 8 can be determined using equation (8) with $F_{desired,x}$ and $F_{desired,y}$ , and ultimately, the magnitudes and directions of $F_{c,x}^{\mathrm{\prime }}$ and $F_{c,y}^{\mathrm{\prime }}$ of the central rotor must match $F_{desired,x}$ and $F_{desired,y}$ , as expressed in equation (9). Therefore, $F_{c,z}^{\mathrm{\prime }}$ can be expressed simply using the Pythagorean theorem, as shown in equation (7). Therefore, utilizing the methods derived from equation (4) for calculating forward kinematics and equation (6) for geometric interpretation, one can determine the angles ${\theta }_1$ and ${\theta }_2$ of the servo motor as shown in equations (10)–(15).

$$F_{\mathrm{c}}^{\mathrm{\prime }}={\left[\begin{array}{ccc}{F}_{c,x}^{\mathrm{\prime }}& F_{c,y}^{\mathrm{\prime }}& F_{c,z}^{\mathrm{\prime }}\end{array}\right]}^T$$

(6)

$$F_{c,z}^{\mathrm{\prime }}=-\sqrt{{|F_{\mathrm{c}}^{\mathrm{\prime }}|}^2-{(F_{desired})}^2}$$

$$=-\sqrt{{|F_{\mathrm{c}}^{\mathrm{\prime }}|}^2-{(F_{c,x}^{\mathrm{\prime }})}^2-{(F_{c,y}^{\mathrm{\prime }})}^2}$$

(7)

where

$$F_{desired}=\sqrt{F_{desired,x}^2+F_{desired,y}^2}$$

(8)

$$F_{c,x}^{\mathrm{\prime }}=F_{desired,x},F_{c,y}^{\mathrm{\prime }}=F_{desired,y}$$

(9)

$$F_c=[F_c^{\mathrm{\prime }}1{]}^T{=}^b{T}_H^{}{F}_H$$

(10)

$$\begin{array}{rl}& \left[\begin{array}{c}\begin{array}{c}{F}_{c,x}^{\mathrm{\prime }}\\ F_{c,y}^{\mathrm{\prime }}\\ F_{c,z}^{\mathrm{\prime }}\end{array}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{S}_{\theta 1}{S}_{\theta 2}& -C_{\theta 1}& S_{\theta 1}{C}_{\theta 2}& 0\\ C_{\theta 2}& 0& -S_{\theta 2}& 0\\ C_{\theta 1}{S}_{\theta 2}& S_{\theta 1}& C_{\theta 1}{C}_{\theta 2}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}\begin{array}{c}0\\ 0\\ -|F_{\mathrm{H}}|\end{array}\\ 1\end{array}\right]\\ & =\left[\begin{array}{c}\begin{array}{c}-|F_{\mathrm{H}}|S_{\theta 1}{C}_{\theta 2}\\ |F_{\mathrm{H}}|S_{\theta 2}\\ -|F_{\mathrm{H}}|C_{\theta 1}{C}_{\theta 2}\end{array}\\ 1\end{array}\right]\end{array}$$

(11)

$$tan{\theta }_1={\displaystyle \frac{F_{c,x}^{\mathrm{\prime }}}{F_{c,z}^{\mathrm{\prime }}}={\displaystyle \frac{F_{c,x}^{\mathrm{\prime }}}{-\sqrt{{|F_H|}^2-F_{c,x}^{\mathrm{\prime }2}-F_{c,y}^{\mathrm{\prime }2}}}}}$$

(12)

Figure 8.

Relation between central rotor force and desired force.

Thus,

$${\theta }_1=atan\left({\displaystyle \frac{F_{\mathrm{c},x}^{\mathrm{\prime }}}{-\sqrt{{|F_{\mathrm{H}}|}^2-F_{\mathrm{c},x}^{{}^{\mathrm{\prime }}2}-F_{\mathrm{c},\mathrm{y}}^{{}^{\mathrm{\prime }}2}}}}\right)$$

(13)

From

$$sin{\theta }_2=\frac{F_{c,y}^{\mathrm{\prime }}}{|F_H|}$$

(14)

$${\theta }_2=asin\left({\displaystyle \frac{F_{\mathrm{c},y}^{\mathrm{\prime }}}{|F_{\mathrm{H}}|}}\right)$$

(15)

The obtained ${\theta }_1$ and ${\theta }_2$ are the angles of the servo motors that satisfy the $F_{desired}$ . Finally, the magnitude of $F_H$ , $|F_H|$ , is the thrust generated by the central rotor and is nonlinear. Therefore, the thrust data for the 6S EDF Motor (Galaxy X7 by XFLy-Model) for various throttle settings is obtained through thrust measurement experiments, as shown in Figure 9. Using the least squares method, an approximation equation is derived as shown in equation (16).

$$F_H=21.265t^2-0.03731t-0.0133$$

(16)

where $0\le t\le 1$ , ( $t$ = throttle ratio).

Figure 9.

Thrust graph of 6S EDF motor.

Dynamic modeling of central-rotor type pentacopter

The dynamic modeling of a center-rotor pentacopter can basically be interpreted based on the modeling of a quadcopter. The absolute position of the pentacopter in the inertial coordinate system is represented by $\zeta =[x,y,z{]}^T$ , and its attitude is expressed as Euler angles $\eta =[\varphi ,\theta ,\psi {]}^T$ . R is expressed as in equation (17) and is the rotation transformation matrix from the body frame to the inertial coordinate system, following the rotation order of z-y-x.^16–18

$$R(\psi ,\theta ,\varphi )=\left[\begin{array}{ccc}{C}_{\psi }{C}_{\theta }& C_{\psi }{S}_{\theta }{S}_{\varphi }-S_{\psi }{C}_{\varphi }& C_{\psi }{S}_{\theta }{C}_{\varphi }+S_{\psi }{S}_{\varphi }\\ S_{\psi }{C}_{\theta }& S_{\psi }{S}_{\theta }{S}_{\varphi }+C_{\psi }{C}_{\varphi }& S_{\psi }{S}_{\theta }{C}_{\varphi }-C_{\psi }{S}_{\varphi }\\ -S_{\theta }& C_{\theta }{S}_{\varphi }& C_{\theta }{C}_{\varphi }\end{array}\right]$$

(17)

The central rotor of the pentacopter can be analyzed using the same method proposed by Lenski. ¹⁹ However, Lenski's method assumes that the rotational center of the centrally mounted propeller differs from the center of mass, resulting in displacement and angular acceleration. In contrast, this paper assumes that the central rotor is located at the center of the aircraft, thus not generating a moment due to the thrust of the central rotor. Therefore, the dynamic model of the central rotor-type pentacopter can be expressed as transformation and rotation systems, given by equations (18) and (24), respectively.

$$m\dot{\zeta }=G+R{F}_B+R{F}_{\mathrm{c}}^{\mathrm{\prime }}+F_w$$

(18)

where

$$G=\left[\begin{array}{c}0\\ 0\\ mg\end{array}\right]$$

(19)

$$F_B=\left[\begin{array}{c}0\\ 0\\ -T\end{array}\right]$$

(20)

$$T=k\sum _{i=1}^4{w}_i^2$$

(21)

$$F_w={\displaystyle \frac{1}{2}\rho C_{d}A{v}_a^b||v_a|{|}_2}$$

(22)

where

$$v_a^b=v_w^b-v_b$$

(23)

$$\ddot{\eta }=J^{-1}(\tau +{\tau }_{\mathrm{c}}-C(\eta ,\ddot{\eta })\ddot{\eta })$$

(24)

where

$$\tau =\left[\begin{array}{c}{\tau }_{\varphi }\\ {\tau }_{\theta }\\ {\tau }_{\psi }\end{array}\right]=\left[\begin{array}{c}lk({\omega }_2^2+{\omega }_3^2-{\omega }_1^2-{\omega }_4^2)\\ lk({\omega }_1^2+{\omega }_2^2-{\omega }_3^2-{\omega }_4^2)\\ {\tau }_{M1}-{\tau }_{M2}+{\tau }_{M3}-{\tau }_{M4}\end{array}\right]$$

(25)

$${\tau }_{M}i=b{\omega }_i^2+I_r{\dot{\omega }}_i,(i=1,\dots ,4)$$

(26)

$${\tau }_{\mathrm{c}}=r_H\times F_c^{\mathrm{\prime }}$$

(27)

In equations (18)–(23), m represents the mass of the aircraft, and g is the gravitational acceleration. $F_B$ represents the thrust generated by the four main rotors in the $z_b$ direction of the body frame, and T is the sum of the thrusts. Here, k represents the thrust coefficient, and ${\omega }_i$ denotes the angular velocity for each rotor of QRP and it generates $F_i$ in the direction of the rotor's axis. $F_w$ is the wind force. We simply applied a model of the wind based on a model of the aerodynamic forces on the drone.^20,21 Here, $\rho$ is the standard air density, $C_{d}A$ is the drag area of the drone, $v_a^b$ is the airflow velocity in the body frame. And $v_w^b$ is the wind speed in the body frame, and $v_{w,nominal}$ is the wind speed in the inertial coordinate system. Therefore, $v_w^b$ can be calculated as $v_w^b=R^T{v}_{w,nominal}$ . In equations (24)–(27), $\tau$ is composed of torques ${\tau }_{\varphi },{\tau }_{\theta ,}{\tau }_{\psi }$ for the angles of each axis $x_b,y_b,z_b$ in the body frame, ${\tau }_{M}i$ is the torque generated by the rotor's angular velocity and acceleration, where b in equation (26) is the drag constant and $I_r$ is the inertia moment of the rotor. In general, the effect of ${\omega \dot{}}_i$ is considered very small and thus it is omitted. And ${\tau }_{\mathrm{c}}$ represents the torque generated by the rotor of the CRP. Here, $r_H$ is the position vector from the center of mass of the aircraft to the center of the central rotor, as shown in Figure 7 and l is the distance between the rotors of the QRP and the center of the aircraft. $J(\eta )$ is a Jacobian matrix from the angular velocity of the aircraft ( $\dot{{\varphi }_b},\dot{{\theta }_b},\dot{{\psi }_b}$ ) to the angular velocity in the inertial frame ( $\dot{\varphi },\dot{\theta },\dot{\psi })$ , and it is given by equation (28). $W_{\eta }$ is the transformation matrix for angular velocities from the inertial frame to the body frame, and I is the moment of inertia of the aircraft. $C(\eta ,\dot{\eta })$ in equations (30)–(31) is the Coriolis term.

$$J(\eta )=W_{\eta }^{T}I{W}_{\eta }=\left[\begin{array}{ccc}{I}_{xx}& 0& -I_{xx}{S}_{\theta }\\ 0& I_{yy}{C}_{\varphi }^2+I_{zz}{S}_{\varphi }^2& (I_{yy}-I_{xx})C_{\varphi }{S}_{\varphi }{C}_{\theta }\\ -I_{xx}{S}_{\theta }& (I_{yy}-I_{zz})C_{\varphi }{S}_{\varphi }{C}_{\theta }& I_{xx}{S}_{\theta }^2+I_{yy}{S}_{\varphi }^2{C}_{\theta }^2+I_{zz}{C}_{\varphi }^2{C}_{\theta }^2\end{array}\right]$$

(28)

where

$$I=\left[\begin{array}{c}\begin{array}{ccc}{I}_{xx}& 0& 0\end{array}\\ \begin{array}{ccc}0& I_{yy}& 0\end{array}\\ \begin{array}{ccc}0& 0& I_{zz}\end{array}\end{array}\right],W_{\eta }=\left[\begin{array}{ccc}1& 0& -S_{\theta }\\ 0& C_{\varphi }& C_{\theta }{S}_{\varphi }\\ 0& -S_{\varphi }& C_{\theta }{C}_{\varphi }\end{array}\right]$$

(29)

$$C(\eta ,\dot{\eta })=\left[\begin{array}{c}{c}_{11}{c}_{12}{c}_{13}\\ c_{21}{c}_{22}{c}_{23}\\ c_{31}{c}_{32}{c}_{33}\end{array}\right]$$

(30)

where

$$\begin{array}{rl}& c_{11}=0\\ & c_{12}=(I_{yy}-I_{zz})(\dot{\theta }{C}_{\varphi }{S}_{\varphi }+\dot{\psi }{S}_{\varphi }^2{C}_{\theta })+(I_{zz}-I_{yy})\dot{\psi }{C}_{\varphi }^2{C}_{\theta }\\ & -I_{xx}\dot{\psi }{C}_{\theta }\\ & c_{13}=(I_{zz}-I_{yy})\dot{\psi }{C}_{\varphi }{S}_{\varphi }{C}_{\theta }^2\\ & c_{21}=(I_{zz}-I_{yy})(\dot{\theta }{C}_{\varphi }{S}_{\varphi }+\dot{\psi }{S}_{\varphi }{C}_{\theta })+(I_{yy}-I_{zz})\dot{\psi }{C}_{\varphi }^2{C}_{\theta }\\ & +I_{xx}\dot{\psi }{C}_{\theta }\\ & c_{22}=(I_{zz}-I_{yy})\dot{\varphi }{C}_{\varphi }{S}_{\varphi }\\ & c_{23}=-I_{xx}\dot{\psi }{S}_{\theta }{C}_{\theta }+I_{yy}\dot{\psi }{S}_{\varphi }^2{S}_{\theta }{C}_{\theta }+I_{zz}\dot{\psi }{C}_{\varphi }^2{S}_{\theta }{C}_{\theta }\\ & c_{31}=(I_{yy}-I_{zz})\dot{\psi }{C}_{\theta }^2{S}_{\varphi }{C}_{\varphi }-I_{xx}\dot{\theta }{C}_{\theta }\\ & c_{32}=(I_{zz}-I_{yy})(\dot{\theta }{C}_{\varphi }{S}_{\varphi }{S}_{\theta }+\dot{\varphi }{S}_{\varphi }^2{C}_{\theta })+(I_{yy}-I_{zz})\dot{\varphi }{C}_{\varphi }^2{C}_{\theta }\\ & +I_{xx}\dot{\psi }{S}_{\theta }{C}_{\theta }-I_{yy}\dot{\psi }{S}_{\varphi }^2{S}_{\theta }{C}_{\theta }-I_{zz}\dot{\psi }{C}_{\varphi }^2{S}_{\theta }{C}_{\theta }\\ & c_{33}=(I_{yy}-I_{zz})\dot{\varphi }{C}_{\varphi }{S}_{\varphi }{C}_{\theta }^2-I_{yy}\dot{\theta }{S}_{\varphi }^2{C}_{\theta }{S}_{\theta }-I_{zz}\dot{\theta }{C}_{\varphi }^2{C}_{\theta }{S}_{\theta }\\ & +I_{xx}\dot{\theta }{C}_{\theta }{S}_{\theta }\end{array}$$

(31)

Figure 10 shows a pentacopter in contact with an outer wall. The forces $F_x$ , $F_y$ , and $F_z$ represent the thrust generated by the central rotor in the x-, y-, and z-axis directions, respectively. $F_H$ is the thrust of the center rotor, $F_N$ is the normal force, and $F_{\mu ,omni}$ is the friction force of the omni wheel. In addition, ${\theta }_1$ and ${\theta }_2$ represent the pitch and roll angles of the center rotor, and $\alpha$ represents the torsion angle of the omni wheel.

Figure 10.

Diagram of a pentacopter contacting an outer wall.

The thrust generated by the center rotor can be represented by equations (32)–(34).

$$F_x=F_H\sin {\theta }_1\cos {\theta }_2$$

(32)

$$F_y=F_H\cos {\theta }_1\sin {\theta }_2$$

(33)

$$F_z=F_H\cos {\theta }_1$$

(34)

In addition, the $F_N$ generated by $F_x$ is related to the displacement of the springs on either side of the omni wheel axis, as shown in Figure 4, and is determined by the displacement of eight springs, two per omni wheel, for the four omni wheels of the WCP. If the force generated by $F_x$ is applied uniformly to the four omni wheels, $F_N$ acting on the pentacopter is equal to equation (34).

$$F_N=\{\begin{array}{c}8k_s\mathrm{\Delta }{x}_{s}if{F}_x\stackrel{<}{=\phantom{{}_x}}\mathrm{\Delta }{x}_{s,max}\\ F_{x}if{F}_x>\mathrm{\Delta }{x}_{s,max}\end{array}$$

(35)

where, $k_s$ is the spring constant, $\mathrm{\Delta }{x}_s$ is the displacement of the spring, and Δ $x_{s,max}$ is the maximum displacement of the spring within the elastic deformation.

Next, the maximum static frictional force ( $F_{\mu ,omni})$ acting on the omni wheel can be expressed as equation (36). Here, ${\mu }_{omni}$ represents the maximum static friction coefficient of the omni wheel.

$$F_{\mu ,omni}={\mu }_{omni}{F}_N$$

(36)

Therefore, the minimum force for the pentacopter to touch the wall and move vertically is equal to equation (37), and the minimum force for it to move side to side is equal to equation (38).

$$\{\begin{array}{c}{F}_B+F_z>4F_{\mu ,omni}+mgif+z_{wall}\\ F_B+F_z<-4F_{\mu ,omni}+mgif-z_{wall}\end{array}$$

(37)

$$if{F}_B+F_z=mg,$$

$$\{\begin{array}{c}{F}_y>|4F_{\mu ,omni}|if+y_{wall}\\ -F_y>|4F_{\mu ,omni}|if-y_{wall}\end{array}$$

(38)

Design of control system for central-rotor type pentacopter

Configuration of control system for central-rotor type pentacopter

The control system of a central-rotor type pentacopter is configured as shown in Figure 11. Using the Pixhawk4 Flight Controller (FC), the control system drives the ducted fan motor and two servo motors of the central rotor, as well as the four BLDC motors of the main rotors, based on external control inputs. Additionally, for aircraft control, the system utilizes a Lite-Lidar v3 (ToF Lidar—Time of Flight Lidar) sensor and PX4 Flow (Optical Flow) for altitude estimation and speed estimation.

Figure 11.

Control system diagram.

Control of central-rotor type pentacopter

As a method for controlling drones, PID control is the most widely used control algorithm. PID control is used for altitude and attitude control of drones, and it is applied to pentacopter.^22–25 Figure 12 depicts the control configuration of the central-rotor type pentacopter. It consists of Quad Rotor Control (QRC) for controlling the four propellers of the QRP and Central Rotor Control (CRC) for controlling the central rotor of the CRP, controlled independently. The QRC section depicted in Figure 12 utilizes PID control to regulate the aircraft's attitude and altitude. Equations (39)–(46) represent the P-PID controllers applied to the pentacopter.

$${\tau }_{\varphi }=\left(K_{\varphi ,P_r}\left(e_{\varphi }-\dot{\varphi }\right)+K_{\varphi ,I_r}\underset{0}{\overset{t}{\int }}\left(e_{\varphi }-\dot{\varphi }\right)d\tau +K_{\varphi ,D_r}\left({\stackrel{.}{e}}_{\varphi }-\stackrel{..}{\varphi }\right)\right)I_{xx}$$

(39)

where

$$e_{\varphi }=K_{\varphi ,P}({\varphi }_d-\varphi )$$

(40)

$${\tau }_{\theta }=\left(K_{\theta ,P_r}(e_{\theta }-\stackrel{.}{\theta })+K_{\theta ,I_r}\underset{0}{\overset{t}{\int }}(e_{\theta }-\stackrel{.}{\theta })d\tau +K_{\theta ,D_r}\left({\stackrel{.}{e}}_{\theta }-\stackrel{..}{\theta }\right)\right)I_{yy}$$

(41)

where

$$e_{\theta }=K_{\theta ,P}({\theta }_d-\theta )$$

(42)

$${\tau }_{\psi }=\left(K_{\psi ,P_r}(e_{\psi }-\stackrel{.}{\psi })+K_{\psi ,I_r}\underset{0}{\overset{t}{\int }}(e_{\psi }-\stackrel{.}{\psi })d\tau +K_{\psi ,D_r}\left({\stackrel{.}{e}}_{\psi }-\stackrel{..}{\psi }\right)\right)I_{zz}$$

(43)

where

$$e_{\psi }=K_{\psi ,P}({\psi }_d-\psi )$$

(44)

$$T=\left(g+K_{z,P_r}(e_z-\stackrel{.}{z})+K_{z,I_r}\underset{0}{\overset{t}{\int }}(e_z-\stackrel{.}{z})d\tau +K_{z,D_r}\left({\stackrel{.}{e}}_z-\stackrel{..}{z}\right)\right){\displaystyle \frac{m}{C_{\varphi }{C}_{\theta }}}$$

(45)

where

$$e_z=K_{z,P}(z_d-z)$$

(46)

Figure 12.

Control configuration of the central-rotor type pentacopter.

The CRC section illustrated in Figure 12 enables the pentacopter to maintain its speed or hover by comparing the target speed ( ${\dot{x}}_d,{\dot{y}}_d)$ and the pentacopter's estimated speed ( ${\dot{x}}_b,{\dot{y}}_b)$ through the optical flow sensor and IMU sensor.

In addition, for the convenience of control, the value of $|F_c^{\mathrm{\prime }}|$ is assumed to be constant. This allows the magnitude of $F_{desired}$ to be determined only by the roll ( ${\theta }_2)$ and pitch ( ${\theta }_1)$ values of the central rotor. The values of $F_{desired,x}$ and $F_{\mathrm{desired},y}$ obtained by the P controller determine the $F_{desired}$ in Figure 8, and this determines the force vector ( $F_c^{\mathrm{\prime }})$ of the central rotor to satisfy it. Equations (47) and (48) represent the P controller.

$$F_{desired,x}=K_{\dot{x},P}({\dot{x}}_d-{\dot{x}}_b)$$

(47)

$$F_{\mathrm{desired},y}=K_{\dot{y},P}({\dot{y}}_d-{\dot{y}}_b)$$

(48)

Ideally, if $|F_{\mathrm{desired}}|$ is determined, the $|F_{\mathrm{c}}^{\mathrm{\prime }}|$ required to generate that force should always be the same. However, since the $|F_{\mathrm{c}}^{\mathrm{\prime }}|$ is physically limited, it is necessary to separate the cases where $|F_{\mathrm{desired}}|$ is larger or smaller than $|F_{\mathrm{c}}^{\mathrm{\prime }}|$ and control them differently.

Therefore, equations (49) and (50) normalizes the vector to obtain $F_{n,x}$ and $F_{n,\mathrm{y}}$ .

$$F_{n,x}=\{\begin{array}{cc}{\displaystyle \frac{F_{\mathrm{desired},\mathrm{x}}}{|F_{desired}|}|F_{\mathrm{c}}^{\mathrm{\prime }}|}& \mathrm{if}|F_{desired}|>|F_{\mathrm{c}}^{\mathrm{\prime }}|\\ F_{\mathrm{desired},x}& \mathrm{otherwise}\end{array}$$

(49)

$$F_{n,y}=\{\begin{array}{cc}{\displaystyle \frac{F_{\mathrm{desired},y}}{|F_{desired}|}|F_{\mathrm{c}}^{\mathrm{\prime }}|}& \mathrm{if}|F_{desired}|>|F_{\mathrm{c}}^{\mathrm{\prime }}|\\ F_{\mathrm{desired},y}& \mathrm{otherwise}\end{array}$$

(50)

The values of $F_{n,x}$ and $F_{n,\mathrm{y}}$ obtained from equations (49) and (50) are used instead of $F_{c,x}^{\mathrm{\prime }}$ and $F_{c,y}^{\mathrm{\prime }}$ in equations (10)–(15). By using these values, we can calculate the angles ${\theta }_1$ and ${\theta }_2$ of the central rotor. With these angles, we can determine the direction of the thrust $F_c^{\mathrm{\prime }}$ of the central rotor that satisfies the desired force $F_{\mathrm{desired}}$ .

Simulations

Based on the modeling of the pentacopter obtained earlier, simulations are conducted. The parameters used for the simulations are shown in Table 2. To verify the horizontal motion of the pentacopter controlled by the central rotor of the pentacopter, the target roll ( ${\varphi }_d$ ), pitch ( ${\theta }_d$ ), and yaw ( ${\psi }_d$ ) were set to 0°, and the target altitude ( $z_d$ ) was set to 2 m.

Table 2.

Parameters for simulations.

Hardware parameter	Value	Hardware parameter	Value
$m$	5.2 kg	$d_0,d_1,d_2,l_1$	0.1 m
$I_{xx}$	0.25 kgm2	$l_0,l_2,l_3$	$0$
$I_{yy}$	0.29 kgm2	$|F_H|$	3 N
$I_{zz}$	0.43 kgm2	$l$	0.37 m
$r_H$	$[-0.0464m,0.00059m,0.143m{]}^T$

Controller Gain	Value	Controller Gain	Value
$K_{\varphi ,P},K_{\theta ,P}$	3	$K_{z,P}$	1
$K_{\varphi ,P_r},K_{\theta ,P_r},K_{\psi ,P_r}$	15	$K_{z,P_r}$	3
$K_{\varphi ,I_r},K_{\theta ,I_r},K_{\psi ,I_r}$	0.8	$K_{z,I_r}$	0.8
$K_{\varphi ,D_r},K_{\theta ,D_r},K_{z,D_r}$	10	$K_{z,D_r}$	2
$K_{\dot{x},P},K_{\dot{y},P}$	0.1

Additionally, after setting the central rotor's thrust at 3 N, a step input of 1 m/s in the x-direction was applied after 5 s. The simulation results are shown in Figure 13 (center). It takes about 2 s to reach the target altitude of 2 m after takeoff, during which time the pentacopter maintains an attitude of 0°. The maximum change in the pitch angle of about −0.2° during initial takeoff is due to the weight center being slightly biased in the $x_b$ direction. Furthermore, it can be observed that it takes about 2 s to reach the target speed ( $\dot{x_d}$ ) of 1 m/s, and the pitch angle ( ${\theta }_1$ ) of the central rotor rapidly approaches the target speed after the speed command is given by maximizing the angle at −90°, returning to 0° as it approaches the target speed. During movement, the pentacopter's attitude, roll $(\varphi )$ , and pitch $(\theta )$ , show minimal changes of about 0.0032° and 0.732°, respectively, indicating that the pentacopter maintains its attitude and moves forward. Next, we perform simulations on the quadcopter to compare the performance of a conventional quadcopter with that of a center-rotor pentacopter. To regulate the speed of the vehicle without using a center rotor, we design a control system using equations (51)–(54). These equations are derived by adding a P-controller for speed control through attitude to equations (39)–(46). The simulation results are shown in Figure 13 (right).

$${\tau }_{\varphi }=\left(K_{\varphi ,P_r}\left(e_{\varphi }-\dot{\varphi }\right)+K_{\varphi ,I_r}\underset{0}{\overset{t}{\int }}\left(e_{\varphi }-\dot{\varphi }\right)d\tau +K_{\varphi ,D_r}\left({\stackrel{.}{e}}_{\varphi }-\stackrel{..}{\varphi }\right)\right)I_{xx}$$

(51)

where

$$e_{\varphi }=K_{\varphi ,P}({\varphi }_d-\varphi ),{\varphi }_d=K_{\dot{y},P}({\dot{y}}_d-\dot{y})$$

(52)

$${\tau }_{\theta }=\left(K_{\theta ,P_r}(e_{\theta }-\stackrel{.}{\theta })+K_{\theta ,I_r}\underset{0}{\overset{t}{\int }}(e_{\theta }-\stackrel{.}{\theta })d\tau +K_{\theta ,D_r}\left({\stackrel{.}{e}}_{\theta }-\stackrel{..}{\theta }\right)\right)I_{yy}$$

(53)

where

$$e_{\theta }=K_{\theta ,P}({\theta }_d-\theta ),{\theta }_d=K_{\dot{x},P}({\dot{x}}_d-\dot{x})$$

(54)

Figure 13.

Simulation results of controlling a center-rotor pentacopter (center) and a quadcopter (right) for a target input (left).

When the same target input as in Figure 13 (left) is given, it can be observed that the pentacopter tilts up to a maximum of approximately 4.58° in pitch while moving forward. By comparing the case with and without using a central rotor, it can be concluded that when using a central rotor, the attitude changes during flight are significantly reduced. The following is a simulation of whether the pentacopter can maintain its position under the force of the center rotor without changing its attitude when subjected to a sudden gust of wind. The parameters of the pentacopter are the same as in Table 2, with a standard air density $(\rho )$ of 1.225 $kg/m^3$ and a pentacopter drag area $(C_{d}A)$ of 0.1741 $m^3$ . According to the research by Park J.K et al., when measuring wind speed for bridges in Korea for 10 min, the maximum average wind speed was measured at 5.51 m/s. ²⁶

Therefore, in this study, the wind speed for sudden gusts is assumed to be 6 m/s for simulation (i.e., $North:v_{w,nominal}=6/\sqrt{2}[100{]}^T,$ $East:v_{w,nominal}=6/\sqrt{2}[010{]}^T)$ .

Figure 14 is the wind input, generate a north wind between 5 and 9 s and an east wind between 7 and 11 s. The results of the pentacopter's response to the wind are shown in Figure 15. In the case of (a), it can be seen that the pentacopter is moved by the gust because no speed control using the central rotor or attitude control was applied to the changes in $\dot{x}$ and $\dot{y}$ . In the case of (b), speed control was done using only attitude control in response to the gust. The changes in $\dot{x}$ and $\dot{y}$ in this case are a maximum of 0.09 m/s and 0.13 m/s, with averages of 0.0078 m/s and 0.00856 m/s, respectively. The roll and pitch angles are a maximum of −6.9° and −3.15°, respectively. In the cases of (c) and (d), simulations were conducted to see how well the pentacopter could withstand gusts using only the central rotor without using attitude-based speed control. In (c), the thrust of the central rotor was set to 3 N. The changes in $\dot{x}$ and $\dot{y}$ are a maximum of 0.51 m/s and −0.0006 m/s, with averages of 0.086 m/s and 0.118 m/s, respectively. The roll and pitch angles are a maximum of 0.6° and −0.6°, respectively. In (d), the simulation was conducted with the central rotor's thrust close to its maximum at 10 N, as shown in Figure 9. The changes in $\dot{x}$ and $\dot{y}$ are a maximum of 0.09 m/s and 0.08 m/s, with averages of −0.0008 m/s and −0.02 m/s, respectively. The changes in roll and pitch are 1.26° and −2.1°, respectively. Comparing (b) and (c), it can be seen that in the case of (b), the speed changes less, making it better at withstanding gusts, but the attitude changes are greater than in (c). In the case of (d), the increased thrust of the central rotor results in not only less speed change, similar to (b), but also significantly less attitude change.

Figure 14.

Wind input.

Figure 15.

Simulation result for gust. (a) Simulation results without using the central rotor and attitude-based speed control. (b) Simulation results using attitude-based speed control without using the central rotor. (c) Simulation results using only the central rotor without using attitude-based speed control. $(|F_H|=3N)$ (d) Simulation results using only the central rotor without using attitude-based speed control. $(|F_H|=10N)$ .

Experimental results

Table 3 and Figure 16 show the specifications and appearance of the designed and manufactured center-rotor pentacopter. The weight is about 5.2 kg, the dimensions of the airframe are 940 × 1020 × 325 mm, and the flight time is about 10 min. The following are the experimental results conducted by inputting a 1 m/s command in the x-axis direction to evaluate the horizontal movement performance. Figure 17 shows that the target input is reached within about 5 s after entering the command in the $x_b$ direction.

Figure 16.

Completed prototype of the central rotor type pentacopter.

Figure 17.

Velocity control results for horizontal movement in the $x_b$ -direction.

Table 3.

Specifications of the central rotor type pentacopter.

Section	Specification
Size (width × length × height)	940 × 1020 ×325 mm
Weight	5.2 kg
Propeller	15 inch 5 pitch
Flight time	10 min

Figure 18 shows the variation of the roll angle and pitch angle when flying as in Figure 17. According to Table 4, we can see that the roll angle remains at a mean of −0.47298° with a deviation of 0.000509 and the pitch angle at a mean of −0.3445° with a deviation of 0.000179 when traveling horizontally. Figure 19 shows the experimental results of on continuous vertical movement in the − and + directions in the y-axis direction. Figure 20 represents the changing roll and pitch angles during continuous movement.

Figure 18.

Roll and pitch angles of a center-rotor pentacopter during horizontal movement in the $x_b$ -direction.

Figure 19.

Velocity control results for horizontal movement in the $y_b$ -direction.

Figure 20.

Roll and pitch angles of a center-rotor pentacopter during horizontal movement in the $y_b$ -direction.

Table 4.

Average and variance of roll and pitch angle during horizontal directional movement.

Angle	Average	Variance
Roll angle	−0.47298°	0.000509
Pitch angle	−0.3445°	0.000179

As shown in Table 5, the angles of roll and pitch maintain an average of −0.00124° and 0.026977°, respectively, during movement, and the variances are 0.1378 and 0.093012, respectively. One of the purposes of the central rotor-type pentacopter is to be stably contacted to a wall through horizontal flight. Therefore, experiments are conducted to verify whether the pentacopter can be contacted to the wall. In addition, it is necessary to measure the force exerted when the pentacopter is contacted to the wall.

Table 5.

Average and variance of roll and pitch angle during vertical directional movement.

Angle	Average	Variance
Roll angle	−0.00124°	0.1378
Pitch angle	0.026977°	0.093012

Figure 21 shows a wall contact device that can measure the contacting force when the pentacopter is contacted to the wall. The wall contact device is constructed using a load cell that can measure up to 5 kg. Figure 22 is a snapshot of the process of the pentacopter being contacted to the wall, and Figure 23 shows the results of measuring the normal force between the wall and the contact device. To measure the force of contact with the wall, we conducted an experiment to measure the normal force when the pentacopter was placed in contact with a wall using the center rotor, and the thrust of the center rotor was generated at 3 N and 5 N in the forward direction of the pentacopter $(x_b)$ , respectively.

Figure 21.

Normal force measurement device using loadcell sensor.

Figure 22.

Snapshots of the wall contact process.

Figure 23.

Normal force measurement data graph (up: $F_H$ = 3N, down: $F_H$ = 5N).

Sections (a)–(c) represent the pentacopter traveling until it is contacted to the wall, with a measurement of 0 g. Sections (d)–(e) represent the collision with the wall, with the normal force increasing to approximately 1200 $gf$ (=12 N) due to the impact. Finally, section (f) represents the section where the pentacopter is in stable contact with the wall, and the corresponding wall contact force measurements are shown in Table 6. The fact that the normal force in the measurements shown in the table is slightly lower than the force generated by the center rotor could be the result of the center rotor's angle not being kept constant by the external environment, resulting in a distributed thrust. Figure 24 is a snapshot illustrating the process of horizontal flight after the pentacopter is contacted to the wall. The experiment was conducted in a location with minimal wind to test the aircraft's performance. The pentacopter flies a total distance of 6 m ((1) to (6)).

Figure 24.

Snapshots of the horizontal flight process after wall contact.

Table 6.

Wall contacting force measurement data according to velocity.

$F_H$ [N]	Average normal force (N)
3	2.545
5	4.3

Additionally, to evaluate the effectiveness of the contact to the wall, a distance sensor is contacted to the front of the pentacopter to measure the distance between the pentacopter and the wall. The experimental procedure is as follows: First, the pentacopter elevates its altitude using the four main rotors and then contacts itself to the starting point labeled as (1) using the central rotor. Subsequently, in section (1) to (3), the pentacopter performs a rightward horizontal movement using the central rotor, while in section (3) to (4), the pentacopter lowers its altitude using the main rotors. Finally, sections (4) to (6) represent the process of the pentacopter moving horizontally to the left using the central rotor. The experimental results are presented in Table 7. During the total 6 m flight, the roll and pitch angles showed minimal variation, measuring 0.007° and 0.015° respectively, indicating stable orientation. The distance from the wall was measured at 0.064 m, confirming successful contact. Furthermore, the pentacopter exhibited a y-axis velocity of 0.131 m/s during the movement in sections (1) to (3), while the velocity during the movement in sections (4) to (6) was 0.121 m/s.

Table 7.

Horizontal movement experimental results after wall contact.

Measurement items	Value
Roll average ((1)∼(6))	0.007685°
Pitch average ((1)∼(6))	0.015719°
Average distance from the wall ((1)∼(6))	0.064 m
y-axis average speed ((1)∼(3))	0.131 m/s
y-axis average speed ((4)∼(6))	−0.121 m/s

Ensure that the pentacopter can measure the cracks smoothly and can measure the width of the cracks well. Figure 25 (left) shows the pentacopter shooting with the camera at point A, where the actual measurements were performed. Figure 25 (right) shows the actual measurements of 16 cracks. The camera used in the pentacopter was a Samsung Galaxy A52 s phone camera with a 64MP resolution and a field of view of 0.705 m (W). The phone mounted on the pentacopter was positioned 0.3 m away from the outer wall. Figure 26 shows some images of the actual measured crack width (left) and the crack width measured by counting the number of pixels in the crack image (right). Table 8 shows the measured and calculated values for cracks 1–16. The error between the actual measured and calculated values is 0.079 mm on average, with a maximum error of 0.12 mm, which shows that the error is very small with simple image processing. In the same manner as Figure 26, Figure 27 shows the measurement of crack widths on a bridge with instantaneous wind speeds of up to 4.1 m/s. The crack widths could be measured as small as 0.0917 mm. Through this, it is understood that the measurement of crack widths in various concrete exterior walls is possible, and stable imaging is achievable even in gusty conditions.

Figure 25.

Experiment on measuring cracks in bridges.

Figure 26.

Actual measurement of cracks (left) and calculated values (right).

Figure 27.

Crack measurement results for different concrete exterior walls.

Table 8.

Compare actual measured and calculated values for crack numbers.

Crack Num.	AM	Calc.	E	Crack Num.	AM	Calc.	E
1	0.67	0.6676	0.0024	9	0.7	0.7336	0.0336
2	1.2	1.1194	0.0806	10	0.3	0.2338	0.0662
3	0.08	0.1227	0.0427	11	0.4	0.4127	0.0127
4	0.1	0.1697	0.0697	12	0.2	0.3227	0.1227
5	0.8	0.752	0.048	13	1.1	1.2062	0.1062
6	0.6	0.521	0.079	14	0.6	0.87	0.27
7	0.5	0.5978	0.0978	15	0.2	0.321	0.121
8	1.4	1.3036	0.0964	16	0.4	0.4152	0.0152

AM: actual measurement; E: error.

Conclusions

The purpose of this study is to propose a mechanism and control method for a center-rotor type pentacopter as a method for detecting cracks in the outer walls of concrete structures such as dams and bridges and to accurately measure the width of the cracks. The proposed pentacopter can fly in a stable attitude without tilting or leaning by adding an EDF motor to the center of gravity of the aircraft to generate thrust. This allows it to make stable contact with external walls and perform vertical and horizontal maneuvers without changing its attitude after contact. To verify this, this paper (1) established a mathematical model of a central-rotor type pentacopter and conducted simulations to verify the differences from general drones, and confirmed through experiments that there is almost no attitude change when the pentacopter flies horizontally. (2) Simulated the ability of the pentacopter to cope with sudden gusts of wind and found that there is little attitude change in a 6 m/s gust and no significant change in speed. (3) Analyzed and experimentally verified the normal forces that occur when a center-rotor pentacopter contacts an outer wall. (4) Conducted experiments to test whether the center-rotor pentacopter can stably contact the outer wall and move after contact. (5) To verify the efficiency of the pentacopter, we measured the actual cracks on a bridge in a GPS-unavailable area and compared them with the cracks photographed using the pentacopter and found that the width of the cracks can be accurately measured with simple image processing. Therefore, we believe that the center rotor type pentacopter proposed in this paper can be used to detect cracks in concrete and accurately measure the width of cracks. In addition, we believe that it is possible to inspect in areas without GPS coverage.

However, the pentacopter studied in this paper was researched on concrete structures without curves. Therefore, the currently applied WCP form has difficulty adapting to curved walls, and additional research on WCP is needed. Additionally, since the pentacopter is piloted by a human, the pilot's flying skills are important, and since the photographed cracks are simply counted as the number of pixels, it is necessary to consider how to measure the width of the crack from where to start.

Therefore, if the positioning technology using UWB is further supplemented by combining technologies such as image processing and deep learning, it is expected to overcome the problems of infrastructure inspection and be widely applied to delivery services in high-rise buildings and apartments in the future.